Journal of Monetary Economics | Macro Paper Warehouse

Payment data, information disclosure, and privacy

Thu, 01 Jan 2026 00:00:00 +0000

Layer 1: Overview

Research question and motivation: Digital payments generate vast, high-frequency, transaction-level data that several central banks (Bank of Canada, Swiss National Bank, Eurosystem members) already use for nowcasting, and regulatory initiatives (the EU’s PSD2, the UK’s Open Banking Standard, prospective CBDCs) are broadening system-wide data access. The paper asks how improved aggregate-demand forecasts enabled by payment data affect economic activity and through which channels; what the optimal communication policy for disseminating such forecasts is and how it depends on the monetary-policy stance; whether a competitive market in which private banks produce and sell forecasts is socially optimal; and how privacy concerns over individual transaction data affect optimal policy.

Model setup: The authors build a Lagos-Wright / Rocheteau-Wright general-equilibrium monetary model with infinitely-lived buyers and sellers (unit measure each) and periods split into a centralized market (CM) and decentralized market (DM). Each period a stochastic fraction theta_t of buyers becomes ‘active’ and wants the DM good; theta_t takes two values, theta_B < theta_G (bad/good aggregate state) with unconditional mean E[theta_t] = theta-bar. Sellers can pay an effort cost kappa to raise productivity from theta_L to theta_H. Payments use bank deposits fully backed by one-period government bonds costing g > beta (g is the policy variable; r = 1/g - 1). DM terms of trade follow the Kalai (1977) bargaining solution with buyer bargaining power sigma. No agent observes theta_t directly, but aggregating payment data across all banks yields a noisy binary signal s in {o,p} (optimistic/pessimistic), producing an unbiased forecast theta-tilde_t in {theta-tilde_G, theta-tilde_B} with E(theta-tilde_t) = theta-bar.

Main findings (qualitative, as the paper is theoretical with an illustrative calibration): Disclosing forecasts affects welfare through two channels. (1) Demand channel: buyers hold more deposits when expecting high demand, so disclosure raises deposit-holding volatility; even though buyer utility is strictly concave, aggregate welfare w(theta) can be convex or concave. The sign hinges on the statistic T(x) = [u’’(x)]^2 / [u’’’(x)(u’(x)-1/theta)]: w(theta) is convex if T(x) < 1/3 and concave if T(x) > 1 over the relevant range (Lemma 4). (2) Investment channel: sellers underinvest because they capture only fraction (1-sigma) of DM surplus, so disclosure that encourages (discourages) investment raises (lowers) welfare (Lemma 3, thresholds kappa_1 < kappa_2 < kappa_3). Crucially the welfare effect is state-dependent in the monetary stance: with a low bond price/high deposit rate (low g) disclosure tends to reduce welfare (it mainly adds downside volatility and can weaken investment), while with high g (low deposit rate) disclosure tends to raise welfare (Proposition 1; thresholds g, g-bar). Calibrating to the U.S. economy 2016-19, disclosure improves welfare when the utility curvature parameter gamma is small and g is large; the discrete investment channel is inactive over most of the parameter space (Figure 2).

Policy/theoretical implications: A central bank that controls disclosure can do better than binary reveal/withhold by sending noisy messages, a form of Bayesian persuasion (Kamenica-Gentzkow 2011): by committing to send the pessimistic message mb even when the forecast is optimistic (P^b < 1), it raises the posterior theta-tilde_b and induces investment, improving welfare when the investment channel is strong (Figures 4-5; numerical cases g = 1.05 and g = 1.00). A competitive market where private banks pay fixed cost C to produce and sell the forecast yields zero profits and always reveals undistorted information; provided C is below a threshold C-bar the forecast is always produced and sold, possibly causing excessive information production relative to the social optimum. Privacy: a fraction eta of buyers with high privacy costs use cash, shrinking recorded transactions and lowering forecast precision, but this need not reduce welfare; concave privacy costs can make deposit buyers’ preferences less concave, turning welfare convex so disclosure helps via the demand channel, partially but not fully offsetting the privacy cost.

In depth

Q1. What is the modeling/identification strategy, and what are the main threats to it?

This is a theoretical general-equilibrium paper, not an empirical identification exercise. The strategy is to embed payment-data-derived forecasting and central-bank communication into a Lagos-Wright/Rocheteau-Wright monetary search model. Aggregate demand theta_t is a two-state random variable realized at the start of the DM; agents make CM decisions (deposit holdings, investment) under a common prior theta-bar unless a forecast is disclosed. The ’threat’ analog is robustness of the comparative statics to functional-form and parameter assumptions; the authors discipline curvature via the statistic T(x) and use a CRRA-type utility u(x)=(x+gamma)^{1-sigma_u}… so that conditions map cleanly into the parameter gamma. They acknowledge agents in reality observe many macro indicators, but assume the only payment-data-based information is the unbiased binary signal, to isolate the informational value of payment data.

Q2. What are the two main channels, and how are they distinguished?

The demand channel works through buyers’ deposit holdings: optimistic forecasts raise deposits and DM consumption x, pessimistic forecasts lower them; its welfare sign depends on the convexity/concavity of w(theta), governed by T(x) (convex if T<1/3, concave if T>1). The investment channel works through sellers’ discrete investment decision: because sellers capture only (1-sigma) of surplus they underinvest, so disclosure that pushes investment up raises welfare and disclosure that pushes it down lowers welfare. They are distinguished analytically by shutting one off: Lemma 4 and Proposition 1 set theta_L = theta_H to isolate the demand channel; Lemma 3 isolates the investment channel via the cost thresholds kappa_1 < kappa_2 < kappa_3.

Q3. How does the welfare effect depend on monetary policy stance?

The bond price g (inverse of the deposit rate, r = 1/g - 1) is the key policy variable. When g is small (high deposit rate, cheap to hold deposits), consumption x is near its upper bound x*(theta) already under theta-bar, so an optimistic forecast barely raises x while a pessimistic one sharply lowers it, making welfare locally concave and disclosure welfare-reducing; low g also makes DM surplus large so sellers already invest, and a low theta-tilde_B can discourage investment, hurting welfare. When g is large (low deposit rate, costly deposits), x is low under theta-bar so an optimistic forecast substantially raises trade volume, making welfare convex and disclosure welfare-improving (Proposition 1, thresholds g and g-bar). Hence optimal forecast communication should be designed jointly with conventional monetary policy.

Q4. How does the Bayesian persuasion / noisy-message result work?

Instead of fully revealing theta-tilde_t, the central bank sends messages m in {mg,mb} under a committed, publicly known policy phi, choosing posteriors P^g = P(theta-tilde_G|mg) and P^b = P(theta-tilde_B|mb). Lemma 6 gives the policy implementing constant posteriors (requires P^b + P^g != 1). By lowering P^b below 1, the bank sometimes sends mb even when the forecast is optimistic, raising the posterior theta-tilde_b conditional on mb and encouraging sellers to invest; this can outweigh the demand-channel loss when the investment channel is strong. Lowering P^g below 1 adds beneficial noise via the demand channel when w is concave (low g). Numerical exercises with g = 1.05 (welfare locally convex, full transparency P^g=P^b=1 optimal when only demand channel active) and g = 1.00 (welfare locally concave, noisy messages welfare-improving) illustrate this (Figures 4-5).

Q5. Why do buyers and sellers always want to buy the forecast even when disclosure can lower welfare, and what is the market failure?

Lemma 5 shows buyers’ willingness to pay rho^b_t > 0 always and sellers’ rho^s_t >= 0. Knowing theta-tilde_t lets buyers tailor deposit holdings (avoiding the cost of carrying a fixed level since g > beta) and lets sellers tailor investment, yielding strictly higher private surplus. But neither internalizes the social benefit (the increase in total DM surplus), so private willingness to pay can exceed the social value. Proposition 3 shows that for C <= C-bar the forecast is always produced and sold in the competitive equilibrium (banks earn zero profit), which can lead to excessive information production relative to the social optimum. The market always fully reveals; it cannot replicate the central bank’s optimal noisy (persuasion) policy.

Q6. What is the selective-disclosure result?

When the production cost C is neither large nor small, the break-even price may exceed only one side’s willingness to pay, so the forecast is sold only to buyers or only to sellers (Proposition 3). A buyer-only outcome can improve welfare if the forecast helps via the demand channel but hurts via the investment channel; a seller-only outcome helps if the reverse holds. Online Appendix C.3 shows both are possible, but these market outcomes generally do not coincide with the social optimum, so implementing welfare-improving selective disclosure may require the central bank to control the payment data.

Q7. How does forecast precision affect outcomes?

Raising phi_o (precision of the optimistic signal) requires lowering phi_p, sharpening the forecast under both realizations. Through the demand channel, dE[w]/dphi_o = phi-tilde(theta_G-theta_B)[w’(theta-tilde_G)-w’(theta-tilde_B)], which is positive when w is convex and negative when concave. Through the investment channel, more precision raises theta-tilde_G but lowers theta-tilde_B, which can raise or lower investment depending on kappa. With private banks, Proposition 4 shows buyers’ and sellers’ willingness to pay rises with precision, making production (and possible over-production) more likely and selective disclosure less likely. Under Bayesian persuasion, higher precision weakly raises welfare (it expands the feasible policy set); but if private banks also disseminate, the central bank’s persuasion is constrained because agents’ posteriors cannot contain less information than the private forecast.

Q8. How are privacy and cash modeled, and what is the effect on welfare?

A fraction eta in (0,1) of buyers (‘cash buyers’) face sufficiently large privacy costs from deposit-based payments and use lower-return cash; the rest (‘deposit buyers’) prefer deposits. Cash use shrinks the share of recorded DM transactions, lowering forecast precision (unless cash and deposit buyers’ demand is perfectly correlated). By the precision results this can raise or lower welfare; with private production it makes excessive information less likely, while under central-bank noisy-message disclosure lower precision shrinks the feasible policy set and can reduce welfare. If the privacy cost is increasing and concave in DM consumption x, deposit buyers’ net DM utility becomes less concave, making w more likely convex, so disclosure can improve welfare via the demand channel and the optimal policy may switch from non-disclosure to disclosure. This partially but not fully offsets the negative welfare impact of the privacy cost.

Q9. What are the equilibrium-multiplicity and underinvestment results in the benchmark?

With no data sharing, all decisions are state-independent under theta-bar. Strategic complementarity (more sellers investing raises buyers’ deposits, which raises investment payoff) can generate multiple stationary equilibria (lambda=0, lambda=1, and a mixed lambda in (0,1)) when kappa and theta-bar are intermediate (Figure 1). The lambda=1 equilibrium is highest-welfare and Pareto optimal, and the authors impose a refinement selecting it. Sellers can underinvest: there exists kappa for which lambda=0 is the unique equilibrium even though lambda=1 would be socially better, because sellers receive only (1-sigma) of DM surplus. This underinvestment drives the investment-channel welfare results.

Versus Andolfatto-Berentsen-Waller (2014) and Andolfatto-Martin (2013), where assets pay stochastic dividends and information is disclosed at the start of the DM so nondisclosure is always optimal (consumption smoothing), here the forecast is revealed at the start of the CM and affects deposit and investment decisions, so disclosure can be welfare-positive or -negative. Versus Choi-Liang (2023), whose non-monotonic disclosure effects arise from a money-adoption coordination margin, here non-monotonicity arises from how disclosure shapes marginal deposit holdings and investment. It extends the payment-data literature (Garratt-van Oordt 2021; Garratt-Lee 2020; Kang 2024; Amendola-Araujo-Ferraris 2025; Wang 2020, 2023; Cheng-Izumi 2025; Ahnert-Hoffmann-Monnet 2024) by focusing on the macroeconomic forecasting value of payment data and optimal disclosure, and connects to central-bank communication work (Morris-Shin; Jarocinski-Karadi 2020 information channel; Aruoba-Drechsel forthcoming).

Q11. What are the CBDC and privacy-protection implications and their scope conditions?

CBDC can serve as an institutional alternative source of payment data: transactions are recorded on a digital ledger, potentially letting the central bank observe flows directly, and can reduce coverage gaps from financial exclusion (the paper cites the 2021 FDIC survey: 4.5 percent of U.S. households, about 5.9 million, were unbanked). CBDC data could improve welfare via the demand and investment channels. Because privacy is a primary public concern, the authors recommend privacy-preserving architectures: adding statistical noise (differential privacy), randomizing data on the buyer’s device before transmission, keeping data decentralized with only model updates shared (federated learning), and clear governance/consent. Scope condition: incentivizing a cash-to-deposit/CBDC shift is welfare-improving only under sufficient privacy protection and only under the conditions (e.g., concave privacy cost, high g) that make disclosure beneficial; legal hurdles to central-bank access of payment data remain, which CBDC issuance could circumvent.

Q12. What extensions and robustness checks are reported?

Correlated signals: the central bank and private banks may receive correlated but non-identical signals (e.g., the bank has confidential surveys); Online Appendix B.4 shows this does not change the main results because information affects allocations only through agents’ beliefs about theta_t at decision time. The model is calibrated to the U.S. 2016-19 (Online Appendix B.2) for the quantitative figures. Online Appendix C.2 provides a continuous-investment version (under which the investment channel is always active and welfare responses are smoother); the paper deliberately presents the discrete-investment case to highlight the channels. Online Appendix C.1 gives additional noisy-message numerical exercises, and C.3 shows selective-disclosure cases. An alternative to the lambda=1 refinement is a government ‘revenue backstop’ subsidy (Online Appendix B.2).

Key Concepts

Demand channel: The mechanism by which disclosing the aggregate-demand forecast changes buyers’ deposit holdings and hence DM consumption volatility; its welfare sign depends on whether aggregate welfare w(theta) is convex or concave, governed by the curvature statistic T(x), not merely by the concavity of buyer utility.

Investment channel: The mechanism by which disclosure changes sellers’ discrete decision to invest in higher productivity; because sellers capture only fraction (1-sigma) of DM surplus they underinvest, so disclosure that encourages investment raises welfare and disclosure that discourages it lowers welfare.

T(x) statistic: A normalized log-curvature measure, T(x) = [u’’(x)]^2 / [u’’’(x)(u’(x)-1/theta)], that disciplines the curvature of w(theta): w is convex when T(x) < 1/3 and concave when T(x) > 1 over the relevant consumption range, capturing how quickly the marginal DM surplus falls as consumption rises.

Bayesian persuasion via noisy messages: In the paper’s sense, the central bank commits to a publicly known communication policy (choosing posteriors P^g and P^b) that deliberately garbles the forecast - e.g., sending the pessimistic message even when the forecast is optimistic - to shift agents’ expectations (especially to induce socially efficient seller investment), exploiting that Bayes’ rule constrains only the average posterior.

Excessive information production: The outcome under a competitive market for forecasts where, because banks earn zero profit and both buyers and sellers are willing to pay for the forecast even though it may lower aggregate welfare, the forecast is always produced and sold whenever the cost C is below a threshold, over-supplying information relative to the social optimum.

Cash buyers / privacy cost: Buyers facing sufficiently large privacy costs from deposit-based (recorded) payments who choose lower-return cash; their use reduces recorded transactions and forecast precision, but a privacy cost that is concave in consumption can make deposit buyers’ preferences less concave, turning welfare convex so that disclosure becomes optimal and partially offsets the privacy cost.

Aggregate state theta_t: The two-valued (theta_B bad, theta_G good) random fraction of buyers who become active and demand the DM good, equal to the level of aggregate demand; realized at the start of the DM with unbiased forecast theta-tilde_t derived from aggregated payment data.

Merger guidelines for the labor market

Wed, 01 Jan 2025 00:00:00 +0000

Layer 1: Overview

Research question and motivation. Antitrust review of mergers has historically focused almost entirely on harm to consumers (product-market monopoly), ignoring harm to workers (labor-market monopsony). Following the July 2021 White House executive order and the DOJ’s monopsony-based challenge to the Penguin Random House (PRH)/Simon & Schuster (SS) publishing merger, the agencies are now putting buyer power at the center of policy. The paper asks: how should Herfindahl-based merger-review thresholds, designed for product markets, perform if applied to local labor markets, and what efficiency gains would a merger need to leave workers unharmed?

Model and data. The authors extend Berger, Herkenhoff, and Mongey (2022, “BHM”) to allow multi-plant (post-merger) ownership. The model has a representative household supplying labor through a nested-CES system (within-market substitutability governed by eta, across-market by theta, with eta > theta > 0), firms competing in quantities (Cournot/oligopsony), heterogeneous firm productivity, decreasing returns to scale, and capital. Firms set wages as a variable markdown on the marginal revenue product of labor; the markdown depends on the firm’s local payroll share. Markets are defined as 3-digit NAICS by commuting zone. Calibration is taken directly from BHM using confidential US Census data (LBD). Key estimated values: theta = 0.42 and eta = 10.85 (the elasticity-substitution parameters; the paper also reports theta = 0.45 in one passage), productivity dispersion sigma_z, returns to scale alpha, etc. The average market has 113 firms, an HHI of 0.11 (about nine equal firms), the average firm share is ~0.02, and the employment-weighted average markdown is 0.72 (workers paid 72% of marginal revenue product), equivalent to a labor-supply elasticity of 2.57.

Theory. Proposition 1 shows that, absent efficiency gains, a within-market merger equalizes the two merged plants’ markdowns at the level implied by their combined share, depresses both merging plants’ wages, lowers the market wage index and employment, and reduces total worker pay. Non-merging firms’ shares rise and they expand, so the actual rise in concentration is smaller than a “naive” calculation (adding pre-merger shares) would predict. Under the monopsony limit (infinitely many firms, or eta = theta), mergers have no effect.

Main quantitative findings. (1) Model validation: replicating Arnold (2020), the model generates a change in log employment of -9.0 (vs Arnold -14.4, about three-fifths), log earnings -0.7 (vs -0.8), log payroll -10.5 (vs -12.1); earnings fall -4.4% in high-concentration vs -1.1% in medium-concentration markets (Arnold: -3.1% and -0.8%); the naive-concentration regression coefficient is 0.893 (Arnold 0.834), both below one. (2) PRH/SS simulation (PRH 37% share, SS 12%): with no efficiency gains the merger cuts author wages by 5%; the Required Efficiency Gain (REG) for worker-surplus neutrality is 17%. A merger of the two largest publishers gives -10% wages and a 30% REG; the two smallest Big Five give a 13% REG. (3) Applying product-market thresholds to labor markets via a 200,000-market simulation: under the stricter 1982 guidelines (block if post-merger HHI > 1800 and Delta-HHI > 100), the average REG of permitted mergers is 4.68%; under the looser 2010 guidelines (HHI > 2500, Delta-HHI > 200) it is 5.96%. Thus at the standard assumed 5% efficiency gain, 1982-permitted mergers raise the wage index (+0.04%) while 2010-permitted mergers lower it (-0.14%) and harm workers. (4) The Gross Downward Wage Pressure Index (GDWPI) equals (1/theta - 1/eta) times the other plant’s payroll share. Among mergers with GDWPI > 5% at both plants, more than 80% require a REG of at least 5.8% (20th-percentile REG = 5.8%, median 6.4%); among GDWPI > 10% at both plants, more than 80% generate a welfare loss under an assumed 5% efficiency gain.

Implications. Product-market thresholds are too lenient for labor markets because labor is harder to substitute than products (low theta). The framework lets regulators trade off Type I error tolerance and efficiency-gain priors to set concentration thresholds.

In depth

Q1. What is the identification/estimation strategy for the key parameters, and what are the threats to it?

The model is not separately estimated; calibration is inherited wholesale from BHM (2022). The crucial labor-supply substitution parameters theta (across-market) and eta (within-market) are estimated in BHM from tradeable firms’ market-share-dependent employment responses to corporate tax changes, identifying how much firms with different market shares move employment when after-tax returns change. Productivity dispersion sigma_z matches the payroll-weighted HHI, alpha matches labor’s share, gamma the capital share, Z mean firm size, and phi mean worker earnings. Main threats: (i) theta and eta are estimated from tradeable (largely manufacturing) firms and held fixed economy-wide, while the authors acknowledge no economy-wide substitutability estimates exist outside manufacturing; (ii) markets are defined by NAICS3-by-CZ rather than occupation (the conceptually preferred unit), because occupation codes are unavailable for the universe of workers; (iii) the whole exercise relies on the calibrated structure being the right laboratory.

Q2. How is the model validated out of sample?

By replicating Arnold (2020), who estimates causal labor-market effects of US mergers. The authors draw and merge two firms per market, impose a pre-merger employment cutoff (tilde-n = 46, about five times average firm size) so that median pre-merger employment matches Arnold’s sample (116), and run Arnold’s exact regressions on simulated data. The model reproduces the sign and roughly the magnitude of employment and wage declines, the concentration interaction (effects more than three times larger in high-concentration markets), and the sub-one naive-concentration coefficient. This is out-of-sample because none of these moments were targeted in calibration.

Q3. What is the central welfare metric and policy quantity?

Worker Surplus Neutrality: a merger is worker-surplus neutral if the market-level wage index W_j is unchanged (using a household problem in which profits are NOT rebated, to mirror the product-market consumer-surplus standard). The key policy object is the Required Efficiency Gain (REG, Delta-star): the common post-merger productivity gain at both plants needed to keep W_j constant. By Proposition 1.5 the REG is always positive.

Q4. What are the main mechanisms, and what is downward wage pressure specifically?

Market power comes from costly worker mobility within (eta) and across (theta) markets. When two plants merge, hiring at Plant 1 raises the market wage and thus the wage the merged firm must pay its inframarginal workers at Plant 2 (and vice versa). The merged firm internalizes this cross-plant cost, which acts like a per-worker ’labor cannibalization tax,’ lowering the marginal benefit of hiring at both plants, so it hires less and pays less. Downward wage pressure at Plant 1 equals n_2j times the derivative of w_2j with respect to n_1j; in share form DWP_1j = w_1j (1/theta - 1/eta) s_2j. The GDWPI normalizes this by the wage: GDWPI_1j = (1/theta - 1/eta) s_2j, bounded in [0, theta^-1 - eta^-1], interpretable as a wage tax rate. Larger partner share and higher within-market substitutability (eta) raise downward pressure.

Q5. What heterogeneity is documented?

Effects vary strongly with concentration: earnings fall -4.4% in high-concentration markets vs -1.1% in medium-concentration markets (model). Effects depend on the merging firms’ shares: assuming a 5% efficiency gain, fewer than 12.1% of mergers in which the smaller firm’s payroll share exceeds 5% yield a worker-surplus gain. REGs differ across publisher pairings in the PRH case (17% for PRH+SS, 30% for the two largest, 13% for the two smallest). The model also generates wide firm-level variation in markdowns (small firms near competitive, large firms marked down well below 0.72).

Q6. What do the confidence/threshold figures show?

Fixing a 5% efficiency gain, the simulation reports the fraction of mergers yielding a worker-surplus gain by concentration cell. 89.5% of mergers with post-merger HHI < 500 and Delta-HHI < 50 yield gains. Under the 2010 highly-concentrated definition (HHI > 2500, Delta-HHI > 100 in the cited cell), fewer than 34.8% yield gains. A merger with small-firm share 4% and large-firm share 18% has a 69.7% chance of a worker-surplus gain at 5% efficiency, rising to 97.7% at a 10% efficiency gain. This lets a regulator pick thresholds for a desired Type I error tolerance.

Q7. How sensitive are results to the assumed efficiency gain?

Highly. Under 1982 guidelines, permitted mergers change average W_j by -0.40% at 1% efficiency, … up to +0.04% at 5% efficiency; blocked mergers fall -7.39% (1%) to -5.99% (5%). Under 2010 guidelines, permitted mergers fall -0.63% (1%) to -0.14% (5%); blocked mergers fall -10.37% (1%) to -8.61% (5%). The 5% benchmark (Farrell-Shapiro) is itself questioned: Blonigen and Pierce (2016) find roughly zero or negative merger productivity gains, implying even the 1982 thresholds may be too lenient.

It extends BHM by adding multi-plant ownership and merger analysis. Relative to Nocke and Schutz (2018a,b) and Nocke and Whinston (2022), who derive product-market merger comparative statics under Bertrand competition (and, for Nocke-Whinston, CRS), this paper derives results for the LABOR market under nested-CES supply, Cournot competition, decreasing returns to scale, and endogenous household income. Relative to Naidu, Posner, Weyl (2018) and Marinescu-Hovenkamp (2019), who translate downward-wage-pressure concepts but assume symmetric firms, this paper provides a downward-wage-pressure test with firm heterogeneity across and within markets and shows it can be computed from readily available payroll shares and existing eta/theta estimates. It empirically benchmarks to Arnold (2020) and Prager-Schmitt (2021).

Q9. What are the policy implications and their scope conditions?

Product-market HHI thresholds are too lenient when applied to labor markets: at an assumed 5% efficiency gain, 1982 thresholds (1800/100) keep permitted mergers worker-surplus neutral while 2010 thresholds (2500/200) do not. Scope conditions: (i) results hinge on the assumed efficiency gain (which empirical evidence suggests may be well below 5%); (ii) the framework treats product-market effects as ‘out of market’ and should be combined with consumer-harm analysis; (iii) parameters are economy-wide benchmarks that may not fit a specific industry; (iv) market definition (NAICS3-by-CZ) matters, though the low estimated theta makes it consistent with a hypothetical-monopsonist test. The framework can be modified to add monopolistic pricing or variable markups (e.g., Deb et al. 2022).

Q10. Are there internal inconsistencies a reader should note?

Yes. Table 1 reports theta = 0.42 (and 1.49 as the data moment), but the text at one point states ’theta = 0.45, and eta = 10.85, giving theta^-1 - eta^-1 = 2.29.’ The 2010 threshold is described in the abstract/Section 3 as Delta-HHI > 200 but the headline simulation result (4.68% vs 5.96%) compares ‘1800/100’ against ‘2500/200’, and one passage lists the 2010 thresholds as (2500, 200) while the highly-concentrated text uses Delta-HHI of 200 for presumption and 100 in a figure cell. These are presentational; the substantive ranking (1982 stricter, 2010 more lenient) is robust.

Key Concepts

Monetary Policy, Firm Heterogeneity, and the Distribution of Investment Rates

Wed, 01 Jan 2025 00:00:00 +0000

Layer 1: Overview

Research question and motivation. Investment is a sizable and the most volatile component of aggregate GDP, so understanding the investment channel of monetary policy matters for policymakers. Prior work has overwhelmingly studied the effect of monetary policy on the average investment rate. But an estimated average effect can reflect either a uniform rightward shift of the entire distribution (all firms invest a bit more) or a change in the shape of the distribution (a few firms invest a lot more). The paper asks: how does monetary policy reshape the cross-sectional distribution of firm investment rates, and what does that reveal about the frictions driving (heterogeneous) transmission?

Data and empirical strategy. Quarterly firm-level data from Compustat, sample 1986Q1–2018Q4, U.S. nonfinancial firms (financial firms, foreign firms, and firms with incomplete/questionable data excluded). Firm age is merged from WorldScope and Jay Ritter’s database. Accounting capital stocks are converted to real economic capital via a Perpetual Inventory Method (building on Bachmann and Bayer 2014). The investment rate is real capital expenditures (CAPX) net of sales of property/plant/equipment (SPPE), deflated and divided by the lagged real capital stock. The firm-level data are aggregated into quarterly investment-rate distributions and moments. Identification uses monetary policy shocks from the Gertler and Karadi (2015) Proxy SVAR (re-extracted with updated VAR data and high-frequency instruments). Estimation is via two-step quantile/bin local projections (eq. 1), with quarter dummies for seasonality and Newey-West standard errors. Shocks are scaled to reduce the 1-year Treasury yield by 25 basis points (100bp in some distribution figures for readability). As a validity check, an expansionary shock produces hump-shaped increases in investment (peak 1.4%) and GDP (peak 0.35%).

Main findings (three facts). Fact 1: An expansionary shock changes the shape of the distribution — fewer zero and small investment rates and more large ones. The 75th percentile responds significantly more than the 25th (the interquartile range rises significantly); the share of firms in bins [0,2) and [2,4) falls significantly while higher positive bins rise, most sizably in bin [28,infinity); negative investment rates are not meaningfully affected. The spike rate (share with investment rate >10%) rises and the inaction rate (|i|<0.5%) falls. Fact 2: These shape changes are more pronounced and statistically significant among young firms (defined as less than 15 years old) than old firms; spike rates rise more and inaction rates fall more for young firms. These effects persist even among firms unlikely to be financially constrained (low leverage, high liquidity, or dividend payers), arguing against a purely financial explanation. Fact 3: A decomposition (eq. 3) into extensive vs. intensive margins shows the extensive margin accounts for around 60% (intensive 40%) of the effect on the average investment rate, and around 60% (intensive 40%) of the heterogeneous average effect across age groups.

Model and mechanism. The authors build a general-equilibrium New Keynesian heterogeneous-firm model with fixed and convex capital adjustment costs, maintenance investment, and firm entry/exit (life cycles), in the spirit of Khan and Thomas (2008) and Winberry (2021). Calibrated to U.S. data (quarterly, beta=0.99), it replicates all three facts. Fixed costs generate lumpy investment and an extensive-margin channel: an interest-rate cut raises the discounted benefit of investing, inducing some firms to switch from inaction to a sizeable investment. Young firms are on average farther from their optimal capital (higher marginal product of capital under decreasing returns), so they are induced to invest more easily — generating heterogeneity without any financial friction. This implies observational equivalence with the financial accelerator, but with opposite cyclicality: fixed costs imply procyclical policy effectiveness, whereas financial acceleration implies countercyclical effectiveness.

Aggregate/policy implications. Monetary policy is most effective when many firms are “close to paying the fixed cost.” The decline in business dynamism / firm aging since the 1980s has made monetary policy about 12% less effective at stimulating investment; policy is also less effective in recessions than booms (about 22% more effective in a large boom than a deep recession).

In depth

Q1. What is the identification strategy and what are the main threats to it?

The authors use exogenous monetary policy shocks from the Gertler and Karadi (2015) Proxy SVAR, re-extracted after updating both the VAR time-series data and the high-frequency (high-frequency surprise) instruments. These shocks are fed into two-step local projections: in the first step they construct time series of distributional objects (quantiles, interquartile range, the share of firms in each investment-rate bin, the spike rate, the inaction rate); in the second step (eq. 1) they regress the h-period change in each object on the shock, with calendar-quarter dummies to absorb seasonality and Newey-West standard errors for heteroskedasticity and autocorrelation. The validity check is that the shocks produce plausible hump-shaped aggregate responses (investment peak 1.4%, GDP peak 0.35%). The key threats are the standard ones for high-frequency-identified monetary shocks (the shock series being a valid instrument / external to the outcome) and the aggregation step; the paper does not run firm-level panel regressions with firm fixed effects here but instead works on aggregated distributional time series, so threats relate to the time-series identification of the GK shocks rather than firm-level confounding.

Q2. What are the main mechanisms and how are they distinguished empirically?

Two margins: the intensive margin (firms changing the size of investment conditional on adjusting) and the extensive margin (firms changing whether to invest at all). Empirically they are separated via the decomposition in equation (3), which classifies observations into spikes (i>10%) and normal (i<=10%) and writes the average rate as the spike fraction times the conditional spike rate plus the complementary term. The extensive-margin component isolates the change in the average rate coming only from changes in the spike rate; the intensive component isolates changes in conditional investment rates. Two covariance terms are dropped as negligible. The shape change in the distribution (fewer small, more very-large investments, negatives unaffected), plus the rising spike rate and falling inaction rate, are the empirical fingerprints of the extensive margin. The decomposition attributes about 60% of the average effect to the extensive margin.

Q3. What heterogeneity is documented?

Heterogeneity by firm age (young = less than 15 years old, old = 15+). Young firms show larger and more statistically significant shape changes (bigger drop in bin [0,2), bigger rise in bin [28,infinity)), larger spike-rate increases, and larger inaction-rate declines. The disproportionate right-tail (upper-quantile) response holds in both groups but is much more pronounced for young firms. The extensive margin explains roughly 60% of the young-vs-old gap in average effects. Appendix C reports similar but quantitatively weaker results when comparing small vs. large firms instead of young vs. old. The heterogeneous age effect survives within groups unlikely to be financially constrained (low leverage, high liquidity, dividend payers) and is also present among likely-constrained firms.

Q4. How does the model decompose the heterogeneous extensive-margin effect, and what is the ‘heterogeneous size effect’?

Using eq. (22), the heterogeneous extensive-margin effect splits into (i) a ‘heterogeneous hazard rate increase’ — an interest-rate cut raises young firms’ hazard (adjustment probability) more than old firms’, because young firms have a higher marginal product of capital and are farther from optimal size, so the discounted benefit of investing rises more for them; and (ii) a ‘heterogeneous size effect’ — among new adjusters, young firms choose higher conditional investment rates than old firms, so there would be a heterogeneous average effect even if hazard rates rose identically. Both are quantitatively important.

Q5. What role do the different adjustment costs play, and how is the model calibrated?

The model has fixed adjustment costs (random, uniform on [0, xi-bar]), convex adjustment costs (parameter phi), and maintenance investment (parameter chi). In isolation, the fixed cost generates 55% of the heterogeneous average effect and the convex cost only 29%, with the remaining 16% from their interaction (the heterogeneous size effect needs both: hazard changes require fixed costs, differing conditional rates require convex costs). Five parameters (sigma_z=0.07, k0=2.27, xi-bar=0.90, phi=2.20, chi=0.34) are fitted to five moments: standard deviation of investment rates (data 0.20 / model 0.18), average investment rate (0.12/0.13), autocorrelation of investment rates (0.38/0.38), relative size of entrants (0.29/0.29), and relative spike rate of old firms (0.40/0.40). Fixed parameters include beta=0.99, psi=0.58, theta=0.21, nu=0.64, delta=1.93% (giving a 7.7% annual aggregate investment rate), rho_z=0.95, pi_exit=1.625%, phi(Rotemberg)=90, gamma=10, Taylor inflation coefficient phi_pi=1.5, smoothing rho_r=0.75, external capital adjustment cost kappa=11.

Q6. What untargeted moments validate the model?

The model reproduces (i) firm life-cycle profiles — average investment rate highest for newborns and falling with age, decomposed into frequency of adjustment (extensive) and conditional investment rate (intensive), both higher for young firms; (ii) plausible aggregate monetary-policy responses; and (iii) the interest-rate elasticity of aggregate investment. All three investment frictions are needed for the life-cycle profiles: fixed costs generate adjustment frequencies below one, convex costs keep young firms’ conditional investment rates plausible (no instant jump to optimal size), and maintenance investment makes hazard rates decline with age.

Q7. What robustness checks are run?

Robustness to alternative quantile choices (Figure A.1); alternative spike thresholds of 8% and 12% (Figure A.8); using the spike rate vs. hazard rate to identify extensive-margin adjustments in the model (Figure A.12, very similar results); replication of heterogeneous spike/inaction effects within groups unlikely to be financially constrained (Figure A.6) and within likely-constrained firms (Figure A.7); small-vs-large firm comparison (Appendix C); and comparison of extensive-margin contributions across different shocks (aggregate TFP, wage-markup) in Appendix E.4, showing the extensive-margin contribution can differ substantially when a shock directly affects adjustment costs.

It builds on the empirical investment-channel literature (Christiano et al. 2005; Gertler and Gilchrist 1994; Ottonello and Winberry 2020; Jeenas 2023; Cloyne et al. 2023) which focused on aggregate or average investment rates; its novelty is documenting effects on the entire distribution and its moments. Against Cloyne et al. (2023), who interpret stronger young-firm responsiveness through the financial accelerator, this paper shows a non-financial friction (fixed adjustment costs) generates the same age heterogeneity — an observational-equivalence point — though it stresses its findings are ‘consistent with’ and ’not necessarily at odds with’ the financial accelerator (the intensive margin, stronger among young firms, may reflect financial acceleration). On the lumpy-investment theory side it extends Khan and Thomas (2008), Winberry (2021), Koby and Wolf (2020), Reiter et al. (2013, 2020), Fang (2023) by adding firm life cycles. Relative to contemporaneous work by Lee (2023), which examines spike rates of small vs. large firms, this paper studies young vs. old firms and the entire distribution; relative to Gourio and Kashyap (2007), who study unconditional spike-rate cyclicality, this paper studies responses to monetary shocks.

Q9. What are the policy implications and their scope conditions?

Monetary policy stimulates aggregate investment mainly because a few firms switch from inaction to sizeable investment (extensive margin), not because many firms invest a little more. Effectiveness is state-dependent: it is higher when many firms are ‘close to paying the fixed cost’ — i.e., in booms and in high-business-dynamism economies with many young, growing firms. Scope conditions/quantification: the post-1980s decline in business dynamism / firm aging has made policy about 12% less effective; the impact effect on aggregate investment is 1.44% in baseline, 1.61% (about 11.5% larger) under a high-dynamism calibration (13% entrant share, as in 1984) and 1.32% (about 8.5% smaller) under low dynamism (3.375% entrant share); policy is about 22% more effective in a large boom than a deep recession. Critically, the cyclicality direction differs from the financial accelerator: fixed costs imply procyclical effectiveness, financial acceleration implies countercyclical — a distinction that matters for policy and aligns with evidence (Tenreyro and Thwaites 2016) that policy is weaker in recessions. A key caveat from general equilibrium: a higher young-firm share does not automatically raise effectiveness, because higher investment demand raises the price of capital and crowds out investment; state dependence only arises when the price elasticity of aggregate investment is sufficiently low (as in their model).

Q10. What are the main caveats and open questions?

The extensive-margin channel cannot rationalize the entire young-old responsiveness gap — the intensive margin is also quantitatively relevant and may reflect financial acceleration. The roughly-60% extensive-margin share of the heterogeneous effect cannot be rationalized by the classical Bernanke-Gertler-Gilchrist (1999) financial accelerator, which operates on the intensive margin. The spike rate is used as an empirical proxy for the model’s unobservable hazard rate. The paper leaves open why young firms grow slowly, how the relevant frictions respond to economic policy, and how policy effects are shaped by these frictions, pointing to non-financial constraints like productivity/demand uncertainty (Jovanovic 1982; Chen et al. 2023) as further avenues.

Key Concepts

Policy transition risk, carbon premiums, and asset prices

Wed, 01 Jan 2025 00:00:00 +0000

Layer 1: Overview

Research question and motivation: Central bankers, regulators, and investors increasingly worry about climate “transition risks” — abrupt shifts in climate policy, green technology breakthroughs, or consumer-preference shifts that re-price assets (Carney’s “tragedy of the horizon”). Rather than use the fixed NGFS-style stress-test scenarios, the authors ask how policy transition risk — modeled as stochastic, reversible jumps between climate-policy regimes — endogenously affects carbon pricing, asset prices, risk premiums, the risk-free rate, and the speed of the green transition.

Model setup: A global two-sector continuous-time DSGE macro-finance model of the climate and economy (building on Hambel, Kraft, van der Ploeg 2024). Two sectors produce perfectly substitutable final goods via Cobb-Douglas in capital and a CES energy composite of fossil fuel and renewables; sector 1 is “green” (renewables-intensive) and sector 2 is “brown” (fossil-intensive). Investment carries quadratic intertemporal adjustment costs and brown-to-green capital reallocation carries quadratic intrasectoral costs (a dollar of brown converts to less than a dollar of green). Temperature rises in cumulative emissions (TCRE specification). Households have Epstein-Zin recursive preferences; dividends are leveraged consumption (D=C^phi, phi>1). Capital is exposed to Brownian shocks plus Barro-style macro-disaster jumps; learning-by-doing lowers renewable costs. The core model has a two-state policy Markov chain — BAU (no carbon pricing) and CAP (carbon pricing internalizing damages and enforcing a Tcap=2C cap; if the cap is breached, fossil use is forced to zero). Policy tips with transition intensity calibrated at lambda_x = 4% per year from BAU to CAP. Model solved by finite differences; 20,000 simulated paths to 2100. Calibration: RRA gamma=2.977, EIS psi=1.5, time preference delta=0.0346, initial GDP $116tn, initial brown-capital share S0=0.876, TCRE=1.8 C/TtC, T0=1.27C.

Main quantitative findings: (1) Under pure BAU, the green transition is slow and temperatures reach on average 3.9C above pre-industrial by 2100; risk-free rate and risk premiums are almost unaffected (TFP damage alone cannot generate a temperature premium). (2) With policy transition risk, by 2100 about 28% of paths stay below 1.8C, 46% land between 1.8C and 2.5C, and the rest exceed 2.5C; roughly 45% of paths adhere to the 2C cap; 94% of paths have active climate policy by 2100. On the illustrative path tipping to CAP in 2045, a carbon price of ~~$700/tC (~~$190/tCO2) is imposed; the green share price jumps +22% and the brown price drops -21.5% on impact. In the ~4% of paths where CAP is adopted in 2021, the carbon tax starts at ~$218/tC ($60/tCO2), about 50% larger than Pigouvian pricing without an enforced cap — because the cap forces policymakers to catch up. (3) The model generates a sizable, positive carbon premium (brown minus green risk premium) that is initially near zero but becomes large when temperature is close to or above the 2C cap and the economy is still carbon-intensive; the dominant channel is the asymmetric temperature-shock impact on the brown sector’s price-dividend ratio (third term of eq. 3.4). Without transition risk (first-best Pigouvian pricing), the carbon premium is slightly negative. (4) The mean risk-free rate starts at 0.8% and is largely stable, but its lower quantile falls sharply when temperature approaches/exceeds the cap as precautionary saving rises. (5) Extensions table: in the pure PIGOU scenario (no cap, no transition risk) climate disasters roughly double the optimal carbon tax from $45/tCO2 (2025) to $91, and adding irreversible climate tipping raises it to $121; in the core BAU->CAP model the average optimal CO2 tax rises from $73 to $108 (disasters) to $134 (tipping). News effects on share prices are far larger for policy tips than for climate or technology tips (climate tipping events move prices ~3-5%; a BAU->CAP tip moves the brown price ~-27% and brown price-dividend ratio ~-13%, green price +18%, green PDR +42%).

Implications: Policy transition risk makes average policy more ambitious than BAU but less than first-best; it produces risk-driven carbon premiums that accelerate the green transition, raises precautionary saving, and depresses the risk-free rate near the cap. Physical risks alone (assumed symmetric across sectors) cannot generate a sizable carbon premium but do raise carbon prices and create a temperature risk premium on all assets.

In depth

Q1. What is the identification strategy, and what are the main threats to it?

This is a calibrated structural (DSGE) model, not an empirical identification design, so ‘identification’ here means the model mechanism that generates carbon premiums plus calibration to external sources. The carbon premium is generated purely endogenously by making the brown sector more fossil-/carbon-intensive than the green sector, with physical risks assumed to load symmetrically on both capital stocks so any premium asymmetry comes from policy transition risk and temperature exposure rather than from differential physical-risk loadings. The main threats the authors acknowledge are: (i) calibration choices for negative-emissions cost curves and transition probabilities are ’tentative’ and partly curve-fit/ad hoc; (ii) exogenous and stark policy states (two or three regimes with given/partly exogenous transition intensities) are a simplified representation of the political process; (iii) global-economy calibration sits uneasily with national-election interpretations of policy tipping. They argue the forward-looking households/firms make the model robust to the Lucas critique.

Q2. What are the main mechanisms, and how are they distinguished?

Three channels for the carbon premium appear in equation (3.4): (1) a stochastic-discount-factor/transition-shock term scaling in transition intensities lambda_x; (2) a diffusive term from the volatility of the brown-capital share affecting the brown price-dividend ratio more (largest when S(1-S) is high, i.e. share neither very high nor very low) and from higher consumption-capital-ratio volatility in the brown sector combined with leverage; (3) a temperature-shock term that becomes large near 2C because the policy transition to CAP becomes potentially devastating (forced phase-out of fossil fuel) and hits the brown PDR much more than the green PDR. The authors state the third (temperature-near-cap) effect is quantitatively the most important. The premium is risk-driven, distinguished from preference-driven mechanisms (Pastor et al. 2021; Pedersen et al. 2021; Zerbib 2022) in which green investors accept lower returns.

Q3. What heterogeneity is documented?

Heterogeneity is across states and paths rather than across firms in data. The carbon premium and risk-free-rate response depend nonlinearly on temperature (large near/above 2C) and on the brown-capital share S (large transition effect when S is high). Across simulated paths the outcomes diverge widely: ~28% below 1.8C, ~46% between 1.8C and 2.5C, the rest above 2.5C by 2100. The price impact of news differs sharply by type: policy tips dominate climate tips and technology tips. The risk-free rate’s lower quantile falls much more in high-temperature paths.

Q4. What robustness checks and extensions are run?

Extensions: (a) recurring temperature-dependent climate disasters (intensity rising linearly in T, lambda_c-hat=0.096, lambda_c(T0)=0.122, expected loss 1.5% vs 25% for macro disasters, alpha_c=65.7); (b) irreversible climate tipping via a 3-state chain raising TCRE from 1.8 to 2.1 to 2.4 C/TtC and adding permanent damages d=0,0.025,0.05; (c) a negative-emissions/technology-breakthrough state (2-state chain, ~50% chance of competitive technology by 2050, intensity 0.0224, cost curve fit to Rebonato et al. 2023); (d) a richer 3-state policy chain BAU/PIGOU/CAP with reversible and partly endogenous transition probabilities (switch to active policy rising toward 75% if T>1.5C; lobbying makes switches depend on brown/green capital shares), giving an 18-state (2x3x3) Markov chain. Core qualitative results (positive carbon premium driven by policy risk near the cap, precautionary saving lowering the risk-free rate) survive all extensions; the carbon premium is smaller in the 3-state model because only ~30% of paths reach CAP. A model variant with exhaustible fossil resources (cap 3000 GtC) found the exhaustibility constraint non-binding.

It extends Hambel et al. (2024), which used a two-sector economy for climate disasters/tipping and first-best carbon prices but did not study policy transition risk or carbon premiums. It builds general-equilibrium structure on the partial-equilibrium reduced-form insights of Hsu et al. (2023) on the pollution premium (who report a 4.42% annual pollution premium). It is most closely related to Barnett (2024), also a DSGE transition-risk model, but adds richer interactions among climate tipping, political risk, and technology breakthrough, imperfect energy substitution, and intrasectoral adjustment costs; Barnett instead emphasizes a climate-policy-driven ‘run on fossil fuel’. It provides a risk-based mechanism for the carbon premium documented empirically by Bolton and Kacperczyk (2021, 2023) and Hsu et al. (2023), while noting contrary evidence (Pastor et al. 2021; Bauer et al. 2022; Aswani et al. 2024; Zhang 2025 — who finds the premium turns negative in the U.S. after a data-lag correction; Hambel and van der Sanden 2024). Calibration of policy scenarios follows Moore et al. (2022).

Q6. What are the policy implications and their scope conditions?

Under policy transition risk, average climate policy is more ambitious than BAU but less ambitious than first-best; policymakers may set carbon taxes even higher than first-best to ‘catch up’ for time lost by predecessors when the economy is close to the temperature cap. Carbon premiums encourage firms to shift investment from brown to green and accelerate the transition. Scope conditions: carbon premiums are large only when the economy is still carbon-intensive (high brown-capital share) AND temperature is near or above the 2C cap; if policymakers implement first-best Pigouvian taxes while ignoring transition risk, the carbon premium is slightly negative. Physical-risk symmetry across sectors is assumed; if physical risk hit sectors differently there would be additional carbon-premium effects.

Q7. What happens to asset prices at the moment of each type of tipping?

At a tip to more ambitious carbon pricing, green share prices rise and brown share prices fall (and conversely when policy weakens). At a climate tip, both green and brown share prices fall (~3-5% each in the illustrative path). When negative-emissions technology becomes available, green prices jump down and brown prices jump up while the carbon price falls (because the brown sector may use fossil fuel again). The brown asset becomes worthless once the transition completes and the brown capital stock is run down; partial stranding occurs when the cap is crossed and fossil use is banned. News effects on prices are much larger for policy than for climate or technology tipping.

Q8. What drives the risk-free rate dynamics?

The risk-free rate (eq. 3.2) combines discounting, consumption-smoothing, standard diffusion and macro-disaster precautionary saving, an uninsurable temperature-risk term (small because consumption volatility is close to capital volatility, and it vanishes under CRRA), and a novel policy-transition-risk term that makes the rate jump with the policy state. Increased transition risk raises precautionary saving and lowers the rate, especially when temperature is close to its cap (where forced fossil phase-out makes expected consumption growth drop). As the transition completes and brown capital shrinks, precautionary saving falls and the rate stabilizes. Mean rate ~0.8%, stable; lower quantile falls over time.

Key Concepts

Policy transition risk: In this paper, the risk arising from stochastic, reversible jumps between discrete climate-policy regimes (no / modest / ambitious carbon pricing), modeled as a Markov chain with given or partly endogenous transition intensities — distinct from fixed NGFS-style scenarios. Financial markets price these regime-change risks even in the BAU state.

Carbon premium: Defined as the difference between the brown and green risk premiums (r^p_2 minus r^p_1). In the model it is a purely risk-driven, endogenous object arising because policy/temperature shocks hit the carbon-intensive brown sector’s price-dividend ratio more than the green sector’s; it is large near the temperature cap and slightly negative under first-best pricing without transition risk.

CAP policy state: The ‘ambitious carbon pricing’ regime in which policymakers set the carbon tax to internalize warming damages AND enforce a hard temperature cap Tcap=2C; if the cap is breached, fossil-fuel use is forced to zero (F1=F2=0) and carbon prices exceed the usual social cost of carbon.

PIGOU policy state: The ‘modest carbon pricing’ regime (added in the extended 3-state chain) that internalizes all global-warming externalities, including risks of climate disasters and tipping, but does NOT impose a temperature cap — yielding lower carbon taxes than CAP.

TCRE (transient climate response to cumulative emissions): The proportionality coefficient (theta/vartheta) translating cumulative net emissions into temperature change; calibrated at 1.8 C/TtC in the core model and allowed to jump irreversibly to 2.1 and 2.4 C/TtC under climate tipping.

Temperature/transition risk premium: A positive risk premium carried by all risky assets stemming from physical climate risk (disasters and tipping) that rises with the level of temperature; distinct from the carbon premium, which is the brown-minus-green differential and is driven mainly by asymmetric policy-transition exposure.

Partial asset stranding: The situation when the temperature cap is crossed and fossil fuel may no longer be burned, so the brown sector — though still operable with renewables — loses the value of its fossil-based capital, causing the brown share price to fall.

Macro and micro of external finance premium and monetary policy transmission

Mon, 01 Jan 2024 00:00:00 +0000

Layer 1: Overview

This paper establishes basic facts about the external finance premium (EFP) faced by euro area firms borrowing from banks, and studies how monetary policy is transmitted to it. The EFP — the extra cost a firm pays for external funds versus the opportunity cost of holding cash — is a central object in financial-accelerator theory (Bernanke-Gertler, Kiyotaki-Moore), but its determinants below the country level have rarely been measured directly. The motivation is that euro area policy discussion treats country-level sovereign spreads as sufficient summary statistics for financial conditions, yet there is little micro evidence on whether country variation actually captures the bulk of loan-level variation.

Data and strategy: The authors use AnaCredit, a loan-level database of all euro area firm loans of at least €25,000, restricted to all new, unsecured loans (so they are not directly affected by Covid government guarantees) in the ten largest euro area economies (Austria, Belgium, Germany, Spain, Finland, France, Ireland, Italy, Netherlands, Portugal), which cover 93% of both the number and value of new euro area loans and 95% of euro area GDP. The sample spans January 2019 to December 2023 and contains about 36 million loans (35,919,600 in the contract tables). Loans are matched to Orbis (firm controls), ECB IBSI and supervisory data (bank balance sheets and capital), CSDB (bank bond yields) and iMIR (aggregate loan rates). The EFP is the loan spread over a maturity-matched OIS rate. They sequentially decompose it via weighted least squares (loan-size weighted) into country-time, then bank-time, then firm-time fixed effects, with contract-level effects as a residual — so each fixed effect is a value-weighted index at that level. Sequence runs aggregate-to-granular so any covariance is attributed to higher aggregation levels, making covariate explanatory power a lower bound.

Decomposition findings: Country-time effects capture 48.5% of the variance; bank-time 23.8%; firm-time 16.3% (bringing country+bank+firm to 88.6%); residual contract-level variation is 11.4%. Banking relationships are highly local — 96% of bank-firm pairs are in the same country (84% value-weighted). At the country level, the relevant covariate is the euro-area average sovereign spread, not the country-specific one: local spreads explain 48% of country-level variation while the EA average explains nearly 80%, and local spreads add no power beyond the EA average — pointing to a common (global) risk factor. The EFP is roughly 2.6 times larger than the sovereign spread. The EFP is countercyclical (higher with lower GDP and higher unemployment). Bank-level: weaker banks (less capitalized, less liquid, more exposed to risky assets, higher funding costs, larger) charge higher EFPs; the 95-5 quantile range of Tier 1 capital implies almost 100 bps higher EFP. Firm-level: smaller, younger, more leveraged, less profitable firms pay more — the 5-95 leverage range implies 90 bps higher EFP, the probability-of-default range about 20 bps, and old (50yr) vs young (5yr) about 30 bps. Crucially, bank-, firm- and contract-level variation remains largely unexplained (R-squared on bank regressions ~0.01-0.05; firm ~0.11-0.18; contract ~0.0001-0.0003).

Monetary policy transmission: Using Jorda local projections on high-frequency identified ECB surprises (Altavilla et al. 2019: Target, Forward Guidance, QE factors from OIS changes around announcements), a null EFP response means exact pass-through. A one-SD Target surprise (8 bps) raises the EFP about 10 bps (peaking 3-5 months); a one-SD QE surprise (€500 bn) lowers the EFP about 20 bps, split roughly equally across bank and firm levels. Effects are asymmetric: policy-rate tightening (not easing) and QE (not QT) are amplified through the EFP. Tightening amplification is mostly at the bank level (bank lending channel, driven by weaker banks); QE additionally narrows the EFP at the firm level (firm balance-sheet channel, helping fragile firms). QT, while fully passed through to tighten lending, leaves the EFP unchanged — attributed to QT’s slower, more predictable, “loud-bang-less” implementation versus QE’s large-envelope announcements (a difference-in-difference on QE envelope months shows a significant EFP decline after envelope announcements). Implication: as the ECB shrinks its balance sheet (lowering liquidity), rate hikes become more likely to generate financial amplification via the EFP, since less-liquid banks respond more to rate hikes. The QT result is caveated by limited sample evidence.

In depth

Q1. What is the empirical strategy for decomposing the EFP, and why does the order of fixed-effect extraction matter?

The EFP (loan spread over maturity-matched OIS) is decomposed sequentially via weighted least squares (each observation weighted by loan size) into country-time, then bank-time, then firm-time fixed effects, with contract-level effects as the residual (Equations 1-3). Each fixed effect is effectively a value-weighted index of spreads at that level. The sequence MUST run from aggregate to granular: starting with loan-level effects would soak up all variance. Because aggregate effects are estimated first, any covariance (e.g., a particular firm type clustering at a particular bank, or a country with a strong/weak banking system) is attributed to the higher aggregation level. This means variance attributed to higher levels may be slightly overstated relative to joint estimation, but covariate explanatory power can be read as a lower bound. The authors avoid simultaneous estimation for two reasons: it is computationally infeasible to estimate ~10 million fixed effects jointly and retrieve their values (which are the dependent variables in the second stage), and the sequential method makes clear exactly where covariances land. A check absorbing firm/bank effects via differencing while explicitly estimating country-time effects yields a 98% correlation between sequential and jointly estimated country-time fixed effects.

Q2. What is the variance decomposition result, and what is its headline interpretation?

Country-time effects capture 48.5% of loan-level variance, bank-time 23.8%, firm-time 16.3% (country+bank+firm = 88.6%), and residual contract-level variation 11.4%. The headline: country-level variation — the usual focus of euro area policy — is the single largest component but only about half the story. Policymakers and researchers must look at more disaggregated (bank and firm) data to understand financial conditions. The ‘proverbial glass is half full.’

Q3. Why is the euro-area average sovereign spread, not the country-specific spread, the relevant covariate at the country level?

Regressing country-time EFP fixed effects on sovereign spreads: country-specific spreads explain 48% of country-level variation, while the EA-average spread explains nearly 80%; adding local spreads on top of the EA average yields no additional explanatory power (the local-spread coefficient is insignificant). This is consistent with variance along the time (t) dimension being much larger than across countries (c), suggesting a common factor — likely global risk aversion — drives country-level EFP variation. The EFP is roughly 2.6 times larger than the sovereign spread (specification 2). Heterogeneity: aggregate (EA) spreads matter most for large firms (multi-country operators) and short-maturity loans; for small firms and long-maturity loans the country-specific spread becomes relevant (verified with a Patton-Timmermann monotonicity test).

Q4. What evidence supports the bank lending channel at the bank level?

Bank-time EFP is regressed on bank balance-sheet and funding-cost variables. Higher EFP is associated with weaker banks: less capitalized, more exposed to risky assets, less liquid, and with higher funding costs. The 95-5 quantile range of Tier 1 capital implies almost 100 bps higher EFP. These covariates (except the interbank rate, which is common across banks and captures time variation) are bank-specific, so they reflect the bank’s own balance sheet rather than its average borrower — the essence of the bank lending channel. Larger banks also charge higher rates, which the authors suggest may reflect market power. Caveat: R-squared values are very low (~0.01-0.05), so most bank-level loan-rate behavior remains unexplained.

Q5. What evidence supports the firm balance-sheet channel at the firm level?

Firm-time EFP (net of country and bank effects) is regressed on firm fundamentals. Smaller, younger, more leveraged, and less profitable firms pay higher EFPs — a clear balance-sheet/financial-accelerator mechanism. Magnitudes from specification (4): the 5-95 leverage range implies 90 bps higher EFP; the probability-of-default distribution implies about 20 bps; old (50yr) versus young (5yr) firms differ by about 30 bps. This is notable because the sequential extraction attributes all bank-firm covariance to banks, yet firm-level drivers still appear. Caveats: covariates explain only about a fifth of firm-time variation, and part of the fit comes from including probability of default (itself a financial price).

Q6. What is found at the contract level?

After controlling for country, bank, and firm effects, residual contract-level variation arises only for firms borrowing multiple times in the same month at different rates. Regressing on loan size and maturity, both are statistically significant but collectively explain a negligible share (R-squared ~0.0001-0.0003). The authors call this a ’nothing to see here’ result and conjecture that unobserved contract characteristics — likely loan covenants — drive it; because these would correlate with size and maturity, there is omitted-variable bias, so they do not interpret the coefficients. Notably these are unsecured loans, so covenants are not about explicit collateral.

Q7. What is the identification strategy for monetary policy transmission, and what are its limits?

The authors estimate Jorda (2005) local projections of cumulative changes in the bank-time and firm-time EFP (h = 0..5 months) on high-frequency identified ECB monetary policy surprises from Altavilla, Brugnolini, Gurkaynak, Motto and Ragusa (2019) — rotated factors from OIS changes in a narrow window around announcements, interpretable as Target, Forward Guidance, and QE surprises (the QE sign is flipped so larger = larger easing). A null EFP response indicates exact pass-through of the policy rate to the loan rate, not ineffectiveness. Limits: at the country level, the analysis acknowledges it does not condition on exogenous variance, so causal claims at the country/macro covariate level are ’not strongly grounded’; the paper frames the country-level work as comovement/fact-finding. The local-projection monetary-policy results are stated as causal. Forward-guidance surprises are too small in this sample (the ECB deliberately withheld guidance) to generate identifying variation, so FG results are relegated to the appendix.

Q8. What are the main asymmetries in monetary policy transmission to the EFP?

Two sign/instrument asymmetries: (1) Policy-rate tightening (but not easing) is amplified via the EFP, mostly at the bank level, driven by weaker (less capitalized, less liquid, higher-NPL) banks. The weaker amplification from rate cuts is linked to limited policy space near the effective lower bound, which binds for cuts but not hikes. (2) QE (but not QT) is amplified via the EFP, reducing it at both bank and firm levels, with the firm-level reduction indicating a firm balance-sheet channel that helps fragile firms. Magnitudes: a one-SD Target surprise (8 bps) raises EFP ~10 bps (peak 3-5 months); a one-SD QE surprise (€500 bn) lowers EFP ~20 bps, split roughly equally bank/firm. QT is fully passed through to tighten lending but leaves the EFP unchanged.

Q9. Why does QT leave the EFP unchanged while QE moves it, and how is this tested?

The authors consider three channels: (i) QE’s signalling channel (signalling an accommodative stance near zero rates) has no QT equivalent; (ii) QE is announced in financial distress while QT occurs in calmer periods — but these concern ‘periods’ not ‘surprises,’ and in the event-study framework many QT surprises actually fall within the QE period as smaller-than-expected QE, so policy-cycle explanations don’t apply directly; (iii) the operationally relevant channel: QE arrives via large ’envelope’ announcements generating sizeable stock and flow effects (‘a loud bang’), whereas QT is implemented slowly, predictably, and designed to be ‘as unsurprising and gentle as possible,’ muting both effects. They test the third channel with a difference-in-difference comparing EFP changes around the five/six QE envelope announcement months (APP/PEPP announcements/recalibrations: September 2019, and March, April, June, December 2020) versus all other months. Both bank- and firm-level panels show no pre-trend divergence but a significant EFP decline after the envelope announcement, beyond the risk-free curve. Caveat: QT results rest on limited accumulated evidence and need reassessment; deviations from gradual balance-sheet normalization could have significant effects.

Q10. How is the bank/firm channel split corroborated via cross-sectional interactions?

Equation (9) adds interactions of monetary policy surprises with bank/firm fragility characteristics (reporting h=3). Consistent with the bank lending channel, transmission of rate-tightening and QE-easing surprises is amplified for banks with weaker regulatory positions, less liquid assets, and higher funding costs. Consistent with the firm balance-sheet channel, the EFP is reduced more strongly for fragile firms (by size, age, leverage, profitability). Two implications: QE narrowed not just sovereign spreads but also the EFP on loans to more fragile firms; and because less-liquid banks respond more to rate hikes and QT lowers system liquidity, QT and rate hikes interact — as the ECB shrinks its balance sheet, rate increases are more likely to generate financial amplification via the EFP.

Q11. What robustness checks are run on the country-level results?

Three main checks (appendix): (A1) excluding 2020 (the Covid year) entirely leaves results unchanged, so country results are not Covid-driven; (A2) restricting to loans where bank country equals firm country strengthens the result, so the irrelevance of local spreads is not driven by bank-vs-firm country matching; (A3) a long macro sample built directly from aggregate iMIR data spanning April 2005 to December 2023 yields similar results, addressing the short-T concern and validating the bottom-up micro construction. Results are also robust to using 2-year or 10-year sovereign spreads, and main results hold under OLS rather than WLS (though equal-weighting overweights small loans — the smallest 90% of loans are just 1.3% of the market). Westerlund-style cointegration tests address potential non-stationarity/spurious regression.

Q12. How does this paper relate to and differ from prior work?

It builds on the financial-accelerator literature (Bernanke-Gertler 1989; Kiyotaki-Moore 1997; Bernanke-Gertler-Gilchrist 1999) resting on a failure of Modigliani-Miller due to information asymmetries. Unlike the applied EFP literature that proxies the premium with bond spreads (Gilchrist-Zakrajsek 2012; Gilchrist-Mojon 2018) — relevant only to firms able to issue bonds, a significant limitation in the bank-intermediated euro area — this paper measures the EFP directly from bank loan rates. Unlike standard microdata work that saturates regressions with fixed effects (Khwaja-Mian 2008; Amiti-Weinstein 2018; Degryse et al. 2019) to separate supply from demand and then discards those fixed effects, this paper makes the fixed effects themselves the objects of study. On asymmetry, it adds to the literature on asymmetric monetary policy over the cycle (Keynes 1936; Cover 1992; Tenreyro-Thwaites 2016) and to the scant literature comparing instrument effectiveness during easing vs tightening (Wei 2022; Crawley et al. 2022), and complements Todorov (2020) showing QE shrinks risk premia for less creditworthy bond-market borrowers.

Q13. What are the policy implications and their scope conditions?

(1) Country-level sovereign spreads are inadequate summary statistics for euro area financial conditions — they capture only half the EFP variance — so monitoring must extend to bank and firm levels. (2) QE is effective at the micro level, narrowing the EFP especially for fragile banks and firms; it is a ‘fine substitute’ for interest-rate policy. (3) QT’s gentle, predictable implementation has so far avoided EFP amplification, but this is contingent on that specific implementation modality — a fast or surprising QT (a tightening-direction ’envelope’) could have significant effects on firm and household lending conditions. (4) Interest-rate and balance-sheet policies are complementary: as the balance sheet shrinks and liquidity falls, rate hikes become more amplifying via the EFP. Scope conditions: country-level/macro comovements are not conditioned on exogenous variance so are not strong causal claims; sovereign spreads are asset prices, not fundamentals; QT conclusions rest on a limited sample and need reassessment; the policy result reflects the specific ECB communication and operational modalities observed in 2019-2023.

Q14. What significant caveats and unexplained findings does the paper itself flag?

The paper is explicitly framed as a ‘fact-finding effort’ rather than a complete causal narrative. Most bank-, firm-, and essentially all contract-level variation remains unexplained by an extensive list of covariates (low R-squared). The finding that larger banks charge more (market power) is presented as an interpretation worth studying, not established. Country-level comovements are not causal. The QT/EFP-unchanged result rests on limited evidence. Contract-level drivers (likely loan covenants) suffer omitted-variable bias and are left uninterpreted. The authors repeatedly invite future work on causal mechanisms and sub-country determinants.

Key Concepts

The Credit Channel of Public Procurement

Mon, 01 Jan 2024 00:00:00 +0000

Layer 1: Overview

Research question and motivation. Public procurement accounts for roughly one-third of government spending (12.6% of GDP and 30% of total government expenditures in OECD countries in 2019). The standard view is that procurement helps firms grow by raising their revenues. Gabriel asks whether procurement also operates through a previously underexplored credit channel: if a procurement contract is a secure future cash-flow stream, firms can pledge it as collateral to obtain more credit. This matters especially in bank-dependent economies (in Portugal and several OECD countries, >80% of nonfinancial corporate debt is bank loans; <1% of Portuguese firms access capital markets), and for small/financially constrained firms.

Data and strategy. The author web-scrapes >1 million Portuguese electronic procurement contracts (2009-2019) from the official BASE registry, matching winners’ tax IDs to firm balance-sheet/income data (IES via BPLIM) and to the monthly Credit Registry (CRC) with loan-level collateral types. Focusing on contracts awarded via public contests (a silent sealed-bid first-price-auction-like setting) for quasi-exogenous variation yields 138,561 contract-winner pairings and 35,675 unique winner-year observations. Average contract award is ~€202,170 (median ~€33,762-34,762), average duration ~297 days, ~3.6 contestants. Identification uses Jordà (2005) local projections (Eq. 1) regressing credit growth (scaled by lagged assets) on the award amount (scaled by lagged assets), with firm and industry×year fixed effects, SEs clustered at the firm level. The identifying assumption is that winning via public contest is not systematically correlated with firm characteristics; conditional on fixed effects, winner/non-winner differences largely disappear (except total assets, which is controlled).

Main findings (with magnitudes). Winning an additional €1 of procurement raises total firm credit by up to €0.07 (3.3 cents drawn credit on impact, plus ~4 cents in potential/undrawn credit lines; total ~7 cents in the award year), and raises cash and bank deposits by ~6 cents. Interest rates fall by over 0.3 percentage points on impact, indicating the increase is supply-driven (winners’ average implicit rate ~6.9%, median ~5.1%). A back-of-envelope calculation gives ~2.5 pp credit growth one year out (vs. ~5 pp in Spain per di Giovanni et al. 2024). The credit increase is almost entirely collateralized; in monthly data, firm personal guarantees (which include future procurement cash flows) account for >66% of the credit increase at month 4, and adding state guarantees, cash-flow-based lending explains ~75%. On the real side: +6 cents of non-current assets/investment (mostly PPE) per euro, persistent employment gains, ~70% rise in sales income one year post-award, positive net income of ~5 cents per euro. cash-flow-based lending is ~44% of firm credit in the sample.

Heterogeneity and aggregate. Investment responses are concentrated in small/constrained firms (β ≈ €7.3 for small/micro vs. −€1.2 for big firms 2 years out; difference significant at 1%); credit responses do not differ significantly by size. Regionally (Eq. 2, NUTS-III, region+year FE, clustered at region), €1 of procurement raises regional GVA by ~€1.3 (€1.32 on impact), implying ~€0.32 crowding-in of private production; the credit channel accounts for ~5% (5.5%) of this. Procurement boosts private R&D but not TFP, with only modest, short-lived inflation and no broad regional credit expansion (suggesting credit redistribution toward winners).

In depth

Q1. What is the identification strategy and what are the main threats to it?

The author exploits public contests, which resemble a silent sealed-bid first-price auction with a costly single bid: the hiring entity does not know who bids and firms do not know their competitors or how many there are, so the winner is not ex-ante predictable. He estimates Jordà (2005) local projections (Eq. 1) of credit growth on the award amount, both scaled by lagged total assets, with firm and industry×year fixed effects and firm-clustered SEs. The key identifying assumption is that winning via public contest is not systematically correlated with other firm characteristics. Threats: (i) selection if contracts go to more productive firms (would overstate effects) or displace private opportunities (would understate); (ii) anticipation, if firms foresee winning and adjust early. He addresses anticipation by including pre-event horizons h=-2, h=-3 (annual) and pre-months (monthly), finding no significant pre-trends, and by focusing on contests (where outcomes are unknown, unlike direct awards) and using yearly aggregation (the announce-to-decision gap was ~4 months in 2020). Figure C.1 shows unconditional winner/non-winner differences mostly vanish once fixed effects are included, except total assets (which is controlled). Appendix C.1 adds a local-projections difference-in-differences robustness check following Dube et al. (2023).

Q2. What is the credit channel mechanism and how is it distinguished from a demand story?

The mechanism is cash-flow-based lending: procurement contracts represent secure future cash flows that firms pledge as collateral (personal/firm guarantees), easing borrowing constraints. It is distinguished from a credit-demand story by the price of credit: a demand-driven increase would raise interest rates, but rates fall by >0.3 pp on impact, consistent with a supply-driven expansion. Two micro-mechanisms raise perceived creditworthiness: (i) collateral value of the contract itself, and (ii) a signaling/certification effect where government endorsement reduces bank information asymmetry. Monthly collateral decomposition (Figure 5) shows the credit increase is overwhelmingly backed by firm personal guarantees (>66% at month 4; ~75% including state guarantees), with asset-based collateral mostly insignificant, directly supporting the cash-flow collateral channel.

Q3. How is the signaling/certification mechanism tested separately?

In Appendix Table C.3 (discussed in Section 3.5) the author compares first-time award recipients to firms with previous awards. First-time winners enjoy significantly higher and more persistent responses in credit, employment, and investment, which he interprets as a reputation/certification effect that partially resolves a banking information-asymmetry problem (banks learn the firm has government demand). This is distinct from the pure collateral mechanism, which is tested with the monthly collateral-type decomposition.

Q4. What heterogeneity is documented?

By firm size (Commission Recommendation 2003/361/CE: small = headcount <50 and turnover/balance-sheet <€10m): credit responses do not differ significantly between small and big firms, but investment and employment responses are much larger and more persistent for small/constrained firms (investment β ≈ €7.3 small vs. −€1.2 big at 2 years, difference significant at 1% and growing with horizon; HAC p-values for employment differences are 0.05 at 1yr and 0.00 at 2yr). This is rationalized via the financial-accelerator hypothesis (Bernanke et al. 1999) and investment-cash-flow sensitivity literature (Fazzari et al. 1988). Employment heterogeneity mirrors Giroud and Mueller (2017). By sector: Construction and Medical Equipment (~60% of 2019 procurement value) account for much of the credit response but show no significant persistent differences in investment/employment. By award history: first-time winners respond more strongly (reputation effect).

Q5. What does the monthly analysis add over the annual analysis?

Using monthly credit/collateral data within the first year (relevant since the median contract lasts <1 year), the credit increase begins at award inception, rises sharply in the first month, and peaks ~3 months after the award (aligning with the annual ~3+ cents/euro). The increase is almost entirely collateralized (unsecured credit shows a muted response) and of sound quality (non-performing credit barely moves). Both long- and short-maturity credit rise, with long-term credit responding more strongly. Crucially, no significant credit movement appears up to three months before signing, reinforcing the no-anticipation conclusion.

Q6. What are the aggregate/regional results and how are they estimated?

The author aggregates procurement by spending location to NUTS-III regions and estimates local-projection multipliers (Eq. 2) with region and year fixed effects, SEs clustered at region, sample matched 2010-2016 (25 regions × 6 years), procurement winsorized at the 95th percentile. A €1 increase in regional procurement raises GVA by ~€1.3 (€1.32 on impact, interpreted as an open-economy relative multiplier à la Nakamura-Steinsson 2014), implying €0.32 crowding-in of private production. Eq. 3 interacts procurement with winners’ credit (following Basso and Rachedi 2021): the positive significant interaction means credit amplifies the multiplier; a 1% credit-to-GVA increase raises the multiplier by 11% on impact, and since winners’ credit is ~0.5% of GVA, the credit channel adds ~(0.11×0.5)% ≈ 5.5% (~~5%). National-accounts regressions (Table 4) show procurement raises private value added (~~€1.2 on impact), private investment, private R&D (innovation), and modest short-lived inflation, but not TFP; aggregate nonfinancial-firm credit is subdued, suggesting credit redistribution toward winners rather than broad expansion.

Q7. What robustness checks and caveats are noted?

Robustness: anticipation tests at multiple pre-horizons (annual and monthly); a local-projections diff-in-diff specification (Dube et al. 2023) in Appendix C.1; fixed-effects conditioning that removes most winner/non-winner differences; winsorizing the regional regressor at the 95th percentile (results sensitive to outliers). Caveats explicitly acknowledged: (i) no loan-level data, so the implicit interest rate is total interest expense / lagged effective credit, and financial covenants cannot be observed (if present, estimates would be conservative); (ii) under Portugal’s Public Procurement Code (Ch. IX), contracts above ~€500k may require a guarantee up to 5% of value, often a bank guarantee that appears as firm-guaranteed credit—but the central message still holds; (iii) procurement coverage is incomplete (web-scraped data ≈ one-third of total procurement, ~3% of GDP), so regional coefficients should be read with caution; (iv) the regional credit measure may not capture the full cumulative credit response and credit increases could partly reflect non-procurement factors; (v) collateral values are not market-adjusted and are often capped at the loan amount.

It contributes to three literatures. (1) Firm-level effects of fiscal policy/procurement (Barrot-Nanda 2020; Goldman 2020; Cox et al. 2024; Ferraz et al. 2021; Lee 2021): prior work emphasizes revenues as the driver; Gabriel adds a new credit/collateral transmission mechanism across all industries. The closest contemporaneous work is di Giovanni et al. (2024) for Spain, who document a positive procurement-credit correlation; relative to them, this paper provides detailed evidence on the credit-supply channel and its investment implications, measures contract heterogeneity, and—unlike their welfare/allocation-system focus—provides the first local procurement multiplier estimates with the credit channel’s share. (2) Government spending and fiscal multipliers, including stronger fiscal effects under tight credit (Ferraresi et al. 2015; Aghion et al. 2014). (3) Financial frictions and collateral type, shifting from asset/liquidation-value collateral (Kiyotaki-Moore 1997) to cash-flow-based collateral (Lian-Ma 2021; Ivashina et al. 2022; Drechsel 2022; Caglio et al. 2022); the novelty is cash flows from sales to the government as collateral. Notably his investment elasticity for small firms (~5 cents/euro cumulative at one year) is smaller than Hebous and Zimmermann’s (2021) ~13 cents.

Q9. What are the policy implications and their scope conditions?

Two implications: (1) Targeting design—because small/financially constrained firms respond more strongly and persistently in investment and employment, targeting procurement to such firms (as pushed by the European Commission/Parliament for SMEs) likely raises aggregate investment and employment, not just efficiency. (2) Financial stability—letting firms pledge procurement contracts as collateral diversifies collateral away from real-estate/asset-based booms (which deplete project information and lead to deep downturns, Asriyan et al. 2022), so procurement could temper collateral-induced financial fluctuations. Scope conditions: external validity is greatest for countries where procurement is a large GDP share and firms rely heavily on bank credit (true for many developed and developing economies, e.g., Portugal where <1% of firms access capital markets); the effect grows more important the more bank-dependent firms are. The interest-rate decline is a firm-level result and should not be read as procurement lowering equilibrium interest rates economy-wide; a procurement shock can be a reallocation of spending rather than higher total spending/deficit.

Q10. What is the nature of the real-side response and why is the sales response not larger?

Winning raises non-current assets by ~6 cents per euro (mostly PPE/tangible, not intangibles or financial investments), comparable to Hebous-Zimmermann’s ~10 cents and to real-estate-collateral elasticities (~6 cents, Chaney et al. 2012; Catherine et al. 2022). Employment rises persistently beyond the first year (Ferraz et al. 2021), though without a matching rise in value added. Sales income rises ~70% one year post-award—less than a one-for-one mapping of public demand to sales—for two reasons: a ‘duration effect’ (contracts spread revenue over years; some last up to a decade) and a ‘capacity constraint effect’ (firms prioritize government contracts, diverting other business to competitors, which also shows up in regional GVA), potentially mitigated by sub-contracting. Despite higher costs of goods sold, net income stays positive at ~5 cents per euro, so contracts are profitable.

Key Concepts

Who bears the costs of inflation? Euro area households and the 2021-2023 shock

Mon, 01 Jan 2024 00:00:00 +0000

Layer 1: Overview

This paper measures the heterogeneous first-order welfare effects of the 2021-2023 inflation surge across households in the four largest euro area countries (Germany, France, Italy, Spain). Motivation: euro area headline HICP inflation peaked at 10.6% (year-on-year) in October 2022, driven mainly by energy and food prices following Russia’s invasion of Ukraine; cumulatively over 2021-23 the price index rose roughly 14% in France and Spain, 16% in Italy and 20% in Germany. The classic question—who wins and who loses from surprise inflation, and through which channels—is the focus.

Method: The authors build a tractable two-period overlapping-generations framework and use the envelope theorem to decompose the “money-metric” welfare change (in euros) into four additive, observable components requiring no functional-form or structural-parameter assumptions: (1) a direct component (raw inflation before fiscal support, holding wages and asset prices fixed; captures heterogeneous consumption baskets and the Fisher revaluation of net nominal positions, labor income, dividends and capital gains); (2) an unconventional fiscal policy component (ad-hoc energy price interventions and transfers); (3) an indirect component (short-run responses of nominal wages, pensions, taxes/fiscal drag, and asset prices); (4) a long-run adjustment component (relative prices returning to pre-shock ratios). They combine micro data—Household Budget Survey (2015 wave) for expenditure shares, HICP micro data for good-specific price changes (20 COICOP-based categories), the 2017 Household Finance and Consumption Survey (HFCS) for budget-constraint components, the Bruegel dataset for fiscal responses, and IMF (Dao et al. 2023) counterfactual prices—with event-study/high-frequency identification (on German HICP release days) for wage, pension, house, stock and bond price responses. Households are sorted into 15 groups: three age classes (25-44 young, 45-64 middle-aged, 65+ retirees) and five consumption (permanent-income proxy) quintiles per country. Welfare is expressed as a share of triennial (3-year) disposable income.

Main findings: (i) Average country-level welfare losses were sizable and heterogeneous: around 3% of triennial income in France and Spain, 7% in Germany, and 9% in Italy. (ii) The episode resembles an age-dependent tax: retirees lost up to 14% (German and Italian high-income retirees), while roughly half of 25-44 year-olds were net winners; young French households gained up to 7% (about EUR 4,000 on average), young Spanish broke even; middle-aged households lost roughly 2-11%. Overall about one quarter of euro area households were net winners. (iii) Losses were quite uniform across consumption quintiles because rigid (sticky) rents hedged the poor; excluding rents, the poor suffer more due to higher energy/food exposure. (iv) Nominal net positions (NNP) were the key driver of cross-household heterogeneity—retirees hold large positive nominal assets, the young hold nominal mortgage debt. (v) Energy prices generated vast individual-inflation-rate variation, but unconventional fiscal policy (especially energy price caps, more so in France where it cut inflation ~2 p.p.) shielded households, reducing first-stage welfare costs by about one-fifth on average. Estimated asset-price elasticities to a 10% inflation surprise: house prices -1.38% (beta x delta = -3.995 x 0.035 = -0.138), stocks -0.410, bonds -0.726. Pensions, being indexed, rose faster than wages; fiscal drag taxed away gains in Italy and Spain (unindexed brackets), much less in France/Germany. The counterpart of household losses is a large government gain from eroded real public debt: governments in France, Italy and Spain were net winners (Italy +4.5 to 5.1% of triennial GDP), while Germany roughly broke even. Policy implication: in a monetary union where monetary policy cannot address country-specific dynamics, fiscal policy was crucial; and redistributing government inflation gains to households could substantially offset their losses.

In depth

Q1. What is the identification/measurement strategy and what are its main threats?

The core strategy is an envelope-theorem decomposition that yields analytical ‘sufficient-statistic’ formulas for money-metric welfare change, requiring only observable budget-constraint quantities and price changes—no structural parameters or functional forms. The key assumption is that, to first order, substitution in consumption baskets and portfolio rebalancing after the shock have only second-order welfare effects, so observed pre-shock quantities (2015 HBS shares, 2017 HFCS positions) can be used. Four structural assumptions define the shock: (1) it is unanticipated; (2) the price-level jump is permanent but inflation is temporary (returns to zero from t=1); (3) the shock is long-run neutral in aggregate and across the distribution—all nominal variables and relative prices realign one-to-one with the new price level by t=1; (4) the government budget constraint accommodates either via the price level (active/FTPL) or via future real surpluses (passive). For asset-price responses they use high-frequency identification: regressing daily REIT, stock and bond returns on the inflation surprise (daily change in 1-year inflation-linked swaps) on German HICP release days, controlling for stock returns. Main threats: the first-order/second-order approximation could fail if substitution effects are large (the authors note that pre/post high-frequency micro data—unavailable to them—could test this); the use of 2015 expenditure shares and 2017 balance sheets to represent the pre-shock state; reliance on counterfactual price series (IMF, OMIE) for what prices would have been absent intervention; and the assumption that relative prices fully return to pre-shock ratios in the long run.

Q2. What are the four channels and how are they distinguished empirically?

(1) Direct component: raw inflation effect on cost of living before fiscal support and before wage/asset-price adjustment; split into average inflation, the ‘pi difference’ from heterogeneous baskets (C), net income/labor-income purchasing power (Y), net nominal positions (NNP), and dividends+capital gains (K). (2) Unconventional fiscal policy (UFP): energy price interventions (changes in good-specific tax/subsidy wedges, requiring counterfactual no-intervention price indices) plus ad-hoc transfers to households. (3) Indirect: short-run changes in nominal wages, minimum wages, pensions, fiscal drag, and asset prices (house, stock, bond) plus the direct effect of monetary-policy-driven interest-rate changes on deposits and debt. (4) Long-run: welfare from relative prices realigning to the new price level, discounted to t=0. They are computed sequentially in stages so each component’s contribution is isolated. NNP is the dominant driver of age heterogeneity; Y is the largest single contributor to losses but is fairly uniform across groups; C matters mainly for poor elderly in Italy and Spain.

Q3. What heterogeneity is documented?

Age is the most pronounced dimension: retirees lose most (driven by large positive nominal asset holdings), the young least (often net winners via mortgage debt revaluation). German and Italian retirees lost up to 14% of triennial income; high-income retirees lost more than EUR 10,000 on average. By contrast, the consumption-quintile (permanent-income) gradient is weak because sticky rents hedge low-income renters; excluding rents reveals a negative inflation-income gradient (poor face higher inflation via energy/food). Cross-country: Italy highest cost (~9%), France lowest (~3%), due to (i) bigger raw price shock in Italy (energy import dependence/market structure), (ii) more effective fiscal offset in France, (iii) nominal wages lagging inflation much more in Italy, (iv) Italian middle-aged/elderly holding larger nominal positions while the young borrow less than in France. Within-bin heterogeneity (homeowners with mortgages vs renters) means about a quarter of households are winners overall; more than half of the young in France and Spain, ~50% in Germany, ~30% in Italy, and ~50% of Spanish retirees (extensive pension indexation) are winners.

Q4. What role did unconventional fiscal policy play?

Fiscal interventions reduced first-stage welfare losses by about one-fifth on average across countries and household types. Energy price caps were more important than transfers, especially in 2022 when caps were active in all countries. In France, interventions reduced the measured inflation rate by about 2 p.p.; in Italy interventions came ex-post via bonuses/transfers and so did not lower recorded inflation. Retirees benefited most, consistent with their higher energy/food shares and targeted measures. Government fiscal support outlays were approximately 1% of triennial GDP in all four countries, though in Italy and Spain a larger share (above 35% of costs) went to firms versus 14% (Germany) and 5% (France).

Q5. How are asset prices treated and what are the estimated elasticities?

House prices: a two-step approach—daily REIT (FTSE EPRA NAREIT Eurozone Residential) returns regressed on inflation surprises (beta = -3.995 on the swap surprise) on German HICP release days, then quarterly house-price returns (2006Q1-2023Q4) regressed on lagged REIT returns (delta = 0.035); the product beta x delta = -0.138 means a 10% inflation surprise lowers house prices ~1.38%. Stock and bond elasticities are larger and negative: -0.410 and -0.726 respectively. The asset-price channel is quantitatively negligible in welfare terms because house elasticity is small and stock/bond holdings are concentrated only at the very top of the consumption distribution. Housing and stocks are therefore not good inflation hedges when inflation has a large cost-push component.

Q6. What about wages, pensions, and fiscal drag in the indirect channel?

Nominal wage increases were modest, generating a welfare gain of only about 3% of disposable income against a direct loss on nominal wages of about 9.5%. Wages rose faster in France (sectoral agreements, over 4% vs 2-3% elsewhere) and for low-quintile German workers (large minimum-wage rise in October 2022). Pensions, being indexed to past inflation, grew more than wages in all four countries, so retirees gained substantially from the indirect channel, especially in Spain (pensions up 9.5% for most pensioners in 2023). However, fiscal drag (unindexed tax brackets in Italy and Spain) taxed away nominal gains—up to 2.5% for higher-quintile pensioners—whereas France and Germany had near-real-time bracket indexation, so drag was small. Higher ECB interest rates (tightening from July 2022) raised mortgage payments for young Spanish households with adjustable-rate mortgages, partly wiping out their NNP gains; the effect was small elsewhere (fixed-rate mortgages, limited deposit-rate pass-through).

Q7. What does the sectoral (government and foreign) analysis show?

Using Euro Area Sector Financial Accounts (2017), the household sector holds positive net nominal positions (total NNP/triennial GDP: 0.28 Germany, 0.31 France, 0.35 Italy, 0.13 Spain), governments hold negative positions, and the foreign sector is a creditor against all except Germany. From the NNP channel alone the household sector lost (as % of triennial GDP): -3.8 Germany, -2.9 France, -3.9 Italy, -0.5 Spain; governments gained +3.5, +4.8, +7.5, +4.5; the foreign sector gained +0.3 in Germany but lost -1.9, -3.6, -3.9 in France, Italy, Spain. Adding fiscal drag (revenue), fiscal support cost (~1% GDP), higher pension cost (~1% GDP, peak 1.7% Italy), and higher government energy purchase cost, total government gains were: Germany -0.6 to +0.5 (roughly breaks even), France +1.3 to 2.1, Italy +4.5 to 5.1, Spain +1.6 to 2.2% of triennial GDP. Cross-country differences in government gains are driven mainly by the outstanding stock of public debt. Redistributing these government gains to households could substantially offset household losses.

Q8. How does this paper relate to and differ from prior work?

It applies the envelope-theorem money-metric approach used by Auclert (2019), Slacalek et al. (2020), Fagereng et al. (2022) and Del Canto et al. (2023), but studies a specific historical episode as an event study rather than identified shocks. It builds directly on Cardoso et al. (2022), who quantify the direct channel for Spain using bank-account data, by adding the other three channels (fiscal, indirect, long-run) and covering four countries. It contributes to the inflation-heterogeneity literature (Kaplan-Schulhofer-Wohl, Jaravel, Hobijn-Lagakos, Argente-Lee) by documenting inflation-rate differentials an order of magnitude larger than pre-pandemic US estimates, and confirms Doepke-Schneider (2006) that age is the key dimension via life-cycle net nominal positions. Unlike fully specified HANK models (Pugsley-Rubinton, Olivi et al., Yang), the sufficient-statistic approach cannot evaluate policy counterfactuals. Most contemporaneous euro-area papers stop at measuring differential inflation; this one quantifies full welfare.

Q9. What are the main caveats and robustness considerations?

The framework is first-order: it assumes consumption and portfolio adjustments have only second-order welfare effects, which the authors flag as testable with high-frequency micro data they lacked. Survey-based (HFCS) nominal asset measures are 2-3 times smaller than financial-account measures because surveys undersample the very rich, so the Section 4 micro results best represent the population excluding the wealth top. Expenditure weights come from the 2015 HBS (judged stable using 2005/2015 HBS and credit-card evidence); inflation expectations (0.4-1.7%/year) come from Consensus Economics early 2021. A robustness note: assuming 0.75%/year trend productivity growth (so part of nominal wage rises reflects trend, not catch-up) increases welfare losses by roughly 1.5% of disposable income. The retiree/young housing trade is modeled as selling/buying one tenth of housing (3/30 over the 3-year long run). The conclusion notes the episode coincided with high pandemic excess savings that cushioned purchasing-power erosion, and that the inflation tax effectively redistributes from retirees to the young, partially offsetting future fiscal adjustment.

Key Concepts

A choice-based approach to the measurement of inflation expectations

Mon, 01 Jan 0001 00:00:00 +0000

Standard survey-based measurement of inflation expectations relies on density forecasts in which respondents assign probabilities to pre-specified inflation bins; this method has been found to induce biases through its bin structure (suggesting that values near zero are more likely), to impose cognitive demands that raise dropout rates, and to become uninformative during high-inflation episodes when responses cluster in open-ended extreme bins—making cross-time and cross-country comparisons unreliable. This paper proposes a new choice-based elicitation method rooted in decision theory that uses a bisection process: respondents first state a minimum and maximum inflation level for which they see almost no chance of actual inflation falling outside the range, avoiding external anchors, and then answer a series of binary choices from which the relevant percentiles of their subjective distribution can be inferred. Two large surveys (UK and US) and a laboratory experiment demonstrate that the method leads to well-defined expectations that fulfil both subjective and objective quality criteria, that it is neither perceived as more difficult nor more time-consuming than the density forecast standard, and that—unlike density forecasts—it is robust to differences in the state of the economy, enabling comparisons across time and countries. The method is portable and can be applied to elicit distributions over other macroeconomic variables beyond inflation.

In depth

Q1. What specific failures of density forecasts motivate the new method?

The paper identifies four problems with the standard density forecast format: (i) bin-structure bias—narrower bandwidths around zero may lead respondents to infer that near-zero inflation is more likely by design, biasing responses toward zero; (ii) cognitive demands that raise dropout rates and may introduce selection bias; (iii) sensitivity to question wording and response-scale changes; and (iv) loss of informativeness during high-inflation episodes when responses bunch in extreme open-ended bins, compounded by the incompatibility of adjusted bin structures across survey waves. During the recent surge in inflation these problems became especially visible, motivating a method more robust to the state of the inflation environment.

Q2. How does the choice-based bisection method work?

The method, building on Baillon (2008), elicits respondents’ subjective inflation distribution via a series of binary choices structured as a bisection algorithm that partitions the state space into equally likely subevents, allowing the relevant percentiles of the distribution to be recovered without imposing external anchors. The procedure begins by asking respondents for a minimum and maximum inflation level for which they believe there is “almost no chance” actual inflation falls outside the interval—avoiding the bin-structure bias of the density forecast by letting respondents define their own relevant range. Subsequent binary choices then narrow down the median, quartiles, and further quantiles according to a strict algorithm.

Q3. What do the field surveys and laboratory experiment show?

Two large surveys—one in the UK testing feasibility across multiple protocol variants, one in the US—and a laboratory experiment demonstrate that the choice-based method produces well-defined expectations fulfilling both subjective and objective quality criteria, and is neither perceived as harder nor more time-consuming than the standard density forecast. The UK survey compared two variants of the proposed “Midpoint method” against existing density forecast formats. The convergence on quality criteria across different samples and settings supports the method’s potential for adoption in large-scale central bank surveys.

Q4. What makes the method robust to the state of the economy, and why does that matter for monetary policy?

In contrast to density forecasts, the choice-based method is robust to differences in the level and volatility of inflation because respondents define their own relevant range rather than choosing among fixed pre-specified bins, so the method does not become uninformative when actual inflation is far from the bins’ central mass. This robustness allows comparisons of inflation expectations distributions across time (including across high- and low-inflation regimes) and across countries—a feature density forecasts cannot deliver without adjusting bin structures in ways that compromise comparability. For monetary authorities that use survey expectations as both an indicator and a policy tool, this portability is a key advantage.

Key concepts

density forecast : the standard survey format in which respondents assign subjective probabilities to pre-specified inflation intervals (bins); the format used by the Federal Reserve Bank of New York’s Survey of Consumer Expectations and widely adopted by central banks.

choice-based elicitation (Midpoint method) : the paper’s proposed alternative; a bisection procedure in which respondents first report a subjective min/max range and then answer binary choices, yielding quantiles of the subjective inflation distribution without imposing an external bin structure or anchors.

bisection process : the algorithmic structure in which each binary choice partitions the remaining probability mass so that successive responses identify the median, quartiles, and further quantiles of the respondent’s subjective distribution.

bin-structure bias : the distortion introduced by the density forecast’s pre-specified bins when narrower intervals near zero suggest to respondents that near-zero inflation is considered more likely by the survey designers, biasing their reported probabilities toward zero.

A model of expenditure shocks

Mon, 01 Jan 0001 00:00:00 +0000

A common observation from account-level bank data is that low-income, low-liquidity households often use additional income to repay debt rather than consume, and that household-level consumption is extremely volatile even though aggregate consumption is smooth. This paper formalizes these patterns using four new facts from the PSID: household consumption is as volatile as income (contradicting PIH); the correlation between household consumption and income growth is only about 0.2 (low); consumption growth is negatively autocorrelated (contradicting both PIH and habit models); and—a finding new to the literature—the cross-sectional correlation between consumption and income growth is far smaller among households experiencing high consumption episodes than in the full sample. The paper proposes an explanation based on stochastic consumption thresholds: unanticipated shocks such as medical expenses or vehicle repairs create time-varying minimum-consumption floors whose violation incurs large utility costs, inducing households to prioritize expenditures on these needs over income-responsive consumption and to rebuild savings after the shock. This mechanism increases the welfare cost of income fluctuations by an order of magnitude relative to standard models.

In depth

Q1. What are the four empirical facts and why do they challenge standard models?

Fact 1: for the average PSID household, consumption is as volatile as income; Fact 2: the correlation between consumption growth and income growth is about 0.2; Fact 3: household consumption growth is negatively autocorrelated; Fact 4 (new): the cross-sectional correlation between consumption and income growth is far smaller among households with high consumption than in the full sample. Fact 1 contradicts the permanent income hypothesis (PIH), under which consumption should be smoother than income. Facts 1 and 2 together cannot both be explained by liquidity constraints (which would tie consumption to current income, producing a high correlation) or by very persistent income shocks (same problem). Fact 3 contradicts habit models (which generate positive autocorrelation) and is inconsistent with PIH (which implies zero autocorrelation). Fact 4 is novel: in standard models the level of consumption barely affects the income-consumption growth relationship, so this fact requires a new explanation.

Q2. What is the expenditure shock mechanism, and how does it rationalize the four facts?

The model introduces stochastic, time-varying consumption thresholds—representing unavoidable expenditures such as medical emergencies, vehicle breakdowns, or appliance repairs—that, if violated, incur large utility costs; this forces households to prioritize meeting these minimum needs over income-proportional consumption. When a threshold shock hits, consumption jumps to meet it regardless of current income (explaining volatile, income-disconnected consumption). After the shock the household rebuilds savings, reducing consumption below its long-run level (generating negative autocorrelation). During high-consumption episodes (threshold shocks), income and consumption growth are decoupled (explaining Fact 4). Meanwhile, without a threshold shock, households are saving to self-insure against future shocks (explaining why low-income households save rather than consume when income rises).

Q3. What does the model imply for the welfare cost of income fluctuations?

The stochastic thresholds increase the welfare cost of income fluctuations by an order of magnitude relative to standard consumption models, because households must maintain precautionary buffers against the risk of hitting a threshold and being unable to meet it. The large welfare cost arises from two sources: the direct cost of violating a threshold (large utility penalty), and the precautionary motive it creates, which forces households to save at the expense of current consumption utility even when no threshold shock is present.

Q4. What empirical evidence does the paper use and what is the scope of the findings?

The PSID (post-1999 comprehensive consumption module) provides panel data on total household consumption and income; the authors use this to document all four facts, including the novel Fact 4. The negative autocorrelation of consumption growth (Fact 3) is documented in the prior literature (Blundell et al. 2008) as indicative of preference shocks or measurement error, but the paper’s model gives it a structural interpretation as evidence of expenditure shocks. The finding that consumption is volatile yet disconnected from income (Facts 1 and 2) is robust to restricting attention to nondurable consumption, ruling out durable goods as the driver. The results hold at the household level; aggregate consumption is smooth because household threshold shocks are largely idiosyncratic and average out.

Key concepts

stochastic consumption threshold : a time-varying, unanticipated minimum consumption level (representing unavoidable expenditures like medical emergencies or vehicle repairs) whose violation incurs large utility costs; the paper’s key modeling innovation.

expenditure shock : an unanticipated increase in the required minimum consumption level, representing events that force households to spend on necessities regardless of current income or savings; the proposed explanation for the four empirical facts about household consumption dynamics.

A traffic-jam theory of growth

Mon, 01 Jan 0001 00:00:00 +0000

Research Question. Finocchiaro and Weil ask whether financial development necessarily promotes long-run economic growth, or whether congestion externalities in R&D markets can offset — and even reverse — the growth benefits of easier credit access. The paper proposes that the empirical coexistence of expanding financial sectors and roughly constant per-capita GDP growth rates (approximately 2% annually in the United States over the last century) can be explained by the interplay of search frictions in two sequential markets: credit and innovation.

Methodology. The authors build a continuous-time endogenous growth model in which all growth is innovation-led. Firms must pass through four sequential stages — creation, fund-raising (Stage 0–1), R&D search (Stage 1–2), and high-productivity production (Stage 2–3) — before being exogenously destroyed. Both the credit market (firms searching for banks/venture capitalists) and the innovation market (firms searching for innovators after securing finance) are characterized by constant-returns-to-scale matching functions with endogenous market tightness. Nash bargaining determines the loan repayment, and free entry drives profits to zero in both markets. The model is then calibrated to annual U.S. data, with the risk-free rate r = 3.5%, separation rate s = 4%, symmetric bargaining power ω = 0.5, a productivity jump γ = 0.023 targeting a baseline growth rate of 2%, credit market duration for creditors just below one month and for firms slightly above one year (consistent with Wasmer and Weil, 2004), a two-year average patent approval time (USPTO 2020), 6% employment in finance (BLS 2020), and 0.5% employment in scientific R&D (BLS 2020).

Core Mechanism. The paper derives a “spillover function” Q(p,g) that links the equilibrium probability of finding an innovator (q) to the probability of finding a bank (p) and the growth rate (g). Because free entry holds profits at zero, easier credit — a higher p — forces q downward: if a firm spends less time raising funds, the innovation market becomes more congested (Qp < 0). This negative spillover between the two markets is the paper’s central traffic-jam analogy: relieving one bottleneck shifts congestion downstream.

Main Findings. The GG curve — the locus of (p, g) pairs consistent with equilibrium — is hump-shaped under the symmetric cost condition c = ωn (flow search cost for firms in credit markets equals the firm’s share of search costs in innovation markets). Growth is maximized when expected credit search time equals expected innovation search time (1/p = 1/q). Beyond that interior optimum, further financial deepening lowers the growth rate. The calibrated economy sits to the right of the hump in a flat region (p > q), so that reducing credit frictions alone has a marginally negative effect on growth: eliminating credit frictions lowers g from 2.000% to 1.997%, a reduction of 0.003 percentage points. Reducing innovation frictions alone raises g modestly to 2.071% (+0.071 pp). Only a simultaneous reduction of frictions in both markets raises g meaningfully, to 2.122% (+0.122 pp). The quantitative effects are deliberately small, consistent with the near-constancy of long-run growth despite financial deepening.

Scope Conditions. The non-monotonicity requires both markets to carry search frictions; when only one friction is present, financial development is unambiguously good for growth (Section 4.3). The hump-shape is established analytically in the symmetric case c = ωn; more generally, the paper shows (via back-of-envelope approximation) that the sign of the finance–growth link depends on whether c/ω is less than or greater than n. The quantitative insensitivity of growth to finance is amplified when the real interest rate is close to the growth rate and when potential growth γ is close to actual growth g: the elasticity of growth with respect to finance is proportional to (γ − g)/γ. Extensions to fixed bank entry costs (introducing a growth-to-finance feedback), endogenous innovator wages (Section 4.2), and frictionless innovation (Section 4.3) all confirm the benchmark conclusions under stated parameter conditions.

Q1: What is the paper’s central theoretical claim about the finance–growth nexus? The paper claims that the finance–growth relationship is non-monotonic: financial development raises growth when credit is scarce (left of the hump on the GG curve) but lowers it when credit is readily available (right of the hump), because easier financing draws more firms into the innovation market, tightening it and reducing the probability of finding an innovator. This congestion spillover from the credit market to the innovation market is the “traffic-jam” mechanism. The non-monotonicity vanishes if either market lacks search frictions.

Q2: What is the “spillover function” and why is it central to the model? The spillover function Q(p, g) is derived from the free-entry zero-profit condition for firms and expresses the innovation-matching probability q consistent with equilibrium for given credit-matching probability p and growth rate g. It has Qp < 0 (easier credit reduces q) and Qg < 0 (faster growth reduces q), capturing the two-way negative interaction between the markets. It is central because all equilibrium and comparative-statics results flow through it: the GG curve is defined by substituting Q into the growth equation g = γ/(1 + s/p + s/Q(p,g)).

Q3: Under what condition is the GG curve hump-shaped, and what is the intuition? The GG curve is hump-shaped when the flow search cost for firms in the credit market c equals the firm’s share of innovation search costs ωn (Proposition 4). The intuition mirrors equalizing travel times across two congested roads: growth is maximized when expected credit search time (1/p) equals expected innovation search time (1/q). When credit is very tight (p small), a marginal increase in p raises the share of innovating firms faster than it tightens the innovation market, so growth rises. Once credit is abundant (p large), the congestion effect on innovation dominates and growth falls.

Q4: What does the benchmark calibration predict about the quantitative effect of financial development on growth? The benchmark calibration, targeting 2% annual U.S. growth, places the economy to the right of the hump in a flat region of the GG curve (p > q). Eliminating credit market frictions alone reduces the annual growth rate by 0.003 percentage points (from 2.000% to 1.997%) while lengthening expected innovation search time from 2 years to 3.4 years. This marginally negative effect arises because the economy is already well to the right of the optimum. The results are deliberately small and consistent with the empirical near-constancy of growth alongside financial deepening.

Q5: What combination of policies does the model recommend for raising growth? Only a simultaneous reduction of frictions in both the credit and the innovation market raises the growth rate meaningfully, to 2.122% in the calibration (+0.122 pp relative to the 2.000% benchmark). Isolated improvements in credit markets have a marginally negative effect; isolated improvements in innovation markets have a marginally positive effect (+0.071 pp). The authors interpret this as supporting the OECD view that growth-stimulating policies should be designed as a system rather than as isolated pro-growth measures.

Q6: How does the elasticity of growth to finance depend on the gap between potential and actual growth? The authors show (referenced as available on request) that the elasticity of the growth rate with respect to financial factors is proportional to (γ − g)/γ, where γ is the potential growth rate (the productivity jump per innovation) and g is the actual equilibrium growth rate. When actual growth is close to potential — as in the benchmark calibration with γ = 0.023 and g = 2.000% — this factor is near zero, making growth nearly insensitive to changes in financial conditions. This provides a structural rationale for why empirically measured finance–growth effects are often small or nil in advanced economies.

Q7: How does introducing fixed bank entry costs (Section 4.1) change the results? When banks bear a fixed licensing cost K (paid each time they enter the credit market), credit market tightness φ becomes an increasing function of (r − g)K: the annuity value of the fixed cost falls as growth rises, inducing more bank entry and reducing credit tightness. This introduces an upward-sloping PP curve (rather than a vertical one) and creates a direct positive feedback from growth to financial deepening. The qualitative conclusions on non-monotonicity are preserved: lower licensing costs shift the PP curve right and steepen it, with the equilibrium effect on growth remaining ambiguous due to the congestion spillover into the innovation market.

Q8: What happens to the spillover function when innovators are paid (Section 4.2)? When innovators receive a Nash-bargained wage, the equilibrium wage (Equation 30) is increasing in innovator productivity (πγ), innovation market tightness (θn), and the growth rate, and decreasing in total credit market search costs K(φ). Easier credit raises both expected revenues and innovator wages for the firm. For innovator bargaining power α sufficiently small (and always for α < 1, as shown in the Appendix), the revenue effect dominates so that Qp < 0 is preserved: finance still creates bottlenecks in the innovation market, and the core non-monotonicity result carries through.

Q9: What does the model predict when only one market has search frictions? When only the credit market is frictional and innovators are found instantly after financing is secured, improving credit market efficiency unambiguously raises growth (Section 4.3, Figure 4). The GG curve becomes g = γ/(s/p + 1), which is strictly increasing in p, and the PP curve shifts in a way that unambiguously raises equilibrium growth. The paper uses this case to isolate the source of non-monotonicity: the negative spillover from credit ease to innovation congestion requires frictions in both markets to operate.

Q10: How does the paper relate to the empirical “too much finance” literature? The paper offers a distinct theoretical mechanism for the inverted-U relationship between credit and productivity growth documented by Arcand et al. (2015), Aghion et al. (2019), and Popov (2018), among others. While Aghion et al. (2019) explain the inverted-U through less-efficient incumbents surviving longer with better credit access, and Malamud and Zucchi (2019) emphasize how financing frictions differentially affect entrant and incumbent composition, Finocchiaro and Weil’s mechanism operates through congestion externalities in sequential search markets — a channel not previously formalized in the innovation-led growth literature.

Search frictions in credit markets: Firms searching for financiers (banks or venture capitalists) and banks searching for firms face a matching technology with constant returns to scale; credit market tightness φ is the ratio of firms searching for banks to banks searching for firms, and the matching probability p(φ) is strictly decreasing in φ. Free entry drives bank profits to zero, pinning equilibrium tightness.

Search frictions in innovation markets: After securing financing, firms search for innovators who can upgrade their productivity by factor γ; innovation market tightness θ is the ratio of firms searching for innovators to innovators, and the matching probability q(θ) is strictly decreasing in θ. The number of innovators is held fixed (analogously to fixed labor supply in Mortensen-Pissarides).

Spillover function Q(p, g): Derived from the free-entry zero-profit condition for firms, Q expresses the equilibrium innovation-matching probability q as a function of the credit-matching probability p and the growth rate g. It has Qp < 0 and Qg < 0, meaning easier credit and faster growth both reduce q by tightening the innovation market. It is the formal embodiment of the traffic-jam mechanism.

GG curve: The locus of (p, g) pairs consistent with the equilibrium growth equation g = γ/(1 + s/p + s/Q(p,g)). Under the symmetric cost condition c = ωn, the GG curve is hump-shaped: it rises from the origin, reaches a maximum interior growth rate, then declines toward an asymptote g∞ < γ. Its shape encodes the non-monotonic relationship between finance and growth.

PP curve: The locus of equilibrium credit-matching probabilities consistent with free entry in the credit market. In the benchmark model it is a vertical line at p* = p(ω/(1−ω) · k/c), independent of q and g. When banks bear a fixed entry cost K, the PP curve becomes upward-sloping, introducing a direct positive feedback from growth to financial deepening.

Potential growth rate γ: The productivity jump per successful innovation; in a frictionless world (p = q = ∞) the economy grows at γ. Actual growth g falls below γ to the extent that search frictions delay the delivery of credit and innovation. The elasticity of g to financial factors is proportional to (γ − g)/γ, so when actual and potential growth are close, financial factors matter little for growth.

Congestion externality in R&D: The mechanism by which financial deepening — raising p — drives more firms to seek innovators, tightening the innovation market and reducing q. This negative spillover (Qp < 0) is the paper’s central departure from models with only a single friction, where finance is always growth-enhancing.

Aggregate demand externality and self-fulfilling default cycles

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question. Why do corporate defaults cluster in recurring episodes rather than occurring smoothly? The paper asks whether observable fundamental factors — firm characteristics and macroeconomic variables — are sufficient to account for the clustered default patterns documented in the data, and, if not, what theoretical mechanism can explain them.

Empirical Motivation. Using Moody’s historical default rate data, the authors document that the long-run average corporate bond default rate during 1866–2008 was approximately 1.50%, yet defaults were highly episodic: the worst three-year period during the Great Depression totaled 12.88%, and the three-year period 1873–1875 after the railroad boom reached 35.80%. A Markov switching regression on post-war default rate data (1951–2017) strongly rejects a linear no-switch model in favor of a two-regime model across all information criteria (AIC, HQ, SC, and log-likelihood). The estimated high-default regime has a mean default rate of 1.93% (unconditional mean µ/(1−ρ)) — roughly eight times the 0.23% mean of the low-default regime — and a standard deviation nearly six times larger. The high-default regime persists on average 5.81 years (transition probability of staying ≈ 0.83), while the low-default regime lasts approximately 7.52 years (staying probability ≈ 0.87).

Model. The authors build a continuous-time general equilibrium model with Dixit-Stiglitz monopolistic competition (CES aggregation with elasticity σ) and an endogenous entry/exit/default mechanism. Households are risk-neutral and also act as entrepreneurs. At each instant, δµ new project blueprints are invented; entrepreneurs borrow to invest, then face an idiosyncratic liquidity shock z drawn from a Pareto distribution G(z). Entrepreneurs continue if z ≤ Z*, a cutoff determined by the continuation value of the firm, and default otherwise. Continuing firms become monopolists for a new variety until that variety becomes obsolete at a Poisson rate δ. Each operating firm must borrow working capital constrained by its firm value Vt (collateral constraint wtnjt ≤ θVjt). The entire equilibrium reduces to a two-dimensional dynamical system in (Mt, Vt), where Mt is the number of operating firms (state variable) and Vt is the firm value (control variable).

Key Mechanism — Demand Externality and Positive Feedback. Under CES aggregation, each firm’s gross revenue is y_jt^(1–1/σ) · Y_t^(1/σ), making individual firm revenue increasing in aggregate output Yt. A decline in Yt lowers firm profits and firm value Vt, which raises the default threshold Z* and increases the fraction of projects that are abandoned. Fewer operating firms further depress Yt, closing a positive feedback loop. This static strategic complementarity (through CES) is combined with dynamic strategic complementarity through the borrowing constraint: higher expected future firm value relaxes current working capital constraints, raising current production.

Multiple Equilibria and Global Dynamics. The two-locus phase diagram (˙Mt = 0 and ˙Vt = 0) yields multiple intersections — and hence multiple steady states — when productivity A lies in an intermediate range (A < A < Ā). When A > Ā, a single good saddle-point equilibrium exists. When A < A, no equilibrium can be sustained. In the intermediate range, a good steady state (low default rate, high firm value) coexists with a bad steady state (high default rate, low firm value). The good steady state is always a saddle; the bad steady state is a sink (locally indeterminate, κ < κ_Hopf) or a source (locally determinate but globally indeterminate, κ > κ_Hopf), depending on parameter κ = 1 + (θ + ρ)/δ.

Bogdanov-Takens Bifurcation. Using global dynamical methods, the paper demonstrates richer indeterminacy than local analysis permits. Near the Bogdanov-Takens point (κ, Ā), the system can exhibit: (a) infinite equilibrium trajectories converging to the bad steady state; (b) saddle-loop bifurcation at κ = κ_SL ≈ 14.25 (under the baseline calibration); (c) stable or unstable periodic orbits for κ ∈ (κ_Hopf, κ_SL) — endogenous business cycles in a perfect-foresight equilibrium; and (d) multiple trajectories from near the source that converge to the good saddle equilibrium.

Simulation of Clustered Defaults. With a two-state Markov process for productivity (Ah = 10, Al = 9.34) and pessimistic sentiment shifts (the “ugly” state), the model replicates the cluster pattern: in the good/high-productivity state, the default rate is near zero; when productivity falls to low and sentiment turns pessimistic, the default rate can spike to approximately 12%, consistent with the Great Depression observation. Critically, the paper shows that the cluster pattern is generated only under global dynamics — restricting to local dynamics produces substantially smaller fluctuations in the default rate, confirming that the ugly (sink) equilibrium is essential.

Policy. A countercyclical subsidy to non-defaulting entrants — financed by a lump-sum tax, calibrated as tr(Vt) = τ(VG − Vt) — shifts the ˙Mt = 0 locus downward and can eliminate the bad steady state entirely, leaving only the good saddle-path equilibrium. The paper provides a closed-form sufficiency condition for τ (Proposition 7).

Scope Conditions. Multiple equilibria require: (i) productivity in the intermediate range A < A < Ā; (ii) the elasticity of substitution σ not too large (below a threshold σ̄ that itself depends on µ); (iii) the borrowing constraint binding (δ > θσ/((σ–1)κ), which can always be ensured by choosing δ sufficiently large). Clustered defaults in the simulation require the joint occurrence of a negative fundamental shock (productivity falling from high to low) and a shift to pessimistic sentiment; either factor alone generates only limited default amplification.

In depth

Q1. What is the core empirical motivation for the model, and what does the regime-switching analysis establish?

The paper documents that the corporate bond default rate, drawn from Moody’s data covering 1866–2008, clusters sharply in episodes: the long-run average is 1.50%, yet the worst three-year period of the Great Depression totaled 12.88% and 1873–1875 reached 35.80%. A Markov switching regression on 1951–2017 data strongly rejects a linear no-regime-switch model across all four criteria (log-likelihood, AIC, HQ, SC). The two-regime model identifies a high-default regime with unconditional mean 1.93% and standard deviation roughly six times the low-default regime’s, a persistence probability of approximately 0.83 (duration ≈ 5.81 years), and a low-default regime with unconditional mean 0.23% and persistence approximately 0.87 (duration ≈ 7.52 years). The regime-switching result supports the prior literature’s claim (Das et al. 2007; Duffie et al. 2009; Azizpour et al. 2018) that observable fundamentals alone cannot account for clustered defaults.

Q2. How does the Dixit-Stiglitz CES structure generate a demand externality that links aggregate output to individual firm default decisions?

Under CES aggregation with elasticity σ, each firm’s gross revenue equals y_jt^(1–1/σ) · Y_t^(1/σ) (equation 7), so aggregate output Yt directly enters individual firm revenue. Each firm takes Yt as given, yet the aggregation of all firms’ output determines Yt. When aggregate output falls — because more firms have defaulted and exited production — each remaining firm’s revenue and profit fall, reducing the firm’s continuation value Vt. A lower Vt tightens the borrowing constraint (wtnjt ≤ θVjt), reduces working capital, and raises the probability that the firm’s idiosyncratic liquidity shock will exceed the default threshold Z*, producing further defaults. This positive feedback constitutes the demand externality: individual firms’ decisions are strategic complements, both statically (through CES demand) and dynamically (through the borrowing constraint on working capital).

Q3. What is the two-dimensional dynamical system that summarizes the equilibrium, and what do the two loci look like in the phase diagram?

The entire equilibrium reduces to two differential equations in (Mt, Vt): ˙Mt = –δ[Mt – µG(Z(Vt))] and ˙Vt = κδVt[1 – F(Vt, Mt)], where F captures the ratio of monopoly profit to firm value including the borrowing constraint. The ˙Mt = 0 locus slopes strictly upward because a higher firm value Vt raises the default cutoff Z* and lowers the fraction of entrants who default, so more firms survive and Mt rises until absorption equals entry. This locus has a minimum at Mm = µG(zm) because firm value must exceed the threshold that sustains the credit market. The ˙Vt = 0 locus is non-monotonic: it first slopes upward (more firms raise aggregate demand and profit through the scale/externality channel) and then slopes downward (more firms tighten the labor market, raising wages and lowering profits). The two opposing channels make the ˙Vt = 0 locus hump-shaped, creating the possibility of two intersections and hence two steady states.

Q4. Under what conditions do multiple steady states exist, and what does each look like?

Multiple steady states exist when productivity A satisfies A < A < Ā, where A and Ā are closed-form thresholds given by Equations (A.3) and (A.4), and the elasticity of substitution σ is below a threshold σ̄ (Equation A.5). When A < A, neither locus intersects and no equilibrium is sustainable. When A > Ā, a single good saddle-point equilibrium exists. In the multiple-equilibria range, the good steady state has a higher firm value and a smaller fraction of firms defaulting; the bad steady state has a lower firm value and a higher default rate. Under the paper’s numerical calibration (A = 10, η = 6.5, Zmin = 0.88), the low default rate at the good steady state is approximately 1.5% and the high default rate at the bad steady state is between 12% and 13%.

Q5. What are the local dynamics around each steady state, and how does parameter κ determine whether the bad steady state is a sink or a source?

Proposition 5 shows that the good steady state is always a saddle point, ensuring a unique convergent path for initial Mt near Mg_0. The bad steady state’s local nature depends on κ = 1 + (θ + ρ)/δ and the critical value κ_Hopf = 1 + ψ/(θMb_0Vb_0). When κ is between 1 and κ_Hopf, the Jacobian trace is negative and the bad steady state is a sink with one order of indeterminacy: given Mt close to Mb_0, infinitely many initial values of the control variable Vt satisfy all equilibrium conditions. When κ > κ_Hopf, the bad steady state is a source point; the economy diverges from it. Because κ does not affect the steady-state locations (Proposition 3), one can vary κ to change the dynamic character without moving the equilibria in the phase diagram.

Q6. What does the global dynamics analysis reveal that local analysis misses?

Global analysis via Bogdanov-Takens bifurcation (Proposition 6) reveals three classes of dynamics absent from local analysis. First, even in the saddle-source case (locally determinate), there exist multiple equilibrium trajectories diverging from near the bad (source) steady state and converging to the good (saddle) steady state; these paths satisfy all equilibrium conditions including transversality but are incorrectly ruled out by local methods. Second, at the critical value κ_SL ≈ 14.25 (under the baseline calibration), a homoclinic saddle-loop orbit connects the saddle point to itself — all trajectories interior to the loop converge to the bad steady state. Third, for κ between κ_Hopf and κ_SL, periodic orbits arise in a perfect-foresight equilibrium with no external shocks. For example, at κ = 14.9, the phase diagram displays a unique periodic orbit around the bad steady state, with two distinct initial values of Vt for any given Mt near the orbit — endogenous, perpetual oscillations without any exogenous driving force. Numerical experiments confirm that Mt = 0.23 admits two rational-expectations values of Vt (2.09 and 3.55) on the saddle path alone, illustrating abundant indeterminacy even at the endpoint.

Q7. How does the paper simulate the clustered default pattern and what is the role of the “ugly” equilibrium?

The paper constructs a three-state Markov economy: “good” (high productivity Ah = 10, single saddle equilibrium, near-zero default rate), “bad” (low productivity Al = 9.34, saddle-path equilibrium, modestly elevated defaults), and “ugly” (low productivity, sink-path equilibrium, sharply elevated defaults). The ugly state is reached when, upon a productivity decline, firms adopt pessimistic expectations and the economy slides to the high-default sink instead of remaining on the low-default saddle path. Transition probabilities are set so that the average ugly-state duration is approximately 6 years and roughly 45% of periods are ugly, consistent with the regime-switching estimates. With Zmin = 0.2 and η = 15, the ugly-state default rate can reach approximately 12%, matching the Great Depression observation. The counterfactual experiment deletes the ugly state (pGU = 0) and resets pGB = 0.45: the resulting default rate stays close to zero with no cluster pattern, demonstrating that global dynamics (the ugly sink) rather than the fundamental shock alone generate the clustering.

Q8. Can purely sentiment-driven cycles generate the clustered default pattern?

Section 6.2 fixes productivity at a low level (A = 9.53) and drives switches between the bad (saddle path) and ugly (sink path) states by pure sentiment shocks alone (πBU and πUB). The simulated default rate does spike upward when sentiment turns pessimistic, but the rises are generally more modest than in the combined fundamental-plus-sentiment exercise, and the default rate can no longer be characterized as countercyclical. The authors conclude that the realistic observed default cluster is the result of a combination of negative fundamental shocks and pessimistic sentiment shifts; either ingredient alone is insufficient to replicate all features of the data.

Q9. How does the collateral constraint on working capital create dynamic strategic complementarity?

Following Jermann and Quadrini (2012), Liu and Wang (2014), and Lian and Ma (2021), each operating firm must borrow to pay wages each period, subject to the constraint wtnjt ≤ θVjt. Since Vt is forward-looking (the discounted present value of the firm’s monopoly profit stream), optimistic expectations about future output raise Vt, relax the borrowing constraint, allow firms to hire more labor and produce more output today, and thereby validate optimism. This intertemporal complementarity means that the equilibrium is sensitive not only to current fundamentals but also to beliefs about the future, opening the channel for sentiment-driven multiple equilibria and self-fulfilling cycles.

Q10. What is the policy remedy for the bad equilibrium, and how does it work?

Proposition 7 establishes that a countercyclical lump-sum-tax-financed subsidy to non-defaulting entrants, tr(Vt) = τ(VG − Vt), with τ exceeding a computable threshold, eliminates the bad steady state. The subsidy works by effectively raising the value of continuing for a firm at any given Vt and Mt, shifting the ˙Mt = 0 locus downward until it lies below the ˙Vt = 0 locus everywhere in the relevant range, eliminating the second intersection and leaving only the good saddle-path equilibrium. The numerical illustration uses parameters from Section 6 with A = 9.67 and τ = 1/3 to demonstrate that the bad steady state vanishes and the phase diagram has a single equilibrium. The subsidy is self-limiting: in normal conditions when firm value is already high (Vt ≈ VG), the transfer is near zero.

Cui and Kaas (2021) show default cycles from self-fulfilling beliefs in a fully competitive firm environment, focusing on intertemporal default coordination. The present paper differs in three respects. First, firms engage in monopolistic competition under CES preferences, and the main novel mechanism is cross-firm default contagion through the demand externality — which can produce multiple equilibria even in a static setting, without any intertemporal coordination. Second, the paper examines the joint role of fundamental shocks and aggregate-demand externalities together, showing that multiple equilibria arise only in the presence of sufficiently low productivity (A < A < Ā), making indeterminacy contingent on external fundamentals rather than structural parameters alone. Third, the continuous-time framework with full global analysis via Bogdanov-Takens bifurcation allows characterization of periodic orbits and the interaction of the ugly sink path with Markov productivity regimes — dynamics not covered in Cui and Kaas (2021).

Q12. What is the markup prediction of the model, and is it consistent with empirical evidence?

Under Dixit-Stiglitz CES with elasticity σ, the equilibrium markup of each intermediate good equals σ/(σ–1) at the firm level. However, the measured gross markup — which includes the effective collateral constraint — is predicted to comove positively with the default rate in the model, and hence the markup is countercyclical. The paper notes this is consistent with the well-documented empirical regularity in Bils (1987) and Rotemberg and Woodford (1999). Additionally, the model replicates the finding in Gilchrist and Zakrajšek (2012) that a low default rate is associated with a high firm entry rate.

Key Concepts

Demand Externality (Dixit-Stiglitz type). In the paper’s sense, this is the mechanism by which individual firms’ revenues depend on aggregate output Yt through the CES aggregator: each firm’s gross revenue is y_jt^(1–1/σ) · Y_t^(1/σ). Each firm takes Yt as given, but the aggregation of all firms’ output determines Yt. This creates a positive spillover: more operating firms raise aggregate output, which raises each firm’s revenue, and vice versa. The paper uses this as the central transmission channel for self-fulfilling defaults, in contrast to prior literature that emphasized debt networks or asymmetric information contagion.

Self-Fulfilling Default Cycle. A dynamic equilibrium path in which pessimistic expectations about aggregate output are validated: if firms anticipate that more other firms will default (lowering Yt), their own continuation value Vt falls, raising the probability that their idiosyncratic liquidity shock will exceed the default threshold, increasing actual defaults, further lowering Yt, and so on. The paper distinguishes this from shock-amplifier stories by constructing a model with multiple rational-expectations equilibria in which the aggregate default rate is determined in part by initial beliefs.

Bogdanov-Takens Bifurcation. A mathematical tool for global dynamics analysis applied to two-dimensional continuous-time systems. In the paper, it is used to characterize system behavior when the parameters (κ, A) are near the point (κ̄, Ā) at which the Jacobian has two zero eigenvalues. Near this point, the system can exhibit saddle-loop bifurcations, Hopf bifurcations, homoclinic orbits, and stable or unstable periodic orbits — all of which are invisible to local linearization analysis. The paper uses this to establish that indeterminacy is more pervasive than local analysis suggests.

Good / Bad / Ugly Steady States. In the paper’s three-regime framework: the “good” state is the unique saddle-point equilibrium under high productivity Ah, with near-zero default rates; the “bad” state is the saddle-path equilibrium under low productivity Al, with modestly elevated defaults; the “ugly” state is the sink-path equilibrium under low productivity, characterized by self-fulfilling high default rates (up to ~12%). The ugly state is reached only when pessimistic sentiment coincides with the low-productivity regime, and it is the ugly state that generates the cluster pattern in simulation.

Collateral Constraint on Working Capital. The firm-level borrowing constraint wtnjt ≤ θVjt, where θ is the collateral ratio and Vjt is the firm’s continuation value. This constraint means that higher expected future profits — by raising Vt — relax the current borrowing limit, increase current labor demand and output, and create dynamic strategic complementarity between current and future production. It is this constraint, combined with the CES demand externality, that makes the dynamical system two-dimensional and generates the non-monotonic ˙Vt = 0 locus.

Global Indeterminacy. The existence, given an initial state variable Mt, of multiple equilibrium trajectories — each satisfying all equilibrium conditions including transversality — that converge to different steady states or follow periodic paths. In the paper, global indeterminacy arises even when the system is locally determinate (e.g., in the saddle-source case): trajectories diverging from near the source steady state can converge to the saddle steady state along multiple paths, none of which is detectable by local linearization.

Periodic Orbit (Endogenous Cycle). In the paper, a closed trajectory in the (Mt, Vt) phase plane that the economy follows indefinitely in perfect-foresight equilibrium without any exogenous shocks. Such orbits exist for κ ∈ (κ_Hopf, κ_SL), are stable if S < 0 and unstable if S > 0 (where S is a computable quantity defined in Equation A.13). Their existence demonstrates that business cycles can arise purely from internal forces — the demand externality and borrowing constraint — consistent with the view in Beaudry, Galizia, and Portier (2020).

AI and task efficiency

Mon, 01 Jan 0001 00:00:00 +0000

AI can improve decisions, raise firm productivity, and accelerate human capital growth through its effect on signal quality in problem-solving tasks, but the consequences are heterogeneous across the skill distribution and depend on how AI changes the hierarchy within firms. This paper proposes a framework in which AI improves the accuracy of the signals that guide human decisions—individually and in groups—and derives implications for firm organization, wages, and productivity. It also examines preliminary evidence: a cross-sectional regression of changes in TFP growth (2024 versus 2022) on sectoral AI exposure (Eisfeldt et al. 2024) for Compustat firms yields a positive relationship, statistically significant at the 10% level at the 3-digit NAICS sector level and at the 5% level at the firm level, with a slope coefficient of 0.206 for the firm-level regression. The paper compares AI to earlier general purpose technologies (GPTs)—electricity and information technology—finding that if there is a productivity delay for AI it appears shorter than the five- and eight-year delays documented for electrification and IT.

In depth

Q1. What is the theoretical framework linking AI to decisions and productivity?

The paper models several mechanisms through which AI may improve outcomes by raising the accuracy of signals that guide problem-solving: when signal accuracy rises, individuals and groups make better decisions, potentially enabling lower-level workers to handle more complex tasks and reducing the need for expensive higher-level solutions. For example, if AI allows managers to understand problems faster, they can handle more problems at a given time, potentially reducing demand for specialized expert judgment at lower hierarchy levels. Alternatively, if AI allows lower-level workers (clerks, nurses) to handle tasks previously requiring specialists (partners, doctors), the demand for specialists may fall and the wage premium for top-tier workers may narrow. The direction of the effect depends on whether AI is a better complement to high-skill or to low-skill tasks.

Q2. What does the empirical evidence show about AI’s current productivity effects?

A cross-sectional regression using 5,009 Compustat firm-level observations for 66 three-digit NAICS sectors finds a positive and statistically significant relationship between sectoral AI exposure in 2022 (from Eisfeldt et al. 2024) and the change in annual TFP growth between 2024 and 2022, with a sector-level slope coefficient that is statistically significant at the 10% level. The firm-level regression (including 3-digit NAICS fixed effects) yields a slope of 0.206 on AI exposure, significant at the 5% level (t-statistic 2.08), with R² = 0.20 and 1,996 observations. The relationship is absent when examining TFP growth levels in any individual year between 2019 and 2022, consistent with AI’s macroeconomic effects only becoming measurable after the release of GPT-4 in March 2023.

Q3. How does AI compare with prior general purpose technologies?

The paper relates AI to the earlier GPT literature, noting that productivity growth tended to be lower at the start of both the electrification and IT eras—with delays of approximately five and eight years respectively before productivity gains became measurable—and that if there is a similar delay for AI it appears shorter based on the preliminary 2024 data. This comparison suggests that AI may be a GPT with unusually rapid diffusion or a shorter learning curve, though the authors caution that the evidence is still preliminary and depends on the dating of AI’s “arrival.”

Q4. Why might AI effects differ across the hierarchy within firms?

AI’s effect on a firm hierarchy depends on whether it complements or substitutes for skills at each level: if AI primarily helps managers (by speeding problem diagnosis), it may reduce demand for specialized lower-level workers; if it primarily helps clerks (by enabling them to handle more complex documents), it may reduce demand for partners while raising demand for lower-level staff. The paper argues that the distributional consequences—whether AI raises or lowers wage dispersion—depend on this complementarity/substitutability pattern, which likely varies by industry, as illustrated by the contrasting cases of automotive assembly (AI may help managers but not line workers) and law firms (AI may help clerks handle more complex work).

Key concepts

AI as signal accuracy improvement : the paper’s framework for thinking about AI’s effect on decision quality: AI raises the precision of the signals that guide problem-solving, which leads to better individual and group decisions regardless of the specific mechanism.

general purpose technology (GPT) delay : the empirical phenomenon documented by Jovanovic and Rousseau (2005) in which productivity growth is lower at the start of a major GPT era before eventually accelerating; the paper examines whether AI exhibits the same pattern, finding that any delay appears shorter than for electrification (five years) or IT (eight years).

An endogenous gridpoint method for distributional dynamics

Mon, 01 Jan 0001 00:00:00 +0000

This paper introduces the Distributional Endogenous Gridpoint Method (DEGM), a novel numerical technique for solving the distributional dynamics that arise in heterogeneous agent macroeconomic models. The core problem is how to efficiently update the distribution of agents over the state space as the economy evolves. The dominant existing approach — the “lottery method” of Young (2010) — discretizes the state space and represents policy functions as lotteries over nearby gridpoints, producing a transition matrix that is linear in optimal policies. This linearity renders the lottery method incapable of capturing nonlinear effects in distributional dynamics, a limitation that becomes quantitatively significant for higher-order perturbation solutions.

DEGM extends Carroll’s (2006) endogenous gridpoint method from individual optimization to the distributional level. Rather than discretizing the density and integrating forward, DEGM works directly on the cumulative distribution function (CDF). The key insight is that when the policy function is monotone — as savings functions typically are — the endogenous gridpoints generated by the policy function trace out exact points on the post-policy CDF without requiring integration. Specifically, if A*_{i,j} = a*(A_i, Y_j) are optimal asset choices from grid point A_i at income Y_j, then the CDF values at those endogenous points are known analytically as F_t(A_i | Y_j). An interpolant using shape-preserving splines constructed through these points allows evaluation of the updated CDF at any point without integration. The income transition step is handled separately via standard quadrature over the discretized income process.

The paper demonstrates DEGM’s performance with two applications. First, in the Aiyagari (1994) economy, DEGM converges to the stationary equilibrium an order of magnitude faster than the lottery method in terms of gridpoints. At nk=40 gridpoints, the lottery method deviates from the benchmark capital stock by 1.72% and the wealth Gini by 2.24% (for nh=5), while DEGM deviates by only 0.09% and 0.12% respectively. Both methods converge to the same solution as the number of gridpoints increases, but DEGM reaches this limit far faster.

Second, the authors introduce a Krusell-Smith style model with aggregate investment risk (capital depreciation shocks calibrated following Barro, 2006, as a 0.4% quarterly probability of 7.5% capital destruction causing a 10% annual GDP drop) as a new baseline for studying aggregate nonlinearities with household heterogeneity. This model overcomes the near-linearity of aggregate capital dynamics in the original Krusell-Smith specification. Using a third-order perturbation solution with DEGM, aggregate investment risk lowers the capital stock by 5 to 11 basis points and increases wealth inequality by up to 11 basis points relative to the non-stochastic steady state, depending on idiosyncratic income risk calibration. The lottery method systematically mispredicts these effects: it always predicts a decrease in wealth inequality in the presence of investment risk, while DEGM predicts an increase. At third order, the lottery method predicts wealth Gini changes of +2.0 bp (persistent calibration) and -149.7 bp (transitory calibration), while DEGM predicts +10.7 bp and +2.1 bp respectively.

The mechanism for increased inequality under investment risk is heterogeneous: for less wealthy households the substitution effect dominates (they reduce saving more in response to risky returns), while for wealthy households the income effect is stronger and precautionary saving motives dominate. The lottery method, by making the distributional transition matrix linear in policies, zeros out the second derivative of the transition matrix with respect to the policy function, missing the term capturing how the density at the pre-image of each asset level is affected nonlinearly. DEGM’s cubic spline interpolant captures all nonlinearities up to third order, enabling economically meaningful results that qualitatively differ from lottery-method predictions on wealth inequality.

Q: What is the fundamental numerical problem that DEGM solves? A: Evolving the distribution of agents forward over time in heterogeneous agent models requires evaluating a Kolmogorov forward equation, which naively demands numerical integration. The lottery method avoids integration by discretizing the state space and expressing transitions as a linear matrix operation, but this forces the distributional dynamics to be linear in optimal policies. DEGM avoids integration by exploiting policy function monotonicity: the endogenous policy gridpoints are the interpolation nodes, so the CDF update requires only interpolation, not integration. This preserves nonlinear effects up to the order of the splines used.

Q: How does DEGM handle the borrowing constraint and the resulting mass point? A: Savings policy functions are typically weakly monotone: constant at the borrowing constraint for sufficiently poor households, then strictly monotone above a threshold. DEGM accommodates this by starting the endogenous grid at the EGM solution corresponding to the borrowing constraint (the threshold a_j above which the policy is strictly monotone), restoring strict monotonicity on the relevant domain. The mass point at the borrowing constraint is captured by evaluating F_t(a_j, Y_j). Echoes of the borrowing constraint diminish as the number of income states increases, and in practice 10 income gridpoints are sufficient to smooth them.

Q: How much faster does DEGM converge relative to the lottery method for the stationary equilibrium? A: In the Aiyagari economy with nk=40 asset gridpoints, the lottery method’s capital stock deviates from the benchmark by 1.72% and the wealth Gini by 2.24% (nh=5), while DEGM deviates by only 0.09% and 0.12% respectively — roughly a 20-fold improvement in accuracy for the same gridpoints. At nk=80, the lottery method still shows 0.56%/0.78% deviations while DEGM shows 0.03%/0.00%. Although for a fixed number of gridpoints the lottery method is faster in wall-clock time (0.35s vs 0.82s at nk=40, nh=20), DEGM is faster for a given level of accuracy because it requires far fewer gridpoints.

Q: Why does the lottery method fail at higher-order perturbations? A: The lottery method constructs its transition matrix as a piecewise linear function of the optimal policy a*, so its second derivative with respect to a* is zero. As a result, it misses the second term in the second-order derivative of the end-of-period CDF: the term involving the derivative of the density at the pre-image of each asset level times the squared linear policy effect. This missing nonlinearity becomes quantitatively important at second and third order. DEGM’s cubic hermitian spline interpolant captures all nonlinearities up to third order, allowing it to correctly represent how the distribution responds nonlinearly to aggregate shocks.

Q: What does the paper find about the effect of aggregate investment risk on the capital stock and wealth inequality? A: Using a third-order perturbation solution with DEGM, aggregate investment risk lowers the capital stock by 5 to 11 basis points from the non-stochastic steady state, depending on whether income risk is persistent or transitory (DEGM third-order: -4.7 bp persistent, -11.4 bp transitory). Wealth inequality increases by up to 11 basis points (DEGM third-order: +10.7 bp persistent, +2.1 bp transitory). The lottery method diverges dramatically at third order, predicting Gini changes of +2.0 bp and -149.7 bp for the persistent and transitory calibrations respectively, compared to DEGM’s +10.7 bp and +2.1 bp.

Q: What is the mechanism through which aggregate investment risk increases wealth inequality? A: The mechanism operates through heterogeneous saving responses across the wealth distribution. For less wealthy households, capital income is a small share of total income, so the substitution effect of risky returns dominates: higher investment risk reduces their incentive to save. For wealthy households, capital income is central, so the income effect is stronger and precautionary saving motives intensify. A capital depreciation shock upon realization compresses the wealth distribution, but the risk of such a shock increases inequality on average because it disproportionately reduces saving among poorer households.

Q: How do the authors extend DEGM to handle aggregate risk and higher-order perturbations? A: The authors follow Reiter (2009) in including the distribution and value functions in the state space, defining a nonlinear difference equation over these objects. Higher-order perturbation of this system proceeds using the algorithms of Andreasen et al. (2018) and Levintal (2017), with second-order terms solved via a generalized Sylvester equation using Kim et al.’s (2008) doubling algorithm. The implementation handles up to 3,200 variables at second order and 220 variables at third order. For the second-order solution, the Bayer-Luetticke (2020) state-space reduction and its refinement in Bayer et al. (2024) yield results identical to the full unreduced system.

Q: What is the state-space reduction procedure and how much does it compress the system? A: The full system uses 402 states and 412 controls (persistent calibration). A copula representation of the distribution reduces this to 213 states and 412 controls; adding DCT compression of the value function gives 213 states and 98 controls; further adding a factor representation from the first-order solution yields 111 states and 98 controls — a 75% reduction. The R-squared-like IRF statistic remains 1.00 across all reductions, and ergodic moments are identical (capital: 25.54, Gini: 0.61 for the persistent calibration).

Q: Does DEGM produce different first-order impulse responses than the lottery method? A: For first-order perturbations, DEGM and the lottery method converge to the same solution as the number of gridpoints increases, but DEGM converges faster. For the first-order dynamics of the wealth distribution (wealth Gini IRFs), DEGM reaches convergence with nk=40 gridpoints while the lottery method requires nk=160. For aggregate capital stock IRFs, both methods converge quickly at first order. Quantitative differences become significant only at second and higher orders.

Q: What calibration is used for the investment risk model? A: Capital depreciation deviates from its steady-state value by a shock with second moment sigma_delta = 0.005 and third moment tau_delta = 0.012. This corresponds to a 0.4% quarterly probability that a disaster destroys 7.5% of the capital stock and causes a 10% drop in annual GDP, consistent with the evidence in Barro (2006). The model is solved under both a persistent income calibration (beta=0.98, rho=0.98, sigma_epsilon=0.14, implied Gini=0.66) and a transitory income calibration (beta=0.99, rho=0.88, sigma_epsilon=0.18, implied Gini=0.42).

Distributional Endogenous Gridpoint Method (DEGM): A numerical method for evolving the joint CDF of agents over the state space by constructing an interpolant at endogenous gridpoints A*_{i,j} = a*(A_i, Y_j) — the optimal policy values — at which CDF values are known analytically as F_t(A_i | Y_j), thus updating the distribution through interpolation rather than integration and preserving nonlinearities up to the order of the spline.

Lottery Method (LM): Young’s (2010) standard technique that replaces the continuous distribution with a discrete counterpart and represents optimal policy functions as probability weights over nearby gridpoints, yielding a single transition matrix A* such that f_{t+1} = f_t * A*. The transition matrix is linear in optimal policies, which zeroes out the second derivative of the distributional dynamics with respect to policies and causes systematic misprediction of distributional dynamics under higher-order perturbation.

Kolmogorov Forward Equation (Distributional Dynamics): The law of motion for the joint CDF F_t(a, y) describing how the distribution of households over assets and income evolves given optimal policies and the income transition process. In DEGM, this equation is split into a sub-period for asset choices (where endogenous gridpoints allow integration-free updating) and a sub-period for income transitions (handled by quadrature over the discretized income process).

Higher-Order Perturbation Solution: A Taylor expansion of the model’s nonlinear equilibrium conditions around the non-stochastic steady state beyond first order. Second-order solutions capture precautionary motives and mean deviations from the steady state; third-order solutions additionally capture asymmetric effects of shocks, requiring DEGM’s nonlinear distributional representation to produce accurate results.

Aggregate Investment Risk (Capital Depreciation Shocks): Shocks to the aggregate capital depreciation rate calibrated following Barro (2006) as a 0.4% quarterly probability of a disaster that destroys 7.5% of the capital stock and causes a 10% annual GDP drop. Proposed as a replacement for near-linear Krusell-Smith aggregate productivity shocks to generate genuine nonlinearities in aggregate capital dynamics while remaining equally parsimonious.

State-Space Reduction: A sequence of compression techniques — copula representation of the wealth distribution, discrete cosine transform (DCT) compression of the value function, and factor representation from the first-order solution — that reduce the Reiter (2009) system from 402 states and 412 controls to 111 states and 98 controls (a 75% reduction) with no measurable loss of accuracy in impulse responses or ergodic moments.

Shape-Preserving Interpolation: Interpolation methods (linear spline or piecewise cubic hermitian splines) that maintain the monotonicity of the CDF when constructing the interpolant from endogenous gridpoints. Cubic hermitian splines additionally preserve differentiability, making the distributional dynamics smooth enough for third-order perturbation and capturing all nonlinear effects that the lottery method misses.

Artificial intelligence and cognitive inequality

Mon, 01 Jan 0001 00:00:00 +0000

Artificial intelligence and technological unemployment

Mon, 01 Jan 0001 00:00:00 +0000

Wang and Wong develop a continuous-time labor-search model to assess the dynamic effects of generative AI (GenAI) on labor productivity and unemployment. The paper is motivated by conflicting empirical evidence: micro studies find productivity gains of 14% (Brynjolfsson, Li, and Raymond 2025) and 55.8% faster coding (Peng et al. 2023), while macro estimates suggest modest TFP gains of at most 0.064% annually (Acemoglu 2024), and occupation-level evidence shows a 13% relative employment decline in AI-exposed jobs (Brynjolfsson, Chandar, and Chen 2025).

The model distinguishes GenAI from earlier automation technologies by its learning-by-using mechanism: AI capability grows at rate µ per employed worker (law of motion dAt/At = µHt − δ), raises employed workers’ productivity, and creates a displacement threat through renegotiation. When renegotiation fails, AI replaces the worker, generating technological unemployment. Firms renegotiate wages at a rate ρµAt proportional to AI’s learning rate and the job’s exposure ρ. The joint surplus condition governs whether replacement occurs: AI replaces a worker if and only if πA (AI’s net present value per output) exceeds the post-renegotiation joint surplus St.

The model admits three steady states: (i) a some-AI steady state with finite AI capability, persistent AI adoption (It = 1), expanded job creation but declining employment at H∞ = δ/µ; (ii) an unbounded-AI equilibrium with sustained endogenous growth, no displacement (It = 0), and employment at H∞ = α/(α+σ); and (iii) a no-AI equilibrium reverting to the Mortensen-Pissarides benchmark. In the benchmark model (exogenous job-finding rate, AI-augmented productivity), multiple steady states can coexist—global indeterminacy—when condition (28) holds. In the full model (endogenous job creation via free entry), both global and local indeterminacy are possible, and a continuum of oscillatory transition paths converge to the some-AI steady state.

Calibrated to U.S. data, targeting a pre-AI unemployment rate of 5%, AI elasticity of productivity εy = 1.069 (from Czarnitzki et al. 2023), initial AI productivity boost of 14% (Brynjolfsson et al. 2025), worker exposure ρ = 0.618 (Brynjolfsson et al. 2018’s machine learning suitability index), AI replacement cost ϕ = 0.0043 (from U.S. business GenAI spending), AI learning rate µ = 0.632, and AI error rate δ = 0.462 (Moore’s law half-life of 1.5 years), the model converges to a some-AI steady state. The long-run results are: a 23% employment loss (H∞ = 0.732 vs. H0 = 0.95), AI capability improvement of 321%, and labor productivity gain of 366%. Approximately half of the employment loss—11.5 percentage points—occurs within the first five years, alongside a 49.3% output gain and 45.5% AI capability improvement over that period.

Untargeted moments are validated: the model implies 7.08% labor productivity growth over the first 10 years (consistent with Briggs and Kodnani 2023) and an AI elasticity of vacancies averaging 0.16 over the first five years (consistent with Acemoglu et al. 2022).

On welfare, equilibria are inefficient even when the Hosios condition holds. AI introduces four externalities beyond standard matching frictions: job destruction via displacement, productivity enhancement for employed workers, feedback from AI learning depending on employment, and direct effects on matching surpluses. A constrained-optimal subsidy to jobs at risk of AI displacement is 26.6% in the short run and exceeds 50% in the long run. In the full model, the Hosios condition requires fixing firm bargaining power θ to the vacancy elasticity of matching ξ, but an additional per-output transfer T = µApωA to firm-worker matches is necessary to correct AI adoption inefficiency.

Q: What is the core mechanism by which AI generates unemployment in this model? A: AI capability grows through a learning-by-using process (dAt/At = µHt − δ), improving as it observes employed workers. As capability rises, firms gain a displacement option that arrives at rate ρµAt per matched pair. When renegotiation over wages fails—i.e., when the AI’s NPV πA exceeds the joint surplus—firms replace workers with AI, causing unemployment. This creates a feedback loop: higher employment accelerates AI learning, which increases displacement pressure and reduces employment.

Q: What are the three steady states and what distinguishes them? A: The some-AI steady state features finite AI capability, persistent displacement (It = 1), and long-run employment H∞ = δ/µ; it involves technological unemployment. The unbounded-AI steady state features infinite AI capability, no displacement (It = 0), endogenous productivity growth, and employment H∞ = α/(α+σ) as in the standard Mortensen-Pissarides model. The no-AI steady state has A∞ = 0 with the same H∞ = α/(α+σ) but no AI contribution. Employment is higher in the unbounded-AI equilibrium than in the some-AI equilibrium.

Q: What does the calibration imply for long-run employment and productivity? A: The calibrated full model converges to a some-AI steady state with a 23% employment loss (H∞ = 0.732), a 321% improvement in AI capability, and a 366% gain in labor productivity. The parameters yield a unique equilibrium under the baseline calibration (πA = 1.949 > sAI = 0.8735 confirms some-AI existence). These results reflect a large worker replacement effect under the calibrated AI learning and error rates, while the job creation effect is relatively modest.

Q: How fast does technological unemployment materialize? A: Approximately half of the total 23% employment loss occurs within the first five years; specifically, employment falls by 11.5 percentage points over that period. Over the same five years, AI capability improves by 45.5% and output rises by 49.3%. Over the first 10 years, AI capability improvement accumulates to 94.0% and output gain to 103% (approximately double the five-year output gain).

Q: How does the full model differ from the benchmark model in transition dynamics? A: In the full model, job-finding rates are endogenous: firms post vacancies until a free-entry condition (κyt = ftΠt) is satisfied, tying job-finding rate αt to the surplus ratio st via αt = α(st). This endogeneity implies that as AI raises labor productivity, firms create more vacancies, slowing the employment decline relative to the benchmark model with a fixed job-finding rate. At the same time, AI capability grows faster in the full model because higher employment accelerates AI learning.

Q: What is global indeterminacy and when does it arise? A: Global indeterminacy occurs when both the some-AI and unbounded-AI steady states coexist, so the long-run outcome depends on initial conditions or expectations. In the benchmark model this requires condition (28): 0 < r + σ + α(1−θ) − (1−b)/πA ≤ εy(µα/(α+σ) − δ). In the full model, global indeterminacy is plausible when firm bargaining power rises to θ = 0.95 given the baseline AI replacement cost ϕ = 0.0043. The region of global indeterminacy is larger when firm bargaining power is higher.

Q: What is local indeterminacy and what does it imply for transition paths? A: Local indeterminacy means there is a continuum of equilibrium paths converging to the some-AI steady state in the neighborhood of that steady state, rather than a unique saddle path. In the full model, under alternative parameters (θ = 1, ξ = 0.765, εy = 6), the eigenvalues feature a negative real root and two complex roots with negative real parts, yielding oscillatory local dynamics in employment and AI capability. This implies short-run cycles in productivity and unemployment, consistent with the wide range of empirical findings on AI’s labor-market effects.

Q: Why does the Hosios condition fail to deliver efficiency in this model? A: The Hosios condition eliminates the standard matching externality by setting firm bargaining power to the vacancy elasticity of matching. But AI introduces four additional externalities: (i) job destruction through displacement, (ii) productivity enhancement for employed workers, (iii) feedback from AI learning that depends on aggregate employment, and (iv) direct effects on matching surpluses and job-finding rates. These externalities mean the standard Hosios rule alone is insufficient; additional instruments are required.

Q: What is the constrained-optimal policy response? A: In the simple model, the constrained optimal AI adoption threshold differs from the equilibrium threshold because firm bargaining power θ distorts adoption decisions: AI is over-adopted when πA > (1−b)/(r+σ+α(1−θ)) and under-adopted when (1−b)/(r+σ+α) < πA ≤ (1−b)/(r+σ+α(1−θ)). In the full model, constrained optimality requires setting θ = ξ (Hosios) plus a per-output subsidy T = µApωA to firm-worker matches exposed to AI displacement. This targeted subsidy is 26.6% in the short run and exceeds 50% in the long run.

Q: How does AI compare to computers in this model’s counterfactual? A: The paper reports that exogenous productivity growth from computers reduced unemployment only modestly—by 0.16 percentage points. By contrast, AI’s learning-by-using and displacement features imply a nearly 20% long-run employment loss in a comparable counterfactual. The key distinction is that computers lack the self-learning improvement and associated renegotiation-triggered displacement that characterize GenAI in this model.

Q: How is AI exposure parameterized and what does it capture? A: The exposure parameter ρ captures the degree to which a job is subject to AI-driven replacement risk. It is calibrated using Brynjolfsson et al. (2018)’s suitability for machine learning (SML) index: on a 1–5 scale, SML averages 3.47 across 964 O*NET occupations, translating to (3.47−1)/(5−1) = 61.8%, so ρ = 0.618. The effective exposure measure is ρµ, which is higher when facing a faster-learning AI.

Q: What is the predator-prey analogy in the model’s dynamics? A: The dynamical system for AI capability (At) and employment (Ht) in the simple model resembles the Lotka-Volterra predator-prey system. Employment (prey) feeds AI learning; as AI capability (predator) grows, it displaces workers faster, reducing employment; lower employment then slows AI learning, causing capability to decay; and the cycle repeats with diminishing magnitude until the steady state is reached. This mechanism operates only when the AI learning rate µ is neither too high nor too low, with the convergence path being a spiral when µα < 4δ²(1 − δ(α+σ)/(µα)).

Q: What is the labor-share implication of the unbounded-AI equilibrium? A: In the unbounded-AI steady state, employment is higher than in the some-AI steady state (H^AJJ > H^AI) and labor productivity grows without bound. However, the labor share is lower in the unbounded-AI equilibrium if the firm’s bargaining power θ is sufficiently low. This implies that while workers are not fully displaced and rising AI-augmented productivity sustains employment, workers’ income share may still decline even in the more favorable unbounded scenario.

Technological unemployment: A phenomenon in which AI adoption raises labor productivity and expands job creation, yet still causes sizable employment losses because the worker displacement effect (driven by renegotiation failure when AI’s NPV πA exceeds the joint surplus) dominates the job-creation effect. In the calibrated model this amounts to a 23% employment loss despite a 366% productivity gain.

Learning-by-using AI: The model’s representation of GenAI as a technology whose capability At grows through reinforced learning from employed workers at rate µ per worker, so aggregate AI growth is µHt, offset by deterioration at rate δ. This distinguishes GenAI from earlier automation technologies (computers, robotics) that do not self-improve through usage.

Some-AI steady state: A long-run equilibrium with finite AI capability (gA∞ = 0), persistent AI adoption (It = 1), and employment pinned at H∞ = δ/µ—the ratio of AI’s error rate to its learning rate. Characterized by expanded job creation but lower employment than the no-AI benchmark, constituting the model’s primary calibrated outcome.

Unbounded-AI steady state: A long-run equilibrium with infinite AI capability (A∞ = ∞), no displacement (It = 0), and endogenous growth at rate gA = µH^AJJ − δ. Employment equals the Mortensen-Pissarides level H∞ = α/(α+σ), and labor productivity grows without bound, complementing Aghion, Jones, and Jones (2019)’s idea production framework.

Global indeterminacy: Coexistence of multiple steady states (some-AI and unbounded-AI) such that the long-run equilibrium depends on initial conditions or expectations rather than being uniquely determined. Arises in the benchmark model when condition (28) holds and becomes more likely with higher firm bargaining power θ.

Local indeterminacy: A continuum of equilibrium transition paths converging to a single steady state from nearby initial conditions, rather than a unique saddle path. Arises in the full model under certain parameter configurations (e.g., θ = 1, ξ = 0.765, εy = 6), implying oscillatory short-run dynamics in employment and AI capability.

AI exposure (ρ): A firm-level parameter capturing the degree to which a job-match is subject to AI-driven displacement risk. The displacement option arrives at rate ρµAt per matched pair; ρ is calibrated at 0.618 using the average suitability-for-machine-learning score across O*NET occupations. The effective exposure measure is the product ρµ.

Renegotiation-proof displacement: Proposition 1’s result that the joint surplus Snt is independent of the renegotiation round n, so the AI adoption decision It is also round-invariant. This simplifies the model to a single indicator function: AI replaces the worker if and only if πA exceeds the joint surplus St, regardless of how many renegotiation rounds have occurred.

Automated credit limit increases and consumer welfare

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question. Should regulators restrict banks from proactively raising credit card limits using machine-learning algorithms, and if so, how? The paper asks: to what extent are bank-initiated credit limit increases directed toward revolving borrowers (those who carry interest-accruing balances month-to-month), and what are the welfare consequences of policies that constrain such increases?

Data. The empirical analysis uses the Federal Reserve’s Capital Assessments and Stress Testing (Y-14M) regulatory data, January 2014 to December 2024, covering monthly account-level records for all credit cards issued by large stress-tested banks (assets > $100B). The 26 banks in the sample collectively represent more than 70% of U.S. credit card balances. A 0.5% sample yields more than 150 million observations across more than 3.6 million unique active credit cards. A key advantage of Y-14 over credit bureau data is that it identifies whether each limit change was bank-initiated or consumer-initiated — a distinction not available in other datasets.

Stylized Facts. Credit limit increases are an important and understudied source of consumer credit. During the post-pandemic period, limit increases generate more than $40 billion of additional available credit per quarter, roughly 60% of the approximately $70 billion coming from new card originations; prior to the pandemic the figure was about $30 billion, or roughly half of new issuance. The number of accounts undergoing a limit increase each quarter is on average 30% higher than the number of new cards issued. Consistent with “low-and-grow” lending strategies, limit increases are disproportionately important for lower credit-score borrowers: average subprime credit limits rise from $700 at origination to $2,700 by five years after origination (a 285% increase) and to nearly $5,000 by eight years, while average superprime limits rise only from approximately $12,000 to $15,000 (a 25% increase). About 30% of total revolving balances are made possible by limit increases, with the share reaching 60% for subprime borrowers but only 12% for superprime borrowers. Approximately 75–80% of all limit increases — both by dollar amount and by number of cards — are bank-initiated rather than consumer-initiated. Banks that more frequently reference “artificial intelligence” or “machine learning” in their 10-K filings support a larger share of revolving balances through limit increases. Bank-initiated increases are roughly 1.5–2 times more prevalent among accounts that have revolved in the prior three months, whereas consumer-initiated increases show essentially no differential by revolving status.

Empirical Analysis. Using a linear probability model with card-portfolio-group fixed effects, month fixed effects, and controls for credit score, income, prior limit changes, and other account characteristics, the authors show that the probability of a bank-initiated limit increase follows an inverse-U shape in revolving utilization: accounts with revolving utilization in the moderate range (roughly 0.2–0.7) are most likely to receive an increase, while those near zero or near 1.0 are not. An account with revolving utilization in the (0.2, 0.3] bin is approximately as likely to receive a limit increase as an account whose credit score just rose by 66 points. Transacting utilization, by contrast, follows a logistic growth pattern: the probability rises monotonically until about a utilization of 0.3 and is flat above that. An event study shows that after a bank-initiated limit increase, revolving utilization rebounds to its pre-increase level within approximately 8 months; on average, revolving balances increase by about 40% of the limit increase, with approximately 30% of the limit increase going toward revolving balances. This rebound occurs even for accounts with revolving utilization below the pre-increase mean of 0.28, indicating that the effect is not confined to liquidity-constrained borrowers.

Model. The authors develop a life-cycle consumption–saving model with credit card borrowing, uninsurable income and employment risk, potential default (Chapter 7 style), and heterogeneous preferences following Nakajima (2017) and Gul–Pesendorfer (2001, 2004). Two household types coexist: 60% with standard exponential-discounting preferences (calibrated β = 0.92) and 40% with temptation preferences (calibrated β = 0.96, temptation parameter λ = 0.28 from Kovacs et al., 2021). The credit limit increase function is calibrated using Y-14M data via a latent-variable formulation, replicating the empirical inverted-U relationship between revolving utilization and limit increase probability. The four internally calibrated targets are: share of households with revolving credit card debt (data: 45%, model: 41.8%); utilization rate conditional on debt (data: 35%, model: 28.9%); default probability (data: 0.94%, model: 0.94%); debt-to-income ratio (data: 8.6%, model: 6.8%).

Main Findings — Baseline. Through the model, tempted agents are disproportionately likely to receive credit limit increases because they are more likely to revolve. For customers with utilization above 50%, the majority of credit limit increases are detrimental from the borrower’s own perspective. Standard agents almost always benefit from higher credit limits.

Counterfactual 1 — UK-style (prohibit limit increases for revolving borrowers). This policy reduces the annual probability of limit increases from roughly 5.5% to approximately 1.0%. The default probability falls from about 0.9% to near zero. The debt-to-income ratio declines by roughly 2 percentage points. Aggregate welfare improves by 1.12% in consumption equivalent variation (CEV) when the social planner internalizes the psychological cost of temptation (0.98% without). Standard households incur a modest welfare loss of 0.21% from reduced consumption-smoothing flexibility, while tempted households gain approximately 3.12% in CEV.

Counterfactual 2 — Canada/EU-style (require consumer consent). This policy reduces the annual limit-increase probability from 5.5% to approximately 1.9%. Aggregate welfare improves by 1.16% in CEV (1.04% without psychological costs). Standard households lose 0.19%, while tempted households gain approximately 3.19%. Under the baseline assumption of sophisticated tempted households, results are nearly identical to the UK-style policy. However, when the fraction of naïve tempted households is large, the consent-based policy becomes ineffective (naïve consumers accept limit increases they will regret), whereas the UK-style revolving-borrower ban remains welfare-improving regardless of the naïve share.

Robustness. When the firm is allowed to re-optimize its credit limit increase policy, it endogenously reallocates more limit increases toward standard consumers. Welfare gains remain positive but are attenuated: the UK-style policy yields 0.21% CEV (vs. 1.12% in the baseline calibration) and the consent-based policy yields 0.27% CEV.

Policy Implications. The U.S. lacks regulation of bank-initiated proactive credit limit increases (existing rules under ECOA and ability-to-pay provisions are largely non-binding for this purpose). The authors conclude that banks’ revealed preference for targeting revolvers constitutes an implicit targeting of consumers with self-control issues, and that if a meaningful share of households have self-control issues, there are strong consumer protection grounds for regulating algorithmic credit limit increases.

In depth

Q1. Why do the authors use Y-14M data rather than credit bureau data, and what does this data uniquely enable?

A: The Y-14M dataset allows the authors to distinguish between bank-initiated and consumer-initiated credit limit changes — a distinction not observable in credit bureau data. It also contains actual payment information enabling identification of revolvers (those carrying interest-accruing balances) rather than just total balances. The sample covers more than 70% of U.S. credit card balances and more than 150 million monthly observations over the January 2014 to December 2024 period.

Q2. How large are credit limit increases relative to new card originations in the U.S. credit card market?

A: During the post-pandemic period, limit increases produce more than $40 billion of additional available credit per quarter, roughly 60% of the approximately $70 billion created by new card originations. Prior to the pandemic the figure was approximately $30 billion, or about half of new issuance. On a count basis, the number of cards undergoing a limit increase each quarter is on average 30% higher than the number of new cards issued.

Q3. What is the “low-and-grow” strategy, and how large is the subsequent credit expansion?

A: The low-and-grow strategy involves originating higher-risk borrowers at low initial credit limits and then expanding limits based on observed borrowing behavior. For the average subprime credit card, the initial limit of $700 grows to $2,700 by five years after origination (a 285% increase) and to nearly $5,000 by eight years. For superprime borrowers, the initial limit of approximately $12,000 grows only to $15,000 (a 25% increase) by five years and then is approximately unchanged.

Q4. How does a borrower’s revolving status affect the probability of receiving a bank-initiated limit increase?

A: Bank-initiated increases are approximately 1.5–2 times more prevalent among accounts that have revolved at least once in the prior three months, compared to non-revolving accounts. By contrast, consumer-initiated increases show essentially no differential between revolvers and non-revolvers. This reveals a bank-side revealed preference for targeting revolvers.

Q5. What is the shape of the relationship between revolving utilization and the probability of a bank-initiated limit increase, and how large is its economic magnitude?

A: The relationship follows an inverted-U shape. Accounts with revolving utilization in bins between approximately 0.2 and 0.7 have the highest probability of receiving an increase; accounts near zero or near full utilization are as unlikely to receive an increase as zero-utilization accounts. The effect of being in the (0.2, 0.3] revolving utilization bin has approximately the same positive effect on the probability of receiving a limit increase as a 66-point increase in credit score, making it economically large relative to standard risk signals.

Q6. How does transacting utilization relate to bank-initiated limit increases, and how does this differ from revolving utilization?

A: Transacting utilization follows a logistic growth pattern rather than an inverted-U. The probability of receiving a limit increase rises monotonically with transacting utilization until about a utilization of 0.3, above which the probability does not vary with utilization. This contrasts with revolving utilization, where very high utilization (above 0.9) is actually no more predictive than zero utilization.

Q7. What does the event study show about borrowing behavior following credit limit increases?

A: After a bank-initiated limit increase, revolving utilization (as a share of the credit limit) drops mechanically but then rebounds to pre-increase levels within approximately 8 months. On average, revolving balances increase by about 40% of the amount of the limit increase, with approximately 30% of each dollar of new credit limit going toward revolving balances. These magnitudes are somewhat larger than the 13% (Gross and Souleles, 2002) and 18% (Aydin, 2022) found in prior work, which the authors attribute to the non-causal nature of their event study, higher average utilization in their sample, and their focus on revolving rather than total utilization.

Q8. Is the post-increase borrowing rebound driven by liquidity-constrained borrowers?

A: No. The authors show that limiting the sample to accounts with revolving utilization below the pre-increase mean of 0.28 — accounts that are unlikely to be liquidity constrained — yields very similar results. This finding is consistent with the presence of self-control issues rather than binding credit constraints.

A: The model features two types: 60% with standard exponential-discounting preferences (estimated discount factor β = 0.92) and 40% with temptation preferences (β = 0.96, temptation parameter λ = 0.28 set from Kovacs et al., 2021). The 40% tempted share is internally estimated via the Method of Simulated Moments targeting four aggregate moments: share with revolving credit card debt (45% in data, 41.8% in model), utilization rate conditional on debt (35% vs. 28.9%), default probability (0.94% vs. 0.94%), and debt-to-income ratio (8.6% vs. 6.8%).

Q10. How do tempted and standard households differ in their credit card usage within the model?

A: In the model, 76% of tempted agents carry revolving credit card debt, with an average utilization rate of 73.6%, a debt-to-income ratio of 15.4%, and a default probability of 2.22%. Standard agents carry debt only 18.9% of the time, with average utilization of 4.1%, a debt-to-income ratio of 1.1%, and a default probability of 0.08%. Tempted agents also pay a substantially higher share of income on credit card interest.

Q11. How does the model capture the mechanism by which credit limit increases harm tempted households?

A: The Gul–Pesendorfer temptation utility function makes household welfare depend on both actual consumption and the most tempting consumption alternative available (the budget-set maximum). When credit limits rise, the most tempting alternative ˜c_t increases, which raises the utility cost of self-restraint even for households that do not succumb to temptation. This mechanism is distinct from hyperbolic discounting: temptation imposes a psychic cost even on those who ultimately choose not to over-borrow.

Q12. What are the quantitative welfare effects of the UK-style policy prohibiting limit increases for revolving borrowers?

A: The policy yields an overall welfare gain of 1.12% in consumption equivalent variation (CEV) when the social planner internalizes the psychological cost of temptation (0.98% without). Standard households suffer a modest welfare loss of 0.21% from reduced consumption-smoothing flexibility. Tempted households gain approximately 3.12% in CEV, because the benefit from reduced temptation and lower interest expenditure outweighs the cost of reduced credit access.

A: The consent-based policy yields an overall welfare gain of 1.16% in CEV (1.04% without psychological costs). Standard households lose 0.19%, and tempted households gain approximately 3.19%. Under the baseline assumption of fully sophisticated tempted households, results are nearly identical to the UK-style ban.

A: The UK-style ban on limit increases for revolving borrowers remains welfare-improving regardless of whether tempted households are sophisticated or naïve — the welfare impact is approximately flat as the naïve fraction rises from zero to one. The consent-based policy, by contrast, exhibits a negative linear relationship between the naïve fraction and welfare impact, with welfare gains disappearing as the naïve fraction approaches one. Naïve consumers accept limit increases they would regret, so the policy’s effectiveness depends on households accurately recognizing their own self-control issues.

Q15. What happens when the firm is allowed to re-optimize its credit limit increase policy in response to regulation?

A: With firm re-optimization, both counterfactual policies continue to improve welfare but the magnitudes are attenuated. The UK-style policy yields 0.21% CEV overall (tempted: 0.89%) and the consent-based policy yields 0.27% overall (tempted: 0.98%), compared to 1.12% and 1.16% without re-optimization. The re-optimizing firm reallocates more limit increases toward standard consumers, which reduces the number directed at tempted households but also limits the welfare gains from regulation.

Q16. What do lenders’ 10-K filings reveal about the role of AI/ML in targeting revolvers for limit increases?

A: Banks that mention “artificial intelligence” or “machine learning” above the median number of times in their 2024 10-K filings support a higher share of revolving balances through credit limit increases, for all credit score groups. This difference is not driven by differences in credit limits at origination between higher-AI and lower-AI lenders, suggesting that AI/ML adoption affects the targeting of limit increases toward revolvers rather than the initial credit allocation.

Key Concepts

Revolving utilization. In this paper, revolving utilization is defined as the portion of overall credit card utilization attributable to balances that the borrower carries from one month to the next without full repayment, thereby accruing interest. It is measured as revolving balances divided by credit limit, averaged over the prior three months. This is distinct from transacting utilization (new purchases as a share of limit) and is the primary signal banks use — implicitly, via their algorithms — to select accounts for proactive limit increases.

Bank-initiated vs. consumer-initiated credit limit increase. A bank-initiated limit increase is one in which the lender proactively raises a borrower’s credit limit without a request from the borrower. A consumer-initiated increase is one explicitly requested by the borrower. The Y-14M data uniquely identify the source of each change. The paper documents that approximately 75–80% of all limit increases are bank-initiated, and that bank-initiated increases are strongly correlated with revolving utilization whereas consumer-initiated increases are not.

Low-and-grow strategy. The practice of originating higher-risk borrowers at low initial credit limits and then expanding those limits over time based on observed borrowing behavior. In the paper this is a documented empirical pattern, not an assumption: subprime accounts start at an average $700 limit at origination and reach nearly $5,000 by eight years, a 285% increase versus only 25% for superprime accounts over the same horizon.

Temptation preferences (Gul–Pesendorfer). A utility framework in which household welfare depends not only on actual consumption but also on the most tempting consumption alternative within the budget set. The disutility from temptation arises even when the household does not succumb — it reflects the psychological cost of self-restraint. In the paper, λ (set to 0.28) parameterizes the weight of this temptation cost relative to standard utility. Temptation preferences are time-consistent, which facilitates welfare analysis, and are preferred to hyperbolic discounting in this setting because they predict that individuals may pay to have tempting options removed even without acting on them.

Revealed preference for targeting revolvers. The paper’s characterization of banks’ credit limit increase behavior as reflecting a systematic preference for giving increases to revolving borrowers, inferred from the empirical pattern in the Y-14M data (the inverted-U shape between revolving utilization and limit increase probability). Because banks’ algorithms are proprietary and unobserved, the paper interprets the observed allocation of limit increases as a revealed preference, consistent with banks’ profit motive since revolvers generate the majority of credit card interest income.

Consumption equivalent variation (CEV). The welfare metric used throughout the paper’s counterfactual analysis. CEV is defined as the percentage change in consumption in every period and state that would make households indifferent between the baseline policy regime and the counterfactual policy. A positive CEV indicates that the counterfactual policy improves welfare; a negative CEV indicates harm. The paper considers two versions: one in which the social planner internalizes the psychological cost of temptation (consistent with tempted households’ actual preferences), and one in which the planner ignores that cost (λ = 0 for the planner) but households still face temptation.

Persistent revolving debt (UK regulatory definition). In the UK Financial Conduct Authority’s framework, a borrower is considered in “persistent revolving debt” when the cumulative amount paid toward interest and fees exceeds the cumulative amount of principal repaid over a 12-month period. The UK rule prohibits lenders from increasing credit limits for borrowers meeting this definition. The paper models a stylized version: any account currently carrying a revolving balance is ineligible for a bank-initiated limit increase in the UK-style counterfactual.

Balance-Sheet Policy and the Term Premium: High-Frequency Evidence

Mon, 01 Jan 0001 00:00:00 +0000

When a central bank shrinks its balance sheet, how much do long-term interest rates actually move — and through which channel? Using minute-by-minute market data around balance-sheet announcements, the authors estimate that much of the long-rate response works through the term premium rather than through changed expectations of future short rates. The result is an estimate for their 2009–2024 sample under their identifying assumptions — evidence consistent with a term-premium channel, not a universal constant.

In depth

Q1. Does balance-sheet policy move long rates through the term premium or through expected short rates?

The paper estimates that a substantial share of the long-rate response operates through the term premium, with a smaller role for revised short-rate expectations — though it frames this as identification within their window, not a structural decomposition that holds in all regimes. This sits against a literature that has split the response into a signaling channel and a portfolio-balance channel; the contribution here is using intraday yields to isolate the announcement effect from contaminating macro news.

Q2. How is the effect identified, and why high-frequency?

By measuring yield changes in narrow windows around scheduled balance-sheet announcements, so that other macroeconomic news is unlikely to move rates within the window. The maintained assumption is that within a tight enough window, the announcement is the dominant shock — a standard high-frequency identification premise. The authors note the assumption is weaker around unscheduled communications, and restrict the main sample accordingly.

Q3. What does this imply for the pace of balance-sheet runoff?

If transmission runs through the term premium, the pace and predictability of runoff plausibly matter for long rates — but the paper presents this as suggestive, stopping short of a calibrated policy rule. The reading is that quantity and communication interact, consistent with prior work on announcement effects, rather than that runoff has a single mechanical effect on yields.

Key concepts

term premium: The extra return investors require for holding a long-term bond instead of rolling over short-term ones — here, the part of long rates not explained by expected future short rates.
balance-sheet policy: A central bank changing the size or composition of its asset holdings (expansion via purchases, runoff via “quantitative tightening”) as a policy tool distinct from setting the short-term rate.
high-frequency identification: Inferring a policy action’s effect from price moves in a very short window around the announcement, on the assumption that little else moves markets inside that window.

Bayesian inference in proxy SVARs with incomplete identification: Re-evaluating the validity of monetary policy instruments

Mon, 01 Jan 0001 00:00:00 +0000

Beyond the headline: How personal exposure to inflation shapes the financial choices of households

Mon, 01 Jan 0001 00:00:00 +0000

Biased expectations and labor market outcomes: Evidence from German survey data and implications for the East–West wage gap

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research question. The paper asks two questions: (1) How do workers’ biased expectations about job finding and job separation shape the labor market equilibrium and wages? (2) Are differences in expectation biases across workers a quantitatively important driver of wage differentials, specifically the East–West German wage gap?

Data. The empirical analysis uses the German Socio-Economic Panel (SOEP), a nationally representative longitudinal survey of approximately 30,000 participants per wave. The working-age sample (ages 25–65) covers nine biennial survey waves from 1999 to 2015, yielding 67,772 observations for job separation expectations and 6,423 for job finding expectations. Perceived transition probabilities are reported on a 0–100 scale in steps of 10 percentage points. Actual (statistical) transition probabilities are constructed by estimating probit models that predict realized transitions within 24 months using a rich set of individual, job, and employer characteristics, and are rounded to the nearest decile for consistency with the survey scale.

Main empirical findings. Employed workers in Germany overestimate their job separation probability by 6.4 percentage points on average (perceived: 19.8%; actual: 13.3%), a pessimistic bias significant at the 1% level. Unemployed workers overestimate their job finding probability by 8.2 percentage points on average (perceived: 57.0%; actual: 48.8%), an optimistic bias also significant at the 1% level. The East–West divergence is striking. East German workers exhibit a pessimistic job separation bias of 12.1 percentage points, compared to only 4.7 percentage points in the West, despite broadly similar actual separation rates (15.1% vs. 12.8%). For job finding, West Germans overestimate their probability by 12.9 percentage points, while East Germans overestimate by only 2.0 percentage points — meaning East Germans are also substantially less optimistic about re-employment. These East–West differences survive controls for compositional differences and alternative definitions of job separation (dismissals only; selected reasons; spell-based) and job finding (including those out of the labor force). The biases are stable over the 1999–2015 sample period with no discernible trend. A cohort analysis shows that the excess pessimism in East Germany is concentrated among cohorts who were already in the labor market at the time of German reunification (born in the 1950s and 1960s), consistent with persistent effects of the communist GDR experience. Individuals do not systematically learn over time: mean changes in individual-level absolute deviations between consecutive waves are close to zero. Individual deviations between perceived and actual rates have statistically significant but quantitatively negligible predictive power for subsequent transitions (a 1 pp higher perceived job separation is associated with only a 0.001 pp higher realized separation rate), ruling out private information as a first-order explanation for the biases.

Model. The authors extend the Diamond–Mortensen–Pissarides (DMP) frictional labor market framework by (i) allowing workers to hold biased perceived transition rates (λw for job finding, σw for job separation) while firms have rational expectations, and (ii) introducing wage contracts of explicit length T periods after which parties re-bargain. Common knowledge of each party’s perceived values is assumed, and generalized Nash bargaining is applied. The contract length T is a key parameter: there exists a critical threshold T* such that a pessimistic job separation bias raises the equilibrium wage for T < T* (the continuation-value effect dominates) and lowers it for T ≥ T* (the within-contract discounting effect dominates). An optimistic job finding bias unambiguously raises the equilibrium wage by inflating the perceived value of unemployment and hence the reservation wage.

Quantitative results. The model is calibrated to East Germany. The job separation bias (∆σ = 0.0194) and job finding bias (∆λ = 0.0044) are set to SOEP-based estimates. The critical threshold implied by calibrated parameter values is T* = 10 quarters. The baseline contract length, constructed from the share of permanent (88%) and temporary (12%) contracts in SOEP and average remaining tenure until retirement, is T = 67 quarters (a lower bound). This exceeds T*, so the pessimistic separation bias depresses wages in the baseline. A counterfactual experiment assigns West German bias levels to East German workers, while holding all other parameters fixed. For the preferred calibration range (γ ∈ {0.35, 0.50}, T ∈ {67, 106, 159}), East German wages rise by 1.07 to 2.36 percent. This corresponds to a reduction in the conditional East–West German wage gap (23 percent) of 4.6 to 10.6 percent, and a reduction in the unconditional gap (30 percent) of 3.6 to 7.9 percent. Although wages rise, equilibrium unemployment increases by 0.70 to 1.01 percentage points, widening the already large East–West unemployment gap (approximately 7 percentage points). Net of the unemployment effect, expected lifetime income (computed at actual, unbiased transition rates) rises by 0.7 to 1.88 percent for East German workers under West German biases, implying an unambiguous welfare gain. Under a biennial calibration (robustness), wages increase by up to 3.3 percent and expected lifetime income rises by up to 2.23 percent.

Scope conditions. Results apply to a stationary environment (no aggregate fluctuations). Firms are assumed to have rational expectations; an extension shows results hold provided firm bias is smaller than worker bias. Workers are assumed homogeneous in their bias levels; learning is abstracted from. The quantitative magnitudes are sensitive to the workers’ bargaining power γ and the contract length T, both of which are subject to uncertainty in calibration.

In depth

Q1. How are actual (statistical) transition probabilities constructed, and why are probit-predicted probabilities preferred over realized sample means?

A: Realized transition rates in the sample mix transitions for various idiosyncratic reasons that vary substantially across population groups, so raw sample means do not reflect the probability a given individual faces at interview time. The authors estimate probit models separately for job separation (employed sample) and job finding (unemployed sample), including a rich set of covariates — age, gender, education, tenure, firm size, unemployment experience, industry, survey year, and East Germany indicator, among others — and predict individual-level probabilities at the time of the interview. For consistency with the survey’s discrete response format, probit-predicted probabilities are rounded to the nearest decile (0%, 10%, …, 100%). The bias is computed as the individual-level difference between perceived and probit-predicted actual probabilities, averaged over the sample.

Q2. What is the magnitude and direction of the aggregate expectation biases in Germany?

A: Employed workers overestimate job separation by 6.4 percentage points on average (perceived 19.8% vs. actual 13.3%), a pessimistic bias significant at the 1% level. Unemployed workers overestimate job finding by 8.2 percentage points (perceived 57.0% vs. actual 48.8%), an optimistic bias also significant at the 1% level. Both directions are statistically robust across alternative definitions of separation and finding, as well as to trimming extreme responses (0% and 100% answers) and adjusting for directional rounding.

Q3. How large are the East–West differences in expectation biases, and do they survive controls for compositional differences?

A: East German workers exhibit a pessimistic job separation bias of 12.1 percentage points, more than 2.5 times the West German level of 4.7 percentage points, despite actual separation rates being broadly comparable (15.1% vs. 12.8%). For job finding, West Germans are optimistic by 12.9 percentage points while East Germans are optimistic by only 2.0 percentage points, a difference of 10.9 percentage points. The paper states these differences persist after accounting for compositional differences between regions, and are robust across all alternative definitions of job separation (Dismissals, Selected, Spell) and job finding (out of U or O). The table of robustness results (Table 2) confirms that in all specifications, the pessimistic separation bias is substantially larger in the East and the optimistic finding bias is substantially smaller.

Q4. What cohort analysis is conducted to explore the origins of greater East German pessimism?

A: The authors conduct a regression of the individual-level bias on birth-cohort indicators, controlling for age, demographic, and economic characteristics. They find that the pessimistic job separation bias is most pronounced among cohorts born in the 1950s and 1960s — those who experienced adult working life in the communist GDR and lived through reunification — and is smaller for cohorts born before 1950 and substantially smaller for cohorts born after 1970. For job finding, the optimistic bias is comparably low among cohorts born in the 1960s and earlier, but rises significantly for later-born East German cohorts. This cohort pattern is consistent with a long-lasting “experience effect” of communist institutions and the reunification shock on beliefs, analogous to findings in the broader literature on the persistent effects of communism.

Q5. Is there evidence that individuals update their biased expectations over time?

A: To assess learning, the authors use the panel dimension and compute for each individual in two consecutive survey waves the absolute value of the deviation between perceived and actual transition probabilities, then examine the change in this absolute deviation between waves. The histograms of individual-level changes show substantial dispersion but means close to zero in all four sub-groups (East/West, job separation/finding), indicating no systematic convergence of beliefs toward actual rates. Biases are also stable in the time-series dimension, with perceived and actual rates moving largely in parallel across survey waves from 1999 to 2015, leaving the aggregate bias level roughly constant.

Q6. How does the model rule out private information as an alternative explanation for the biases?

A: If biases reflected private information about idiosyncratic risk not captured by observable characteristics, individual-level deviations between perceived and actual rates should predict subsequent realized transitions. The authors add the individual-level deviation as an additional regressor in the probit transition models. The estimated coefficients are statistically significant and positive, but quantitatively negligible: a 1 percentage point higher expected job separation probability is associated with only a 0.001 percentage point higher realized separation probability, and a 1 percentage point higher expected job finding probability with a 0.002 percentage point higher realized finding probability. These magnitudes are too small to materially alter the interpretation of the biases as reflecting systematic expectation errors rather than private information.

Q7. What is the role of contract length T in the model, and what is the critical threshold T*?

A: The wage contract length T determines which of two opposing effects of pessimistic job separation expectations dominates in bargaining. The first (negative wage) effect: a pessimistic worker discounts future wages within the current contract more heavily than the firm does, so the worker values the contract less and accepts a lower wage. The second (positive wage) effect: a pessimistic worker also discounts the continuation value of future contracts more heavily, making it less attractive to remain in the match, so the firm must offer a higher wage to retain the worker. For short contract lengths (T < T*), the second (positive) effect dominates, so the pessimistic bias raises wages. For long contracts (T ≥ T*), the first (negative) effect dominates, so the pessimistic bias depresses wages. The critical threshold T* is the smallest positive integer such that T*/λw(θ) < β times a weighted sum involving σw and T*. Using calibrated parameter values for East Germany, T* = 10 quarters (2.5 years). The baseline contract length is T = 67 quarters (approximately 16.8 years), well above T*, placing the economy in the regime where pessimism depresses wages.

Q8. How does the optimistic job finding bias affect equilibrium wages and unemployment?

A: An optimistic job finding bias (λw > p(θ)) raises the perceived value of unemployment U because workers expect to escape unemployment sooner. A higher value of unemployment raises the worker’s outside option in bargaining, increases the reservation wage, and thereby pushes up the bargained wage. In general equilibrium, the job creation condition (which is unaffected by worker expectations) is unchanged, so the upward rotation of the wage curve reduces labor market tightness θ, raises equilibrium unemployment, and extends average unemployment duration. This comparative static holds unambiguously for any contract length T.

Q9. What are the quantitative results of the counterfactual experiment assigning West German biases to East German workers?

A: The counterfactual assigns West German bias levels (smaller pessimistic separation bias, larger optimistic finding bias) to East German workers while holding all other parameters at East German calibrated values. For the preferred calibration with γ ∈ {0.35, 0.50} and T ∈ {67, 106, 159}, wages in East Germany rise by 1.07 to 2.36 percent. This implies a reduction in the conditional East–West wage gap (23 percent) of 4.6 to 10.6 percent and a reduction in the unconditional gap (30 percent) of 3.6 to 7.9 percent. Equilibrium unemployment in East Germany rises by 0.70 to 1.01 percentage points as a side effect. Net of the unemployment effect, ex-ante unbiased expected lifetime income rises by 0.7 to 1.88 percent, confirming a positive welfare effect of reducing East German pessimism to West German levels. Under the biennial calibration robustness check, wage increases reach up to 3.3 percent, the conditional wage gap narrows by up to 11 percent, and lifetime income rises by up to 2.23 percent.

Q10. How is the bargaining power parameter γ calibrated and why does it matter for the results?

A: The paper considers a range γ ∈ {0.35, 0.50, 0.65}, rather than a single calibrated value, because γ plays a crucial role in the sensitivity of wages to expectation biases. Lower bargaining power reduces the equilibrium wage directly; however, because lower wages spur job creation, the model requires a higher vacancy cost κ to match the empirical job finding rate, which in turn increases the elasticity of wages with respect to the bias (see the wage equation, which shows that the bias effect scales with κθ/p(θ)). The paper argues that γ = 0.65 is inconsistent with the empirical wage–bias relationship estimated in SOEP data (which is negative and about twice as negative in East Germany as in the West), while γ ∈ {0.35, 0.50} is consistent. Lower bargaining power is also argued to be realistic for East Germany given weaker union representation there relative to the West.

Q11. How does the empirical relationship between the job separation bias and wages serve as a model validation target?

A: Using SOEP data, the authors regress log hourly wages on the individual-level difference between perceived and actual job separation rates, controlling for individual fixed effects and other covariates, and allow the slope to differ between East and West Germany. They find a statistically significant and negative relationship in both regions, with the effect approximately twice as large in East Germany as in the West. The estimate implies that if East German workers’ job separation pessimism were reduced to West German levels, hourly wages in the East would be about 1 percent higher. This empirical gradient is used as an external validation check — not a calibration target — to assess which combinations of (γ, T) in the model are quantitatively plausible.

Q12. What does the model predict about the general equilibrium effects on unemployment from reducing East German pessimism?

A: Reducing East German pessimism — both the pessimistic separation bias and the low optimistic finding bias — shifts the wage curve upward in equilibrium. Because the job creation condition is unaffected by worker beliefs (firms have rational expectations), higher wages reduce the firm’s incentive to post vacancies, lowering labor market tightness θ. This leads to higher equilibrium unemployment and longer average unemployment duration. The counterfactual with West German biases implies that East German unemployment would rise by 0.70 to 1.01 percentage points, further widening the approximately 7 percentage point East–West unemployment gap. The authors note this is a welfare-relevant trade-off, but show that the wage gain dominates the unemployment cost in terms of expected lifetime income.

Q13. What robustness checks are performed on the quantitative results?

A: The paper considers (i) a narrower definition of job separation (dismissals only) to match the most likely interpretation of the survey question; (ii) targeting the officially reported East German unemployment rate (14.5% average from the Federal Employment Agency) rather than the SOEP-implied rate of 8.6% as a calibration target; (iii) a biennial calibration frequency instead of quarterly. The main results — wage increases and narrowing of the wage gap — are quantitatively similar across these alternatives, with one exception: the biennial calibration yields substantially larger wage increases (up to 3.3%), a larger reduction in the conditional wage gap (up to 11%), and larger lifetime income gains (up to 2.23%).

Key Concepts

Expectation bias (job separation / job finding). In this paper, a bias in expectations is defined as a systematic average difference between an individual’s perceived transition probability and the actual (statistically predicted) transition probability for their demographic and job group. A pessimistic job separation bias means workers overestimate the probability of losing their job (σw > σ); an optimistic job finding bias means unemployed workers overestimate the probability of re-employment (λw > p(θ)). Biases are not attributed to private information but to systematic expectation errors.

Actual (statistical) transition probability. The paper defines actual transition probabilities not as raw sample transition rates but as individual-level predicted probabilities from probit models estimated on realized transitions within 24 months, conditional on a comprehensive set of individual, job, and employer characteristics observed at interview time. These are rounded to the nearest decile for comparability with the survey’s discrete response format.

Wage contract length (T). The contract length T is the number of periods for which a bargained wage is fixed before the match parties re-bargain. A job match consists of a sequence of consecutive wage contracts of length T. The paper departs from the standard DMP assumption of period-by-period bargaining (T = 1) and shows that T is central to how job separation expectations feed into the bargained wage. A permanent job approximates T → ∞.

Critical contract length (T).* A theoretically derived threshold: the pessimistic job separation bias raises equilibrium wages for contract lengths T < T* and depresses wages for T ≥ T*. Specifically, T* is the smallest positive integer such that T*/λw(θ) < β times a weighted sum involving β, σw, and T*. In the East German calibration, T* = 10 quarters.

Generalized Nash bargaining with common knowledge / agree to disagree. The model assumes that both the worker and the firm know each other’s perceived values of the job match and outside options and accept them as the basis for bargaining, even though they differ. Workers use their biased perceived transition rates to value employment and unemployment; firms use actual rates. There is no private information. The paper refers to this as workers and firms “agreeing to disagree.”

Ex-ante unbiased expected lifetime income (EI_{W,U}). A welfare measure defined as the present discounted value of income for an individual entering the economy, computed at actual (unbiased) job separation and job finding probabilities rather than at workers’ perceived (biased) rates. This measure captures the net welfare effect of changing expectation biases because it correctly accounts for actual employment transitions, even though the behavioral responses in equilibrium are driven by biased perceptions.

Effective discount factor (β(1 − σw)). When a worker holds pessimistic job separation expectations, future payoffs within the current contract are discounted not at the pure time discount factor β but at β(1 − σw), which is smaller when σw is larger. A more pessimistic worker therefore effectively discounts future wage payments more steeply, and this differential discounting relative to the firm (which uses β(1 − σ)) is the key mechanism generating the contract-length dependence of the wage effect.

Bridging micro and macro production functions: The fiscal multiplier of infrastructure investment

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper investigates the fiscal multiplier of infrastructure investment, specifically by incorporating firm-level investment decisions — a dimension absent from prior literature. The central analytical challenge is bridging the micro (firm-level) and macro (state-level) production functions for infrastructure, given that public capital is non-rivalrous: it can be used simultaneously by all firms without being depleted. The paper demonstrates that this non-rivalry generates a systematic discrepancy between firm-level and aggregate-level estimates of the elasticity of substitution between private and public capital, and it shows how this discrepancy shapes the magnitude of the fiscal multiplier.

Data and Methodology

The authors build and estimate a heterogeneous-firm general equilibrium model. Firms operate a constant-elasticity-of-substitution (CES) production function using private capital, non-rivalrous public capital (infrastructure), and labor. Firms are subject to idiosyncratic productivity shocks and make lumpy investment decisions subject to both fixed and convex capital adjustment costs, following Cooper and Haltiwanger (2006) and Winberry (2021). The economy has two regions — one with poor infrastructure and one with good infrastructure — motivated by the near-invariant cross-state distribution of infrastructure spending observed in U.S. data.

The model is estimated via an extended Simulated Method of Moments (SMM) that treats market clearing prices as additional parameters estimated simultaneously with structural parameters, reducing computational cost relative to standard GE estimation. Estimation uses a multi-block Metropolis-Hastings algorithm. Target moments include lumpy investment fraction (0.14, from Zwick and Mahon 2017), average investment-to-capital ratio (0.10), standard deviation of i/k (0.16), private-to-infrastructure capital ratio (0.75, from BEA), high-infrastructure region’s private capital share (0.83, from Census BDS), and total working hours (0.33).

The identification of the key parameter — the firm-level elasticity of substitution between private and public capital (λ) — comes from the relative size of private capital stocks across the two infrastructure groups: under greater complementarity, regions with more infrastructure should hold relatively more private capital.

External validation is provided by estimating the state-level elasticity from the model’s simulated data using a nonlinear least squares method following An et al. (2019), and comparing it to empirical state-level estimates from actual U.S. state data.

Main Findings with Quantitative Magnitudes

Firm-level vs. aggregate-level elasticity gap. The estimated firm-level elasticity of substitution is λ = 1.185, implying gross substitutability between private and public capital at the firm level. The state-level elasticity implied by the same model is 0.48 (or 0.35 in a decreasing-returns-to-scale specification), implying gross complementarity. The empirical state-level counterpart estimated from actual U.S. data is 0.445. The paper proves theoretically (Proposition 1) that, given non-rivalry and under mild conditions, firm-level gross substitutability implies aggregate-level gross complementarity. Proposition 2 further shows that this same mechanism micro-founds the increasing-returns-to-scale assumption in Baxter and King’s (1993) Cobb-Douglas aggregate production function.
Fiscal multiplier (baseline, 2-year horizon). The aggregate output multiplier over a 2-year horizon in the heterogeneous-firm general equilibrium model is 1.088 in response to a one-time unexpected infrastructure spending shock equal to 1% of steady-state GDP, financed by a lump-sum tax. The corresponding partial-equilibrium output multiplier (holding prices fixed at steady state) is 1.858; the gap reflects crowding out of private investment induced by the general equilibrium interest rate response. In the baseline, the interest rate rises by 0.39% after the shock; the investment multiplier is -0.043.
Comparison with representative-agent model. When the same implied returns-to-scale parameters are used in a representative-agent model (following Baxter and King 1993), the output multiplier is 0.991 and the investment multiplier is -0.157, both substantially lower than the heterogeneous-firm baseline. The key mechanism: under convex adjustment costs, the Jensen’s inequality effect implies that heterogeneous firms face a greater average adjustment burden than the representative firm, making their investment less responsive to the general equilibrium crowding-out pressure.
Sensitivity to elasticity of substitution. Across the heterogeneous-firm model: at λ = 3 (high substitutability), the output multiplier falls to 0.672; at λ = 0.5 (complementarity), it rises to 1.364. The multiplier is significantly more sensitive to λ in the heterogeneous-firm model than in the representative-agent model, because non-rivalry amplifies the effect of any given elasticity value through each firm’s production function.
Cross-state distribution of gains. Under the baseline spending allocation (81% to Good states, 19% to Poor states), per $1 of infrastructure spending, Good states receive $1.072 of the $1.088 total output gain, while Poor states receive only $0.016. In a counterfactual with equal spending across states, the total output multiplier falls to 0.873, Good states’ output multiplier falls to 0.810, and Poor states’ output multiplier rises to approximately 0.062 (about four times the baseline level of 0.016). This quantifies a sharp efficiency-equality trade-off in the allocation of infrastructure investment.
Employment and earnings effects. Compared to steady state, the baseline fiscal shock produces an average annual increase of 0.304% in employment and 0.389% in wages, yielding a $0.713 increase in earnings and a $0.148 increase in consumption per $1 of fiscal spending in general equilibrium. In partial equilibrium (no price changes), earnings increase by $1.294 and consumption by $0.605 per $1 spent.

Scope Conditions

Results are conditional on: (i) lump-sum tax financing of the fiscal shock; (ii) a one-time unexpected (MIT) shock with no persistence; (iii) a closed-economy framework with endogenous real interest rate; (iv) the estimated two-region structure calibrated to U.S. state-level infrastructure data; (v) firm-level investment dynamics calibrated to Compustat and BDS moments. The authors note that incorporating time-to-build assumptions (tested in an appendix) reduces the aggregate fiscal multiplier, consistent with Ramey (2020).

In depth

Q1. What is the core theoretical result connecting firm-level and aggregate-level elasticities, and what is the intuition?

A: Proposition 1 proves that, given non-rivalrous public capital and mild data conditions (at least one firm has private capital below total infrastructure, and aggregate private capital exceeds total infrastructure), if the firm-level elasticity of substitution λ ≥ 1 (gross substitutes), then the aggregate-level elasticity ξ < 1 (gross complements). The intuition is that a marginal increase in public capital raises the marginal product of private capital for every firm simultaneously due to non-rivalry; the sum of these MPK gains across all firms exceeds any single firm’s gain. To represent this amplified benefit within an aggregate production function, a stronger complementarity is required than what any single firm faces. Put differently, non-rivalry means aggregate private and public capital “look” more complementary than they truly are at the firm level.

Q2. How does non-rivalry micro-found the Baxter-King aggregate production function?

A: Proposition 2 shows that if firms use a CES production function with gross substitutability (λ ≥ 1) and non-rivalrous public capital, then fitting aggregate output with a Cobb-Douglas production function (as in Baxter and King 1993, H(K,N,L) = zK^α L^{1-α} N^ζ) yields ζ > 0, implying increasing returns to scale (IRS). This is the paper’s micro-foundation for a widely-used but previously ad hoc assumption in the macro-fiscal literature. The corollary states that both gross complementarity in the aggregate CES function and IRS in the aggregate Cobb-Douglas follow from the same non-rivalry mechanism at the firm level.

Q3. Why does the heterogeneous-firm model produce a higher output multiplier than the representative-agent model?

A: Two mechanisms drive the difference. First, due to Jensen’s inequality and the convexity of adjustment costs, heterogeneous firms face a higher average adjustment burden than the representative (average) firm; this means heterogeneous firms are less responsive to interest rate changes that crowd out investment. The investment multiplier is -0.043 in the heterogeneous-agent baseline versus -0.157 in the representative-agent model. Second, the fixed adjustment cost (present in the baseline but absent from the representative-agent model) further dampens investment sensitivity via the extensive margin. Because less private investment is crowded out, more of the direct output boost from infrastructure spending survives into the aggregate multiplier, yielding 1.088 versus 0.991.

Q4. What is the novel estimation procedure and why is it necessary?

A: Standard SMM applied to GE models requires solving for market-clearing prices for every candidate parameter vector, creating a nested optimization loop that is computationally prohibitive. The authors extend SMM by treating market-clearing prices (wage w and marginal utility of consumption p) as additional parameters and appending market-clearing conditions as additional target moments — effectively requiring those moments to equal zero. A multi-block Metropolis-Hastings algorithm jointly draws from the price block and the parameter block. This approach generates posterior draws that simultaneously satisfy market clearing and fit empirical moments, without the inner loop. The resulting market-clearing accuracy is e^{-4} at the posterior mean.

Q5. How is the firm-level elasticity of substitution (λ) identified from the data?

A: λ is identified from the cross-state difference in private capital stocks between high- and low-infrastructure regions. Under the model, if private and public capital are more complementary (lower λ), high-infrastructure regions should attract relatively more private capital. The data moment used is the Good region’s share of aggregate private capital (0.83 from Census BDS data). This identification strategy is analogous to Bartik-instrument approaches in the empirical literature, where a parameter governing cross-state sensitivity to aggregate shocks is identified from cross-sectional variation.

Q6. How is the model validated externally?

A: The authors compute the state-level elasticity from the estimated model by fixing firm-level parameters and re-estimating only the elasticity and regional productivity from the model’s simulated state-level data, using the same NLLS estimator as An et al. (2019). The model-implied state-level elasticity is 0.349 (DRS specification) or 0.482 (CRS specification). The empirical estimate from actual U.S. state-level data following the same estimator is 0.445. Both indicate gross complementarity at the state level, consistent with the theoretical prediction. This external validation is not used in the estimation itself, providing an independent check.

Q7. What are the roles of extensive vs. intensive investment margins in the crowding-out effect?

A: Table 9 decomposes the investment multiplier of -0.043 by investment margin. When only the extensive margin (the discrete decision of whether to invest) is allowed to respond, the investment multiplier is -0.032 — approximately 74% of the baseline crowding-out effect. When only the intensive margin (investment size conditional on adjusting) responds, the multiplier is -0.011 — about 25% of the total. Thus the extensive margin is the dominant channel through which higher interest rates crowd out private investment. When both margins are held fixed, the output multiplier rises to 1.139, confirming that investment crowding-out reduces the output multiplier by about 0.05.

Q8. How does the elasticity of substitution affect the fiscal multiplier quantitatively, and why does this matter more in the heterogeneous-firm model?

A: In the heterogeneous-firm GE model: λ = 3 gives an output multiplier of 0.672, λ = 1.185 (baseline) gives 1.088, and λ = 0.5 gives 1.364 — a range of 0.692. In the representative-agent model, the comparable range across the implied ζ values is much narrower (0.970 to 0.998). The amplification in the heterogeneous-firm model occurs because non-rivalry means each firm’s production function directly incorporates the public capital stock, so the elasticity parameter has first-order consequences for every firm’s investment incentive response to a fiscal shock. This heightened sensitivity underscores why accurately estimating λ at the firm level — rather than importing a state-level estimate — is critical for quantifying infrastructure multipliers.

Q9. What is the efficiency-equality trade-off in cross-state infrastructure allocation?

A: Under the baseline allocation (81% of infrastructure spending to Good states, 19% to Poor states), per $1 of infrastructure spending, the Good states receive $1.072 of output gains and Poor states receive only $0.016. In the equal-spending counterfactual, the total output multiplier falls from 1.088 to 0.873. The Poor states’ output multiplier rises from $0.016 to $0.062 (approximately fourfold), while the Good states’ falls from $1.072 to $0.810. The Poor states also see earnings multipliers more than double (from $0.017 to $0.042). This trade-off arises because Good states have both more private capital (benefiting from non-rivalry) and higher estimated TFP — so each dollar of infrastructure is more productive there. Equal allocation reduces aggregate efficiency while partially mitigating regional inequality.

Q10. How do the paper’s multiplier estimates compare to the existing literature?

A: In partial equilibrium (no GE adjustment), the authors find an output multiplier of 1.858, consistent with Chodorow-Reich’s (2019) cross-sectional multiplier of approximately 1.8. Once the general equilibrium interest rate effect is included, the multiplier falls to 1.09, which falls within the 0.6-1.2 range from Ramey (2011). Literature using representative-agent models without non-rivalry (e.g., Ramey 2020) typically reports multipliers of 0.3 to 0.8 using returns-to-scale parameters of 0.07-0.12; the paper shows these correspond to fiscal multipliers of 0.847-0.882 in the representative-agent framework. The heterogeneous-firm model, once it incorporates the non-rivalry-corrected elasticities, yields a meaningfully higher multiplier of 1.088.

Q11. What role does time-to-build play, and how does the paper handle it?

A: The baseline model assumes a time-to-build period s = 1 year (one-year lag before new infrastructure is productive). The paper notes in Appendix H that incorporating extended time-to-build reduces the aggregate fiscal multiplier, operating through two channels: a news effect (agents adjust behavior upon anticipating future infrastructure) and a general equilibrium effect endogenous to the news effect. This finding is consistent with Ramey (2020). The baseline results are therefore reported under the minimal one-year time-to-build assumption, with longer lags serving as a robustness check.

Q12. What is the role of region-specific TFP heterogeneity in the model?

A: The model includes two regions that differ both in infrastructure levels and in region-specific productivity (TFP) levels. The TFP of the Good region is estimated to be approximately double that of the Poor region (x = 2.064 for Good vs. 1 for Poor). This productivity difference is estimated to partially capture heterogeneous congestion effects (which are not separately modeled) and is estimated jointly with the infrastructure elasticity. The productivity differential is identified from the Good region’s share of aggregate output (0.849 in the data). The large TFP gap is also the reason why equal spending on Poor states generates a much smaller output gain than spending on Good states: not only is infrastructure utilization lower (fewer firms), but underlying productivity is also lower.

Key Concepts

Non-rivalry of public capital: The property by which infrastructure stock (Nj,t) enters each firm’s production function at the full regional level, not divided among firms. Formally, a single marginal unit of public capital raises every firm’s marginal product of private capital simultaneously, so the aggregate marginal product gain summed across firms exceeds any single firm’s gain. This is the central mechanism driving the micro-macro elasticity discrepancy in the paper.

Firm-level elasticity of substitution (λ): The elasticity governing the degree of substitutability between private capital (k) and public infrastructure (N) in the firm’s CES production function. At λ = 1 the production function is Cobb-Douglas; λ > 1 is gross substitutability; λ < 1 is gross complementarity. In the paper’s estimation, λ = 1.185, meaning private and public capital are gross substitutes at the firm level.

Gross substitutability vs. gross complementarity: Two inputs are gross substitutes (complements) if an increase in the quantity of one raises (lowers) the demand for the other, holding output price fixed. In the paper’s framework, private and public capital are gross substitutes at the firm level (λ = 1.185 > 1) but gross complements at the state level (ξ ≈ 0.48 < 1), with non-rivalry explaining the inversion upon aggregation.

Convex adjustment cost: A cost C(I,k) = (µ/2)(I/k)² · k that scales quadratically with the investment rate. In the heterogeneous-firm model, this cost plays a critical role: by Jensen’s inequality, heterogeneous firms’ average adjustment burden under a convex cost exceeds that of the representative (average) firm, making aggregate investment less sensitive to interest rate changes and thereby dampening crowding out.

Fixed adjustment cost (ξ): A one-time overhead cost drawn from a uniform distribution [0, ξ̄], paid only when a firm makes a large-scale investment outside the “inaction band” [−νk, νk]. This cost generates lumpy investment at the firm level, with about 14% of firms making lumpy investments in any given year. It also creates an extensive margin of investment adjustment that accounts for approximately 74% of the baseline crowding-out effect.

Fiscal multiplier (as defined in this paper): The ratio of the present value of aggregate output deviations from steady state to the present value of the fiscal spending shock, both summed over a T-year horizon. For the short run, T = 2 years; for the long run, T = 5 years. This is computed as a perfect-foresight transition path response to a one-time MIT shock equal to 1% of steady-state GDP.

MIT shock (one-time unexpected shock): An unanticipated, non-persistent one-period deviation in infrastructure spending. The term “MIT shock” refers to a deterministic transition experiment where agents have perfect foresight about all future values after the initial shock occurs. This contrasts with persistent policy rules and allows isolating the dynamic effects of a one-time fiscal impulse.

Extended SMM with market-clearing moments: The paper’s estimation innovation. Rather than solving for market-clearing prices at each parameter candidate (the standard costly inner loop), wages (w) and marginal utility of consumption (p) are treated as parameters with associated moments being the market-clearing conditions set to zero. A multi-block Metropolis-Hastings algorithm draws from the price block and the parameter block separately, generating posterior draws that jointly satisfy market clearing and empirical moment conditions.

Cash or card? A structural model of payment choices

Mon, 01 Jan 0001 00:00:00 +0000

Lippi and Moracci (2026) ask how euro area households choose between cash and card payments, and whether existing theoretical models can explain observed behavior. They draw on ECB payment diary surveys (SUCH and SPACE waves I–III, 2015–2024) covering transaction-level records that include purchase size, payment method chosen, cash on hand before each transaction, and merchant acceptance of cards. This granular data allows the authors to isolate unforced payment choices — transactions in which the consumer had sufficient cash, the merchant accepted cards, and the consumer held a card — from mechanically constrained ones.

The authors document three empirical patterns. First, roughly 39% of individuals in the sample violate the simple transaction-size threshold rule of Whitesell (1989): their largest unforced cash payment exceeds their smallest unforced card payment. Second, between 27% and 49% of unforced transactions are settled by card across survey waves, contradicting the “cash burns” policy of Alvarez and Lippi (2017) under which cards are used only when cash is exhausted. Third, and most novel, the probability of card use rises sharply as implied residual cash holdings (m′ = m − s) approach zero — that is, when a cash payment would nearly deplete the wallet. This suggests a precautionary motive: consumers maintain a cash buffer to cover purchases at merchants who do not accept cards.

To rationalize these facts, the authors build an inventory-theoretic model with a compound Poisson expenditure flow (random arrival times and random transaction sizes drawn from a lognormal distribution), imperfect card acceptance (fraction ϕ of merchants accept cards, set at 0.89 for 2023–24), a fixed cost b per cash withdrawal, a fixed cost κ per card transaction (sign unrestricted), and a utility penalty u per missed purchase. The optimal policy takes an (s,S) form for withdrawals and a state-dependent threshold for payment choice. When 0 < κ < b, the agent uses cards for purchases large enough that paying cash would push balances below a threshold m̃, thereby avoiding a costly withdrawal or the risk of missing a future purchase. The critical transaction size above which cards are used, s(m), rises with cash on hand, generating the interaction the data reveals.

The model is calibrated by minimum distance to four moments from the 2023–24 SPACE wave: average cash balances relative to daily expenditure, annual withdrawal frequency, the unforced card expenditure share, and realized purchase frequency. The estimated annual cost of managing consumption transactions for the average euro area household is approximately 15 euros — a remarkably small burden. Three counterfactual experiments quantify welfare implications. Removing card access raises the annual cost from 15 to about 50 euros, implying a card ownership value of roughly 35 euros per year. Near-universal card acceptance (ϕ = 0.99) reduces the annual cost by nearly 75%, from 15 to about 4 euros, while average cash holdings fall from 130% to about 20% of daily expenditure. A complete ban on cash would cost the average consumer approximately 60 euros per year more than the current mixed system. A cashless equilibrium requires both near-universal acceptance (ϕ above 99%) and card costs at or below zero (κ ≤ 0); neither condition alone is sufficient given the estimated magnitude of the missed-purchase cost u.

Q: What is the central empirical puzzle the paper addresses? A: Existing models predict either a pure transaction-size threshold (Whitesell 1989) or a pure cash-burns rule (Alvarez and Lippi 2017). The data shows both rules are violated: 39% of individuals with observed unforced transactions of both types violate the threshold rule, and 27–49% of unforced transactions are paid by card despite available cash. Neither model alone accounts for the novel finding that card usage spikes precisely when a cash payment would nearly exhaust the wallet.

Q: What data does the paper use and what is its key advantage? A: The authors use ECB payment diaries from four survey waves: SUCH (2015–16) and SPACE I, II, III (2019, 2021–22, 2023–24). For each transaction the diary records payment method, purchase size, and cash on hand, along with merchant acceptance of each payment method. Critically, the combined information on cash holdings and acceptance allows the authors to distinguish forced from unforced payment choices, which is essential for identifying the behavioral determinants of payment method selection.

Q: What is the novel empirical fact the paper contributes? A: The paper documents that the probability of card use increases sharply as implied residual cash (m′ = m − s) approaches zero. This pattern holds across all survey waves. It is consistent with a precautionary motive: consumers use cards to avoid depleting a cash buffer that provides insurance for encounters with merchants who do not accept cards.

Q: How does the theoretical model generate the precautionary motive for cash? A: Cards are accepted in only fraction ϕ of stores; when a merchant does not accept cards and the consumer lacks cash, the purchase is missed at utility cost u. This creates an incentive to maintain positive cash balances. Combined with a fixed withdrawal cost b and a fixed card cost κ, the agent optimally targets a cash level m* and withdraws before the wallet empties (trigger m̄ > 0), holding a buffer against card-rejection events.

Q: What is the key proposition characterizing the optimal payment policy? A: Proposition 1 establishes three regimes. When κ ≤ 0, the card always dominates and is used for all purchases. When κ ≥ b, cash always dominates and cards are used only for forced transactions. In the intermediate case 0 < κ < b, a threshold m̃ ∈ (m̄, m*) divides behavior: for m < m̃ the agent uses cash for all transactions; for m ≥ m̃ the agent uses a card for any purchase exceeding a size threshold s(m), where s(m) is increasing in m. The threshold s(m) distinguishes this policy from Whitesell (1989)’s fixed threshold.

Q: How does the payment threshold s(m) vary with cash on hand, and why? A: s(m) is the purchase size above which the value loss from paying cash — pushing the agent closer to m̄ and raising the probability of a missed purchase or costly withdrawal — exceeds the fixed card cost κ. As m rises, a larger cash payment is needed to trigger this concern, so s(m) increases. This means card use becomes less frequent as cash balances grow for most of the state space, consistent with the empirical finding that cash probability rises with cash on hand.

Q: What are the calibrated parameter values and what do they imply? A: The withdrawal cost b is estimated at 0.003 EUR — very small. The per-transaction card cost κ is about 60% of b, meaning cards are cheaper to use per transaction than visiting an ATM. The cost of a missed purchase u is approximately 1 EUR. The arrival rate λ is calibrated so that about 2% of purchase opportunities are missed under the estimated card acceptance rate of 0.89. These values imply that the payment system imposes a small but non-trivial welfare burden, concentrated in the precautionary costs of maintaining cash.

Q: What is the estimated annual cost of managing consumption transactions? A: Under the optimal policy for 2023–24 parameters, the annual cost C is approximately 15 euros per household. This decomposes into opportunity costs of holding cash (RM), withdrawal costs (bn), card usage costs, and the disutility from missed purchases. The authors characterize this as “remarkably small,” suggesting the current payment system is relatively efficient from the household’s perspective.

Q: How does this cost compare across demographic groups and over time? A: Until 2019 the estimated annual cost was around 20 euros; it stabilized around 15 euros from 2021–22 onward, with the decline driven primarily by households holding less cash in the post-pandemic period. Across age groups, education levels, income brackets, and gender, each subgroup faces a very similar cost as a proportion of their expenditure, indicating limited distributional variation in payment system costs.

Q: What is the welfare value of owning a payment card? A: Setting ϕ = 0 (cash-only economy), the annual cost rises from 15 to approximately 50 euros. The value of card ownership is therefore approximately 35 euros per year. The savings come primarily from lower opportunity costs of holding cash (since card access reduces the precautionary motive) and lower disutility from missed purchases; withdrawal cost reductions play a negligible role.

Q: What happens under near-universal card acceptance (ϕ = 0.99)? A: Average cash holdings fall from about 130% of daily expenditure to about 20% of daily expenditure, a reduction of approximately 110 percentage points. The unconditional card expenditure share rises by 17 percentage points to about 93%, mostly through an increase in forced card transactions (agents more often lack cash). Unforced card expenditure falls by about 10 percentage points because the precautionary motive for using cards — preserving a cash buffer — weakens when acceptance is near-universal. The annual management cost falls by nearly 75%, from 15 to approximately 4 euros.

Q: Under what conditions does a cashless economy emerge? A: The model identifies two jointly necessary conditions: card acceptance near universal (ϕ above 99%) and card costs at or below zero (κ ≤ 0). Raising ϕ alone from the estimated 0.89 to 0.99 reduces cash use substantially but does not eliminate it, because the estimated cost of missed purchases u is large enough that consumers still maintain a small cash buffer. For κ ≤ 0, cash holdings M/e are insensitive to κ and depend only on ϕ. With current card usage costs, even near-universal acceptance would not produce a cashless economy.

Q: What is the cost of a complete cash ban? A: Under a cashless policy, the annual cost is approximately 75 euros — about 5 times the 15-euro baseline and about 25 euros more than the cash-only cost of 50 euros. A complete ban on cash would increase transaction management costs by approximately 60 euros per year for the average consumer. This is because at ϕ = 0.89, nearly 11% of purchase encounters would result in missed transactions.

Q: How does card acceptance affect cash management in the model and data? A: As ϕ falls, the precautionary motive for holding cash strengthens: the withdrawal trigger m̄ rises, average cash holdings increase, and withdrawals occur when the wallet is still substantially full. This prediction is qualitatively consistent with the empirical finding that in areas with lower card acceptance, individuals hold higher cash balances and withdraw at higher residual cash levels.

Q: What are the main limitations the authors acknowledge? A: Three caveats are identified. First, the model has no exogenous cash inflows (wage payments, gifts); incorporating Miller-Orr-style inflows could affect cash resilience estimates. Second, the card cost κ is fixed and independent of transaction size s; allowing κ(s) = κ₀ + κₛ·s would better capture reward-program economies relevant for the US. Third, merchant card acceptance is treated as exogenous; endogenizing it as a game between merchants would allow a joint welfare evaluation of acceptance decisions, payment choices, and cash management.

Unforced transactions: Transactions in which both cash and card payments are feasible — specifically, cash holdings exceed the purchase size, the merchant accepts cards, and the consumer holds a card. Isolating unforced transactions is necessary to identify behavioral determinants of payment choice, stripping out mechanical constraints imposed by cash insufficiency or merchant non-acceptance.
Precautionary cash buffer: A positive cash balance maintained above the withdrawal trigger (m̄ > 0) to insure against purchases at merchants who do not accept cards. In the model, this buffer arises because card non-acceptance combined with insufficient cash results in a missed purchase at utility cost u; the precautionary motive is stronger when ϕ is lower.
Transaction-size threshold s(m): The purchase size above which a consumer with cash holdings m optimally pays by card (when cards are available and 0 < κ < b). Unlike the fixed threshold of Whitesell (1989), s(m) is increasing in m, generating a novel interaction between cash on hand and payment method choice that the ECB diary data confirms.
Cash burns policy: The policy of Alvarez and Lippi (2017) in which cards are used only when cash is fully exhausted (m = 0). The paper documents that 27–49% of unforced transactions are settled by card across survey waves, constituting a systematic violation of this rule that the model resolves by introducing transaction-size heterogeneity and a precautionary motive.
Imperfect card acceptance (ϕ): The exogenous fraction of merchants willing to accept card payments, set at 0.89 for 2023–24 in the calibration. Imperfect acceptance is the primary driver of the precautionary demand for cash; it also determines the frequency of missed purchases under a cashless policy and is the key parameter governing whether a cashless economy can emerge.
Annual transaction management cost (C): The total yearly household cost of operating within the payment system, defined as C = RM + bn + κ·(number of card purchases) + u·(number of missed purchases). Estimated at approximately 15 euros for the average euro area household in 2023–24, decomposed across opportunity costs of cash holdings, withdrawal costs, card usage costs, and missed-purchase disutility.
Ss withdrawal policy: The optimal cash replenishment rule characterized by a trigger level m̄ and a target level m*. The agent withdraws whenever cash falls to m̄, resetting balances to m*. A strictly positive trigger (m̄ > 0) reflects the precautionary motive: the agent refills before cash is exhausted in order to maintain insurance against card non-acceptance events.

Central bank communication by ??? The economics of monetary policy leaks

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper investigates the economics of monetary policy leaks — anonymous disclosures of confidential information by insiders to the media — focusing on three central questions: (1) Are leaks random accidents, strategic individual disclosures, or institutionally authorized “plants”? (2) Do leaks shape public (financial market) views, and by how much? (3) Can attributed (named) communication by central bank officials mitigate the effects of leaks?

Data and Setting

The authors study the Eurosystem (ECB and euro area National Central Banks) over January 2002 to December 2021. Their primary data source is a novel database of 368 unique policy-relevant leaks — assembled by manually filtering and classifying more than a million news items from Reuters, Bloomberg, and Market News International archives — with precise minute-level timestamps. Topics covered include: policy rates (178 leaks), unconventional monetary policy/UMP (207 leaks), economic growth (47), inflation (41), and euro exchange rate (36); individual leaks may cover multiple topics. They complement this with a dataset of 7,883 attributable public statements by ECB Governing Council members, identified via keyword filtering and machine learning classification of the Reuters News Archive.

Methodology

The paper employs four main empirical strategies. First, high-frequency event studies using asymmetric windows (5 minutes before to 30 minutes after an event) compare absolute market reactions in OIS rates across the full term structure (3M to 10Y) and in the EURO STOXX 50 across leaks, 5,000 randomly sampled placebo events, and attributable statements. Second, Poisson regression models relate the number of leaks per policy meeting to proxies for Governing Council disagreement (Italian-German sovereign yield spread, inter-quartile range of national inflation rates, number of attributable statements per meeting) and a dummy for quarterly macroeconomic projection releases. Third, a regression framework tests whether leaks move market expectations toward the subsequent policy outcome — identifying whether leaks are informative about the direction of policy. Fourth, an augmented version of the Tillmann (2021) model relates end-of-day changes in longer-term OIS rates to high-frequency monetary policy surprises, interacted with dummies for post-announcement leaks and attributable statements.

Main Findings

Incidence and timing. The number of Eurosystem leaks peaked at 36 in 2019 (more than four per policy meeting on average) before declining by more than one third following the start of Christine Lagarde’s presidency in November 2019. Leaks cluster around policy meetings and, since 2015, have shifted notably from before meetings to after meetings, a shift driven by leaks related to UMP. Leaks occur even during the ECB’s quiet period, when policy-makers are formally restricted from public statements on policy-sensitive topics.

Leaks are not accidents. Poisson regressions reveal that the number of leaks per meeting is significantly and positively associated with proxies for Governing Council disagreement: every additional percentage point in the Italian-German sovereign yield spread is associated with approximately half an additional leak per meeting. The propensity of a policy change increases by four to six percentage points with each additional pre-meeting leak (statistically significant at the 5% or 10% level). The specification explains around 15% of the variation in leak counts.

Market impact. Market movements around leaks are up to 85% larger than those around placebo events. Leaks trigger market reactions that are consistently larger than those of attributable statements by individual Governing Council members across the entire OIS term structure and in equities — a result robust to controlling for distance to policy meetings. Rate leaks mainly move the short and medium end of the yield curve; UMP leaks affect the long end and equities. Leaks about general economic conditions (growth, inflation, exchange rate) produce little statistically significant market response.

Leaks are uninformative about policy direction. Conditional on a pre-meeting leak occurring, the average leak does not move market rates closer to the levels prevailing directly after the subsequent policy announcement. By contrast, attributable statements systematically do reduce this distance. This asymmetry implies that leaks predominantly reflect minority opinions within the Governing Council. Consistent with this, leaks counteract prevailing trends in market expectations at the short end of the yield curve (as established by a negative coefficient on the interaction between the prevailing seven-day pre-leak trend and the leak dummy).

Leaks are not plants; attributed communication mitigates their effects. Post-announcement leaks dampen the transmission of monetary policy surprises to longer-term rates (negative and significant interaction coefficient in the augmented Tillmann framework). Attributed statements by ECB Executive Board members, by contrast, systematically move in the direction opposite to the preceding leak across most of the yield curve, partially reversing leak-induced market moves. More intense pre-leak attributable communication is also associated with lower market impact of the subsequent leak, across most maturities. These results jointly indicate that most Eurosystem leaks originate from individual insiders with minority opinions rather than constituting institutional plants.

Scope Conditions

Results pertain to the Eurosystem committee setting, where decision-making is broadly consensus-based and voting records are not published; they may not fully generalize to institutions with concentrated decision-making power. The study measures effects on financial markets, not broader public opinion.

In depth

Q1. How is a “leak” defined in this paper, and how are Eurosystem leaks identified empirically?

A leak is defined as a disclosure of confidential information by an insider to the media with an expectation of anonymity. Eurosystem leaks are identified from Reuters, Bloomberg, and Market News International archives (2002–2021) using keyword-driven pre-filtering followed by manual classification of “candidate” items. The resulting database contains 1,253 news items that aggregate to 368 unique policy-relevant leaks with minute-level timestamps. Policy-relevant leaks touch on: policy rates, unconventional monetary policy tools, economic growth, inflation, or the euro exchange rate; leaks about local economic conditions, banking regulation, or managerial appointments are excluded.

Q2. What are the broad trends in the number and topic composition of Eurosystem leaks over 2002–2021?

The number of leaks rose sharply in the second half of the sample, peaking at 36 in 2019 (more than four per meeting on average). Since Christine Lagarde took over the ECB presidency in November 2019, leaks fell by more than one third from that peak. The topic composition shifted substantially over time: policy-rate leaks predominated in the earlier period, while leaks related to UMP came to dominate in the 2015–2021 sub-period.

Q3. How does the timing of leaks within the policy meeting cycle change across sub-periods?

In the full sample, leaks cluster in the run-up to policy meetings and immediately following announcement days (both on the announcement day itself and the following Friday). Since 2015, a notable shift occurs from pre-meeting to post-meeting timing, driven specifically by leaks related to UMP. The authors attribute this shift to the expectation-management role of UMP: post-meeting leaks allow dissenting insiders to reshape market expectations that are otherwise guided by official press releases and press conferences.

Q4. What regression evidence supports the view that leaks are not random accidents?

Poisson regressions of the number of leaks per meeting on disagreement proxies find significant positive coefficients on: the lagged Italian-German sovereign yield spread (about half a leak more per meeting for each additional percentage point of spread), the inter-quartile range of national inflation rates, and the number of attributable statements per meeting. Meetings coinciding with the release of quarterly macroeconomic projections also attract significantly more leaks. These results are robust to replacing the disagreement proxies with a binary dissent index based on Q&A sessions at ECB press conferences (Tillmann, 2021), even after excluding disagreement-related leaks from the dependent variable to address endogeneity. The model explains about 15% of the variation in leak counts.

Q5. Does the number of pre-meeting leaks predict policy changes?

Yes. The propensity of a monetary policy change increases by four to six percentage points with each additional pre-meeting leak (significant at the 5% or 10% level). This signal about the propensity of change (not the direction) is hard to square with the random accidents hypothesis.

Q6. How large are the financial market reactions to leaks relative to placebo events and to attributable statements?

Market movements around leaks are up to 85% larger than the average size of market reactions to 5,000 randomly sampled placebo events. When leaks are compared directly to attributable statements (with leaks as the baseline and fixed effects for year, month, weekday, and hour), average absolute market moves around leaks are consistently larger across the entire term structure of OIS rates and for the EURO STOXX 50. This result is robust to differences in distance to policy meetings, with size differences across the full term structure persisting for periods far from meetings; near meetings, differences narrow but the average market reaction to leaks never falls below that to attributable statements.

Q7. Do the market effects of leaks differ by topic?

Yes. Leaks about policy rates primarily move the short and medium end of the yield curve. Leaks about UMP tools affect the long end of the curve and equities. Leaks about general economic conditions (growth, inflation, euro exchange rate) do not produce statistically significant market reactions, consistent with the interpretation that economic condition leaks require more interpretation before their implications for the policy path become apparent.

Q8. Do leaks move market expectations in the direction of the subsequent policy outcome?

No. The average pre-meeting leak does not reduce the absolute distance of market rates to post-announcement levels. This result holds across maturities from 3M to 10Y and is robust to separating leaks inside and outside the ECB’s quiet period. Attributable statements, by contrast, systematically reduce this distance (Table 7). The failure of leaks to align expectations with outcomes is interpreted as evidence that leaks predominantly reflect minority views within the Governing Council rather than information held by the decisive voter.

Q9. Do leaks counteract or reinforce prevailing trends in market expectations?

Leaks counteract prevailing trends. The regression of market reactions to leaks and placebo events on the seven-day pre-event trend reveals a significantly negative interaction between the trend and the leak dummy at the short end of the yield curve. This result is driven specifically by leaks about policy rates.

Q10. Do post-announcement leaks dampen the transmission of monetary policy surprises to longer-term rates?

Yes. In the augmented Tillmann (2021) framework, the interaction of the high-frequency 2Y monetary policy surprise with a dummy for post-announcement leaks is negative and significant for 2Y, 5Y, and 10Y OIS rates. In contrast, the interaction with a dummy for post-announcement attributable statements is positive and significant across maturities, indicating that attributed communication reinforces the official policy signal. These two results jointly show that leaks weaken official policy announcements while attributed communication strengthens them.

Q11. Does more intense pre-leak attributable communication reduce the market impact of subsequent leaks?

Yes. Using an intensity measure that weights each attributable statement by the inverse of its distance in hours to the subsequent leak (covering a window from 36 hours to 30 minutes before the leak), the paper finds a significant negative relationship between pre-leak communication intensity and the absolute market reaction to the leak, controlling for year, month, weekday, and hour fixed effects. This holds across most maturities.

Q12. Does the market impact evidence support the “plant” hypothesis?

No. If leaks were institutional plants intended to prepare markets for new policy, one would expect the ECB Executive Board — which controls official communication — to subsequently reinforce the signal from leaks. Instead, attributable statements by ECB-affiliated Governing Council members are systematically negatively correlated with the market direction of the preceding leak across the yield curve, with significant coefficients at medium maturities. NCB Governor statements show weaker and more ambiguous effects, potentially because their statements generate smaller average market movements rather than reflecting a lack of willingness to counteract leaks.

Q13. Why do markets react to leaks even though leaks are generally uninformative about policy outcomes?

The paper offers three candidate explanations: (1) automated trading algorithms that do not distinguish between attributed and anonymous communication; (2) leaks serve as a coordination device in the spirit of Morris and Shin (2002), amplifying even noisy signals; (3) media-reporting models such as Nimark (2014) and Chahrour et al. (2021) predict that “man-bites-dog” news — unusual events such as revelations of committee disagreement — shift beliefs beyond their true information content. Leaks are unusual both in frequency (far less common than attributed statements) and in content (they reveal disagreement that rarely surfaces in official communication).

Q14. What are the implications for the measurement of monetary policy shocks from high-frequency identification?

The paper notes that Eurosystem leaks frequently occur shortly before or after official policy announcements. Pre-announcement leaks can shift market expectations before the start of standard event windows, reducing the measured surprise component of official announcements. Post-meeting leaks dampen the end-of-day effects of announcements. In both cases, standard high-frequency surprise instruments extracted from official announcements alone may miss the full extent of new information available to market participants, suggesting that accounting for leaks could improve the relevance of high-frequency instruments used in monetary policy identification.

Q15. What are the implications for the design of central bank quiet periods?

The ECB’s quiet period ends with the policy announcement, whereas the Federal Reserve’s extends to the day after the meeting. Based on the finding that post-announcement leaks dampen policy announcement effects while post-announcement attributed statements reinforce them, the paper suggests that permitting attributed communication shortly after policy decisions may help mitigate the market impact of post-announcement leaks.

Key Concepts

Monetary policy leak (“sources story”): In this paper, a leak is defined as a disclosure of confidential information emanating from an insider within the Eurosystem (ECB or NCB staff or policy-makers) that is transmitted to financial media with an expectation of anonymity for the source. The paper excludes whistle-blower cases and focuses on leaks where anonymity keeps attention on the content rather than the identity of the source. Leaks are distinct from “plants” (formally authorized institutional disclosures intended to advance the institution’s goals) and from “pleaks” (the middle ground).

Plant: An authorized or semi-authorized anonymous disclosure of confidential information made for the purpose of advancing the public institution’s own goals and interests, as distinct from a leak that originates from an individual insider’s personal agenda. The paper tests and rejects the plant hypothesis for most Eurosystem leaks on the basis that ECB Executive Board members’ attributed statements systematically counteract the market impact of leaks.

Single voice principle: The ECB’s communication norm requiring that Governing Council members discuss and resolve disagreements internally while publicly representing the official policy stance. This principle creates a setting where individual members with minority views may resort to anonymous communication as a way to express dissent “off-protocol.”

Quiet period (purdah): The ECB’s rule requiring policy-makers to refrain from public statements on policy-related topics in the seven days before each Governing Council monetary policy meeting. Leaks cluster during this period despite the restriction, supporting the non-random interpretation of leaks.

Attributable (named) statement: A public statement clearly attributed to a specific, named member of the ECB Governing Council, reported as a breaking-news headline. Attributable statements serve both as a comparison benchmark for measuring the market impact of leaks and as a mitigation instrument when they counteract leak-induced market moves.

Pre-leak communication intensity (lambda): The paper’s measure of the intensity of attributable communication in the 36-hour window before a given leak, defined as the sum of inverse time distances (in hours) from each attributable statement to the leak. A higher value means more recent and/or more numerous attributed statements precede the leak.

High-frequency event study window: The paper uses an asymmetric window starting 5 minutes before and ending 30 minutes after a leak’s timestamp. Market reactions are measured as the change in the median OIS quote during the 10 minutes after the window versus the 10 minutes before, matching methodology used for both leaks and attributable statements to ensure comparability across communication types.

Post-announcement leak dummy: An indicator taking the value of one if at least one leak occurs between the end of the official ECB monetary policy announcement window (15:50 CET) and end of trading hours on the announcement day. Used in the augmented Tillmann (2021) regression to measure whether leaks dampen the transmission of monetary policy surprises to longer-term rates.

Central bank reputation with noise

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question. How does noise in the mapping from central bank actions to realized inflation affect the existence and character of reputational equilibria in monetary policy? Specifically, can a central bank that faces uncertainty about whether it is perceived as “hawkish” or “dovish” sustain a pure strategy separating equilibrium, and how should each type behave as a function of its current reputation?

Model and Methodology. Amador and Phelan build on the monopolistic-competition, cash-in-advance framework of Chari, Christiano, and Eichenbaum (1998) and extend it to allow for (i) two central bank types — hawkish (type 1, high penalty γ₁ for inflationary actions) and dovish (type 2, lower penalty γ₂ < γ₁) — whose identity is private information; (ii) type switching governed by a Markov process, with probability δ that a hawkish bank is replaced by a dovish one and probability ε that a dovish bank is replaced by a hawkish one; and (iii) noise between the central bank’s chosen action μᵢ and realized money growth μₐ, which is drawn from a density f(μₐ|μᵢ) with full support. The equilibrium concept is pure symmetric Markov perfect equilibrium, in which all strategies are functions only of the public Bayesian posterior ρ that the current central bank is hawkish. The paper proceeds analytically to characterize no-pooling results and then computationally to demonstrate existence of separating equilibria.

Main Findings.

No pooling equilibria exist (analytical). Propositions 2 and 3 establish that no pure symmetric Markov equilibrium can have both types choosing the same positive action for any reputation ρ, as long as γ₁ ≠ γ₂ and Assumption 1 (pricing distortion sufficiently severe) holds. The intuition: if both types pool, realized inflation is uninformative, reputation does not change, and there are no dynamic incentives — but different static incentives (γ₁ ≠ γ₂) then imply different optimal actions, a contradiction.
Without sufficient noise, separating equilibria also fail to exist. In the no-noise limit, Bayesian updating forces the dovish bank’s reputation to jump to its maximum after one period of mimicking the hawkish action, making mimicry cheap when the discount factor β is high or the type-persistence probability ε is low. This makes the incentive-compatibility constraint for the dovish bank very difficult to satisfy, potentially precluding existence of a separating equilibrium.
With sufficient noise, pure strategy separating equilibria exist and have appealing properties (computational). The benchmark parameterization sets α = 1, σ = 5, β = 0.99, h(μ) = 0.5μ², ε = δ = 0.02, and the noise distribution such that the hawkish type’s unconstrained target would deliver mean inflation of 2% and the dovish type’s 3%. Under these parameters:
- In the full-information (known-type) world: price P = 1.313 for the hawkish type and P = 1.338 for the dovish type, with E[log(c) − αc] = −1.0297 and −1.0320 respectively, versus the efficient benchmark of −1.
- In the reputational equilibrium, both types choose lower inflationary actions than they would absent reputation considerations — because reputation is valuable (higher ρ lowers household prices and thus improves welfare for both types).
- Both types’ optimal actions are U-shaped in reputation ρ: they are most restrained — choosing the lowest inflationary actions — when ρ is middling (interior), because Bayesian updating is most sensitive (and thus the reputation cost of inflating is greatest) at interior beliefs, while it is difficult to move extreme beliefs.
- Average equilibrium inflation is 2.1%, which lies below the weighted average of unconstrained type targets (2.5% given equal switching probabilities), demonstrating that reputation concerns compress inflation outcomes.
Ergodic distribution of reputation remains interior. Starting from ρ = 0.5, expected reputation conditional on being hawkish stays below 0.63 and conditional on being dovish stays above 0.38, reflecting that noise and type switching prevent reputation from collapsing to its extremes.
Welfare implications. The hawkish type is made worse off by ongoing household uncertainty (relative to the reference game in which type is immediately revealed), while the dovish type is made better off. Households are better off under continuing uncertainty than under immediate revelation, unless reputation is near its maximum — because uncertainty suppresses inflationary temptations for both types.

Scope Conditions. Results apply within a monopolistic-competition, cash-in-advance economy with discrete time, infinite horizon, and Markov strategies. The no-pooling result requires Assumption 1 (the pricing distortion is sufficiently severe that the central bank has a positive incentive to inflate from μ = 0). The no-noise existence failure is an informal argument holding fixed discount and type-switching parameters. Computational results are specific to the benchmark parameterization but are verified to be robust to variation in β, σ, γ₁, γ₂, ε, and δ.

In depth

Q1. What is the fundamental time-inconsistency problem in the underlying Chari et al. (1998) economy, and how does the paper extend it?

A1: In the Chari et al. (1998) monopolistic-competition cash-in-advance economy, households exploit market power when setting prices, and the cash-in-advance constraint depresses consumption efficiency; this creates an ex-post temptation for the central bank to inflate and partially offset these distortions, even though in equilibrium such inflation is anticipated and only worsens inefficiencies. Equilibrium consumption equals (1/α) × ((σ−1)/σ) × (β/(1+μ)), compounding a monopoly distortion (σ−1)/σ < 1 and a cash-in-advance distortion β/(1+μ) < 1 below the efficient level 1/α. Amador and Phelan add household uncertainty about the central bank’s type — captured by the Bayesian posterior ρ that the bank is hawkish — allowing reputation to be endogenously determined and to feed back into equilibrium pricing.

Q2. Why does reputation matter only through differences in inflation costs γᵢ and not through differences in effective discount factors alone?

A2: Proposition 1 establishes that if γ₁ = γ₂ (equal inflation penalties), then even if the two types have different effective discount factors β₁ = β(1−δ) ≠ β₂ = β(1−ε), there exists a pooling Markov equilibrium in which both types choose the same action μ* and reputation plays no role. When both types have identical static incentives, they will always choose the same action given that reputation doesn’t affect payoffs in such an equilibrium. Hence the relevant dimension of heterogeneity for reputation to matter is the inflation cost parameter γᵢ, not patience.

Q3. What is the formal argument that no pooling equilibrium can exist when γ₁ ≠ γ₂?

A3: Propositions 2 and 3 provide the formal argument. If both types pool at any reputation ρ with a common positive action μ, Bayesian updating implies that ρ⁺ is independent of the money growth realization μₐ. The first-order condition for type i then reduces to the static condition (∂E[log(c) − αc|μ]/∂μ) = γᵢh’(μ), which cannot hold simultaneously for types 1 and 2 since γ₁ ≠ γ₂ and h’(μ) > 0 for μ > 0. This logic rules out pooling at the stationary reputation ρ* = ε/(δ+ε) in Proposition 2 and at any reputation where μ > 0 in Proposition 3.

Q4. Why does noise facilitate the existence of separating equilibria?

A4: Without noise, if types separate, observing the hawkish action reveals the bank is hawkish with certainty, pushing reputation to its maximum (1−δ) in a single period. This makes mimicry extremely cheap for the dovish type when β₂ is large or ε is small: the incentive compatibility condition requires that the dovish type’s static gain from choosing its own action exceeds the value gain from jumping to the best possible reputation, which is a very stringent requirement. With noise, mimicry generates only a probabilistic shift in beliefs rather than a discrete jump to the extreme, so the dovish type must maintain the hawkish action repeatedly to achieve a reputational gain — making mimicry costly enough that the incentive compatibility condition can be satisfied.

Q5. What is the “reference game” and what analytical purpose does it serve?

A5: The reference game is a variant in which the central bank’s type is fixed and is revealed to households immediately after they set prices at date t = 0. From t = 1 onward, the game reduces to the full-information, single-type game of Section 4. This allows the authors to isolate the “direct” effect of reputation — the fact that expected type affects equilibrium prices today — from the “indirect” or strategic effect of the central bank actively managing its reputation. In the numerical example, the reference-game prices form the upper dashed line in Figure 1, while the actual game’s prices form the lower solid line, with the gap between them attributable to the central bank’s incentive to restrain inflation in order to protect reputation.

Q6. What are the equilibrium price and welfare levels in the benchmark numerical example, and how do they compare to efficient and full-information benchmarks?

A6: The efficient benchmark delivers log(c) − αc = −1 with consumption c* = 1/α = 1. Under full information with only the hawkish type present, P = 1.313 and E[log(c) − αc] = −1.0297; under only the dovish type, P = 1.338 and E[log(c) − αc] = −1.0320. In the reputational equilibrium, prices lie below the full-information mixed benchmark for any given ρ (the solid line in Figure 1 lies below the dashed reference-game line), reflecting that the central banks’ desire to maintain reputation leads both types to restrain inflation beyond what the direct price effect alone would induce.

Q7. How does the U-shape of optimal central bank actions in reputation arise, and what does it imply for policy?

A7: The U-shape arises because Bayesian updating is most powerful at interior beliefs: for extreme reputations (near ε or 1−δ), any given realization of money growth moves the posterior relatively little, so the reputational cost of inflating is small. For interior (middling) reputations, the same action shifts the posterior substantially, making reputation more sensitive to inflation choices and thus increasing the marginal cost of inflating. Both types therefore choose their minimum inflationary actions at middling reputations. The policy implication is that a hawkish central bank with a very low reputation (following a run of high realized inflation outcomes) should not dramatically tighten, because further contraction does relatively little for its reputation until nature delivers enough favorable realizations to move it to a more interior range.

Q8. What happens to the ergodic distribution of reputation and inflation, and what does this imply about the persistence of reputational dynamics?

A8: Starting from ρ = 0.5, expected reputation remains in the interior: above 0.38 for the dovish type and below 0.63 for the hawkish type. The ergodic distribution of ρ (Figure 5) concentrates at interior values rather than the poles, showing that noise and type switching prevent reputation from stabilizing at extremes. The ergodic inflation distribution (Figure 6) has an average of 2.1%, compared to 2% under an all-hawkish world and 3% under an all-dovish world. Because ε = δ (types are equally likely in the long run), the unconstrained-type-weighted average would be 2.5%, so reputational incentives reduce equilibrium average inflation by approximately 0.4 percentage points.

Q9. Who gains and who loses from ongoing type uncertainty relative to immediate revelation?

A9: The hawkish type’s value function (Figure 3a) lies below the reference-game dashed line for intermediate reputations, indicating that the hawkish type is made worse off by uncertainty — it must bear the cost of restraining inflation beyond what is statically optimal in order to signal its type, but the households partially “blame” it for high realized inflation regardless. The dovish type (Figure 3b) is made better off under continuing uncertainty because its reputation benefits from households’ inability to perfectly distinguish types. Households (Figure 3c) are better off under uncertainty unless reputation is very high, because uncertainty suppresses inflation temptations for both types and keeps prices lower.

Q10. What happens to equilibrium behavior under robustness checks on key parameters?

A10: When the discount factor β or the elasticity of substitution σ decreases, both types inflate more and prices rise. When the hawkish type’s penalty γ₁ decreases (becomes less hawkish), both types inflate more and prices rise. When the dovish type’s penalty γ₂ decreases (becomes more dovish), the dovish type inflates more and, somewhat counterintuitively, the hawkish type inflates less, leaving prices roughly unchanged but slightly higher. When switching probabilities ε or δ increase, prices rise and both types inflate more, analogously to a decrease in β. Across all robustness exercises, the dovish type never inflates less than the hawkish type — consistent with Proposition 1’s implication that the inflation-cost difference γ₁ − γ₂ is the fundamental driver of separation.

Key Concepts

Hawkish type (type 1): A central bank that receives a relatively large negative payoff γ₁h(μᵢ) for taking inflationary actions, where γ₁ > γ₂. In the paper’s own sense, this type is not behavioral — it optimizes fully and can choose any action — but has a strong intrinsic cost to inflation, making it prefer lower money growth rates ceteris paribus.

Dovish type (type 2): A central bank with a lower penalty parameter γ₂ < γ₁ for inflationary actions. Like the hawkish type, it is fully strategic and optimizing, differing only in the magnitude of its intrinsic inflation cost.

Reputation (ρ): The Bayesian posterior probability that households assign to the current central bank being the hawkish type. It is the single payoff-relevant state variable in the Markov equilibrium, evolving through Bayes’ rule applied to realized money growth and type-switching probabilities.

Pure symmetric Markov perfect equilibrium: An equilibrium in which all households set the same price and consume the same amount (symmetry), and all strategies — prices P(ρ), central bank actions μ₁(ρ) and μ₂(ρ), and household consumption c(μₐ, ρ) — depend on history only through the current reputation ρ (Markov). The paper focuses exclusively on pure (non-mixed) strategy equilibria.

Pooling equilibrium: An equilibrium in which both types choose the same action μ₁(ρ) = μ₂(ρ) at some reputation ρ. The paper proves analytically that no pooling equilibrium can exist when γ₁ ≠ γ₂ and the pricing distortion is sufficiently severe (Assumption 1).

Separating equilibrium: An equilibrium in which μ₁(ρ) ≠ μ₂(ρ) for all ρ, so that realized money growth outcomes are informative about type and reputation evolves non-trivially. The paper argues that sufficient noise is necessary for such equilibria to exist.

Effective discount factor (βᵢ): The discount factor net of type-switching: β₁ = β(1−δ) for the hawkish type (which survives as hawkish with probability 1−δ) and β₂ = β(1−ε) for the dovish type. Central banks care only about payoffs while they are active, so effective discounting captures both time preference and expected tenure.

Noise (disconnection between actions and outcomes): The stochastic wedge between the central bank’s chosen action μᵢ and realized money growth μₐ, governed by a density f(μₐ|μᵢ) with full support. In the paper’s framework, noise is not merely a nuisance but a structural feature that makes reputational equilibria possible by preventing single-period complete revelation of type.

Climate change and the macroeconomics of bank capital regulation

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper asks two related questions about the intersection of climate policy and bank capital regulation. First, can differentiated bank capital requirements — imposing higher equity charges on loans to fossil energy firms — serve as a quantitatively meaningful climate policy instrument, in particular relative to carbon taxes? Second, how should optimal bank capital requirements respond to a carbon-tax-induced clean energy transition?

Methodology

The authors build a quantitative multi-sector DSGE model with two layers of default: corporate default at the firm level and bank failure at the bank level. Three intermediate goods sectors are modeled — non-energy, fossil energy, and clean energy — linked via a nested CES final-good production structure. Banks collect deposits from households (who value deposits for liquidity services) and issue defaultable loans to all three sectors. Deposit insurance, combined with limited liability for bank owners, generates an inefficiently high bank risk-taking motive, creating a role for capital regulation. The Ramsey-optimal capital requirement balances the social benefit of liquid deposit provision to households against the social cost of bank failure.

The model is calibrated to quarterly data, targeting a 0.7% annualized bank failure rate, a 2% annualized corporate default rate, a 30% loan recovery rate, a deposit spread of -100 basis points, and a baseline Ramsey-optimal equity requirement of 8% (consistent with Basel III). Sectoral parameters follow Bartocci, Notarpietro, and Pisani (2022) and Fried, Novan, and Peterman (2022): the energy-to-non-energy elasticity of substitution is 0.2, the clean-to-fossil energy elasticity is 3, and full abatement occurs at carbon taxes exceeding 125 $/tonne of carbon (ToC). The clean transition experiment imposes a linear carbon tax path from zero to 10 $/ToC over 40 quarters, announced as an unanticipated but fully credible shock.

Main Findings

Finding 1 — Fossil-penalizing capital requirements are quantitatively negligible as climate policy. Raising the capital requirement on fossil loans from the baseline 8% to 12% (a 150% risk-weight, consistent with current BB- treatment) reduces the fossil capital share within the energy sector by only 0.06 percentage points (from 80.00% to 79.94%) and cuts aggregate emissions by only 0.08%. A 1 $/ToC carbon tax, by contrast, achieves a 5.23% emission reduction while modestly reducing the fossil capital share to 79.80%. The difference arises because capital requirements affect only the size and financing cost of fossil firms, leaving abatement incentives unchanged; the loan-rate effect on fossil firms is small (loan rate rises from 124 bps to 128 bps), consistent with Kashyap, Stein, and Hanson (2010).

Finding 2 — Sustainability-linked capital requirements remain insufficient. Conditioning the fossil capital requirement on firms’ abatement effort (κ_f = 0.12 − η_t) induces an optimal abatement effort of 2.69% and an effective fossil requirement of approximately 9.5%. The implied emission reduction remains far below even a modest carbon tax: the authors state the induced emission reduction falls short by a factor of almost 100 relative to full abatement.

Finding 3 — Ramsey-optimal capital requirements decline monotonically along the transition (in the baseline real model). When a carbon tax gradually rises from zero to 10 $/ToC over 40 quarters, aggregate loan demand contracts permanently because clean, fossil, and non-energy goods are imperfect substitutes and the shock is recessionary for GDP. Banks reduce balance sheets, deposit supply falls, the deposit spread widens by approximately 8 basis points in the long run, and corporate default rates across all sectors rise by almost 0.1 percentage points from the baseline of 2.05% (in steady state). To counteract the deposit scarcity and associated firm risk-taking, the Ramsey-optimal capital requirement declines symmetrically and monotonically to a lower long-run level. Bank capital regulation cannot affect impact default rates because leverage decisions are made before the transition is announced.

Finding 4 — Nominal rigidities produce a temporary tightening before the long-run relaxation. When debt is denominated in nominal terms and Rotemberg price adjustment costs are added, the clean transition is inflationary in the short run (consistent with Ciccarelli and Marotta 2021). Inflation makes deposit financing more attractive, inducing firms to temporarily increase nominal loan issuance; real deposits rise briefly, the deposit spread narrows by around 2 basis points, and the optimal capital requirement tightens over the initial phase of the transition before converging to the same lenient long-run level as the baseline. The short-run tightening is followed by a permanent relaxation.

Finding 5 — Differentiated sector-specific capital requirements are only warranted when banks are not diversified across sectors. In the baseline, perfectly diversified banks face a symmetric aggregate loan demand contraction, so uniform adjustment suffices. When sector-specific banks are introduced (an extreme case meant to bound concentration effects), fossil banks experience a strong reduction in deposit supply while clean banks experience the opposite. The optimal response is temporarily tighter capital requirements for clean banks and relaxed requirements for fossil banks. In the long run, both converge to an aggregate risk-weight of approximately 99.85% relative to the baseline (a small but symmetric relaxation), very close to the diversified baseline.

Scope Conditions

All results are derived within a model calibrated to match broad financial-market and macroeconomic regularities rather than a specific country. Physical risk from climate change is abstracted away throughout. The carbon tax is set exogenously (not derived from a climate policy optimum). Firms cannot switch technologies, providing a conservative lower bound on the sectoral reallocation. Results are robust to halving the deposit demand elasticity parameter (γ_D = 0.6 versus 1.5 in the baseline) and to raising the energy/non-energy substitution elasticity to 3 from 0.2.

In depth

Q1. What is the core trade-off that determines the optimal level of bank capital requirements in this model?

A: The optimal capital requirement balances two welfare-relevant effects of bank leverage. Tighter requirements reduce bank failure rates, limiting the resource losses (proportional to deposits under DIA management) and the inefficient risk-taking that deposit insurance induces. At the same time, tighter requirements force banks to reduce deposit-financed lending, shrinking the supply of liquid deposits that households value directly in utility. The Ramsey planner chooses the capital requirement that equates the marginal welfare benefit of lower bank failure against the marginal welfare cost of reduced deposit provision. In the baseline calibration this optimum is at 8%.

Q2. Why does raising capital requirements on fossil loans have such a small effect on carbon emissions?

A: Capital requirements affect the deposit-financing wedge for fossil loans — the share of loans that can be funded via cheap, deposit-financed sources — but they do not enter firms’ first-order condition for abatement. Firms respond by modestly reducing leverage and investment (the loan rate for fossil energy firms rises from 124 bps to 128 bps), but the emission intensity of fossil production is unchanged. In equilibrium, the fossil capital share within the energy sector declines by only 0.06 percentage points (from 80.00% to 79.94%), reducing total emissions by 0.08%. A 1 $/ToC carbon tax produces a 5.23% emission reduction, many times larger, because carbon taxes directly alter the return to abatement and the profitability of fossil relative to clean production.

Q3. How does the sustainability-linked capital requirement work and why is it still insufficient?

A: Under sustainability-linked capital requirements, the fossil loan charge is set as κ_f = κ̃ − η_t, so firms that abate more face lower capital requirements on their loans and thus lower financing costs. This creates a direct financial incentive for abatement that the simple penalizing factor lacks. With κ̃ = 0.12, the equilibrium abatement effort is 2.69% and the effective fossil requirement falls to approximately 9.5%. Despite this improvement relative to the plain fossil factor, the climate impact remains far smaller than even a modest carbon tax: the induced emission reduction falls short by a factor of almost 100 relative to full abatement. The fundamental limitation is that the feedback from abatement to financing cost is attenuated by deposit-financing wedge mechanics, making the instrument too weak to substitute for direct carbon pricing.

Q4. What are the impact, short-run, and long-run effects of the clean transition on default rates and bank failure?

A: On impact, the unexpected compliance cost increase raises fossil firms’ default threshold, causing a sharp but short-lived uptick in fossil firm default rates (from 2.05% to approximately 2.08% in the baseline transition) and a brief increase in bank failure. Clean firm defaults fall slightly on impact due to higher clean energy prices. In the short run, clean firms increase risk-taking (higher leverage) because the relative attractiveness of debt financing improves as deposit spreads widen; fossil firms deleverage. In the long run, aggregate corporate default rates rise by almost 0.1 percentage points from the baseline of 2.05% (equivalently 2.7% in the Appendix B long-run analysis), driven by the widening of the deposit spread (approximately 8 bps), which raises the deposit financing wedge for all firms. Bank failure rates are always tied to binding capital requirements and revert quickly to their steady-state level.

Q5. Why can bank capital regulation not mitigate the impact default spike when the transition is announced?

A: At the moment of announcement, leverage decisions for the current period have already been made. The bank capital requirement binds on new lending decisions but cannot alter the existing capital structure of banks or firms. Therefore the regulator faces a “bygone” on impact: changing the capital requirement in the announcement period does not affect current corporate default rates or bank failure rates. The regulator’s tool only becomes effective for lending decisions going forward, implying that the transition-induced impact default surge cannot be smoothed by macroprudential policy.

Q6. Why do Ramsey-optimal capital requirements decline along the transition rather than tighten to address higher default risk?

A: The key channel is that aggregate loan demand contracts permanently as imperfect substitutability across sectors makes the carbon tax recessionary. Banks shrink their balance sheets, reducing deposit supply. The resulting deposit scarcity makes deposits more valuable to households (widening the spread), which also makes deposit financing cheaper for banks, partially offsetting the loan demand decline but at the cost of higher corporate leverage. The welfare loss from reduced liquidity provision and higher firm default rates dominates, so the planner relaxes capital requirements to stimulate deposit supply. The dominant effect is the large, permanent decline in credit demand, which makes it welfare-improving to allow banks to operate at lower capital ratios to rebuild deposit provision.

Q7. What is the role of the deposit financing wedge in transmitting carbon tax shocks to the entire corporate sector?

A: The deposit financing wedge (Ξ_t) reflects the benefit for banks of funding loans through deposits rather than equity, combining the liquidity premium households pay on deposits and the deposit insurance put (expected repayment is only 1 − F(μ_{t+1}) per unit of deposits issued). When aggregate loan demand falls due to carbon taxes, deposits become scarcer relative to their steady-state level, making the wedge larger. Through the loan pricing condition, all sectors — not just fossil — face more attractive deposit-financed debt, causing clean and non-energy firms to also increase their leverage and default risk along the transition. This is the mechanism through which a sector-specific shock has symmetric aggregate effects that shape optimal bank regulation.

Q8. How do nominal rigidities change the optimal path of capital requirements along the clean transition?

A: With Rotemberg price adjustment costs and nominally denominated debt, the clean transition is inflationary in the short run (consistent with empirical evidence in Ciccarelli and Marotta 2021). Inflation lowers the real value of outstanding nominal loan obligations, incentivizing firms across all sectors to temporarily increase nominal borrowing. Banks accommodate this demand by increasing deposit issuance, which briefly narrows the deposit spread by around 2 basis points. With deposit supply temporarily elevated, the regulator’s trade-off tilts toward reducing bank failure rather than stimulating deposit provision, so optimal capital requirements tighten during the inflationary phase before reverting to the lenient long-run path of the baseline model. The long-run level is unchanged.

Q9. Under what conditions are sector-specific capital requirements welfare-improving?

A: Sector-specific requirements are only welfare-improving when banks are not perfectly diversified across sectors, so that the transition has heterogeneous effects on sector-specific deposit supply and bank failure rates. In the baseline with perfectly diversified banks, the loan demand decline affects all banks uniformly, so a symmetric uniform adjustment is optimal. When sector-specific banks are introduced as an extreme case of carbon concentration, fossil banks experience a sharp reduction in deposit provision while clean banks see deposits temporarily increase. The planner responds by temporarily relaxing requirements for fossil banks and tightening them for clean banks. In the long run, both converge to approximately the same aggregate relaxation as the diversified baseline (aggregate risk-weight of 99.85%).

Q10. How does the carbon tax shock experiment relate to the perfect-foresight transition analysis?

A: In the carbon tax shock experiment, the tax level follows an AR(1) process with persistence ρ_τ = 0.9, starting from a long-run level of 10 $/ToC, with a one-standard-deviation shock implying an additional 10 $/ToC on impact. Fossil firm default rates spike from 2% to approximately 2.8% on impact and revert relatively quickly. Emissions decline by slightly more than 10% on impact and revert as the shock dissipates. The macroeconomic dynamics — GDP, investment, loan demand, and bank failure rate responses — closely resemble the impact and short-run effects of the perfect-foresight transition. Optimal capital requirements decline temporarily in both cases, confirming that the transition-path results are not an artifact of the specific perfect-foresight assumption.

Q11. What is the “forced safety effect” and how does it interact with the model’s capital requirement trade-off?

A: The “forced safety effect” (following Bahaj and Malherbe 2020) refers to the positive effect of tighter capital requirements on loan supply that operates through reducing bank failure probability. When banks are less likely to fail (lower F(μ_{t+1})), the expected bank productivity conditional on not failing — (1 − G(μ_{t+1})) — rises toward one, reducing the discount applied to future loan payoffs in the bank’s stochastic discount factor. This improves the profitability of lending and expands loan supply. In the model, this effect partially offsets the direct loan-supply reduction from higher equity requirements but does not dominate, so the overall effect of tighter requirements on deposit supply is still negative, preserving the core trade-off.

Q12. What robustness checks are performed and do they materially change the main results?

A: The authors consider three main robustness checks. First, reducing the deposit demand elasticity parameter from γ_D = 1.5 to γ_D = 0.6 (recalibrating ω_D = 0.012 to preserve the -100 bp deposit spread target) has almost no effect on the optimal path of capital requirements. Second, raising the energy/non-energy substitution elasticity from ε̃ = 0.2 to ε̃ = 3 (and adjusting the energy weight to maintain a 10% energy share) produces much stronger fossil investment declines and smaller clean investment responses, but aggregate loan demand and bank deposits contract only slightly less, so the relaxation in capital requirements is slightly smaller than in the baseline. Third, recalibrating to a 2% annualized bank failure rate (versus the baseline 0.7%) does not materially change results. The conclusion that capital requirements should decline along the transition is robust across all specifications.

Key Concepts

Deposit financing wedge (Ξ_t): The gain for banks from funding loans via deposits rather than equity. It comprises two components: (i) the liquidity premium — households value deposits for their liquidity services, so the deposit rate lies below the risk-free rate; and (ii) the deposit insurance put — the expected repayment obligation per unit of deposits is only 1 − F(μ_{t+1}), not one, since the DIA covers depositors in the event of bank failure. A larger wedge makes deposit-financed lending more profitable, expanding loan supply. In this paper the wedge is the central transmission mechanism through which capital requirements and aggregate loan demand interact.

Bank failure threshold (μ_t): The realization of the bank-specific idiosyncratic risk shock below which a bank cannot service depositors and transfers all assets and liabilities to the deposit insurance agency. It depends on the ratio of deposit repayment obligations to the aggregate realized loan portfolio return. In the model the threshold increases when aggregate loan payoffs fall (as in a carbon tax shock), temporarily raising bank failure rates.

Ramsey-optimal capital requirement: The sequence of sector-specific (or uniform) capital ratios chosen by a benevolent government planner to maximize household welfare, treating the capital requirement as the sole policy instrument. In this model the Ramsey problem is solved nonlinearly along the perfect-foresight transition path. The planner internalizes that tighter requirements simultaneously reduce bank failure probability and shrink deposit supply; the optimum trades off these two objectives.

Sustainability-linked capital requirement: A capital requirement on fossil loans that explicitly depends on the abatement effort undertaken by fossil firms (κ_f = κ̃ − η_t), creating a direct financing-cost incentive for emission reduction. This contrasts with a plain fossil penalizing factor, which affects only the financing cost of fossil capital without altering abatement incentives. The paper shows that even sustainability-linked requirements are quantitatively negligible as climate policy relative to carbon taxes.

Carbon compliance cost per unit of fossil production (ξ_t): A summary statistic combining the direct carbon tax payment and the abatement cost at the optimal abatement effort. It measures the total policy-induced wedge that reduces the profitability of fossil capital and raises fossil firms’ break-even default threshold. In the transition experiment, compliance costs rise from zero to approximately 4% of fossil production value as the tax increases from 0 to 10 $/ToC.

Asset stranding channel: The mechanism through which an unanticipated tightening of carbon policy raises fossil firms’ default probability on impact (by increasing compliance costs above the level priced into existing loan contracts) and subsequently reduces their loan demand permanently. The paper contrasts its treatment of this channel — where stranding affects bank regulation through aggregate deposit supply effects — against models (such as Carattini, Melkadze, and Heutel 2023) where stranding causes an inefficient credit crunch via a financial accelerator.

Deposit spread (s^D_t): Defined as the annualized difference between the deposit rate and the risk-free rate, expressed in basis points. Because households value deposits for liquidity services, the deposit rate lies permanently below the risk-free rate (spread is negative). In the baseline calibration the target is -100 bps. The spread widens (becomes less negative) when deposits become scarcer, which is the case along the carbon tax transition as bank balance sheets contract.

Comment on "Artificial Intelligence and Technological Unemployment" by Wang and Wong

Mon, 01 Jan 0001 00:00:00 +0000

This comment, written by J. Carter Braxton (University of Wisconsin), discusses the paper “Artificial Intelligence and Technological Unemployment” by Wang and Wong (2025), which develops and quantifies an equilibrium labor search model to evaluate the employment effects of spreading AI. Wang and Wong’s central finding is that improvements in AI quality will increase productivity by a factor of three while reducing employment by 23%, with approximately half of the employment decline occurring within the next five years. Braxton’s comment serves two purposes: first, to clarify the model’s structural channels through which AI affects employment; and second, to bring empirical evidence from the spread of computers in the 1980s–2000s to bear on the relative magnitude of those channels.

Braxton identifies two competing forces within Wang and Wong’s framework. The job destruction channel arises from endogenous separations: as AI quality improves, firms increasingly replace matched workers with AI, raising outflows from employment. The job creation channel arises from the free-entry condition: rising AI quality increases firm profits on all matches, inducing firms to post more vacancies, which raises workers’ job-finding rates and employment inflows. Whether aggregate employment rises or falls depends on which channel dominates — a quantitative question the authors resolve through calibration, finding the job destruction channel dominant. Braxton notes that three modeling choices (learning-by-using, the requirement that firms must be matched with a worker to adopt AI, and disembodied technological change) each push against the job-destruction result, making the authors’ findings more striking.

Braxton then evaluates the relative strength of these channels using the historical spread of personal computers. Drawing on Bick, Blandin, and Deming (2024), he notes that workplace AI adoption in 2024 follows nearly the same time trend and income-distribution profile as computer adoption in 1984, making computers a plausible historical analog. Using the CPS Computer Supplement (1984–2003), Braxton measures the change in computer usage by occupation and regresses it against the change in employment-to-unemployment (EU) transition rates by occupation. The estimated coefficient is 0.0146 (robust SE 0.0064), indicating that occupations with higher computer adoption rates saw higher flows into unemployment — confirming that a job destruction channel was active during the computer era. However, regressing the change in log occupation-level employment (1980–2000 Census) on the change in computer usage yields a coefficient of 0.7761 (robust SE 0.2658), with a positive slope indicating that occupations more exposed to computers saw higher employment growth. For the computer episode, therefore, the job creation channel dominated the job destruction channel — the opposite of Wang and Wong’s AI projection.

Braxton also cites his own prior work showing that even when job creation and destruction balance in aggregate, workers displaced by technological change face lasting earnings losses and elevated permanent income risk, raising the question of how to optimally insure these workers.

The comment concludes by identifying avenues for future research: introducing occupational heterogeneity (with some occupations more exposed to AI than others) and worker heterogeneity (skills that are complements versus substitutes to AI). The central open question is whether AI is qualitatively different from prior episodes of technological change, and if so, why.

Q1: What are the two central channels through which AI quality affects employment in Wang and Wong’s model, and how do they operate? The job destruction channel operates through endogenous separations: as AI quality (At) improves, firms that are matched with workers are more likely to replace them with AI at rate ρ, adding the term ρµAt Ht It to outflows from employment in the law of motion for employment. The job creation channel operates through the free-entry condition: higher AI quality raises firm profits on all existing matches (because technological change is disembodied, benefiting matches formed today with future AI gains), inducing firms to post more vacancies, which via free entry reduces the firm’s matching probability but raises the worker’s job-finding rate αt and thereby increases employment inflows. The net employment effect depends on which channel quantitatively dominates.

Q2: What is Wang and Wong’s quantitative finding about the aggregate employment and productivity effects of AI? Using a calibrated equilibrium labor search model, Wang and Wong find that the spread of AI will increase productivity by a factor of three while reducing employment by 23%. Approximately half of the employment decline is projected to occur within the next five years. A version of the model holding job-finding rates fixed yields a similar result, indicating that through the lens of their model the job creation channel is quantitatively small and the job destruction channel dominates.

Q3: What three modeling choices push against Wang and Wong’s job-destruction result, and why does Braxton view this as making the finding more striking? First, AI improves through “learning by using” — it learns from all output being produced — which creates an incentive for employment to remain elevated to accelerate AI learning, dampening job destruction. Second, firms can only adopt AI if currently matched with a worker, which creates an incentive for vacancy posting and pushes in favor of job creation. Third, AI improvements are disembodied (raising productivity in all matches, including those formed before the improvement), which increases the value of forming new matches today and strengthens job creation. Because each of these assumptions pushes against the job destruction result, Braxton argues that finding job destruction dominant despite these model features makes the result more striking.

Q4: How does Braxton use the historical spread of computers to assess the job destruction and job creation channels? Braxton measures occupation-level computer adoption as the change in the share of CPS Computer Supplement respondents who reported using a computer at work between 1984 and 2003 (denoted ΔCPUo,84–03), using occupation codes from Autor and Dorn (2013). He then regresses the occupation-level change in EU transition rates (ΔEUo,84–03, from monthly CPS micro data) on ΔCPUo,84–03 to measure the job destruction channel, and separately regresses the change in log occupation-level employment (Δlog Eo,80–00, from the 1980 and 2000 Census IPUMS) on ΔCPUo,84–03 to assess the net employment effect. A positive coefficient on the employment regression indicates job creation dominates; a negative coefficient indicates job destruction dominates.

Q5: What do the regression results show about the job destruction and job creation channels during the computer era? The job destruction regression yields a coefficient of β = 0.0146 (robust SE = 0.0064, R² = 0.0178), indicating that occupations with higher computer adoption rates did see higher employment-to-unemployment transition rates — the job destruction channel was present. However, the employment-level regression yields a coefficient of β = 0.7761 (robust SE = 0.2658, R² = 0.0348), with a positive slope indicating that occupations more exposed to computers experienced higher employment growth between 1980 and 2000. Thus, for the computer episode, the job creation channel dominated the job destruction channel — the opposite of what Wang and Wong project for AI.

Q6: What is the basis for treating the computer episode as a relevant analog to the spread of AI? Braxton cites Bick, Blandin, and Deming (2024), who show that AI adoption in the workplace in 2024 is following nearly the same aggregate time trend as the spread of personal computers in the early 1980s. Moreover, the distribution of AI usage across the income distribution in 2024 is nearly identical to computer usage across the income distribution in 1984: for both technologies, workplace usage peaks between the 80th and 90th percentiles of the income distribution before declining modestly at the top. Bick et al. (2024) also show the similarities hold by education level and age.

Q7: Even if job creation and destruction balance in aggregate, what does prior work suggest about the distributional consequences for workers? Braxton and Taska (2023) show that workers in occupations more exposed to technological change (measured by changes in computer and software task requirements) suffered larger earnings losses following displacement. Braxton, Herkenhoff, Rothbaum, and Schmidt (2024, forthcoming AER) show that workers in occupations more exposed to technological change experienced larger increases in permanent income risk between the 1980s and 2010s. These findings imply that even if AI does not reduce aggregate employment, workers who are displaced will face deteriorating labor market prospects, raising the question of how to optimally provide insurance.

Q8: What policy implication does Braxton draw from the distributional consequences of technological change? Braxton and Taska (2025, forthcoming Review of Economic Dynamics) show that technological change expands the motive for governments to provide retraining subsidies. Braxton argues that if AI represents an acceleration of technological change, even larger retraining subsidies — and potentially other forms of insurance — may be needed for displaced workers.

Q9: What are the main avenues for future research identified in the comment? Braxton identifies two principal directions. First, introducing occupational heterogeneity into the Wang-Wong framework, so that some occupations are more exposed to AI displacement than others, would allow the model to generate richer distributional implications. Second, allowing worker heterogeneity in skills — distinguishing skill dimensions that are complements to AI from those that are substitutes — would permit the model to capture differential effects across the workforce. The overarching research question is whether AI is qualitatively different from prior technological change episodes, and if so, to identify the precise mechanisms that make it different.

Job destruction channel: In the Wang-Wong model, the increase in endogenous separations driven by firms replacing matched workers with AI as AI quality improves. Formally, this is the term ρµAt Ht It in the law of motion for employment, representing separations that occur when a firm adopts AI and the worker and firm cannot renegotiate a mutually acceptable wage.

Job creation channel: The increase in vacancy posting and worker job-finding rates induced by rising AI quality. Because higher AI quality raises firm profits on all matches (via disembodied technological change), the free-entry condition implies firms post more vacancies, lowering the firm’s matching probability but raising the worker’s job-finding rate αt, increasing employment inflows.

Free-entry condition: The equilibrium condition equating the cost of posting a vacancy (κt) to the expected benefit (the probability of matching ft times the firm’s match surplus Πt). This condition pins down the job-finding rate for workers: when firms find it more profitable to post vacancies, αt rises.

Disembodied technological change: The modeling assumption that AI quality improvements raise productivity in all existing matches, not just those formed after the improvement. This means future AI gains benefit matches formed today, increasing the incentive to create new matches and pushing in favor of the job creation channel.

Learning by using: The mechanism in Wang-Wong whereby AI quality (At) improves as a function of current aggregate employment (Ht) and the learning rate µ. Because AI learns from all output being produced, maintaining higher employment accelerates AI improvement, creating a motive that partially offsets the job destruction channel.

Employment-to-unemployment (EU) transition rate: The rate at which employed workers flow into unemployment in a given occupation, used by Braxton as the empirical measure of the job destruction channel during the computer episode. Measured from monthly CPS micro data.

Capitalization effect: The tendency for firms to post more vacancies today in anticipation of future productivity improvements, because the cost of posting is paid upfront while the benefits of a future-better-AI accrue to the match going forward. Referenced by Braxton as relevant to understanding the job creation channel in Wang-Wong’s framework (citing Pissarides (2000), Chapter 3).

Comment on: Is it AI or data that drives market power?

Mon, 01 Jan 0001 00:00:00 +0000

This paper is a published comment by Miao Ben Zhang (USC Marshall School of Business) on Mihet, Rishabh, and Gomes (2025), “Is It AI or Data That Drives Market Power?” Zhang identifies three contributions of the commented paper and benchmarks each against the existing literature, offering targeted suggestions for strengthening the analysis.

The first contribution Zhang discusses is the commented paper’s distinction between raw data, AI capability, and processed data. Raw data is modeled as a by-product of production linearly related to firm size; processed data is modeled as the abundance of signals improving the precision of firms’ next-period productivity predictions. The commented paper’s key modeling innovation is a formula linking raw data (n_{i,t}), firm-level AI capability (z_i), and processed data (n_{i,t}-tilde): processed data equals a weighted sum of an information entropy effect — e^(-z_i) * (-n_{i,t} * ln(n_{i,t})) — and an AI capability effect — (1 - e^(-z_i)) * n_{i,t} * e^(n_{i,t}). Zhang notes this formula implies that the marginal value of raw data can turn negative for firms with low AI capability, consistent with information-theoretic constraints from the rational inattention literature (Sims, 2003). Zhang requests more empirical support for this equation, specifically asking whether low-AI firms exhibit lower TFP than high-AI firms at similar data-intensity levels, and encouraging discussion of existing measures of data-processing ability such as human capital in data engineering and ML pipeline automation.

The second contribution is the commented paper’s modeling of a secondary market for trading processed data among firms. Zhang notes that facilitating processed data markets — for example via APIs or structured knowledge sharing — can, per the commented paper’s simulation and empirical analysis, democratize innovation and reduce market concentration, enabling even low-AI firms to compete. Zhang flags that the paper is silent on firm acquisition as an alternative channel for accessing processed data, arguing this omission is significant given that processed data, unlike ideas or technologies, is less portable and cannot be obtained simply by poaching skilled employees.

The third contribution is the commented paper’s empirical strategy. The commented paper constructs firm-level proxies for AI intensity and data intensity, then exploits two exogenous technological shocks — the advent of AWS cloud computing and transformer-based architectures — to identify causal effects of improvements in compute and processed data accessibility. The evidence shows that compute improvements disproportionately benefit data-rich firms, while processed data access disproportionately benefits low-AI firms. The central empirical message is that access to raw data tends to foster market concentration, whereas access to processed data tends to reduce market concentration. Zhang raises a measurement concern: the commented paper relies on firm-level Herfindahl-Hirschman Index (HHI) calculations based on time-varying, text-based industry definitions (Hoberg and Phillips, 2016). Zhang argues a positive effect on this HHI could reflect either genuine firm growth relative to competitors or reclassification of the firm into different, possibly more concentrated, sectors — making the HHI measure alone insufficient to support claims about product market concentration. Zhang recommends complementing this with industry-level concentration measures anchored to fixed baseline industry codes (FIC codes from Hoberg and Phillips, 2016), constructed at the FIC-year level, following the approach of Gutierrez and Philippon (2017) on industries’ growth and median Q.

No quantitative magnitudes from regressions or calibrations are reported in the comment itself, as this is a discussion piece rather than an original empirical paper. All claims above are drawn directly from the text.

Q: What are the three contributions of Mihet, Rishabh, and Gomes (2025) that Zhang identifies? A: First, the paper explicitly models the distinct roles of raw data, AI capability, and processed data, linking the information entropy literature to firm production. Second, it models a secondary market for trading processed data among firms, relevant for policy on data sharing platforms. Third, it empirically tests the model’s predictions using firm-level proxies and two exogenous technological shocks.

Q: What is the core formula linking raw data, AI capability, and processed data in the commented paper? A: Processed data (n_{i,t}-tilde) equals e^(-z_i) * (-n_{i,t} * ln(n_{i,t})) plus (1 - e^(-z_i)) * n_{i,t} * e^(n_{i,t}), where z_i is firm-level AI capability and n_{i,t} is raw data. The first term captures the information entropy effect (which can reduce or negate the value of raw data for low-AI firms) and the second captures the AI capability effect (where AI turns raw data into abundant useful signals).

Q: Why can the marginal value of raw data turn negative, according to the framework? A: Information-theoretic constraints — long studied through concepts like Shannon entropy and Sims’s rational inattention — imply that unprocessed raw data may harm rather than help firms that lack adequate processing capabilities. Zhang situates this in the broader macro-finance literature on information choice (Sims, 2003; Veldkamp, 2011).

Q: What empirical suggestion does Zhang make regarding the raw data versus AI capability distinction? A: Zhang asks whether, in the commented paper’s sample of publicly-traded firms with measures of data intensity and AI intensity, low-AI firms exhibit lower TFP (following Imrohoroglu and Tuzel, 2012) than high-AI firms when controlling for similar levels of data intensity. Zhang also encourages discussion of anecdotal evidence for negative information entropy effects and of existing measures of data processing ability such as human capital in data engineering, annotation, cleaning, or ML pipeline automation (Abis and Veldkamp, 2024).

Q: What is the policy relevance of the secondary market for processed data? A: The commented paper’s simulation and empirical analysis shows that facilitating processed data markets (e.g., via APIs or structured knowledge sharing) can democratize innovation and reduce market concentration, enabling even low-AI firms to compete. This aligns with recent literature on secondary markets for structured data and foundation model outputs (Gans, 2018, 2024; Conti et al., 2023, 2024; Athey, 2019). Platforms may have incentives to restrict processed data access, potentially reinforcing incumbent power (Carballa Smichowski et al., 2023).

Q: What channel does Zhang argue the commented paper neglects in its analysis of market concentration? A: Zhang argues the paper is silent on firm acquisition as an alternative means by which firms access processed data, noting that processed data is less portable than ideas or technologies — it cannot be obtained simply by poaching a skilled employee. Zhang contends this acquisition channel appears central to the paper’s focus on market concentration and encourages the authors to include a discussion of it.

Q: What is the central empirical finding of the commented paper regarding raw versus processed data and market concentration? A: Access to raw data tends to foster market concentration, while access to processed data tends to reduce market concentration. The evidence shows that compute improvements (proxied by the AWS shock) disproportionately benefit data-rich firms, while processed data accessibility (proxied by the transformer architecture shock) disproportionately benefits low-AI firms, consistent with theoretical predictions.

Q: What is Zhang’s specific concern about the HHI measure used in the commented paper? A: The commented paper constructs firm-level HHI using time-varying, text-based industry definitions (Hoberg and Phillips, 2016). Zhang argues a positive effect on this HHI is ambiguous: it could reflect genuine firm growth relative to competitors or reclassification of the firm into different, possibly more concentrated, sectors. Zhang concludes that the HHI measure alone is not strong enough to support claims about product market concentration.

Q: What robustness check does Zhang recommend for the empirical analysis? A: Zhang recommends constructing industry-level concentration measures at the FIC-year level using fixed baseline FIC codes from Hoberg and Phillips (2016), available at the Hoberg-Phillips Data Library. The authors could then analyze how industries with high versus low average or median AI intensity and data intensity respond to the two technological shocks in terms of concentration. Zhang cites Gutierrez and Philippon (2017) as an example of this approach and notes it would help distinguish within-industry dynamics from shifts in firm business focus, aligning with best practices from De Loecker, Eeckhout, and Unger (2020) on persistent market power.

Raw data: A by-product of firms’ production, modeled as linearly related to firm size; represents unprocessed observations that have not yet been transformed into useful signals. Distinguished from processed data, which is what actually improves productivity predictions.

Processed data: Modeled as the abundance of signals that improves the precision of firms’ predictions of their next-period productivity (following Farboodi and Veldkamp, 2022). Unlike ideas or technologies, processed data is less portable and cannot easily be transferred by poaching skilled employees.

AI capability (z_i): Firm-level ability to transform raw data into processed data. Firms with low AI capability may receive negative marginal value from additional raw data due to information entropy effects; firms with high AI capability extract large gains from the same raw data.

Information entropy effect: The component of the raw-to-processed-data transformation — e^(-z_i) * (-n_{i,t} * ln(n_{i,t})) — that captures the information-theoretic cost of possessing raw data without adequate processing capability. At low AI capability, this effect can reduce or negate the precision of signals.

Secondary market for processed data: A market in which firms trade processed data, modeled in the commented paper as a platform or API-based exchange. The commented paper’s analysis shows this market can democratize innovation and reduce market concentration by enabling low-AI firms to access processed data they cannot produce internally.

Firm-level HHI (text-based): Herfindahl-Hirschman Index calculated using time-varying, text-based industry definitions (Hoberg and Phillips, 2016). Zhang identifies a measurement ambiguity: a positive effect on this measure could reflect genuine competitive gains or reclassification into more concentrated sectors.

Committed to flexible fiscal rules

Mon, 01 Jan 0001 00:00:00 +0000

A central debate in fiscal policy is whether fiscal rules—numerical constraints on budget deficits or debt levels—impair a government’s ability to respond to adverse economic shocks, creating a fundamental trade-off between debt stabilization and macroeconomic stabilization. This paper uses data on large, random natural disasters as exogenous shocks to address the endogeneity of rule adoption and provides new empirical and theoretical evidence on this trade-off. Contrary to the trade-off hypothesis, countries with fiscal rules perform significantly better following such disasters than countries without rules: GDP and private consumption are persistently higher, and fiscal policy is significantly more expansionary. The superior performance is shown to depend on the existence of prior fiscal space and the presence of escape clauses in the rules. A model of sovereign default with endogenous fiscal space and tax plans rationalizes these findings: tight rules prevent myopic governments from accumulating excessive debt in good times, which creates fiscal space for deficit spending when disasters strike, keeping sovereign spreads lower and enabling more expansionary fiscal responses.

In depth

Q1. What is the identification strategy and why do natural disasters solve the endogeneity problem?

Large natural disasters serve as a source of exogenous, random adverse economic shocks; by interacting disaster exposure with the presence or absence of fiscal rules, the paper identifies the effect of rules on macroeconomic performance without confounding from the non-random adoption of rules. Endogeneity is a central concern in the fiscal rules literature because countries that adopt rules may differ in politically or economically relevant ways from those that do not (e.g., more disciplined political environments, stronger institutions). Using large disasters as quasi-experimental variation removes this concern: the timing and magnitude of natural disasters are uncorrelated with which countries happened to adopt fiscal rules, isolating the effect of rules on crisis response.

Q2. What are the main empirical findings?

Countries with fiscal rules show significantly higher output and private consumption following large natural disasters, and implement significantly more expansionary fiscal policy, compared to countries without rules—holding over a 1970Q1–2018Q4 quarterly panel—with confidence bands at the 68% and 90% levels based on 500 Monte Carlo draws. The result directly contradicts the commonly held view that fiscal rules restrict governments’ ability to respond to shocks. Moreover, the paper finds that the superior performance of rule-constrained countries is conditional on two features: the existence of fiscal space prior to the shock (low debt or deficit positions), and the presence of escape clauses that allow rules to be suspended during severe adverse events.

Q3. What is the model mechanism?

In the sovereign default model, a fiscal rule prevents a myopic government from over-borrowing in good times out of political economy considerations (e.g., electoral incentives to spend); this forced restraint creates fiscal space—lower debt, lower sovereign spreads—which allows the government to run deficits when a shock hits without triggering a default episode or a sharp rise in borrowing costs. The model predicts that, relative to a no-rule economy, when a disaster strikes in a rule-constrained economy: sovereign spreads spike by less, the fiscal policy response is more expansionary, and output and consumption are higher. Escape clauses in the rules are important: they allow the government to depart from the rule explicitly in crisis situations without destroying the credibility of the rule in normal times.

Q4. What is the policy implication for the COVID-19 fiscal response?

The paper’s findings directly address the suspension of fiscal rules during COVID-19: the theoretical and empirical results suggest that rules with escape clauses do not impair crisis response and may actually improve it, by ensuring fiscal space is available when needed. The paper’s evidence implies that the COVID-era suspension of rules in many countries (including the EU’s Stability and Growth Pact) was not necessarily required to enable expansionary fiscal responses—countries with well-designed rules including escape clauses could have responded expansively while maintaining rule credibility.

Key concepts

escape clause : a provision in a fiscal rule that explicitly permits departure from the rule’s numerical target under defined circumstances (severe recessions, natural disasters, etc.); the paper finds that the presence of escape clauses is one of the two conditions for rule-constrained countries to outperform non-rule countries after adverse shocks.

fiscal space : the buffer of low debt and deficit levels that allows a government to increase spending or cut taxes during a shock without triggering unsustainable debt dynamics or elevated sovereign spreads; the paper shows fiscal space is created by rules in good times and consumed in bad times.

Competition and the Phillips curve

Mon, 01 Jan 0001 00:00:00 +0000

Fujiwara and Matsuyama ask whether the well-documented flattening of the New Keynesian Phillips curve (NKPC) and the concurrent rise in market concentration and markup rates are causally linked or merely coincidental. Under the canonical New Keynesian model with CES demand, competition is irrelevant to the Phillips curve regardless of whether entry is endogenous — concentration neither changes its slope nor affects inflation directly. This paper overturns that irrelevance result by extending the canonical model in two directions: (1) incorporating endogenous firm entry and exit following Bilbiie, Ghironi, and Melitz (2008) and Bilbiie, Fujiwara, and Ghironi (2014), and (2) replacing CES with the Homothetic Single Aggregator (HSA) demand system (Matsuyama and Ushchev 2017, 2020b), a flexible, tractable class of homothetic demand systems that nests CES and Translog as special cases.

The paper’s theoretical results depend on two of Marshall’s laws of demand. The Second law states that the price elasticity of demand rises with the firm’s own price; the Third law states that the rate of increase in that elasticity falls with price. Together these conditions imply that the markup rate and pass-through rate are endogenous to the competitive environment.

The main findings, delivered under both Rotemberg (1982) and Calvo (1983) pricing, are that higher entry costs — leading to market concentration — cause Phillips curve flattening through two distinct, complementary channels:

Structural (steady-state) effect. Under Rotemberg pricing, the slope of the NKPC is proportional to the price elasticity zeta(z); market concentration reduces z, hence reduces zeta(z) under the Second law, directly flattening the curve. Under Calvo pricing, the slope is proportional to the pass-through rate rho(z); the Third law implies that concentration reduces rho(z), again flattening the curve. The Calvo–Rotemberg equivalence, which holds under CES to first order (Roberts 1995), breaks down under HSA: each pricing mechanism highlights a different channel.
Observational (omitted variable bias) effect. Endogenous entry generates an endogenous cost-push shock through strategic complementarity in price setting. Because the number of firms N_t is omitted from a naive regression of inflation on real marginal cost, and because N_t is positively correlated with the marginal cost under the Second law, the omitted variable bias is negative — the estimated slope is biased downward. This bias is amplified with greater concentration under the Third law (Rotemberg case) and under both the Second and Third laws (Calvo case).

Quantitatively, the paper simulates under three parametric HSA families — CES, Translog, and Co-PaTh (Constant Pass-Through). De Loecker, Eeckhout, and Unger (2020) document that aggregate markups rose from 21% above marginal cost to 61% — a rise of approximately 40 percentage points. The authors’ simulations imply this increase corresponds to an entry cost roughly 3.5 times higher under Translog and roughly 2.5 times higher under Co-PaTh with pass-through rate rho = 0.5. Under these parameterizations, the accompanying market concentration can halve the slope of the NKPC. Impulse responses confirm that the responses of inflation to both technology shocks and monetary policy shocks become smaller as market concentration deepens.

Scope conditions: results require departure from CES (the Second and/or Third law must hold); endogenous entry is necessary for the dynamic cost-push channel; the structural flattening requires only the Second law under Rotemberg but additionally the Third law under Calvo; the omitted variable bias requires the Second law under Rotemberg and both laws under Calvo. The model is closed-economy, with symmetric monopolistic competition and Rotemberg or Calvo price adjustment.

Q1: What is the irrelevance result the paper overturns, and why does CES produce it? Under CES, the market share function takes the form s(z) = gamma * z^(1-theta), yielding a constant price elasticity zeta = theta and a pass-through rate rho = 1, regardless of the number of firms or entry costs. As a result, concentration neither alters the slope of the NKPC nor generates any endogenous cost-push shock; competition is simply irrelevant to inflation dynamics. This irrelevance holds even with endogenous entry under CES.

Q2: What is the Homothetic Single Aggregator (HSA) and why is it used? HSA is a class of homothetic demand systems, originally proposed by Matsuyama and Ushchev (2017), in which the market share of each intermediate input variety depends solely on its own price normalized by a single price aggregator A_t. This single aggregator serves as a sufficient statistic summarizing all competitive pressure effects on pricing behavior, including the markup rate and pass-through rate. HSA nests CES and Translog as special cases, is analytically tractable (equilibrium existence and uniqueness are straightforward to ensure with endogenous entry), and is flexible enough to accommodate both the Second and Third laws of demand.

Q3: What are Marshall’s Second and Third laws as defined in the paper? The Second law states that the price elasticity of demand zeta(z) is increasing in the normalized price z (equivalently, increasing in the single price aggregator A_t, which rises with fewer firms). The Third law, as defined by Matsuyama and Ushchev (2023b), states that the rate of increase in the price elasticity is decreasing in z. Together they ensure that both markup rates and pass-through rates respond systematically to changes in competitive pressure.

Q4: How does market concentration structurally flatten the NKPC under Rotemberg pricing? Under Rotemberg pricing, the slope of the NKPC equals (zeta(z) - 1) / chi, where chi is the Rotemberg price adjustment cost parameter. Higher entry costs reduce the equilibrium number of firms, which reduces competitive pressure and lowers z. Under the Second law, lower z reduces zeta(z), directly shrinking the slope coefficient. This is the steady-state effect of concentration: the structural slope of the curve declines because the price elasticity falls.

Q5: How does market concentration structurally flatten the NKPC under Calvo pricing? Under Calvo pricing, the slope of the NKPC is positively related to the pass-through rate rho(z) rather than the price elasticity. The Third law implies that lower z (more concentration) reduces rho(z). Market concentration therefore causes structural flattening through the pass-through channel under Calvo. This is why the Calvo–Rotemberg equivalence — which holds to first order under CES — breaks down under HSA: Rotemberg highlights the Second law / price elasticity channel and Calvo highlights the Third law / pass-through channel.

Q6: What is the endogenous cost-push shock and how does it arise? When the number of operating firms N_t changes endogenously, it alters the single price aggregator A_t and therefore the competitive environment facing each firm. Under the Second law, firms exhibit strategic complementarity in price setting: a firm reduces its markup when other firms lower their prices (A_t falls with more entry). Consequently, movements in N_t directly enter the NKPC as an additional term — (1/chi) * (1 - rho(z)) / rho(z) * N_hat_t — acting as an endogenous cost-push shock. This channel is absent under CES because rho = 1 makes the coefficient zero.

Q7: How does the endogenous cost-push shock create a negative omitted variable bias? A naive regression of inflation on real marginal cost omits the N_hat_t term. Under the Second law, N_t is positively correlated with the marginal cost (more entry drives markups down, consistent with marginal cost movements), so the omitted variable N_hat_t is positively correlated with the included regressor. Because the true coefficient on N_hat_t in the NKPC is negative, omitting it biases the estimated slope on marginal cost downward (negative omitted variable bias). The estimated relationship between inflation and marginal cost is therefore weaker than the true structural relationship.

Q8: How is the omitted variable bias amplified by concentration? Under the Third law (Rotemberg case) and under both the Second and Third laws (Calvo case), greater market concentration amplifies the magnitude of this negative bias. The intuition is that higher concentration makes the pass-through rate rho(z) smaller, which increases the coefficient on N_hat_t in the NKPC and thereby raises the magnitude of the bias when N_hat_t is omitted. Greater concentration thus generates both more structural flattening and more observational flattening simultaneously.

Q9: What are the quantitative magnitudes of Phillips curve flattening in the simulations? De Loecker, Eeckhout, and Unger (2020) document that aggregate markups rose from 21% above marginal cost to 61% — approximately 40 percentage points. The paper’s simulations imply this corresponds to an entry cost increase of roughly 3.5 times under Translog and roughly 2.5 times under Co-PaTh with rho = 0.5. According to Figure 2, the accompanying market concentration can halve the slope of the NKPC. The slope declines more steeply for demand systems with smaller pass-through rates (rho further from 1).

Q10: How do impulse responses change with market concentration? As entry costs rise (deeper concentration), the responses of the inflation rate to both technology shocks and monetary policy shocks become smaller in magnitude. Under the Second law, a positive technology shock increases the number of firms through a wealth effect, but strategic complementarity in price setting reduces markups, muting the inflation response relative to CES. The dynamic effect of endogenous entry thus weakens the transmission of real economic shocks to inflation — a supply side effect of monetary policy that parallels Baqaee, Farhi, and Sangani (2021) but operates through firm entry rather than the misallocation channel.

Q11: What is the cyclicality of the markup rate under HSA, and why is it ambiguous? Under CES with flexible prices, the markup is constant. Under CES with sticky prices, the markup is procyclical (marginal cost falls with a positive technology shock but the price is rigid in the short run). Under the Second law with flexible prices, a positive technology shock increases firm entry, which reduces markups, making the markup countercyclical. In a sticky price equilibrium under the Second and Third laws, the cyclicality is therefore ambiguous: it depends on the tension between nominal rigidities (pushing toward procyclicality) and the pass-through rate (pushing toward countercyclicality).

Q12: Why do the three price indices in the model differ, and which is used for the NKPC? The model features three aggregate price measures: the final goods price (CPI) P_t, which captures productivity effects of entry; the single price aggregator A_t, which captures competitive effects of entry and is the reference price for firms; and the average price index (PPI) p_t, which is not affected by entry effects and is the measured price index. Because entry effects shift P_t and A_t in ways that are not directly observed, the paper evaluates NKPC responsiveness in terms of p_t (PPI inflation), the measurable index.

Q13: How does this paper relate to Wang and Werning (2022) and Baqaee, Farhi, and Sangani (2021)? Wang and Werning (2022) use a dynamic oligopoly model with exogenous entry and CES/Kimball demand, showing that higher concentration amplifies real effects of monetary policy and generates inflation persistence and endogenous cost-push shocks. Baqaee, Farhi, and Sangani (2021) use monopolistic competition with exogenous entry and Kimball demand under Calvo pricing, showing flattening through real rigidities and a misallocation channel (supply side effects of monetary policy). This paper uses monopolistic competition with endogenous entry and HSA under both Rotemberg and Calvo pricing; it produces supply side effects through firm entry rather than misallocation, and uses HSA rather than Kimball because HSA more readily guarantees equilibrium uniqueness with endogenous entry.

Q14: What parametric families of HSA are used in simulations and what are their properties? Three families are used: CES (constant price elasticity theta, pass-through rho = 1, benchmark); Translog (satisfies the Second law, variable markups and pass-through); and Co-PaTh or Constant Pass-Through (proposed by Matsuyama and Ushchev 2020a, constant pass-through rate rho in (0,1) under flexible prices, containing CES as a limit as rho approaches 1). For Calvo pricing, a fourth family — PEM (Power Elasticity of Markup, proposed by Matsuyama and Ushchev 2023b) — is used; PEM satisfies the Third law in its strong form and contains Co-PaTh as a limit case. Translog is noted to behave similarly to Co-PaTh with rho = 0.5.

Q15: What are the policy implications for central banks? Rising market concentration, by flattening the NKPC both structurally and observationally, reduces the effectiveness of monetary policy in achieving price stability through real economic activity — consistent with the concerns expressed by Federal Reserve officials (Clarida, Daly, Williams) quoted in the paper. The results suggest that empirical estimates of the NKPC slope that omit endogenous entry dynamics will be systematically biased downward, potentially leading central banks to underestimate the true structural responsiveness of inflation to demand conditions. Competition policy and barriers to entry thus have macroeconomic consequences beyond standard allocative efficiency considerations.

Homothetic Single Aggregator (HSA): A class of homothetic demand systems in which the market share of each input variety depends solely on its own price normalized by a single price aggregator A_t, which serves as a sufficient statistic for all competitive pressure effects on firm pricing behavior including the markup rate and pass-through rate. Nests CES and Translog as special cases.

Marshall’s Second Law of Demand (as used in the paper): The condition that the price elasticity of demand zeta(z) is strictly increasing in the firm’s normalized price z. Under this condition, markup rates and pass-through rates vary endogenously with competitive pressure, and strategic complementarity in price setting arises.

Marshall’s Third Law of Demand (as used in the paper): The condition, defined by Matsuyama and Ushchev (2023b), that the rate of increase in the price elasticity is decreasing in z. This law determines how the pass-through rate responds to concentration changes and is the relevant condition for structural flattening under Calvo pricing.

Pass-through rate rho(z): The fraction of a cost change that a monopolistically competitive firm passes through to its price under flexible pricing, defined as rho(z) = [1 - dln(zeta/(zeta-1))/dln(z)]^(-1). Under CES, rho = 1 (complete pass-through); under the Second law, rho < 1 (incomplete pass-through); it declines with concentration under the Third law.

Endogenous cost-push shock: The direct effect of changes in the endogenous number of firms N_t on inflation in the NKPC, arising from strategic complementarity in price setting under HSA. This term is absent under CES (where the coefficient is zero) and generates an omitted variable bias in naive regressions of inflation on marginal cost.

Steady-state (structural) flattening: The reduction in the true structural slope of the NKPC caused by market concentration operating through lower price elasticity (Rotemberg channel) or lower pass-through rate (Calvo channel). This is the first of the paper’s two reasons for observed Phillips curve flattening.

Observational (omitted variable bias) flattening: The downward bias in empirically estimated NKPC slopes arising because naive regressions omit the endogenous cost-push shock term. The bias is negative and is amplified by greater market concentration under the Third law and/or Second law depending on the pricing mechanism.

Consumer durables and monetary policy according to HANK

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

Consumer durables account for a disproportionately large share of household expenditure fluctuations despite their small share of total private consumption. Two stylized facts motivate the paper: (1) durable expenditure is far more interest-rate sensitive than nondurable expenditure following monetary policy shocks, and (2) durable and nondurable expenditures comove positively and persistently—both reaching trough in the same quarter. Standard two-sector New Keynesian models struggle to generate this positive conditional comovement because asymmetric sectoral price rigidity induces large relative-price movements that push the two sectors in opposite directions. This paper asks what model features are necessary and sufficient to reproduce both the sectoral comovement pattern and the hump-shaped aggregate dynamics observed in the data, and how the answer changes across households sorted by liquid asset holdings.

Data and Methodology

Empirical identification. The authors employ a local projection instrumental variables (LP-IV) strategy using Romer-Romer monetary policy shocks updated by Wieland and Yang (2020), over the sample 1969:Q1–2007:Q3. Impulse response functions (IRFs) are normalized to a cumulative 100 basis-point increase in the Federal Funds Rate over five years. Household-level evidence is drawn from the Consumer Expenditure Survey (CEX) and the Survey of Consumer Finances (SCF); households are classified as liquidity-constrained if liquid assets are below $1,000.

Model. The authors develop a two-sector Heterogeneous Agent New Keynesian (HANK) model in which households maximize utility over nondurable consumption and a durable stock (Cobb-Douglas aggregation), face convex adjustment costs on durable purchases, and update expectations infrequently in the Mankiw-Reis sense (probability of not updating: Xi = 0.918 per period). The general equilibrium version features asymmetric Rotemberg price stickiness (Calvo probability 0.671 for nondurables, 0.797 for durables), nominal wage stickiness (Calvo 0.802), and a Taylor rule with inflation coefficient 1.105, output coefficient 1.440, and smoothing 0.988.

Main Findings and Quantitative Magnitudes

Sectoral magnitude gap. At trough (approximately 8 quarters after the shock), the durable expenditure response to monetary tightening is an order of magnitude larger than the nondurable response—a fact the calibrated HANK model is designed to match.
Positive comovement. Both durable and nondurable expenditures contract and reach trough in the same quarter, contradicting TANK models (Monacelli 2009) in which savers shift portfolios toward durables and generate negative comovement for that group.
Relative-price dynamics. The relative price of durables rises following monetary tightening (nondurables deflate more), but the rise is modest and cannot overturn the positive comovement result.
Role of the direct interest-rate effect. Across liquid-asset groups, the direct effect accounts for 73–87% of the cumulated durable expenditure response and 37–91% of the cumulated nondurable expenditure response. This direct channel—operating through intertemporal substitution—is quantitatively first-order for durables in a way it is not in standard single-sector HANK models where income effects dominate.
Role of sticky information. A full-information HANK variant produces a counterfactually high durable elasticity (35.24 times the baseline) and no hump-shaped dynamics. Infrequent information updating (Xi = 0.918) is essential to match the hump-shaped propagation of both sectoral and aggregate expenditures.
Income effects and fiscal policy. For a fiscal subsidy specifically targeting durable purchases, intertemporal substitution incentives generate a large shift toward durables and, without income effects, a counterfactual crowding-out of nondurable spending. Income effects are essential to protect nondurable spending, and the aggregate consumption effect of such a policy is at best modest—consistent with Mian and Sufi’s (2012) evidence on cash-for-clunkers.

Scope Conditions

All empirical results are conditional on the LP-IV sample 1969:Q1–2007:Q3 and Romer-Romer shocks as instrumented by Wieland-Yang. The household-level comovement result is established for both liquidity-constrained (liquid assets below $1,000) and unconstrained savers using CEX/SCF data. Model quantitative results are specific to the calibration targeting moments from Fagereng et al. (2021) marginal propensities and BEA depreciation data (delta = 0.054).

In depth

Q1. What is the core empirical puzzle the paper addresses, and why do standard models fail?

Standard two-sector New Keynesian models predict that asymmetric sectoral price stickiness generates large relative-price movements between durables and nondurables following a monetary shock. These relative-price shifts tend to produce negative conditional comovement—when durables contract, nondurables expand—contradicting the data. The authors document that both categories exhibit positive and persistent comovement, both reaching their trough at approximately 8 quarters, which standard models cannot replicate.

Q2. What are the key empirical facts established via LP-IV?

Using Romer-Romer shocks over 1969:Q1–2007:Q3, normalized to a cumulative 100bp Federal Funds Rate increase, the authors find: (1) aggregate expenditure follows a hump-shaped contraction with trough at roughly 8 quarters; (2) the durable expenditure response is an order of magnitude larger than the nondurable response at trough; (3) both categories reach their trough in the same quarter; and (4) the relative price of durables rises modestly after monetary tightening (nondurables deflate more), but not enough to reverse comovement.

Q3. How is the partial equilibrium model calibrated, and which moments does it target?

Key calibrated parameters include CRRA sigma = 2.640, Cobb-Douglas weight on nondurables theta = 0.607 (implying durable expenditure share 0.193), adjustment cost alpha = 8.299, information stickiness Xi = 0.918, depreciation rate delta = 0.054, steady-state real rate r = 0.03/4, discount factor beta = 0.915 (matching a 30% share of liquidity-constrained households with liquid assets-to-income ratio of 0.26), and borrowing wedge kappa = 0.05. Moments matched include quarterly MPC on nondurables (22.94%), quarterly MPX on durables (24.15%), interest-rate elasticity of durable expenditure (3.35, within the empirical range of 1.1–5.0), price elasticity of durable demand (29.59), and durable stock skewness relative to nondurable consumption (0.695, consistent with Bertola et al. 2005).

Q4. How does the paper decompose monetary policy transmission?

The paper decomposes transmission into three channels: (1) the direct effect of real interest rate changes, which operates through intertemporal substitution and accounts for the quantitatively largest share of the durable response; (2) the relative-price effect, which is modest and redistributive but cannot overturn positive comovement; and (3) pure income effects, which are key for persistence of the nondurable response but not for the sign of comovement.

Q5. What do counterfactual models reveal about the role of each model ingredient?

A sticky-information RANK produces positive comovement but the dynamics are front-loaded and less inertial than in the data. A sticky-information TANK delivers results similar to RANK—income effects do not qualitatively change the story. A full-information HANK produces a counterfactually high durable interest-rate elasticity (35.24 times the baseline) and no hump-shaped dynamics, demonstrating that sticky information is the ingredient generating realistic propagation, not heterogeneity per se.

Q6. What does the household-level evidence from CEX and SCF show about comovement across the wealth distribution?

Classifying households as liquidity-constrained if liquid assets are below $1,000, the LP-IV estimates show positive comovement between durables and nondurables for both constrained and unconstrained savers. This contradicts TANK models (Monacelli 2009), in which savers shift portfolios toward durables following a monetary shock, generating negative comovement for the saver group. After controlling for income and relative prices, the direct interest-rate effect operates uniformly across financial status groups.

Q7. How does the direct effect vary across liquid asset groups quantitatively?

Decomposing across four liquid asset groups (below $1k, $1k–$10k, $10k–$20k, above $20k), the direct effect accounts for 73–87% of the cumulated durable expenditure response and 37–91% of the cumulated nondurable expenditure response. Income effects are more important for nondurable spending prolongation among liquidity-constrained households, but the direct channel dominates durable expenditure for all groups.

Q8. How does the general equilibrium two-sector HANK model differ from the partial equilibrium setup?

The GE model adds asymmetric sectoral price stickiness (Calvo probabilities 0.671 for nondurables and 0.797 for durables), nominal wage stickiness (Calvo 0.802), a Taylor rule (inflation coefficient 1.105, output coefficient 1.440, smoothing 0.988), and fiscal lump-sum taxes responding to debt (coefficient 0.191). These features generate the relative-price dynamics observed in the data while preserving the positive comovement result.

Q9. What does the fiscal policy application reveal about the role of income effects?

A fiscal subsidy targeting durable purchases generates a much larger shift in the relative price of durables than monetary policy does. Without income effects, intertemporal substitution dominates and nondurable spending falls—a counterfactual result inconsistent with the data. With income effects present, nondurable spending is protected. The aggregate consumption effect of such a durable-targeted fiscal policy is at best modest, consistent with Mian and Sufi’s (2012) evidence from the cash-for-clunkers program.

Q10. What is the broader implication for the literature on HANK versus RANK transmission?

In standard single-sector HANK models, income effects (the indirect channel) typically dominate monetary transmission. The presence of consumer durables restores a quantitatively important role for the direct interest-rate channel, which operates through intertemporal substitution in durable purchases. This rebalances the direct-versus-indirect decomposition relative to the conventional HANK wisdom and shows that the durable goods sector is essential to understanding the full transmission mechanism.

Key Concepts

Sectoral comovement (conditional on monetary policy shocks) The empirical regularity that durable and nondurable expenditures both contract following monetary tightening and reach their respective troughs in the same quarter. In this paper, comovement is defined conditional on identified monetary policy shocks (LP-IV with Romer-Romer instruments), not unconditionally. Standard two-sector NK models predict negative conditional comovement due to relative-price effects; replicating positive comovement is the central discipline imposed on the model.

Direct effect (of real interest rate changes) The component of monetary transmission that operates through the intertemporal substitution incentive induced by changes in the real interest rate, holding income and relative prices fixed. Distinct from the income effect (indirect channel) and the relative-price effect. In this paper’s decomposition, the direct effect accounts for 73–87% of the cumulated durable expenditure response across liquid-asset groups.

Sticky information (Mankiw-Reis) Households update their information sets infrequently, with probability (1 - Xi) per period; Xi = 0.918 means only about 8.2% of households update each quarter. This mechanism is essential in the model for generating the hump-shaped, inertial impulse response dynamics observed in the data. Without it (full-information HANK), the durable elasticity is counterfactually large (35.24 times baseline) and dynamics are front-loaded.

MPX (Marginal Propensity to Expend on durables) Analogous to the MPC for nondurables, the MPX measures the additional durable expenditure flow induced by an income windfall. Calibrated to 24.15% quarterly, matching estimates from Fagereng et al. (2021). Distinct from the MPC because durable purchases represent investment in a stock, not immediate consumption flow.

Liquidity-constrained households Households with liquid assets below $1,000, identified in the CEX and SCF. In the model, the 30% share of such households is targeted by the discount factor (beta = 0.915) and the borrowing wedge (kappa = 0.05). The paper’s key finding is that positive comovement holds for both constrained and unconstrained households, contradicting TANK predictions.

HANK (Heterogeneous Agent New Keynesian model) A New Keynesian general equilibrium model in which households are heterogeneous in their liquid asset holdings (and thus face binding borrowing constraints), so that the distribution of assets matters for aggregate dynamics. Distinguished from RANK (Representative Agent NK) and TANK (Two-Agent NK, which approximates heterogeneity with one unconstrained and one hand-to-mouth agent). In this paper, HANK is extended to a two-sector setting with durables and nondurables.

Convex adjustment costs on durable purchases A cost of adjusting the durable stock that is convex in the size of the adjustment (calibrated parameter alpha = 8.299). This smooths the durable expenditure response and prevents counterfactually sharp jumps in durable purchases following interest rate changes, contributing to realistic propagation dynamics alongside sticky information.

Customer accumulation, returns to scale, and secular trends

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks how rising returns to scale in production contributed to three concurrent U.S. secular trends since 1980: declining business dynamism, rising markups, and growing firm expenditures on customer acquisition. The author constructs a firm dynamics model in the Hopenhayn (1992) tradition with endogenous entry and exit, heterogeneous markups, and customer accumulation grounded in directed search in the product market. Firms compete for customers through both prices and selling activities; larger firms gain a competitive edge when returns to scale rise because their marginal costs fall more than those of smaller firms—even though the technological shift is uniform across firms. This demand-based channel triggers winners-and-losers dynamics and the rise of superstar firms.

The empirical foundation rests on Compustat data for U.S. publicly traded firms (1977–2014) and Business Dynamics Statistics (BDS) for aggregate and sector-level dynamism measures. Production-function estimation using Ackerberg, Caves, and Frazer (2015) augmented with sales-share controls documents that aggregate returns to scale rose from approximately 1.0 in 1980 to approximately 1.05 by 2014—a within-sector increase, not a reallocation effect. Over the same period, the cost-weighted markup rose by 42%, the firm entry rate fell by 33%, the excess reallocation rate fell by 29%, and selling costs relative to production costs rose by 60%–90% depending on the measure used.

The model is calibrated to 1980 steady-state moments (firm life-cycle patterns, markups, entry and reallocation rates). A 5% increase in returns to scale—matching the empirical estimate—accounts for: a +15 percentage point rise in the average cost-weighted markup (vs. +42% in the data); a 33% decline in the entry rate (exactly matching the data); a 21% decline in the reallocation rate (vs. 29% in the data); and a 23% increase in selling costs relative to production costs (vs. 60%–90% in the data). The model also generates a 53% rise in the share of firms aged 11 years or older (vs. 50% in the data) and a 58% decline in the employment share of firms aged 5 years or younger (vs. 56% in the data), closely tracking the aging of the U.S. firm population. Firm-level responsiveness to productivity shocks declines by 0.08 in the model, versus about 0.01 in Compustat and 0.09 in Decker et al. (2020).

Sector-level panel regressions with sector fixed effects confirm the model’s directional predictions: within-sector increases in returns to scale are associated with lower entry rates (coefficient −2.89, significant at 1%), lower reallocation rates (−1.16, significant at 1%), higher markups (+3.15, significant at 1%), and higher selling costs relative to production costs (+1.85 for the advertising-based measure; +8.52 for adjusted SG&A).

A key scope condition is that the model yields a constrained-efficient allocation: directed search and full internalization of returns to scale imply decentralized equilibrium efficiency, making the paper a laboratory for assessing how far efficient firm responses to technological change can explain the secular trends without invoking market failures. The model fits the post-2000 transition dynamics better than the 1980s–1990s period, and explains a substantial but incomplete share of the trends, suggesting complementary—possibly inefficient—forces also contributed.

Q: What is the core mechanism through which rising returns to scale generate winners-and-losers dynamics?

A: The marginal cost of production under increasing returns to scale (alpha > 1) is MC(z,n) = l(n,z)^(1−alpha) × (1/alpha) × (W/e^z), which depends on firm size l(n,z). A uniform rise in alpha rotates the marginal cost schedule clockwise by firm size: larger firms see a proportionally larger cost reduction than smaller firms, even though the technological change is identical across all firms. Because firms compete for the same pool of customers, this asymmetric cost advantage allows large firms to offer lower prices while sustaining higher margins, attracting customers away from small firms. The result is a demand-based channel that generates winners-and-losers dynamics and increases market concentration.

Q: How does the model capture customer accumulation, and why is it central to the paper’s argument?

A: The model introduces directed search in the product market, where firms post advertisements and customers—including those already matched with a firm—choose which submarket to enter by trading off offered utility against matching probability. A constant-returns-to-scale matching function governs match creation; in submarket with tightness theta, customers match with probability m(theta) = theta(1+theta)^(−1) and firms attract customers with probability q(theta) = (1+theta)^(−1). The customer accumulation motive creates an investment-harvest trade-off: firms can either post high promised utility (low prices) to grow their customer base or extract surplus through high prices. Rising returns to scale amplify large firms’ ability to resolve this trade-off favorably, linking the technological change directly to markup dynamics, entry incentives, and selling expenditures.

Q: What is the directed search framework’s role in ensuring equilibrium uniqueness and efficiency?

A: The author introduces firm-side commitment contracts—specifying price, separation probability, and continuation utility contingent on productivity realizations—combined with directed search. Because search is directed on both sides and firms fully internalize returns to scale, the decentralized equilibrium is constrained-efficient. This delivers uniquely determined heterogeneous prices in equilibrium (solving the indeterminacy problem common in customer-market models) and establishes the paper’s efficient-mechanism benchmark: it tests how far profit-maximizing firm responses to technological change—without any market failure—can account for the secular trends.

Q: How are prices structured in the model, and what life-cycle pattern do they generate?

A: Each firm charges two distinct prices in each period: one to incumbent customers (the same for all incumbents, since they are identical conditional on being attached to the same firm) and one to newly acquired customers (which varies based on the promised utility in the submarket searched). Firms that are expanding their customer base offer greater promised utility and therefore charge lower prices to attract customers; firms harvesting their existing base charge higher prices. Because firms enter small and grow, this dynamic generates a price life cycle: young firms invest via low prices and mature firms harvest through higher prices, which the model reproduces as a rising markup pattern over the firm life cycle—an untargeted moment the model fits well.

Q: What does the calibration target and what untargeted moments does the model reproduce?

A: The model is calibrated to 1980 using: the number of employees of entrant firms (pinning entry customer base n_e), employees of age-5 firms (pinning convex cost chi_1), share of firms aged 11+ years (pinning chi_2), average firm size (operating cost f), entry rate (entry cost kappa), excess reallocation rate (exit shock delta), and average cost-weighted markup (linear cost c). Untargeted moments reproduced include: a sales-weighted markup of 0.28 (vs. 0.25 in De Loecker et al. 2020), endogenous customer turnover of approximately 9% (vs. 15% in Gourio and Rudanko 2014), and an elasticity of customer base shrinkage to price of 0.08 (within the 0.01–0.16 range from Paciello et al. 2019). The model also matches markup and selling-cost life-cycle patterns that are typically overlooked.

Q: How large is the quantitative contribution of the 5% rise in returns to scale to each secular trend?

A: Comparing the 1980 steady state (alpha = 1) to the 2014 steady state (alpha = 1.05): the average cost-weighted markup rises by 15% in the model versus 42% in the data; the entry rate declines by 33% in the model, exactly matching the data; the reallocation rate declines by 21% in the model versus 29% in the data; and selling costs relative to production costs rise by 23% in the model versus 60%–90% in the data. The model thus explains a substantial share of each trend while leaving a residual requiring additional mechanisms.

Q: How does the model explain the aging of U.S. firms, and how well does it match the data?

A: The winners-and-losers mechanism shifts activity toward larger, older firms, which mechanically ages the firm population. The model generates a 53% increase in the share of firms aged 11 years or older (vs. 50% in the data) and a 58% decline in the employment share of firms aged 5 years or younger (vs. 56% in the data). This aging arises because rising returns to scale increase the cost of customer acquisition, acting as a barrier to entry that disproportionately hurts new, small firms while allowing large incumbents to remain viable at lower productivity thresholds.

Q: What is the channel through which rising returns to scale reduce business dynamism specifically?

A: The unequal reduction in marginal costs intensifies competition for customers and raises customer acquisition costs. This operates through two simultaneous effects on the exit threshold: (i) lower marginal costs allow large firms to remain viable at lower productivity levels despite higher customer acquisition costs; and (ii) heightened competition forces smaller firms to require higher productivity to survive in a market that has become increasingly costly to operate in. Higher customer acquisition costs therefore function as an endogenous barrier to entry, reducing the entry rate and the reallocation of resources across firms.

Q: Does the model attribute the secular trends entirely to efficient firm behavior, and what does it conclude about residual explanations?

A: No. The model is explicitly designed as a constrained-efficient benchmark, and the paper finds that while rising returns to scale account for a substantial share of the trends—particularly in magnitude—the transition dynamics show a less accurate fit before the 2000s. The author concludes that complementary mechanisms, likely involving inefficiencies (such as market power from horizontal product differentiation or barriers to entry beyond those captured by the model), played a significant role in the earlier evolution of these trends and in the portion of the trends not explained by the efficient channel.

Q: What evidence supports the rising returns to scale finding, and what are its limitations?

A: Production-function estimation using the Ackerberg-Caves-Frazer method with sales-share controls on Compustat data shows returns to scale rising from approximately 1.0 in 1980 to approximately 1.05 by 2014, driven primarily by within-sector increases rather than reallocation toward high-returns sectors. A translog production function finds limited evidence of heterogeneous increases across firm sizes within Compustat. However, Compustat predominantly covers large publicly traded firms; smaller firms outside the sample may have experienced minimal or no increase in returns to scale. If technology adoption involves fixed costs, the aggregate impact could be larger than estimated, meaning the quantitative exercises likely represent a conservative lower bound.

Q: How does the paper relate to and extend the directed search literature in product markets?

A: The paper builds on Gourio and Rudanko (2014) and Roldan-Blanco and Gilbukh (2020), where customers are locked in once matched, by introducing labor-search tools from Schaal (2017) to allow: (i) incumbent customer switching between firms at rates of 10%–25% annually (Gourio and Rudanko 2014), and (ii) a non-zero price sensitivity of incumbent customers (Paciello et al. 2019). It also allows firms to invest in demand through selling expenditures, which prior directed search models in product markets typically abstracted from, making it possible to study how technological changes affect customer reallocation and firms’ cost structures jointly.

Customer capital: The stock of customers a firm has accumulated through prior selling and pricing decisions; treated as a state variable that firms invest in (by offering low prices and spending on advertisements) or harvest from (by charging high markups), with a customer turnover rate estimated at 10%–25% annually in the literature.

Directed search in the product market: A market structure in which both firms and customers choose which submarket (indexed by the promised utility level) to enter, trading off match probability against terms; delivers constrained-efficient equilibrium and uniquely determined heterogeneous prices.

Investment-harvest trade-off: The firm’s dynamic choice between offering high promised utility (low prices, low current markups) to grow the customer base versus extracting surplus through high prices from an existing customer base; shaped by the firm’s current size, productivity, and the cost structure implied by returns to scale.

Returns to scale (alpha): The curvature of the production function y = e^z × l^alpha; equals 1.0 under constant returns and approximately 1.05 by 2014 in the empirical estimates; the paper’s central technological change parameter, whose rise disproportionately reduces marginal costs for larger firms.

Winners-and-losers dynamics: The reallocation of customers and market share from small to large firms triggered by the asymmetric cost advantage large firms obtain when returns to scale rise; the demand-based channel through which superstar firms emerge.

Cost-weighted markup: The average markup aggregated using each firm’s costs as weights, as opposed to sales-weighted markup; the primary measure of market power used in the paper, rising by 42% in the data between 1980 and 2014.

Constrained-efficient allocation: An equilibrium outcome in which, given the frictions present (search-and-matching in the product market), no social planner operating under the same constraints could improve welfare; the paper uses this as a benchmark to assess how far efficient firm responses explain secular trends without invoking market failures.

Selling costs relative to production costs: The ratio of customer acquisition expenditures (advertising or adjusted SG&A) to cost of goods sold; rose by 60%–90% in the data between 1980 and 2014 and by 23% in the model’s steady-state comparison.

Disincentive effects of unemployment insurance benefits

Mon, 01 Jan 0001 00:00:00 +0000

This paper isolates the disincentive effects of pandemic unemployment insurance (UI) benefits on employment recovery, separating them from the simultaneously operating stimulative (demand) effects that previous studies conflate. The authors study the largest UI expansion in U.S. history — the CARES Act of March 2020 — which introduced three simultaneous provisions: a $600 weekly income supplement (FPUC) through end of July 2020, a 13-week extension of maximum benefit duration (PEUC), and expanded eligibility to workers previously ineligible for UI (PUA), together raising the median replacement rate to 145% and more than doubling the number of UI recipients.

The empirical strategy uses high-frequency establishment-level data from Homebase (HB), a scheduling and payroll provider covering approximately 140,000 small U.S. businesses — predominantly restaurants and retailers — matched to Yelp price-tier data and Safegraph foot-traffic and spending data. The final estimation sample is 4,595 businesses within 1,195 local-industry cells, observed at weekly frequency from January 2019 to December 2020.

The identification rests on comparing employment recovery of low-wage versus high-wage businesses within the same narrow local labor market (four-digit zip code), industry (two-digit NAICS), and price tier. Because neighboring businesses largely share the local demand stimulus from UI, differencing within local-industry cells removes common demand effects. The key variation is the expiration of the $600 supplement, which differentially compresses the replacement-rate gap between low- and high-wage businesses depending on local average wages — labor markets where the gap falls more sharply are the treated group.

The main empirical finding is that a 100 percentage point decline in the replacement rate gap is associated with a 5.7 percentage point rise in low-wage business employment recovery relative to high-wage business employment recovery at 12 weeks after the $600 expiration. For the average labor market, the expiration of the $600 supplement decreased the replacement rate gap by 46 percentage points, implying a 2.6 percentage point closing of the low-versus-high-wage employment gap within 12 weeks. Importantly, hours per employee and hourly wages grew faster in low-wage businesses over the same period, consistent with a labor supply rather than a demand mechanism. When the comparison is conducted at the U.S. state level rather than within local-industry cells — as in Finamor and Scott (2021) — the effect disappears and reverses sign, illustrating how local demand effects obscure disincentive effects at broader geographic aggregations.

To quantify the aggregate employment impact, the authors build and calibrate a McCall-style labor search model with heterogeneous firm wages, a UI-eligible and non-UI unemployed pool, and equilibrium reservation wages. The model is extended to include a probability (calibrated at 16.5%) that workers lose UI eligibility upon refusing a job offer, which reconciles the model with the empirical estimates; without this feature the baseline model substantially overstates the differential employment effect of the $600 expiration.

The full model-implied aggregate employment loss from all CARES Act UI provisions combined is 3.4 percentage points on average between April and December 2020, representing approximately 20% of the average employment shortfall in the Leisure and Hospitality sector over that period. When each provision is implemented in isolation, the effects are modest ($600 supplement: 0.2 pp; extended duration: 0.2 pp; expanded eligibility: 1.0 pp), but their interaction generates the large combined effect. Expanded eligibility is identified as the most disruptive provision, particularly for low-wage businesses, because it depletes the pool of non-UI unemployed who are the primary source of hires for these firms. The unemployment duration elasticities implied by the model are modest and in line with the low-to-middle range of pre-pandemic estimates.

The paper’s scope is restricted to the disincentive channel and deliberately excludes the stimulative effects of UI; it studies small, in-person service sector businesses and the April–December 2020 recovery period only.

Q: What is the core identification challenge this paper addresses? A: Prior empirical studies find only modest net effects of pandemic UI on employment, but it is unclear whether this reflects small disincentive effects or the near-cancellation of two opposing forces — UI suppressing labor supply while simultaneously stimulating local consumer demand. Identifying the disincentive effect alone requires a design that neutralizes the demand channel. The authors accomplish this by comparing low-wage and high-wage businesses within the same narrow local market, industry, and price tier, so that common local demand shifts from UI are differenced out.

Q: What data does the empirical analysis use, and how is the sample constructed? A: The primary data source is Homebase, covering approximately 140,000 small U.S. businesses with daily employment, hourly wages, and hours worked. The estimation sample is restricted to 4,595 businesses present throughout 2019, matched to Yelp price-tier classification and Safegraph weekly foot traffic and credit-card spending. Businesses are grouped into 1,195 local-industry cells defined by four-digit zip code, two-digit NAICS industry, and Yelp price tier (inexpensive vs. expensive). Within each cell, businesses are classified as low-wage or high-wage, with high-wage businesses paying on average $1.80 per hour more — about 8% above the average hourly wage of $10.90.

Q: How is the replacement rate defined in the empirical framework? A: The business-specific replacement rate is the ratio of average UI receipts (state benefit plus the pandemic supplement, converted to hourly units) to the pre-pandemic average hourly wage of that business. Because the supplement is uniform across workers, businesses with lower pre-pandemic wages face higher replacement rates; the replacement rate gap between low- and high-wage businesses within a local market is therefore a function of both state benefit levels and the local wage dispersion.

Q: What does the event-study analysis around the $600 expiration show? A: The event study exploits cross-labor-market variation in how much the replacement rate gap between low- and high-wage businesses declined when the $600 FPUC supplement expired at end of July 2020. Labor markets with a larger decline in the gap see faster relative recovery in low-wage business employment after expiration. A 100 percentage point decline in the replacement rate gap is associated with a 5.7 percentage point rise in the low-versus-high-wage employment recovery gap at 12 weeks post-expiration. For the average labor market, the $600 expiration reduced the replacement rate gap by 46 percentage points, implying a 2.6 percentage point narrowing of the employment recovery gap.

Q: Why does the estimated effect disappear when broader geographic aggregations are used? A: When businesses are compared within U.S. state borders rather than within local-industry cells, the estimated coefficient on the replacement rate gap turns positive and statistically insignificant. This occurs because at the state level, low-wage areas benefit disproportionately from the purchasing power increase that generous UI provides to local unemployed workers, so demand effects swamp and reverse the supply-side disincentive. This finding explains why Finamor and Scott (2021), using Homebase data with state fixed effects, find no negative association between replacement rates and labor market re-entry.

Q: What evidence supports a labor supply rather than demand interpretation of the differential recovery? A: During the period of the $600 supplement, hours per employee and hourly wages grew faster in low-wage businesses than in high-wage businesses, even as low-wage businesses lagged in employment levels. If the differential recovery reflected demand deficiencies at low-wage businesses, hours per employee and wages should have grown faster at high-wage businesses instead. The observed pattern is consistent with labor supply shortfalls at low-wage firms.

Q: What is the structure of the quantitative labor search model? A: The model features a unit measure of workers and a fixed measure of firms, each posting a constant idiosyncratic wage drawn from an exogenous distribution. Unemployed workers receive job offers at a rate determined by labor market tightness and accept offers above their reservation wage. Reservation wages are equilibrium objects because UI benefits depend on the worker’s previous wage. The unemployed are split into UI-eligible and non-UI pools; the non-UI pool accepts jobs from lower in the wage distribution and is the primary supply source for low-wage firms. The model is calibrated to pre-pandemic U.S. service sector averages, with a pre-pandemic UI replacement rate of 0.51, a UI recipiency probability of 14%, and a non-UI replacement rate of 0.15.

Q: Why does the baseline model overstate the empirical effect, and how is this reconciled? A: The baseline model dramatically overstates the differential employment impact of the $600 expiration because the CARES Act’s expanded eligibility (modeled as a rise in the recipiency probability from 14% to 70%) nearly empties the non-UI unemployed pool, which is the dominant labor supply source for low-wage firms. In the data, the share of unemployed receiving UI nearly tripled for in-person leisure and hospitality workers, but not to the degree that the model’s implied employment collapse would require. The model is reconciled by introducing a 16.5% probability that a worker loses UI eligibility upon refusing a suitable job offer — consistent with UI law — which reduces the effective outside option and raises acceptance rates for low-wage firms.

Q: What are the aggregate employment losses implied by the model? A: When all three CARES Act provisions are implemented jointly, the model estimates that the disincentive effects held back aggregate employment recovery by 3.4 percentage points on average between April and December 2020 — approximately 20% of the average employment shortfall in the Leisure and Hospitality sector. Implemented in isolation, each provision generates only modest losses: the $600 supplement alone accounts for 0.2 percentage points, extended duration for 0.2 percentage points, and expanded eligibility for 1.0 percentage points. The large combined effect arises from the interaction of all three provisions, not from any single one.

Q: What are the conditional (interaction) effects of each provision when the other two are in place? A: Conditional on the other two provisions being active, the income supplement holds back employment recovery by 1.6 percentage points, the extended duration by 1.5 percentage points, and expanded eligibility by 2.9 percentage points. This interaction effect is the central quantitative finding: individually modest provisions combine to produce effects far exceeding their sum when implemented simultaneously.

Q: What are the implied unemployment duration elasticities, and how do they compare to the literature? A: The $600 supplement alone raises average unemployment duration by 8% against a 343% rise in the replacement rate, implying an elasticity of 0.02. Extended duration alone raises unemployment duration by 6% against a 150% increase in potential benefit duration, implying an elasticity of 0.03. Expanded eligibility alone raises unemployment duration by 19%, implying an elasticity of 0.04. When each provision is activated on top of the other two, the implied elasticities rise substantially: 0.24 for the $600 supplement, 0.43 for extended duration, and 0.28 for expanded eligibility. These are in the low-to-middle range of pre-pandemic estimates (Katz and Meyer, 1990: 0.3–0.5; Johnston and Mas, 2018: 0.4–0.8; Rothstein, 2011: 0.06; Farber and Valletta, 2015: 0.15).

Q: What is the role of expanded eligibility specifically? A: Expanded eligibility is identified as the most disruptive CARES Act provision, accounting for 1.0 percentage points of employment loss alone and 2.9 percentage points conditional on the other provisions. Mechanically, expanded eligibility converts non-UI unemployed workers into UI-eligible workers, draining the pool of workers willing to accept low-wage job offers. Because low-wage firms depend disproportionately on the non-UI pool for hiring, this provision disproportionately depresses their employment. Using CPS data, the authors document that the share of unemployed workers receiving UI in the in-person leisure and hospitality sector nearly tripled in 2020 relative to the pre-pandemic period.

Q: What are the scope conditions and limitations of the analysis? A: The empirical analysis is restricted to small, in-person service sector businesses (restaurants and retailers) in the Homebase sample, which may not be representative of the broader labor market. The quantitative model is explicitly focused on disincentive effects only and does not capture the stimulative or demand effects of UI. The model also abstracts from re-opening restrictions and other pandemic-specific confounders. The analysis covers April to December 2020; the 2021 pandemic UI extensions are not studied. The job-refusal probability (chi = 16.5%) is a reduced-form calibration target rather than a structurally identified parameter.

Replacement rate gap: The difference in business-specific UI replacement rates between low-wage and high-wage businesses within the same local labor market; defined as UI benefits (state benefit plus supplement) divided by the business’s pre-pandemic average hourly wage. Larger gaps indicate greater relative disincentive for workers to accept jobs at low-wage firms.

Disincentive effect: The negative impact of higher UI replacement rates on workers’ willingness to accept job offers and thus on business employment recovery, isolated from the simultaneous stimulative demand effect of UI spending.

Non-UI unemployed pool: Workers who are ineligible for or have exhausted UI benefits and therefore receive only social benefits at a lower replacement rate (calibrated at 0.15 in the model). This group has a lower reservation wage and constitutes the primary labor supply source for low-wage firms.

Local-industry cell: The paper’s unit of comparison — businesses sharing the same four-digit zip code (covering on average four neighboring zip codes), two-digit NAICS industry, and Yelp price tier. Within-cell differencing is the mechanism that removes common local demand effects.

Benefit recipiency probability: The probability that a newly separated worker enters the UI-eligible unemployed pool, combining UI eligibility and takeup. Pre-pandemic this is calibrated at 14%; under the CARES Act it rises to 70%, targeting the observed near-tripling of UI recipients in the CPS data.

Job-refusal eligibility loss: A probability (calibrated at 16.5%) that a UI-eligible worker who rejects a job offer loses UI status and transitions to the non-UI pool. Motivated by UI law prohibiting refusal of suitable work; reduces the effective outside option and reconciles the model’s predicted employment gap with the empirical estimate.

Equilibrium residual wage dispersion: The wage dispersion observed in equilibrium conditional on worker observables. The model generates realistic dispersion by calibrating the non-UI replacement rate to match the lower half of the wage distribution and the firm wage offer variance to match the upper half; the presence of the non-UI state substantially increases residual dispersion relative to standard search models.

Distorted prices and targeted taxes in the New Keynesian Network model

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks how governments should optimally adjust sector-specific taxes in response to sectoral shocks when monetary policy cannot be tailored to individual sectors. The authors work within a variant of Rubbo’s (2023) New Keynesian Network (NKN) model, augmented to include time-varying sectoral sales taxes and production subsidies. The model features N sectors connected through input-output linkages, with Calvo-type price rigidity that is heterogeneous across sectors, and encompasses both sectoral productivity (supply) shocks and demand shocks.

The central finding, stated as Proposition 1, is that the first-best tax policy requires exactly 2N instruments—one sales tax and one production subsidy per sector—not just instruments in the shocked sector. The mechanism turns on a twofold distortion created by sticky prices. Because only a fraction of firms adjust prices at any time, relative prices are distorted both within sectors (price dispersion among firms) and across sectors (misalignment of relative prices). The production subsidy offsets the effect of shocks on marginal costs, incentivizing price-adjusting firms to leave seller prices unchanged and thereby eliminating within-sector dispersion. The sales tax—which applies to both household purchases and intermediate goods trade—steers demand across sectors so that market prices move as if fully flexible, closing sectoral output gaps even as seller prices remain constant. The optimal sales tax moves exactly one-for-one with the vector of natural prices. Crucially, budget neutrality holds to first order: the sales tax revenues fund the production subsidies.

The strength of each instrument’s response depends on network proximity rather than price rigidity. For supply shocks, adjustment propagates downstream (governed by the Leontief inverse), so sectors that intensively use inputs from the shocked sector require larger responses. For demand shocks, adjustment propagates upstream first and then back downstream, so upstream suppliers to the shocked sector face the largest responses.

Because the first-best policy requires observing sectoral shocks directly, the authors propose a simple 2N rule (Proposition 2) that responds only to observable sectoral seller-price inflation, with rule strength parameter ϕ_i per sector. As ϕ_i → ∞ the simple rule converges to the first-best. Crucially, the rule can be implemented by observing inflation only in the shocked sector and adjusting taxes and subsidies in other sectors proportionally to their input-output distance from that sector.

The quantitative assessment calibrates the model to the U.S. economy using BEA 2017 input-output accounts with N = 373 sectors at the 6-digit classification. Sectoral price flexibility is drawn from Antonova (2025), ranging from 0.052 to 0.989 with a median of 0.277 (implying a median price duration of roughly 4.3 months). Shocks follow AR(1) processes with persistence ρ = 0.97. Supply shocks hit 10 energy-related sectors (roughly 10% of total sales); demand shocks hit 22 service-related sectors (roughly 7% of total sales). The key quantitative finding is that the simple 2N policy—both subsidy and tax together—delivers substantially greater welfare improvement than a subsidy-only policy (N instruments), particularly for supply shocks. When the subsidy is not accompanied by the corresponding sales tax, welfare gains are much smaller.

The paper extends to an open economy with import-price shocks that act simultaneously as supply and demand shocks. Applied to the 2022 Ukraine war energy crisis: a 24% world-energy-price increase (IMF Global Energy Price index, 2022M1–2022M4) is used, with high-dependence Europe (energy import share γ_EU = 0.63, substitution elasticity η_EU = 1) contrasted against low-dependence U.S. (γ_US = 0.17, η_US = 4). In Europe, adverse supply effects dominate so the domestic energy sector contracts; in the U.S., demand substitution effects dominate so domestic energy expands. Simple 2N rules correlate 0.89 with the optimal policy across sectors for Europe and 0.94 for the U.S. A notable normative implication: the optimal policy raises sales taxes on energy to discourage consumption, in contrast to the actual European policy of subsidizing energy consumption during the 2022 crisis.

Q: Why can monetary policy not achieve the first-best allocation in the NKN model?

A: Monetary policy sets a single nominal interest rate that applies uniformly across all sectors, but sectoral shocks generate heterogeneous natural rates. Even if monetary policy stabilizes aggregate output, it cannot simultaneously close all sectoral output gaps and eliminate within-sector price dispersion. Rubbo (2023) shows that optimal monetary policy improves welfare but leaves a significant welfare loss remaining.

Q: What is the core tradeoff in each sector that motivates the 2N result?

A: With Calvo-type staggered pricing, adjusting a sector’s relative price to close its output gap creates price dispersion within the sector because not all firms adjust simultaneously; but holding seller prices constant to avoid dispersion leaves output gaps open due to the absence of relative price adjustment. Two instruments—production subsidy and sales tax—are required to address both sides of this distortion simultaneously, in keeping with the Tinbergen principle.

Q: How exactly do the production subsidy and sales tax each work under the optimal policy?

A: The production subsidy is paid to producers and affects the optimal seller price for a given marginal cost, incentivizing firms that can adjust prices to leave them unchanged. The sales tax is levied on buyers (households and downstream firms) and, because it is applied to both household consumption and intermediate goods trade, it steers demand across sectors to replicate the efficient allocation of expenditure. Under the optimal policy, seller prices are fully stabilized (ps_t = 0) while buyer (market) prices move as pt = τs_t = pn_t, mimicking flexible-price outcomes.

Q: What determines which sectors receive larger optimal tax and subsidy responses?

A: For supply (productivity) shocks, responses are governed by the matrix L̄ = XL, where L is the Leontief inverse measuring downstream proximity; sectors that are more intensive downstream users of the shocked sector require larger responses. For demand shocks, the relevant matrix measures upstream proximity, so sectors that supply inputs to the shocked sector face stronger responses. Critically, the level of the policy response is independent of sector-specific price rigidity; only the network structure matters.

Q: Is the optimal 2N policy budget-neutral, and why only approximately?

A: Budget neutrality holds to first order around the zero-profit steady state. The production subsidy applies to costs while the sales tax applies to sales; at the steady state these coincide, so the subsidy is exactly funded by the tax revenue. The approximation breaks down away from the zero-profit steady state because costs and sales diverge.

Q: What is the simple 2N rule and how does it relate to the first-best?

A: The simple rule sets sp_t = Iϕ · πs_t and τs_t = sp_t, where Iϕ = diag{ϕ_i} is a diagonal matrix of response coefficients for each sector’s seller-price inflation. As ϕ_i → ∞ for all i, the allocation converges to first-best; larger ϕ_i produces a stronger commitment to stabilize sectoral inflation, resulting in muted inflation rather than large tax and subsidy levels. In practice, the rule can be implemented by observing inflation only in the shocked sector and scaling responses in other sectors by their input-output distance from that sector.

Q: What does the three-sector example (Energy, Manufacturing, Services) illustrate about supply vs. demand shocks?

A: Under an adverse energy productivity shock, the optimal policy subsidizes Energy and Manufacturing (proportional to energy use in manufacturing) but not Services, since Services are not energy-intensive and thus not closely connected downstream. Under a positive manufacturing demand shock, the optimal policy subsidizes both Manufacturing and upstream Energy equally, reflecting that demand shocks propagate upstream first.

Q: What does the calibrated quantitative exercise show about the welfare gains from using both instruments versus one?

A: For both supply and demand shock scenarios, the simple 2N policy (subsidy plus tax) delivers substantially greater welfare improvement than using only monetary policy. When the subsidy is not accompanied by the corresponding sales tax, welfare gains are much smaller, confirming that both instruments together—not subsidies alone—are essential. This is identified as a key quantitative finding of the paper.

Q: How robust are results to decreasing returns to scale in production?

A: Under decreasing returns to scale, the optimal policy response is highly similar to the baseline: correlations between the two are 0.98 for supply shocks and 0.99 for demand shocks across sectors. The simple 2N rule continues to deliver significant welfare improvements. One difference is that demand shocks generate relatively higher welfare losses under decreasing returns, while productivity shocks lead to lower losses.

Q: How does the open-economy extension change the analysis for import-price shocks?

A: Import-price shocks enter the model as both supply shocks (raising input costs) and demand shocks (shifting expenditures toward domestic substitutes), so they require a policy response that accounts for both propagation channels simultaneously. The optimal open-economy policy is formally isomorphic to the closed-economy counterpart but with redefined upstream and downstream matrices and shock vectors. The relative importance of the supply versus demand channel depends on the economy’s import dependence and substitution elasticity.

Q: How does the 2022 energy crisis illustrate the difference between the optimal policy and actual European policy?

A: Using a 24% world-energy-price increase (IMF Global Energy Price index, 2022M1–2022M4), the model implies that with high European energy dependence (γ_EU = 0.63, η_EU = 1), adverse supply effects dominate and the optimal policy raises sales taxes on energy to discourage consumption and subsidizes domestic energy users proportional to downstream proximity. Actual European policy partly subsidized energy consumption, which the model identifies as welfare-reducing relative to the optimal response. For the low-dependence U.S. (γ_US = 0.17, η_US = 4), demand substitution toward domestic energy dominates, requiring additional subsidies to domestic energy producers.

Q: How does this paper relate to the Diamond-Mirrlees result on intermediate good taxation?

A: Diamond-Mirrlees (1971) recommends against taxing intermediate goods in an otherwise efficient economy to avoid introducing additional distortions. This paper considers an economy already subject to pricing frictions (Calvo staggered pricing), and shows that taxing intermediate goods through the sales tax—which applies to intermediate goods trade—is part of the optimal policy precisely because it corrects the pre-existing distortions. The paper thus does not contradict Diamond-Mirrlees but operates in a different setting where frictions are already present.

New Keynesian Network (NKN) model: A multi-sector general equilibrium framework with N sectors connected through input-output linkages, Calvo-type staggered price setting that is heterogeneous across sectors, and monopolistically competitive firms; provides the canonical system of sectoral IS curves and Phillips curves used in this paper.

2N policy: The paper’s central result that the first-best tax policy requires exactly two instruments per sector—one production subsidy and one sales tax—for a total of 2N instruments; characterized in Proposition 1 and named for this instrument count.

Production subsidy (sp_t,i): A sector-specific transfer paid to producers that affects the optimal seller price for a given marginal cost; under the optimal policy it offsets the effect of shocks on marginal costs, incentivizing price-adjusting firms to leave seller prices unchanged and thereby eliminating within-sector price dispersion.

Sales tax (τs_t,i): A sector-specific tax levied on buyers—both households and downstream firms purchasing intermediate goods—such that the buyer (market) price equals (1 + τs_t,i) times the seller price; under the optimal policy it replicates the efficient allocation of expenditure across sectors even when seller prices are fully stabilized.

Downstream proximity (Leontief inverse L̄ = XL): A measure of the total direct and indirect use of a sector’s output by other sectors, governing the propagation and optimal policy response to supply (productivity) shocks; the ij-th element of L̄ captures how strongly a shock in sector j affects policy in sector i through downstream input-output linkages.

Upstream proximity: A measure of how closely a sector supplies inputs to another sector, governing the propagation of demand shocks; demand shocks propagate first upstream (to input suppliers) before feeding back downstream.

Budget neutrality: The property that the optimal 2N policy is self-financing to first order—sales tax revenues exactly fund the production subsidies around the zero-profit steady state—so the fiscal intervention does not require net government expenditure.

Simple 2N rule: A practically implementable approximation to the first-best policy that sets subsidies and taxes proportional to observed sectoral seller-price inflation with response coefficients ϕ_i; converges to the first-best as ϕ_i → ∞ and can be implemented using only the inflation rate of the shocked sector plus network-distance weights from the input-output table.

Evaluating macroeconomic outcomes under asymmetries: Expectations matter

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper investigates whether and how assumptions about household and firm expectations alter the macroeconomic implications of asymmetries commonly embedded in macroeconomic models. Specifically, it asks: when a model features a nonlinearity — such as an asymmetric monetary policy rule or a nonlinear Phillips curve — do the longer-run average outcomes and the distributional properties of inflation and unemployment depend on whether agents have rational expectations (RE, accounting for the possibility of future shocks) versus perfect foresight (PF, not anticipating future shocks)?

Methodology

The paper works within a standard three-equation New Keynesian model comprising an IS curve (linking the unemployment gap to the policy rate and the natural rate of interest via Okun’s law with coefficient c ≈ 2), a forward-looking Phillips curve, and a monetary policy rule. The model is parameterized at a quarterly frequency with β = 0.99, κ = 0.01, φπ = 1.5, φu = −0.25, shock persistence ρ_rn = 0.9, and shock standard deviation σ_rn = 0.0025 (calibrated to match a 1-percentage-point standard deviation of the unemployment gap under the symmetric baseline rule).

The key methodological distinction is the specification of the expectations operator. Under RE, agents use the true stochastic transition matrix for the natural rate (approximated via the Rouwenhorst method with 105 grid points). Under PF, agents instead use a transition matrix that always places probability one on the steady-state value of the natural rate next period — i.e., they do not anticipate future shocks. The model is solved globally with a discrete state space projection (parameterized expectations) method, applied identically to RE and PF cases. The authors first derive analytical results in a simplified three-state environment and then present numerical results from 3,000 simulations of 1,000 periods each.

Two types of asymmetry serve as case studies: (i) an asymmetric monetary policy rule — the “Shortfalls rule” — under which the central bank does not tighten in response to a tight labor market (negative unemployment gap), in the spirit of the FOMC’s 2020 framework update; and (ii) a nonlinear (kinked) Phillips curve that steepens by a factor of three when the labor market is tight (unemployment gap < 0), consistent with empirical evidence in Smith, Timmermann, and Wright (2025).

Main Findings

The core finding is that the sign and magnitude of longer-run average outcomes under asymmetric macroeconomic environments can differ substantially — and can even reverse — depending on whether agents have rational expectations or perfect foresight.

For the Shortfalls rule, under PF the model implies a longer-run tradeoff: average unemployment gap is −0.32 percentage points and average inflation gap is +0.25 annualized percentage points relative to the symmetric Deviations rule. PF thus suggests policymakers can lower average unemployment at modest inflationary cost. Under RE, however, this apparent tradeoff disappears entirely: the average unemployment gap is essentially zero (−0.05 percentage points) while average inflation is elevated by approximately 1.02 annualized percentage points. The gap in average inflation outcomes between RE and PF thus exceeds one percentage point, and the labor market benefit implied by PF is absent under RE.

For the nonlinear Phillips curve (under a symmetric deviations rule with φu = 0), the results again diverge across expectations assumptions, and the direction of the effects reverses. Under PF, the kinked Phillips curve implies average inflation of +0.41 annualized percentage points and a near-zero unemployment gap (+0.30 percentage points). Under RE, the average inflation gap is essentially zero while the average unemployment gap rises to +0.63 percentage points — the opposite directional pattern from PF.

The mechanism driving the RE–PF divergence is the interaction between forward-looking price-setters and an inflation-stabilizing central bank. Under RE, anticipated future episodes in which the asymmetry may bind (e.g., the Shortfalls rule providing accommodation, or the Phillips curve steepening) cause firms to set higher prices today. The central bank responds to the resulting pickup in inflation expectations with tighter policy, generating a persistent contractionary offset. This channel is absent under PF because agents expect no future shocks.

Robustness

The main conclusions are robust across three extensions: (i) Bounded rationality (following Gabaix 2020, with m_br = 0.97): outcomes move toward the PF case, confirming that what matters is the degree to which agents internalize the probability of future shocks; (ii) Cost-push shocks instead of natural rate shocks: the RE–PF divergence under a Shortfalls rule is broadly similar in direction and magnitude to the baseline; (iii) Alternative shock specifications: the qualitative conclusions are maintained.

Crucially, under the symmetric Deviations rule the RE and PF solutions are identical in all cases, confirming that the divergence is specific to models with macroeconomic asymmetries, not an artifact of the solution method.

In depth

Q1. What is the central methodological claim about perfect foresight solutions in asymmetric models?

The paper argues that in macroeconomic models with asymmetries or nonlinearities, perfect foresight solutions — in which agents do not account for the possibility that future shocks may occur — can yield longer-run average outcomes and distributions that differ from their rational expectations counterparts in magnitude and potentially in sign. The paper is explicit that this is not a critique of PF methods per se, as PF is often necessary for estimating larger models; rather, the point is that researchers should check the robustness of conclusions about longer-run averages using simplified models solvable under both approaches.

Q2. How is the difference between RE and PF operationalized in the model?

The sole technical distinction lies in the specification of the conditional expectations operator Et. Under RE, this operator uses the true stochastic Markov transition matrix for the natural rate (P^RE), which assigns positive probability to all feasible future states. Under PF, agents use a degenerate transition matrix (P^PF) that assigns probability one to the mean value of the natural rate next period regardless of the current state — effectively, agents expect no future innovations. The same global solution method (discrete state space projection with 105 Rouwenhorst grid points) is applied to both, so differences in equilibrium outcomes are entirely attributable to the expectation specification.

Q3. What are the analytical results for the Shortfalls rule in the simplified three-state model?

In the simplified environment with the natural rate taking three equiprobable values (low, steady-state, high) and no persistence, the analytical solution shows that under PF the average unemployment gap is −Δ/(1 + φπκ) < 0 and the average inflation gap is Δκ/(1 + φπκ) > 0, where Δ parameterizes the degree of additional accommodation in the high-demand state. Under RE, the average unemployment gap is exactly zero and the average inflation gap is Δ/(φπ − 1) > 0. The inflation gap under RE exceeds that under PF by Δ(1 + κ)/[(φπ − 1)(1 + φπκ)] > 0, and the unemployment gap under RE exceeds that under PF by Δ/(1 + φπκ) > 0. Thus, PF spuriously implies an exploitable long-run tradeoff that vanishes under RE.

Q4. What are the analytical results for the nonlinear Phillips curve in the simplified model, and how do the directions of the effects compare to the Shortfalls rule case?

Under PF with a nonlinear (kinked) Phillips curve, the average inflation gap is positive (= Δpc > 0) while the average unemployment gap is zero. Under RE, the signs reverse: the average unemployment gap is positive (= Δpc/κ > 0) and the average inflation gap is zero. The difference is ūRE − ūPF = Δpc/κ > 0 and π̄RE − π̄PF = −Δpc < 0. This sign reversal relative to the Shortfalls rule case illustrates that the directional error introduced by PF is not uniform but depends on the specific asymmetry — the key feature is always the absence, under PF, of the forward-looking price-setting channel interacting with monetary policy.

Q5. What is the quantitative magnitude of the RE–PF divergence in the numerical model for the Shortfalls rule?

In the fully parameterized numerical model (Table 2), under a Shortfalls rule the average inflation gap is 1.02 annualized percentage points under RE versus 0.25 annualized percentage points under PF — a difference of roughly 0.77 percentage points. The average unemployment gap is −0.05 percentage points under RE versus −0.32 percentage points under PF — a difference of 0.27 percentage points. The paper also notes that model-implied averages for inflation and nominal interest rates “under perfect foresight can easily differ by at least one percentage point from their rational expectations counterparts.”

Q6. How do the simulated distributions differ between RE and PF under a Shortfalls rule?

Under PF, the simulated distributions of unemployment and inflation gaps exhibit a pronounced kink near the steady-state value (zero gap), reflecting the asymmetric treatment of expansions and contractions. Under RE, the distributions are substantially more symmetric, shifted to the right for inflation (mean of 1.0 versus 0.25 under PF). Standard deviations of the unemployment and inflation gaps are somewhat larger under PF (1.42 and 1.10, respectively) than under RE (1.33 and 1.03), because under RE the contractionary force from inflation expectations moderates the amplitude of fluctuations. These distributional differences have direct implications for how policymakers interpret the risks associated with state-contingent policies.

Q7. What is the role of the forward-looking pricing–central bank interaction in generating RE–PF differences?

The key mechanism is as follows: under RE, the possibility that the asymmetry may bind in the future (e.g., a positive demand shock triggering more accommodation under the Shortfalls rule, or a tight labor market steepening the Phillips curve) causes forward-looking firms to raise prices today in anticipation of future inflation. This increase in current inflation leads the central bank — whose mandate includes inflation stabilization — to raise policy rates, generating a contractionary offset even when the economy is not currently in the high-demand state. Under PF, agents do not form these anticipatory expectations, so this channel is entirely absent, and the asymmetry affects outcomes only when it directly binds.

Q8. Does the RE–PF divergence arise under a symmetric Deviations rule?

No. The paper shows analytically and numerically that when the monetary policy rule is symmetric (the Deviations rule, responding equally to deviations above and below target), the RE and PF solutions are identical. Unemployment and inflation gaps are both zero on average under either expectations assumption, and the policy rate gap is essentially zero (0.01 annualized percentage points) in both cases. This equivalence result confirms that the RE–PF divergence is not an artifact of the solution method or parameterization but is specifically generated by the interaction between an asymmetry and agents’ forward-looking behavior.

Q9. What do the bounded rationality results imply about the mechanism?

The extension following Gabaix (2020), with a myopia parameter m_br = 0.97, produces results that lie between the full-RE and PF cases: the adoption of the Shortfalls rule yields average unemployment of −0.26 percentage points (intermediate between RE’s −0.05 and PF’s −0.32) and average inflation of 0.62 annualized percentage points (between RE’s 1.02 and PF’s 0.25). This gradient confirms that the key driver is the extent to which agents internalize the probability of future shocks: the more forward-looking agents are, the more strongly the anticipatory pricing channel operates and the less favorable (and more inflationary) the apparent policy tradeoff becomes.

Q10. What are the results for the nonlinear Phillips curve in the numerical model?

Under the numerically calibrated nonlinear Phillips curve model (Panel B.3 of Table 3, with the slope increasing by a factor of three when the unemployment gap is negative), the average unemployment gap under RE is 0.63 percentage points versus 0.30 under PF, and the average inflation gap under RE is essentially zero (0.01 annualized percentage points) versus 0.41 under PF. The authors note that “the average outcomes for both unemployment and inflation can differ by roughly 0.3 to 0.4 percentage points between rational expectations and perfect foresight” in this case.

Q11. What is the paper’s advice for researchers who must use perfect foresight methods?

The paper explicitly states that PF methods remain valuable, especially for estimating or simulating larger models with heterogeneity at the micro level where RE solutions are computationally prohibitive. The authors recommend that researchers relying on PF to solve larger models “check the robustness of their conclusions on longer-run averages and the distribution of outcomes using simplified models which can be solved under both perfect foresight and rational expectations.” To support this, the authors provide multiple versions of code for solving simple macroeconomic models under various asymmetries and expectations assumptions.

Q12. How does the paper position its contribution relative to prior work on RE vs. PF in asymmetric models?

The paper acknowledges that Adam and Billi (2007) and Nakov (2008) previously documented that, at the zero lower bound, households’ anticipation of future ZLB episodes leads to lower average inflation — an RE–PF difference in the spirit of this paper’s findings. However, the paper’s contribution is to show that the sign and quantitative implications of a given asymmetry can change depending on the expectations assumption, and to systematically characterize this sensitivity across multiple types of asymmetry (asymmetric policy rules and nonlinear Phillips curves). The paper also categorizes the existing literature by expectations assumptions in Table A.1, showing that many papers examining macroeconomic asymmetries use only one approach.

Key Concepts

Shortfalls Rule: A monetary policy rule, motivated by the FOMC’s 2020 Statement on Longer-Run Goals and Monetary Policy Strategy, under which the central bank responds only to shortfalls of employment from its maximum level — i.e., it does not tighten policy in response to a tight labor market (negative unemployment gap) during an expansion. Formally, it = φπ πt + φu ut when ut ≥ 0 (labor market slack), and it = φπ πt only when ut < 0 (labor market tight). Contrasts with the symmetric Deviations rule that responds to deviations of employment in both directions.

Deviations Rule: A symmetric monetary policy rule in which the central bank responds to the unemployment gap regardless of its sign — tightening in expansions and easing in contractions. Serves as the baseline against which the Shortfalls rule is compared, and as the case in which RE and PF solutions are identical.

Perfect Foresight (PF) Equilibrium: An equilibrium in which agents solve their optimization problems assuming that no future shocks will occur — they expect all endogenous variables to converge to their longer-run (steady-state) values next period, regardless of the current state. In the paper’s notation, the PF transition matrix P^PF assigns probability one to the mean state next period. In linear models, PF and RE yield identical outcomes; in models with asymmetries, they diverge.

Rational Expectations (RE) Equilibrium: An equilibrium in which households and firms correctly account for the full stochastic distribution of future shocks in forming their expectations. Agents use the true Markov transition matrix P^RE for the natural rate process. This allows forward-looking pricing behavior to incorporate the possibility that the economy may enter states in which asymmetries bind in the future.

Nonlinear (Kinked) Phillips Curve: A Phillips curve in which the slope coefficient κ̃t is state-contingent, increasing when the unemployment gap is negative (labor market is tight). In the paper’s numerical implementation, the slope triples (κ̃ = 3κ) when ut < 0, consistent with empirical evidence in Smith, Timmermann, and Wright (2025) on structural breaks in the Phillips curve. The nonlinearity generates an asymmetric inflationary response: a given level of unemployment produces more inflation when the labor market is tight than when it is slack.

Stochastic Steady State: The equilibrium to which the economy converges in the absence of additional shocks, taking into account the stochastic nature of the environment (i.e., accounting for the possibility of future shocks). Used as the initial condition for computing impulse response functions under RE. Contrasts with the deterministic steady state (zero gaps), which serves as the initial condition under PF.

Parameterized Expectations (Global Solution) Method: The numerical solution algorithm used in the paper to solve for equilibrium policy functions for unemployment and inflation gaps over the state space. Implemented identically for RE and PF cases, differing only in the transition matrix used. Applied with 105 Rouwenhorst grid points for the natural rate. The paper shows this method is orders of magnitude faster than the more common shooting algorithm (0.04 seconds vs. 10.8 seconds) while yielding identical policy functions.

Bounded Rationality (Gabaix 2020): An extension of the baseline model in which agents discount the influence of future expectations by a myopia parameter m_br ∈ (0, 1), applied to both the IS curve and the Phillips curve. The parameter m_br = 0.97 (following McKay, Nakamura, and Steinsson 2017) limits the degree to which distant future states affect current decisions. Produces outcomes intermediate between full RE and PF, confirming that the key dimension of variation is the extent to which agents internalize the probability of future shocks.

Expectation-driven term structure of equity and bond yields

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Research Question. What drives the joint historical dynamics of the term structure of equity yields and nominal bond yields — and can a single unified equilibrium model explain the procyclical equity yield slope, the switch in bond-stock correlation from positive to negative after the late 1990s, the maturity-declining predictability of dividend strip returns, and standard aggregate stock market puzzles?

Key Departure from Prior Literature. Existing equilibrium models (habit formation, long-run risk, disaster risk) rely on time-varying risk premia to explain asset prices. Recent survey evidence challenges this: De La O and Myers (2021) show that most aggregate stock price movements are driven by cash-flow growth expectations rather than return expectations, and Van Binsbergen et al. (2013) show that equity yields are driven mainly by dividend growth expectations. This paper constructs an equilibrium model in which equity (bond) yield variation is attributable to subjective dividend growth (GDP growth) expectations, with a constant subjective risk premium implied by CRRA utility.

Model Architecture. The representative agent has CRRA utility with risk-aversion coefficient γ = 4 and subjective discount factor β = 1.0065 (calibrated to the average 10-year equity yield). The agent departs from rational expectations by having the “belief in the law of small numbers” (Tversky and Kahneman 1971): she perceives small samples to represent their population as well as large samples, leading to subjective learning gains that differ from the rational Kalman gain. The subjective belief updating rule is a modified Kalman filter in which the likelihood is exaggerated by factor (1+θ), producing a subjective learning gain ν that exceeds the Kalman gain K when overreaction applies and falls below it when underreaction applies.

The model has three blocks of fundamentals, each decomposed into a stable and a transitory component. (1) Real GDP growth is decomposed into PCE growth (stable, with a random-walk trend state µ_g) and a volatile gap component (stationary state x_g, persistence ρ_g = 0.941). (2) Inflation is decomposed into core inflation (stable, with trend state µ_π) and a volatile gap (persistence ρ_π = 0.932). (3) Real aggregate dividend is decomposed into a long-duration dividend component dl (levered on log real GDP with leverage λ = 3) and the share of long-duration dividend ds (stationary with persistence ρ_d = 0.94). This cross-sectional decomposition uses firm-level long-term earnings growth (LTG) forecasts from IBES as a model-free equity duration measure.

Estimation. State-space parameters are estimated by maximum likelihood with the Kalman filter on data from NYSE/NASDAQ/AMEX firms (CRSP/Compustat), quarterly, from 1987Q4 to 2019Q4. Subjective learning gains are estimated by minimizing RMSE between model-implied expectations and consensus forecasts: 1-year real GDP growth and inflation from the Survey of Professional Forecasters (SPF, 1981Q3–2019Q4), and 1-year aggregate dividend growth extended from De La O and Myers (2021) to 2019Q4. Equity yield data are from Giglio et al. (2021); bond yields are end-of-quarter zero-coupon nominal yields from Gürkaynak et al. (2007).

Main Findings.

Equity Term Structure Dynamics. The model’s subjective dividend growth expectations drive equity yields. The 1-year model-implied equity yield correlates 0.68 with data; the 10-year correlates 0.79; the 10Y–1Y slope correlates 0.59 with data. Consistent with “belief in the law of small numbers,” the agent overreacts to dividend news (estimated learning gains νl_d = 0.166 and νs_d = 0.458, both below their Kalman gains, which under the level-to-growth translation implies overreaction to dividend growth news, confirmed by negative CG(2015) regression slope coefficients of −0.69 at 1Y and −0.97 at 5Y).
Procyclical Equity Yield Slope. During recessions, the average equity yield slope (10Y–1Y) in the model is −3.77%; during expansions it is +3.96%, matching the data (−5.50% in recessions, +3.93% in expansions). The sign reversal is driven primarily by the dividend-specific component of the decomposition: in recessions, short-run dividend growth expectations fall much more sharply than long-run expectations.
Bond Pricing. The model’s 1-year and 10-year nominal bond yields achieve correlations of 0.92 and 0.95 with their data counterparts, inheriting the explanatory power of Zhao (2020) for the bond market. The agent underreacts to GDP growth and inflation news (estimated learning gains well below Kalman gains, confirmed by positive CG(2015) slope coefficients of +2.08 at 1Y for GDP growth and +1.01 at 1Y for inflation).
Bond-Stock Correlation Switch. In data, 10Y bond vs. dividend strip return correlation (5Y strip) goes from +0.46 before 2000 to −0.49 after 2000. The model produces +0.14 before and −0.56 after (for the 5Y strip). Decomposing the change in bond-stock return covariance: the “inflation real effect” (correlation between expected inflation and real growth) accounts for approximately 27–31% of total changes (for 5Y to 10Y strips); the “real growth correlation” channel — stronger co-movement between real GDP and real dividend growth expectations after 2000 — accounts for approximately 89–95% of total changes. The paper identifies this real bond hedging channel as the dominant and previously unexamined driver.
Dividend Strip Return Predictability. The price-dividend ratio predicts annual market excess returns with R² of 10.3% (data) vs. 9.0% (model). Strip return predictability is downward-sloping by maturity: in data, the R² is 20.2% for 5-year strips and 14.5% for 10-year strips; the model generates 14.2% and 10.4% respectively. This is decomposed into three sources: bond return predictability (small contribution), dividend forecast error predictability (dominant for short maturities), and forecast revision predictability (negative contribution that offsets). The downward slope occurs because current news has smaller impact on long-term dividend expectations.
Aggregate Market Puzzles. The model-implied log dividend-price ratio correlates 0.86 with data, with AR(1) coefficient 0.96 (data: 0.95). Model-implied average market return is 9% (data: 8%); annualized return volatility 12% (data: 16%). The model replicates the switch of the bond-stock aggregate return correlation from +0.13 before 2000 to −0.46 after 2000 (data: +0.39 to −0.64).

Scope Conditions. Results apply to U.S. equity and bond markets over 1987Q4–2019Q4 (with bond learning using data back to 1959Q1). The model assumes a representative agent with CRRA utility and constant subjective risk premium. It is silent on the term structure of expected returns in the statistical sense (which requires identification of latent states under the physical measure). The aggregate market results require a reduced-form specification for stochastic equity duration H_t linked to the value-weighted LTG average.

In depth

Q1. What is the core psychological mechanism generating subjective beliefs, and how does it differ from the diagnostic expectations approach?

The agent has the “belief in the law of small numbers” (Tversky and Kahneman 1971): she treats small samples as equally representative of their population as large samples. Formally, this is embedded by exaggerating the likelihood in the Bayesian update: p(x_t|I_t) ∝ p(y_t|x_t)^{1+θ} × p(x_t|I_{t-1}), where θ captures the magnitude of cognitive bias. The resulting subjective learning gain ν = (1+θ)P̃ / [(1+θ)P̃ + σ²_ε] can exceed the Kalman gain K when θ is large (overreaction) or fall below it when θ is small (underreaction). This differs from diagnostic expectations (Bordalo et al. 2019, 2020a,b), which are based on the representativeness heuristic; the paper notes the two notions of news are highly correlated in simulation (Table IA.2) and that both can imply overreaction.

Q2. Why does the model generate overreaction to dividend growth news even though the dividend-level learning gains are smaller than the Kalman gains?

The model separates dividend learning into level and growth. Section 2.2 derives that underreaction to dividend level news (νl_d < Kl_d, νs_d < Ks_d, estimated values 0.166 and 0.458 against Kalman gains 0.19 and 0.49 respectively) translates into overreaction to dividend growth news. This is confirmed by the CG(2015) rationality test: regressing forecast errors on lagged forecast revisions yields slope coefficients of −0.69 (1Y) and −0.97 (5Y) for real dividend growth, both statistically significant (t-statistics −3.63 and −3.22). In contrast, the same test yields positive slope coefficients for GDP growth (2.08 at 1Y) and inflation (1.01 at 1Y), confirming underreaction for these series.

Q3. How well does the model match subjective dividend growth expectations in the survey data?

The model-implied 1-year subjective dividend growth forecast is estimated by minimizing RMSE against the consensus dividend growth forecast series (extended from De La O and Myers 2021 to 2019Q4, with a replication correlation of 0.92 over the overlapping sample). The unconditional correlation between model-implied and data 1-year forecasts is 0.80. Although only 1-year forecasts are used in estimation, the model also achieves a correlation of 0.80 for 2-year forecasts, providing an out-of-sample validation.

Q4. What explains the higher volatility of short-term equity yields relative to long-term equity yields?

Short-term subjective dividend growth expectations are more volatile because the agent’s short-run expectation mean-reverts toward the less volatile long-run (levered) GDP growth expectation. In the model’s two-component dividend structure, the transitory dividend-share component xd has persistence ρ_d = 0.94 and its effect on equity yields decays as maturity increases (via the factor (1−ρ^n_d)/n). Similarly, the effect of the transitory GDP growth state x_g decays with maturity. Long-term equity yields are thus anchored by the slower-moving trend components µ_g and µ_d. In the data from Giglio et al. (2021), 1-year yields have a standard deviation of 8.89% annualized vs. 2.70% for 10-year yields; the model generates 8.22% and 1.89% respectively.

Q5. What is the quantitative importance of the “real growth correlation” channel vs. the “inflation real effect” channel in explaining the bond-stock correlation switch?

For the switch in bond-stock return correlation (using the 10-year nominal bond and various maturity dividend strips), the decomposition in Table 4 shows that the “real growth correlation” channel accounts for 89.1% (5Y strip), 92.1% (7Y strip), and 94.8% (10Y strip) of total bond-stock covariance changes, while the “inflation real effect” (correlation between expected inflation and expected real growth) accounts for 27.3%, 29.3%, and 31.1% respectively. The “volatility of shocks to expected inflation and real growth” makes a negative contribution (−16.4%, −21.4%, −25.9%), mostly attributable to more volatile beliefs during the 2008 global financial crisis. The real growth correlation channel reflects that after 2000, real bonds provide a better hedge to aggregate real dividend risks because real GDP growth expectations and real dividend growth expectations became more positively correlated.

Q6. Does the same real growth correlation story hold for the “Fed model” (bond-stock yield correlation)?

Yes, but with a quantitatively different balance. For yield correlations (Table 5), the “real growth correlation” channel accounts for 72.4%–80.1% of bond-stock yield covariance changes (5Y to 10Y strip), while the “inflation real effect” now accounts for 41.2%–43.9%. The inflation real effect is proportionally larger for yield levels because persistent expected inflation correlates strongly with the level of expected real GDP growth — even though inflation expectations do not move fast enough at high frequency to explain return correlation, they co-move strongly with expected growth at low frequency.

Q7. How does the model generate a downward-sloping term structure of return predictability?

The strip excess return is decomposed into three components (Equation 44): maturity-matched bond excess return (Bond), dividend forecast error within the holding period (FE), and forecast revision regarding dividend growth after the holding period (FR). For short maturities, bond predictability contributes little (R² ≈ 6.7% for 5Y strip), while FE predictability (R² ≈ 31.5%) and FR predictability (R² ≈ 35.6%) dominate. As maturity increases, the current news has smaller impact on long-term dividend expectations, reducing the predictability of FE (R² ≈ 26.6% for 10Y) and FR (R² ≈ 26.5% for 10Y). Taken together, total model-implied strip R² declines from 14.2% (5Y) to 10.4% (10Y), matching the data pattern (20.2% to 14.5%). The paper identifies forecast revision predictability as a new channel not previously documented.

Q8. Why do forecast errors and forecast revisions have opposite signs in the predictability regressions?

Bad news (high equity yields, i.e., low current stock prices) triggers excessively pessimistic subjective dividend growth expectations because the agent overreacts to dividend news. These overly pessimistic forecasts tend to be disappointed in the future — actual dividend realizations exceed the forecast — producing positive subsequent forecast errors (FE is positively predicted by high yields, with R² ≈ 31.5% for 5Y strips). However, as dividend levels mean-revert, higher subsequent realizations cause the agent to revise down the forecast for dividend growth thereafter, leading to negative forecast revisions (FR is negatively predicted by high yields, with R² ≈ 35.6% for 5Y strips, opposite sign from FE). The net effect on return predictability is thus a combination of positive (FE) and negative (FR) contributions.

Q9. How does the model handle the aggregate market dividend-price ratio and its persistence?

The aggregate stock price is modeled as the sum of dividend strip prices up to a stochastic horizon H_t, which is parameterized as a linear function of the value-weighted average of LTG forecasts: H_t = a + b·LTG_t. Parameters a and b are estimated by minimizing RMSE between model-implied and data log dividend-price ratio. The model-implied ratio achieves a correlation of 0.86 with data, an AR(1) coefficient of 0.96 (data: 0.95), and an annualized volatility of 26% (data: 30%). The time-variation is driven entirely by strip yield variations and exogenous LTG movements.

Q10. Is the overreaction to dividend news and underreaction to GDP/inflation news consistent in a single framework?

Yes. The model’s subjective learning framework (based on “belief in the law of small numbers”) generates both over- and underreaction depending on the estimated subjective learning gain relative to the Kalman gain. For GDP growth and inflation, the learning gains (ν*_g = 0.012, νgap_g = 0.065; ν*_π = 0.049, νgap_π = 0.228) are below their Kalman gains (0.29 and 0.67 for GDP components; 0.67 and 0.48 for inflation components), producing underreaction. The paper hypothesizes this is related to the Fed’s dual mandate: agents rationally assign lower weight to GDP and inflation shocks expecting the Fed will stabilize them. For dividend growth, a level-to-growth translation converts level underreaction into growth overreaction.

Q11. What are the robustness checks, and what do they show?

The paper checks three alternative equity duration measures: those from Dechow et al. (2004), Weber (2018), and Gonçalves (2021b), as well as the book-to-market ratio following Lettau and Wachter (2007). Table IA.1 shows that replacing LTG with these measures still produces model-implied equity yields that replicate key data moments with high time-series correlations. Changing the cross-sectional breakpoint for long-duration dividends from the median LTG to the 40th or 60th percentile leaves results similar. The paper also presents an Internet Appendix extension in which the agent has ambiguity about real GDP and dividend growth (model misspecification fear), yielding equity yields and returns even closer to data.

Q12. What is the paper’s contribution to the bond market relative to Zhao (2020)?

The bond pricing block closely follows Zhao (2020), inheriting its explanatory power for bond market stylized facts. The model’s 1-year and 10-year nominal bond yields achieve correlations of 0.92 and 0.95 with data, respectively. The new contribution is the joint model covering both equity and bond markets simultaneously, enabling the decomposition of bond-stock covariance and the identification of the real growth correlation as the dominant driver of the bond-stock correlation switch — a channel not addressed by Zhao (2020), which focused on bond market puzzles alone.

Key Concepts

Equity Yield (Dividend Strip Yield). Defined as ey^(n)_t = (1/n)(d$_t − p^(n)_t), where p^(n)_t is the log price of the n-period dividend strip (a claim to the nominal dividend n periods ahead) and d$_t is the log nominal aggregate dividend. It decomposes into the bond yield, a subjective dividend growth component, and a (constant) risk premium component.

Belief in the Law of Small Numbers. A cognitive bias (Tversky and Kahneman 1971) in which the agent perceives small samples to represent their population as well as large samples. Modeled by exaggerating the likelihood in Bayesian updating: p(x_t|I_t) ∝ p(y_t|x_t)^{1+θ} × p(x_t|I_{t-1}). This generates a subjective learning gain ν that can exceed the Kalman gain (overreaction) or fall below it (underreaction) depending on θ and the signal-to-noise ratio.

Subjective Learning Gain. The coefficient ν in the subjective Kalman filter update ẽ_t x_t = ρẽ_{t-1}x_{t-1} + ν(y_t − ρẽ_{t-1}x_{t-1}). It equals (1+θ)P̃ / [(1+θ)P̃ + σ²_ε], where P̃ is the subjective predictive variance. When ν > K (the rational Kalman gain), the agent overreacts to news; when ν < K, the agent underreacts.

Long-Duration Dividend Component. The portion of aggregate real dividend (dl_t) attributable to “long-duration” firms — those with above-median analyst LTG forecasts in CRSP/Compustat/IBES data. Levered on log real GDP with leverage parameter λ = 3, it carries aggregate risk. The complementary short-duration dividend share ds_t is stationary and carries no aggregate risk. The decomposition allows the model to exploit cross-sectional cash-flow duration information when learning about future aggregate dividend growth.

Real Growth Correlation Channel. A bond-stock covariance component defined as Cov(RGDP^(N), RDIV^(n)), where RGDP^(N) is the real GDP growth expectation component of 10-year nominal bond returns and RDIV^(n) is the real dividend growth expectation component of n-period strip returns. This channel captures whether real bonds hedge aggregate real dividend risks. The paper shows this channel accounts for approximately 89–95% of the post-2000 bond-stock covariance change for dividend strips.

Inflation Real Effect. The covariance component Cov(INFL^(N)_B, RGDP^(n) + RDIV^(n)), defined as the correlation between shocks to expected inflation (embedded in nominal bond returns) and shocks to expected real growth (in strip returns). In the paper’s framework this is distinct from the standard inflation risk premium story, as it concerns the correlation between subjective beliefs rather than realized covariances under the physical measure.

Forecast Error (FE) and Forecast Revision (FR) Predictability. Two of three components of realized strip excess return (Equation 44). FE = ∆d${t+1:t+h} − ẽ_t∆d${t+1:t+h} is the realized dividend growth forecast error within the holding period; FR = (ẽ_{t+h} − ẽ_t)∆d$_{t+h+1:t+n} is the forecast revision for dividend growth beyond the holding period. Because the agent overreacts to dividend news, bad news triggers overly pessimistic forecasts (positive subsequent FE) and, as dividends mean-revert, downward forecast revisions (negative FR). These two have opposite signs in predictive regressions, generating the downward-sloping term structure of return predictability.

Fed Model. The empirical positive correlation between equity yields (real) and nominal bond yield levels. The paper shows that this yield-level correlation switched from strongly positive (≈ 0.85 before 2000) to significantly negative (≈ −0.60 to −0.62 after 2000) for 5Y–10Y dividend strips, and that the same real growth correlation and inflation real effect decomposition applies, albeit with the inflation real effect proportionally larger (≈ 40%) for yield levels than for returns (≈ 30%) because persistent inflation expectations co-move with the level of expected real GDP growth.

Explicit consumption functions with borrowing constraints: A continuous-time approach

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research question. The paper asks whether an explicit, global, closed-form solution exists for the consumption function in the standard income fluctuation problem with a borrowing constraint and constant income, a problem that has resisted closed-form solution since at least Schechtman (1976). All prior continuous-time work (Park 2006, Holm 2018, Fischer 2024) produced only implicit expressions; Achdou et al. (2022) produced explicit expressions valid only locally, near zero assets or as assets diverge to infinity, and only for r > 0.

Model. A single agent with CRRA utility (coefficient of relative risk aversion γ > 0) maximizes discounted utility over an infinite horizon, subject to the flow budget constraint da/dt = ra + y − c, with a borrowing constraint a(t) ≥ 0. The agent receives a constant, deterministic income stream y ≥ 0 and discounts at rate ρ, with the impatience condition ρ > r maintained throughout. The paper takes a continuous-time formulation arrived at by letting the discrete period length Δ → 0, nesting Helpman (1981)’s discrete-time analysis as a special case.

Key analytical device. A one-to-one mapping exists between initial assets a and the time T it takes for the consumer to fully run down her assets. This map, denoted T = h(a; y), is well-defined, strictly increasing, and concave in a (established in Proposition 1 via the Hadamard-Lévy theorem). Expressing the optimal consumption function as c*(a; y) = y · exp(ρh(a;y)/γ) evaluated at t = 0 reduces the problem to explicitly inverting the transcendental equation relating a to T.

Main result (r = 0). For the case of a zero net real interest rate, the transcendental equation can be solved explicitly using the second branch W₋₁(·) of the Lambert W function. The closed-form consumption function is (Theorem 2 and Corollary 2.1):

c*(a; y) = y · exp(ρ h(a;y) / γ), where h(a; y) = −(a/y + γ/ρ) − (γ/ρ) W₋₁(f(a;y)), and f(a;y) = −exp(−b(a + γy/ρ)/y), b := ρ/γ.

This is a global solution (valid for all a ≥ 0), in contrast to the local solutions in prior work. The paper notes that for the illustrative parameter values r = 0.01, γ = 0.5, ρ = 0.08, y = 3 (broadly consistent with average U.S. real interest rates in 2025), there is a visually sizable gap between the constrained and unconstrained consumption functions except as a → ∞, where the two converge (in line with the asymptotic linearity result of Benhabib et al. 2015).

Main result (r > 0). For positive interest rates, the Lambert W function cannot invert a sum of exponentials with different exponents (an open mathematical problem). The paper instead derives a global closed-form approximation valid for r ∼ 0, by expanding e^(−rT) ≈ 1 − rT to first order and applying the same Lambert W inversion. The approximating consumption function has the same structural form but with modified coefficients b_r, c_r, d_r that collapse to their r = 0 counterparts as r → 0 (Proposition 2). Numerical comparison against the implicit-expression solution of Park (2006) confirms the approximation is close for small r.

Characterization of the MPC and supermodularity (Section 3). Leveraging the explicit expression, the paper derives the full Jacobian vector and Hessian matrix of c*(a; y) in closed form (Propositions 3 and 4). Key findings, all proved formally and holding under the impatience condition ρ > r:

Consumption is increasing in both assets and permanent income (both entries of the Jacobian are strictly positive — Corollary 2.2). The second result (∂c*/∂y > 0 for all a) is new for the borrowing-constrained setting; Achdou et al. (2022) provided only suggestive evidence for the limiting case a ∼ 0.
Consumption is strictly concave in both assets and permanent income (both diagonal entries of the Hessian are strictly negative — Corollary 2.3). Concavity in assets was known (Carroll and Kimball 1996); concavity in permanent income under borrowing constraints is new.
The consumption function is supermodular: the cross-derivative ∂²c*/∂a∂y is strictly positive (Corollary 2.3). This means assets and permanent income are complements in generating consumption. Equivalently, the MPC out of permanent income is strictly increasing in the level of initial assets — a counter-intuitive result, since high MPCs are usually associated with poor (low-asset) agents. An identical result was obtained by Commault (2025) for a life-cycle model without borrowing constraints; the current paper confirms it holds in the presence of a borrowing constraint. By symmetry of the Hessian, the MPC out of assets is also strictly increasing in permanent income.

Intuition for supermodularity. When assets are low, an increase in permanent income produces little additional consumption because the risk of hitting the borrowing constraint is high. When assets are higher, the agent has buffer savings, faces a lower constraint-risk, and can smooth the higher future income stream into current consumption.

Scope conditions. Results are derived under CRRA utility, constant (deterministic) income, no stochastic variation, and the impatience condition ρ > r. The exact closed form applies to r = 0; the approximation is characterized as valid for r ∼ 0 and is not a local expansion in assets.

In depth

Q1. What is the longstanding gap in the literature that this paper addresses?

A: Since Zeldes (1989) noted that no closed-form solution exists for the consumption function with stochastic income and CRRA utility, researchers settled for numerical solutions or local analytical approximations. In the constant-income/borrowing-constraint version studied here, Park (2006), Holm (2018), and Fischer (2024) derived only implicit continuous-time expressions. Achdou et al. (2022) gave explicit local solutions valid near a ∼ 0 or a → ∞ under r > 0. No prior work produced an explicit, global closed-form for any case.

Q2. Why does moving to continuous time enable progress that discrete time did not?

A: In discrete time, the consumption function is piecewise linear (Helpman 1981), with kinks at the sequence of asset thresholds µ(T) for T = 0, Δ, 2Δ, …. As Δ → 0, the piecewise-linear function converges to a smooth function whose governing ODE can be solved analytically. This convergence to smoothness, illustrated in Figure 1, is what enables the application of the Lambert W function to invert the resulting transcendental equation.

Q3. What is the role of the Lambert W function, specifically its second branch W₋₁?

A: The optimal asset-depletion time T satisfies the transcendental equation e^(bT) = yT + c (for r = 0), which cannot be solved with elementary functions. Via the change of variables z := −bT − bc/y, the equation reduces to ze^z = α, whose solution is z = W(α). The argument α lies in (−1/e, 0) for a ∈ (0, +∞), and it is precisely on this interval that the Lambert W function is double-valued; the relevant branch is W₋₁ (the second, lower branch), which is well-defined and strictly less than −1 on (−1/e, 0). It is the properties of W₋₁ on this domain — specifically that 1 + W₋₁(α) < 0 — that drive the sign conclusions for the Hessian.

Q4. Why does the Lambert W approach fail for r > 0, and what is the approximation strategy?

A: For r > 0, Equation (8) contains two exponentials with different exponents — e^((ρ−r)T/γ) and e^(−rT) — and their sum cannot be inverted by the Lambert W function, which handles only a linear-plus-single-exponential structure. Inverting a sum of exponentials with different exponents is stated in the paper to be an open problem. The approximation strategy exploits the fact that for r ∼ 0, e^(−rT) ≈ 1 − rT + o(r), reducing the equation to a single-exponential transcendental form (Equation 15) with modified coefficients b_r, d_r, c_r, all of which converge to their r = 0 analogues as r → 0.

Q5. What does Proposition 1 establish, and why is it necessary before stating the main theorem?

A: Proposition 1 establishes that the mapping µ(T) from depletion time T to initial assets a is smooth (infinitely differentiable), bijective (one-to-one and onto) on ℝ₊, and strictly convex. The Hadamard-Lévy theorem then guarantees that its inverse h(a;y) = µ⁻¹(a) exists, is unique, is strictly increasing, and is strictly concave in a. This is a necessary prerequisite for Theorem 2 because h(a;y) is the central object in the closed-form consumption function; without establishing its existence and uniqueness, Theorem 2 would have no well-defined object.

Q6. What does the Jacobian characterization (Proposition 3 and Corollary 2.2) contribute?

A: Proposition 3 gives explicit formulas for ∂c*/∂a = (ρ/γ) · w/(1+w) and ∂c*/∂y in terms of w = W₋₁(f(a;y)). Corollary 2.2 proves both are strictly positive using the property w < −1 on (−1/e, 0), which ensures w/(1+w) > 0 and that the bracketed term in the expression for ∂c*/∂y is strictly positive. The contribution is that the positivity of ∂c*/∂y for all a was previously unproven in a borrowing-constrained setting with constant income.

Q7. What is the structure of the Hessian matrix and what signs do its entries take?

A: All four entries of Hc are proportional to w/(1+w)³. Since w < −1, we have 1 + w < 0, so (1+w)³ < 0, making w/(1+w)³ > 0. The diagonal elements ∂²c*/∂a² = −(ρ²/γ²y) · w/(1+w)³ and ∂²c*/∂y² = −(ρ²a²/γ²y³) · w/(1+w)³ are both strictly negative (concavity). The off-diagonal elements ∂²c*/∂a∂y = (aρ²/γ²y²) · w/(1+w)³ are strictly positive (supermodularity/complementarity).

Q8. What is the precise counter-intuitive implication of supermodularity for MPC heterogeneity?

A: Supermodularity (∂²c*/∂a∂y > 0) means the MPC out of permanent income — conventionally associated with low-wealth households — is in fact increasing in the level of initial assets. This contradicts the conventional narrative that high MPCs are a hallmark of poor agents. The paper’s intuition is that low-asset agents face high risk of hitting the constraint, suppressing their consumption response to income news, while high-asset agents can freely smooth the increased income stream. The same supermodularity implies, by the symmetry of the Hessian, that the MPC out of assets is also increasing in permanent income.

Q9. How does this result relate to Commault (2025)?

A: Commault (2025) proved, in a life-cycle model with a permanent/transitory stochastic income process but without borrowing constraints, that the MPC out of permanent income is increasing in assets. The current paper obtains the same qualitative finding in the opposite environment — constant income with a borrowing constraint. The paper treats these as complementary, noting that the result thus appears robust to these different modeling choices.

Q10. What does concavity in permanent income (∂²c*/∂y² < 0) add that was not previously known?

A: Carroll and Kimball (1996) established concavity of the consumption function in assets for a broad utility class. Concavity in permanent income — that the marginal consumption response to a windfall increase in y is diminishing — had been proved by Commault (2025) only in the absence of borrowing constraints. The current paper provides the first formal proof of this property in a setting with a borrowing constraint (albeit for constant, deterministic income and CRRA utility in continuous time).

Q11. What is the potential use of these closed-form results for numerical methods?

A: The paper notes in the conclusion that the closed-form solutions for r = 0 and the approximation for r ∼ 0 can serve as benchmarks for assessing the reliability of continuous-time numerical methods when computing objects such as the MPC out of assets. Because the exact solution is known analytically, numerical implementations can be compared against it to detect discretization errors or convergence failures.

Q12. What parameter values are used to illustrate the consumption function, and what do they imply?

A: The paper uses r = 0.01, γ = 0.5, ρ = 0.08, y = 3, where r = 0.01 is described as roughly in line with the average real interest rate in the U.S. in 2025. With these values, Figure 1 shows a visually sizable gap between the constrained and unconstrained consumption functions at low to moderate asset levels, with the two converging as a → ∞ as guaranteed by asymptotic linearity (Benhabib et al. 2015).

Key Concepts

Income fluctuation problem (with borrowing constraint): The standard infinite-horizon single-agent savings problem in which the agent faces a non-negativity constraint on assets (a(t) ≥ 0), so that the agent cannot borrow. In the paper’s formulation: maximize ∫ e^(−ρt)u(c(t))dt subject to da/dt = ra + y − c and a(t) ≥ 0, with constant income y and CRRA utility. The borrowing constraint creates the concavity of the consumption function and was the source of intractability in prior closed-form attempts.

Lambert W function (second branch W₋₁): A special transcendental function defined as the solution to we^w = x. It is double-valued on (−1/e, 0); the second branch W₋₁ takes values strictly less than −1 on this interval. In this paper, the transcendental equation linking initial assets to asset-depletion time is reduced to the form ze^z = α, enabling explicit inversion via W₋₁. The property that 1 + W₋₁(α) < 0 on (−1/e, 0) is the algebraic engine driving all sign results in the Hessian.

Asset-depletion time T = h(a; y): The time it takes for the optimal consumer to fully run down her initial assets before settling into perpetual income consumption of y. The paper establishes a bijective mapping from initial assets a to depletion time T (Proposition 1); the closed-form solution is obtained by explicitly inverting this mapping. In the paper’s formulation, h(a; y) = µ⁻¹(a) where µ(T) is derived from the ODE governing the consumption path.

Supermodularity of the consumption function: The property that the cross-derivative ∂²c*/∂a∂y is strictly positive, meaning assets a and permanent income y act as complements in generating consumption. This is an equilibrium property of the consumption function (not an assumption on the utility function), and the paper identifies it as new to the income fluctuation literature. It implies the MPC out of permanent income is increasing in a, and the MPC out of assets is increasing in y.

MPC out of permanent income (∂c/∂y):* The marginal increase in current consumption per unit increase in the constant income stream y, holding initial assets constant. This object is less studied than the MPC out of a transient asset windfall. In the paper’s setting, it is shown to be strictly positive for all a (Corollary 2.2) and, counter-intuitively, strictly increasing in a (supermodularity).

Global vs. local closed-form solution: A global solution holds for all values of the state variable (here, all a ≥ 0), while a local solution is valid only in the neighborhood of a particular value (e.g., a ∼ 0 or a → ∞). Achdou et al. (2022) produced local closed-form expressions; the current paper’s Theorem 2 (r = 0) is the first global explicit closed-form for this class of problems.

Piecewise-linear consumption function (discrete time): In Helpman (1981)’s discrete-time formulation with period length Δ = 1, the optimal consumption function is piecewise linear in assets, with slope changes at the asset thresholds µ(T) for integer T. As Δ → 0, this becomes a smooth function, enabling the passage to the continuous-time closed form derived in the paper.

Financial shocks and leverage of financial institutions: When do they matter?

Mon, 01 Jan 0001 00:00:00 +0000

This paper investigates the role of leverage of financial institutions in amplifying the transmission of financial shocks to the macroeconomy, with particular attention to whether that amplification differs across economic regimes. The authors develop a new endogenous regime-switching structural vector autoregression (RS-SVAR) model with time-varying transition probabilities, in which the probability of switching regime depends on the contemporaneous state of the economy (endogenous switching). The model extends the Sims and Zha (2006) and Sims, Waggoner, and Zha (2008) Markov-switching SVAR framework by: (1) incorporating a time-varying transition matrix in which the probability of staying in a regime is a logistic function of lagged endogenous variables; and (2) introducing new identification techniques for RS-SVARs, including non-recursive zero restrictions, sign restrictions, and narrative sign restrictions, which can in some cases uniquely identify structural shocks rather than merely set-identify them.

The leverage measure is market-based — book assets divided by market equity — constructed from CRSP/Compustat institution-level data covering publicly listed depository institutions, bank holding companies, and nonbank financial institutions. The sample runs monthly from December 1988 to December 2019. The five-variable VAR includes industrial production growth, core CPI inflation, the 2-year Treasury rate, market leverage of financial institutions, and the Chicago Fed’s National Financial Conditions Index (NFCI). The authors estimate three model variants that substitute in turn the leverage of: (i) all depository institutions, (ii) Global Systemically Important Banks (GSIBs), and (iii) securities brokers and dealers.

The model identifies two coefficient regimes — a “financial constraint” regime and “normal times” — using the criterion that the first regime has higher smoothed probability during September 2008 to August 2009. The financial constraint regime covers the end of the Savings and Loan crisis, the 1990/91 recession, the Russian debt default, the Global Financial Crisis (GFC), and the European sovereign debt crisis.

The core finding is that real effects of financial shocks are amplified in the financial constraint regime but not in normal times. In the financial constraint regime, the output response to a financial shock is significantly negative, large, and protracted; GSIB leverage initially rises sharply (as falling asset prices erode equity) and then declines as institutions deleverage. In normal times, the output growth response is negative but non-persistent, and market leverage remains insignificant over the entire horizon.

The counterfactual experiment holding GSIB market leverage constant as of October 2008 is the sharpest quantitative result: if GSIB leverage had not risen further at the onset of the GFC, the decline in industrial production growth would have been approximately 20 percentage points smaller, with a faster subsequent recovery in output growth and inflation and higher short-term interest rates. The counterfactual probability of staying in the financial constraint regime would have fallen as low as 0.1 for some draws, compared to the actual probability remaining elevated. By contrast, for a system using depository institution leverage, the lower-bound counterfactual probability of staying in the constraint regime does not fall below 0.90, indicating substantially weaker heterogeneity effects for the broader depository sector.

Securities brokers and dealers show leverage that rises more on impact than other institutions and then declines immediately, consistent with their willingness to expand balance sheets going into the crisis amplifying losses and forcing a sharp post-crisis contraction.

A separate counterfactual holding the NFCI constant (rather than leverage) shows that the probability of staying in the constraint regime does not decline, confirming that market leverage and the financial conditions index provide distinct characterizations of the financial system and have different implications for shock propagation and regime persistence. Results are robust to substituting the GZ corporate spread for the NFCI and to imposing narrative restrictions for shock identification.

Q: What is the central research question? A: The paper asks whether and how the leverage of financial institutions amplifies the transmission of financial shocks to the real economy, and whether this amplification differs between a financial constraint regime and normal times. A secondary question concerns heterogeneity: do GSIBs, depository institutions broadly, and nonbank securities dealers transmit shocks differently?

Q: What is novel about the econometric framework? A: The RS-SVAR model allows the probability of remaining in a given coefficient regime to vary over time as a logistic function of lagged endogenous variables, so regime switching is endogenous to the state of the economy rather than governed by a fixed transition matrix. The paper also introduces sign restrictions, zero restrictions, and narrative sign restrictions into the RS-SVAR class, enabling identification of both structural shocks and regimes within a single framework; in roughly 20 percent of posterior draws these sign restrictions uniquely identify the financial shock.

Q: Why does the paper use market leverage rather than book leverage? A: Market leverage (book assets divided by market equity) is argued to be more timely than book leverage because book equity incorporates losses with a delay, giving institutions time to adjust book leverage to avoid regulatory limits. Market capitalization reflects market participants’ assessment of an institution’s creditworthiness, and low market-to-book ratios signal that institutions are more leveraged than their books indicate. Market leverage is therefore a more informative early-warning indicator of financial fragility and the need for rapid deleveraging.

Q: How are the two regimes identified? A: For each estimated regime, the authors count the number of months between September 2008 and August 2009 (inclusive) for which the smoothed probability of being in that regime exceeds 0.70; the regime with the higher count is labeled “financial constraint” and ordered first. Shock identification uses sign restrictions: in the financial constraint regime, a positive financial shock must have a contemporaneously negative effect on output, inflation, and the short-term interest rate, but positive effects on the financial conditions index and leverage; in normal times, only the financial conditions index is required to respond positively on impact.

Q: What regimes does the model assign historically? A: The smoothed probability of the financial constraint regime is elevated during the end of the Savings and Loan crisis, the 1990/91 recession, the Russian debt default, the GFC and associated recession (where the probability reaches 1.0 at end-2008 and beginning-2009 before declining sharply to approximately 0.6 percent in 2009/2010), and the European sovereign debt crisis.

Q: What do the impulse responses show in the financial constraint regime? A: In the financial constraint regime, the output response to a positive financial shock (tightening) is significantly negative, large, and protracted. GSIB leverage initially rises due to a sharp decline in asset prices eroding market equity, then falls as GSIBs deleverage in response. The authors interpret this pattern as evidence that deleveraging produces procyclical financial amplification effects with adverse real consequences.

Q: What do the impulse responses show in normal times? A: In normal times, the output growth response is large and negative but non-persistent, in contrast to the financial constraint regime. Market leverage remains statistically insignificant across the entire horizon in normal times, indicating that the leverage amplification channel is inactive outside of financial constraint episodes.

Q: What does the GSIB leverage counterfactual show quantitatively? A: Holding GSIB market leverage constant as of October 2008 implies a decline in industrial production growth that is approximately 20 percentage points smaller than actually occurred, along with a faster recovery in output growth and inflation and higher short-term interest rates. The counterfactual probability of staying in the financial constraint regime declines to as low as 0.1 for some posterior draws, compared to remaining elevated in the actual data.

Q: How do depository institutions compare to GSIBs in the counterfactual? A: For the model using broad depository institution leverage, the lower-bound counterfactual probability of staying in the financial constraint regime does not fall below 0.90, compared to as low as 0.1 for the GSIB specification. This implies that GSIB deleveraging has substantially more detrimental macroeconomic effects and a much larger effect on regime persistence than the broader depository sector.

Q: What is distinctive about securities brokers and dealers? A: Broker-dealer market leverage rises more on impact than leverage of other financial institutions following a financial shock, and then immediately declines due to rapid deleveraging. The authors interpret this as reflecting that dealers’ willingness to expand balance sheets ahead of the crisis amplified growth and losses, followed by a sharp post-crisis contraction — a pattern consistent with the procyclical leverage mechanism described in Adrian and Shin (2014).

Q: How do the authors distinguish the role of market leverage from the financial conditions index? A: A counterfactual holding the NFCI constant (rather than leverage) as of October 2008 shows that the probability of staying in the financial constraint regime does not decline, unlike the leverage counterfactual. This demonstrates that market leverage and the NFCI provide distinct characterizations of financial conditions and have different implications for the propagation of shocks and the persistence of the constraint regime.

Q: How robust are the results? A: Substituting the GZ corporate bond spread for the NFCI yields very similar results, specifically that the probability of staying in the constraint regime declines much more in the counterfactual than in the actual data, suggesting the findings are not driven by the choice of financial conditions proxy. Imposing narrative restrictions for shock identification (exploiting the known high-stress period around Lehman’s failure in September 2008) yields results that are “rather robust” relative to the baseline sign-restriction identification.

Q: What are the policy implications? A: The results confirm the leverage ratio as a useful financial stability indicator, with particular emphasis on market leverage as providing timely information for monitoring. The heterogeneity findings suggest that regulatory attention to GSIB leverage is especially warranted, since GSIB deleveraging can have substantially more detrimental macroeconomic effects and a much larger influence on the persistence of financial constraint regimes than deleveraging by the broader depository sector. The leverage ratio is characterized as complementary to the risk-weighted capital ratio as a regulatory tool.

Market leverage: Measured as book assets divided by market equity (not book equity), constructed from CRSP/Compustat institution-level data at monthly frequency. The paper argues market leverage is more timely than book leverage because market equity immediately reflects losses, preventing institutions from masking fragility through delayed book adjustments.

Financial constraint regime: One of two identified coefficient regimes in the RS-SVAR, characterized by a significantly negative, large, and protracted output response to financial shocks and by active leverage amplification. Identified empirically as the regime with the highest smoothed probability during September 2008 to August 2009.

Endogenous regime switching: A modeling approach in which the probability of transitioning between regimes depends on lagged values of the endogenous variables themselves (via a logistic function), rather than being governed by a fixed constant transition matrix. This allows regime dynamics to respond to the state of the economy.

Time-varying transition probabilities: The diagonal elements of the coefficient-regime transition matrix follow a logistic transformation of a linear function of lagged endogenous variables, so the probability of remaining in any given regime changes each period as a function of current financial and macroeconomic conditions.

Procyclical financial amplification: The mechanism by which financial institution deleveraging in response to falling asset prices further tightens financial conditions and reduces real output, generating a feedback loop. The paper provides empirical evidence for this channel operating specifically in financial constraint regimes.

Heterogeneity of financial institutions: The finding that GSIBs, broad depository institutions, and securities brokers and dealers differ substantially in how their leverage affects the transmission of financial shocks. GSIB deleveraging is shown to have much more detrimental macroeconomic effects and a much larger influence on the probability of remaining in the financial constraint regime than depository institution deleveraging more broadly.

Narrative sign restrictions in RS-SVARs: An identification technique extended from Antolin-Diaz and Rubio-Ramirez (2018) to the regime-switching context, which uses known historical episodes (here, the Lehman failure in September 2008) to impose restrictions on which regime the economy was in or on the sign of structural shocks at particular dates, thereby aiding identification of both shocks and regimes.

Firm dynamics and random search over the business cycle

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

How do aggregate economic fluctuations reallocate workers across the firm productivity distribution over the business cycle? In particular, to what extent do recessions impede workers’ movement up the job ladder toward more productive firms?

Model and Methodology

The paper develops a tractable random search model combining three features that had not previously been integrated in a single quantitative framework: (i) firm dynamics driven by idiosyncratic productivity shocks, with endogenous entry and exit; (ii) on-the-job search, generating a job ladder in which workers gradually move toward more productive firms; and (iii) aggregate productivity shocks. Multi-worker firms post employment contracts, choose hiring rates, and decide whether to continue or exit. The key tractability result — called “size-independence” (Result 1) — shows that, under a constant-returns hiring cost technology, firms’ optimal policies (contract value, hiring rate, exit decision) are all independent of firm size, so the relevant state space reduces from the full joint distribution of firm productivity and size to the employment-weighted distribution of firm productivity alone. A further result (“rank-monotonic equilibrium,” Result 2) guarantees, under a sufficient convexity condition on hiring costs (hc’’(h)/c’(h) ≥ 1), that the optimal employment contract is increasing in firm productivity, so the job ladder maps one-for-one onto the firm productivity ladder. The optimal wage contract then admits a closed-form solution.

The model is calibrated to British data for 1997–2018. Worker-level transition rates (unemployment-to-employment, employment-to-unemployment, and job-to-job) are drawn from the British Household Panel Survey (BHPS). Firm-level data on labor productivity (value added per worker) and employment costs per worker come from the Annual Respondents Database (ARD) and Annual Business Survey (ABS), merged with the Business Structure Database (BSD). The numerical solution adapts ideas from Krusell and Smith (1998), approximating the employment-weighted productivity distribution by a small set of moments and parameterizing value functions as polynomials in the aggregate state; standard linearization methods are inapplicable because endogenous firm entry and exit introduces a discontinuity in value functions.

Main Findings

Model validation via the OP decomposition. The paper’s central validation exercise uses the Olley-Pakes (OP) decomposition of a labor productivity index constructed from firm-level data. The aggregate employment-weighted labor productivity index is decomposed into (a) the unweighted average firm productivity and (b) an interaction term (the “OP term”), which captures the covariance between employment shares and productivity — i.e., how well workers are allocated to productive firms. In the British firm-level data, approximately 20 percent of the variance of the aggregate labor productivity index is accounted for by this interaction (OP) term, with the remaining ~80 percent attributable to the unweighted average of firm productivity. The baseline model, with this moment untargeted, successfully replicates this 80/20 split. By contrast, the leading benchmark model of Moscarini and Postel-Vinay (2016) (MPV2016), calibrated to the same British data, attributes nearly all of the variance of labor productivity to the OP/worker reallocation term, grossly overstating the importance of job-ladder dynamics.

Structural decomposition of labor productivity. Using the calibrated baseline model to decompose the variance of aggregate labor productivity over the post-war British business cycle (“GDP shocks” going back to 1955), the baseline model attributes approximately 30 percent to the direct effect of the aggregate productivity shock, approximately 50 percent to changes in the distribution of active firms (the “firm ladder” or firm selection component), and approximately 20 percent to the worker reallocation component (the OP interaction term). This result is robust to an alternative calibration with a lower curvature of the hiring cost function (c1 = 1).

Persistence and mechanisms. The impact of recessions on the job ladder is persistent: while the aggregate productivity shock is typically close to its pre-recession value four years after a typical recession onset, the overall allocation of workers to firms remains clearly worse relative to the pre-recession level at that same horizon. The Great Recession, viewed through the lens of the model, is a large but not unusually large recession.

Firm selection with multiple aggregate shocks. An unexpected finding concerns the direction of firm selection. With a single aggregate productivity shock, the model generates a standard “cleansing” mechanism: negative shocks raise the firm exit threshold, so surviving firms are on average more productive. However, when additional shocks to the exogenous separation rate (δ) and hiring cost scale (c0) are included — as required to match the volatility of labor market flows — firm selection instead amplifies the decline in labor productivity. The mechanism is a general equilibrium one: a higher separation rate lowers the optimal wage contract (since greater separation risk is passed on to workers), which in turn lowers the entry-exit threshold. Less productive firms become viable because their employees face higher unemployment risk and therefore accept lower wages; moreover, a larger pool of unemployed workers makes it easier for low-productivity firms to recruit.

Wage flexibility tension. The model implies a pass-through elasticity of wages to productivity shocks of approximately 0.7, well above the 0.05–0.2 range typically found empirically.

Scope Conditions

All calibration and quantitative results pertain to Britain for the period 1997–2018 (firm-level data) and 1955–2018 (GDP-based aggregate shocks). The model abstracts from decreasing returns to scale in production and from nominal rigidities. The tractability results rely on specific assumptions about the hiring cost function; the rank-monotonicity condition requires sufficient convexity (hc’’(h)/c’(h) ≥ 1).

In depth

Q1. What is the central tractability result and why does it matter for computational feasibility?

A: Result 1 (“size-independence”) shows that, because both the production technology and the hiring cost function are constant returns to scale, the firm’s present discounted value of profits is linear in employment. As a result, per-worker profits are independent of firm size, and optimal firm policies — the hiring rate, the contract value offered to workers, and the continuation/exit decision — all depend only on the firm’s current productivity, not on its size. This collapses the state space from the full joint distribution of firm productivity and employment size to the employment-weighted measure of firm productivity Lt(p), a uni-dimensional object. Without this result, the model would require tracking the entire joint firm distribution, making it computationally intractable.

Q2. What is a rank-monotonic equilibrium (RME) and what conditions guarantee it?

A: An RME is a recursive equilibrium in which the optimal contract offered by a firm is weakly increasing in that firm’s current productivity realization, for all aggregate states. Result 2 provides sufficient conditions: (i) the Markov process for firm-specific productivity satisfies first-order stochastic dominance (more productive firms today are more likely to be more productive tomorrow), (ii) the distribution of offered contracts is everywhere differentiable (ruling out mass points), and (iii) the hiring cost function satisfies hc’’(h)/c’(h) ≥ 1 — a sufficient convexity condition. The economic interpretation of the convexity condition is that firms must find retention (offering higher wages) sufficiently costly relative to new hiring that more productive firms optimally choose to use the wage margin to limit quits. The baseline calibration yields c1 ≈ 5.9 (so costs are highly convex in the hiring rate), though results are also reported for the minimum permissible c1 = 1.

Q3. What does the optimal employment contract look like in a rank-monotonic equilibrium, and what does it reveal about rent extraction?

A: In an RME, the optimal contract V(p,ω,L) is a weighted average of the value of unemployment U(ω,L) and the firm-workers’ joint surplus S(p,ω,L), where the weights are determined endogenously by the employment-weighted measure of firm productivity L. Specifically, the contract integrates the surplus of all firms with productivity below p, weighted by the share of employed workers at those firms, and divided by the mass of job seekers willing to accept the contract. As the employed workers’ relative search intensity s approaches zero, the contract converges to the value of unemployment — workers receive no rents. The endogenous bargaining weight evolves with the aggregate state over the business cycle, unlike standard Nash bargaining models with a fixed exogenous weight.

Q4. What firm-level moments are used to calibrate the steady-state model, and what is the logic behind the parameter-moment mapping?

A: Eight moments are targeted. From the BHPS worker data: the average UE rate (0.058) pins down the scale of hiring costs c0; the average EU rate (0.003) pins down the exogenous separation rate δ; and the average EE (job-to-job) rate (0.016) pins down the relative search intensity s. From the firm-level ARD/BSD data: average firm size (12.1 employees) pins down the entry probability µ; the share of job destruction from firm exits (0.526) disciplines the flow value of unemployment b; the autocorrelation of firm employment ln(n) (0.949 annually) disciplines the persistence of idiosyncratic productivity ρp; the interquartile range of firm-level labor productivity (1.129 log points) disciplines the volatility of idiosyncratic shocks σp; and the regression coefficient of firm employment growth on lagged labor productivity (0.136) disciplines the curvature of hiring costs c1. The baseline calibration fits all eight moments closely.

Q5. How does the calibrated model match non-targeted moments, and what does this establish?

A: The model generates several realistic features not targeted in calibration. It produces a realistic Pareto tail for the employment-size distribution (Pareto tail exponent of 1.033 in the model vs. 1.066 in the data), which arises from the combination of size-independent growth rates and firm entry and exit — conditions identified in the literature as generating power law distributions. The model also matches the dispersion of employment costs per worker across firms (capturing about 70 percent of the interquartile range of ECi,t), the slope of a regression of employment costs on labor productivity (model: 0.685 vs. data: 0.704), and the slope of a regression of employment growth on employment costs (model: 0.162 vs. data: 0.131). These non-targeted matches provide independent validation of the model’s wage-determination mechanism.

Q6. Why is a single aggregate productivity shock insufficient to match labor market fluctuations, and what additional shocks are needed?

A: With a single aggregate productivity shock calibrated to match the autocorrelation and standard deviation of log GDP, the model generates labor market fluctuations that are roughly an order of magnitude smaller than in the data. For example, the standard deviation of the EU transition rate is 4.1×10⁻⁴ in the single-shock model versus 2.3×10⁻³ in the data. Adding a discount rate shock (ω,r) partially helps but still leaves the job-finding rate (UE) more than 50 percent too smooth. Adding a separation rate shock (ω,δ) substantially increases EU and UE volatility but generates insufficient EE (job-to-job) volatility. The combination (ω,δ,c0) — adding a shock to the scale of hiring costs c0 — brings the standard deviations of EU and UE close to the data (2.0×10⁻³ and 4.0×10⁻⁴ vs. data 2.3×10⁻³ and 2.7×10⁻⁴), though the model still generates slightly under half the observed volatility in EE rates. This combination is the baseline for the quantitative analysis.

Q7. What is the OP decomposition, how is it computed from the firm-level data, and what does it measure in the model?

A: The aggregate labor productivity index LPt is constructed from firm-level data as the employment-share-weighted average of log value added per worker across firms. The OP decomposition writes this as LPt = LPt_bar + OPt, where LPt_bar is the unweighted (simple) average of firm-level productivity and OPt is the covariance between employment shares and labor productivity (the “interaction term”). In the data, OPt increases when workers are disproportionately employed at above-average-productivity firms. In the model, LPt_bar maps onto the average (log) productivity of active firms — the support of the job ladder — while OPt maps onto the difference between the employment-weighted and the unweighted averages of firm productivity, directly measuring how high up the ladder workers are located relative to the set of active firms. Around 20 percent of the variance of LPt in the British data is accounted for by OPt, and the model replicates this.

Q8. How does the Great Recession appear in the OP decomposition, and does the model fit the decomposition during this episode?

A: During the Great Recession (2008q2–2009q3 in the UK), around 20 percent of the overall fall in the labor productivity index is accounted for by the fall in the OP interaction term, with the remaining 80 percent coming from the fall in the unweighted average firm productivity. The model, even though it does not target this decomposition in calibration, successfully matches both the average firm productivity component and the interaction (OP) component during the Great Recession. This matching holds both in the baseline calibration (c1 ≈ 5.9) and in the alternative calibration with c1 = 1. The model also matches the analogous decomposition for employment costs per worker (ECt), an additional non-targeted validation.

Q9. Why does firm selection amplify rather than cleanse in the baseline multi-shock calibration?

A: In the single-shock (productivity ω only) model, a negative productivity shock lowers surplus at all firms, raising the exit threshold pE and thus selecting out low-productivity firms — the standard “cleansing” mechanism. In the multi-shock baseline, the additional separation rate shock (δ) generates a less intuitive mechanism. A higher δ lowers the optimal wage contract (since increased separation risk is passed on to workers: ∂V/∂δ ≤ 0), which reduces the value of continued employment. This lowers the joint firm-worker surplus threshold for exit, making it viable for low-productivity firms to remain active. Moreover, the larger pool of unemployed workers (generated by the δ shock) depresses the outside option of workers and makes it easier for low-productivity firms to recruit. As a result, the entry-exit threshold pE,t falls — the set of active firms becomes less productive on average — producing a negative firm selection contribution to labor productivity and a positive (amplifying rather than cleansing) contribution to the variance of LPt.

Q10. What is the structural variance decomposition of labor productivity in the baseline model?

A: Simulating the baseline model over the post-war British business cycle (1955–2020, GDP shocks), the variance of aggregate labor productivity LPt decomposes into three structural terms: approximately 30 percent (0.296) from the direct effect of the aggregate productivity shock ln(ωt); approximately 50 percent (0.541) from changes in the average productivity of active firms E[KP bar_t(ln p)] — the “firm ladder” or firm selection component; and approximately 20 percent (0.163) from the worker reallocation component OPt = E[LP bar_t(ln p)] − E[KP bar_t(ln p)]. This decomposition implies that roughly 70 percent of fluctuations in labor productivity are driven by worker reallocation broadly defined (the firm ladder plus the interaction term), with the firm selection component being the largest single driver. The result is robust to the alternative c1 = 1 calibration (30/49/22 percent split).

Q11. How does the baseline model compare to MPV2016 in the variance decomposition?

A: In the multi-shock calibration (ω,δ,c0), the MPV2016 model calibrated to the same British data attributes approximately 97.7 percent (0.977) of the variance of LPt to the worker reallocation (OP) term, with essentially none attributed to a firm selection term (since there is no firm entry and exit in MPV2016). This is nearly five times the 20 percent share attributed to worker reallocation in the data and in the baseline model. In the single-shock (ω) calibration, both models attribute a more modest share to worker reallocation (7.2 percent for the baseline model, 0.1 percent for MPV2016 with c1=5), and the difference narrows considerably. The contrast thus stems from the interaction of firm dynamics with multiple aggregate shocks: allowing for endogenous firm entry and exit is critical to prevent the model from overstating the role of the job ladder.

Q12. How persistent is the impact of recessions on the job ladder, based on the model simulations?

A: The paper simulates the structural decomposition of labor productivity starting from each of seven post-war British recessions (defined by two consecutive quarters of negative GDP growth). On average across these recessions, the aggregate productivity shock ln(ωt) is close to its pre-recession level by four years after the recession onset. However, the overall employment-weighted average productivity E[LP bar_t(ln p)] — reflecting workers’ position on the job ladder — remains clearly below its pre-recession value at the four-year horizon, indicating persistent misallocation. The OP interaction term accounts for approximately 20 percent of the total drop in the employment-weighted productivity measure three years after a typical recession onset. Through the model’s lens, the Great Recession is a large recession but not an outlier relative to the historical distribution.

Q13. What does the counterfactual with countercyclical unemployment benefits reveal about the tradeoff between firm selection and worker reallocation?

A: When the flow value of unemployment is made countercyclical (falling in recessions, rising in expansions — mimicking US unemployment insurance extension programs), the model generates a sign reversal in the firm selection (“firm ladder”) component. With countercyclical b, the unemployment value rises in recessions, which raises the minimum wage firms must offer and raises the exit threshold pE,t: fewer low-productivity firms survive, improving the composition of active firms. However, countercyclical benefits also amplify the slowdown in job-to-job reallocation: the higher value of unemployment reduces workers’ willingness to accept job offers, and all firms cut recruitment since optimal wage contracts must rise. The OP interaction term therefore falls more sharply than in the baseline model. The counterfactual with ϵb,ω ∈ {−100, −50} finds that the positive “firm ladder” effect dominates on net, so the overall allocation of workers to firms improves relative to the baseline after a typical recession under countercyclical unemployment benefits.

Q14. What is the numerical solution method, and why are standard linearization approaches inapplicable?

A: The model is solved in two steps. First, aggregate shocks are shut down and the steady-state rank-monotonic equilibrium is solved numerically by discretizing the firm productivity process (401 grid points via Tauchen’s method) and iterating on the value function and the employment-weighted productivity measure until convergence. Second, aggregate shocks are reintroduced using a simulation-based approach adapted from Krusell and Smith (1998): the employment-weighted distribution of productivity is summarized by Nm = 2 moments (plus the unemployment rate), and the value functions are parameterized as polynomials in the aggregate state, with coefficients updated by regression until convergence. Standard linearization methods (Reiter 2009) are inapplicable because the endogenous entry-exit decision creates a kink (discontinuity) in value functions at the productivity threshold pE, making first-order approximations around the steady state inaccurate. Accuracy tests based on den Haan (2010) show that the polynomial approximation generates errors of at most 0.065 percent for value functions and at most 1 percentage point for the unemployment rate across simulation paths.

Key Concepts

1. Rank-Monotonic Equilibrium (RME) A recursive equilibrium in which the optimal state-contingent employment contract V(p,ω,L) offered by a firm is weakly increasing in the firm’s current productivity realization p, for all aggregate states (ω,L). This property implies that the job ladder maps one-for-one onto the firm productivity ladder: workers always prefer to work at more productive firms. The paper shows this property holds under a sufficient convexity condition on hiring costs (hc’’(h)/c’(h) ≥ 1) and first-order stochastic dominance of the productivity process.

2. Size-Independence The property that a firm’s optimal policies — the hiring rate h(p), the employment contract V(p), and the entry/exit decision χ(p) — are all independent of the firm’s current employment size n. This follows from constant returns to scale in production and hiring, which implies that firm profits are linear in employment. Size-independence reduces the model’s relevant state space to the employment-weighted distribution of firm productivity, enabling tractability.

3. Employment-Weighted Distribution of Firm Productivity (L_t(p)) The measure recording, for each productivity level p, the total employment at firms with productivity at most p. This is the sufficient statistic for the state of the job ladder at any point in time: combined with the aggregate shock ω, it determines all equilibrium policy functions and value functions. In the model, it replaces the full joint distribution of firm productivity and employment size that would otherwise be required.

4. OP Decomposition (Olley-Pakes Decomposition) The decomposition of the aggregate employment-weighted labor productivity index LPt into: (a) the unweighted average firm productivity LPt-bar, which summarizes the productivity of active firms (the support of the job ladder); and (b) an interaction term OPt, the covariance between employment shares and firm-level productivity, which measures how well workers are allocated across the productivity distribution (i.e., how high up the ladder workers sit given the set of active firms). In the model, (a) maps to E[KP bar_t(ln p)] and (b) maps to OPt = E[LP bar_t(ln p)] − E[KP bar_t(ln p)].

5. Contract Posting The wage-setting protocol in which each firm commits upon entry to a full state-contingent employment contract — a schedule mapping each future realization of aggregate and idiosyncratic productivity to a wage and continuation decision — and is bound by an equal treatment constraint to offer the same contract to all employees. Workers cannot renegotiate based on outside offers. This protocol produces a well-defined closed-form for the optimal contract in an RME and differs from alternating-offer bargaining (Nash bargaining) in that the bargaining weights are endogenous rather than fixed.

6. Firm-Workers’ Joint Surplus (S_t(p)) The total present discounted value accruing to the firm-worker pair: firm profits per worker plus the contract value promised to workers. Because utility is transferable (risk neutrality) and the firm fully commits to its contract, this surplus depends only on the firm’s current productivity and the aggregate state — not on the promised contract value V. The surplus S_t(p) is the key object determining firm entry/exit (the firm continues if and only if S_t(p) ≥ U_t) and optimal hiring (the marginal return to an additional hire equals S_t(p) − V(p)).

7. Cleansing vs. Anti-Cleansing Firm Selection In models with endogenous firm entry and exit, a negative aggregate shock can either raise or lower the productivity threshold for firm survival. “Cleansing” refers to the standard mechanism where a negative productivity shock raises the exit threshold, selecting out low-productivity firms and improving the average quality of survivors. “Anti-cleansing” (as in the baseline multi-shock calibration) occurs when separation rate or hiring cost shocks lower the optimal wage contract and reduce the exit threshold, allowing less productive firms to survive and worsening average firm productivity.

Firm idiosyncratic risk and productivity investment: Macroeconomic implications

Mon, 01 Jan 0001 00:00:00 +0000

This paper quantifies how idiosyncratic firm-level risk affects aggregate output, TFP, and firm life-cycle growth in an environment where firm productivity evolves endogenously through risky investment. The paper embeds endogenous productivity investment into a Lucas span-of-control model with risk-averse firm owners and endogenous entry and exit, and studies the effects of mean-preserving increases in the variance of returns to productivity investment. A mean-preserving increase in the variance of firm productivity shocks that raises the firm exit rate by 10% (from 0.10 to 0.11) is estimated to cause a 0.73% decline in output, a 0.38% decline in measured TFP, and a 3.69% decline in firm productivity investment; these elasticities remain approximately constant in the empirically relevant range. The driving force is that risk-averse firm owners reduce their risky productivity investment as variance rises; if capital financing constraints are present—as is common in developing economies—these effects are amplified and the increase in uncertainty may also slow firm life-cycle growth. Previously circulated as “Uncertainty, Firm Lifecycle Growth, and Aggregate Productivity.”

In depth

Q1. What distinguishes this paper from standard models of firm misallocation?

Unlike the bulk of firm misallocation literature (Hsieh-Klenow 2009; Gopinath et al. 2017; Sraer-Thesmar 2023), which takes firm productivity as exogenous, this paper models productivity as an endogenous outcome of risky investment, so that idiosyncratic uncertainty affects allocative efficiency not only through selection effects but also through its discouragement of productivity investment by risk-averse owners. The paper incorporates endogenous productivity investment into a standard Lucas span-of-control model, allowing the model to capture how higher uncertainty reduces the incentive to invest in productivity, on top of any selection effects from the exit option.

Q2. What are the two opposing effects of higher idiosyncratic risk?

Higher idiosyncratic firm-level risk has two opposing effects on aggregate productivity: (i) a selection effect—a mean-preserving increase in variance leads to stronger selection and raises the productivity of survivors while reallocating exiters to alternative productive uses—that tends to raise average productivity; and (ii) a productivity investment effect—risk-averse owners reduce risky productivity investment in response to higher variance—that tends to reduce aggregate productivity and firm life-cycle growth. The paper shows quantitatively that the productivity investment effect dominates in the baseline calibration, so that higher idiosyncratic risk reduces output and TFP despite positive selection effects.

Q3. What are the main quantitative findings?

A mean-preserving increase in the variance of firm productivity shocks calibrated to raise the firm exit rate by 10% (from 0.10 to 0.11) results in a 0.73% decline in output, a 0.38% decline in measured TFP, and a 3.69% decline in firm productivity investment; these elasticities remain approximately constant in the empirically relevant range. The exit-rate increase from 0.10 to 0.11 is also associated with a 7.5% increase in the job destruction rate and a 14.6% increase in the standard deviation of firm growth rates—the latter is less than one-fifth of the increases in these risk measures observed when comparing India or Mexico to the U.S.

Q4. How do capital financing constraints interact with the results?

When firms face capital financing constraints—as is common in developing economies—the negative effects of higher idiosyncratic risk are amplified and the increase in uncertainty may also slow firm life-cycle growth. The mechanism is that constrained firms must rely more heavily on internal financing, making risk-averse owners even more sensitive to increases in variance. The paper implies that the macro-financial implications of idiosyncratic risk are more severe in developing economies where both idiosyncratic risk levels and financing constraints are greater—consistent with cross-country patterns of firm growth dynamics.

Key concepts

productivity investment : endogenous spending by firms on activities that shift their productivity process; in the model, this investment exposes firm owners to idiosyncratic risk via the innovation in the productivity process; the key margin through which higher uncertainty reduces aggregate productivity and output. mean-preserving increase in variance : a statistical experiment that increases the spread of the distribution of returns to productivity investment while leaving the mean unchanged; used here to isolate the pure risk effect on firm behavior and aggregate outcomes from any change in expected returns. span-of-control model : the Lucas (1978) model of firm size distribution with decreasing returns to scale in the entrepreneurial input; used as the production environment; extended here by adding endogenous productivity investment and endogenous entry and exit.

FraNK: Fragmentation in the NK Model

Mon, 01 Jan 0001 00:00:00 +0000

Moro and Nispi Landi develop FraNK, a multi-country New Keynesian model designed to study geoeconomic fragmentation — defined, following Aiyar et al. (2023), as a policy-driven reversal of economic integration guided by strategic considerations. The model extends Gali and Monacelli (2005) along three dimensions: it is multi-country rather than small-open-economy; it assumes incomplete international financial markets, relaxing perfect risk sharing; and it incorporates commodities as intermediate inputs in production, capturing both domestic and imported commodity sourcing. A fragmentation shock is modeled as a simultaneous increase in three tax rates imposed on rival countries: a tax on imports of final goods, a tax on imports of commodities, and a tax on the purchase of foreign bonds (capital controls).

The paper proceeds in two stages. First, under a symmetric two-bloc calibration, closed-form analytical results establish the distinct macroeconomic channels of each tax. The good import tax operates through both demand (households reduce consumption of foreign goods) and supply (firms face higher real marginal costs), with the demand channel dominating: output falls unambiguously and PPI inflation decreases, though CPI inflation rises on impact due to the direct pass-through of import prices. The commodity import tax operates exclusively through supply — raising intermediate input costs — so both output and PPI inflation move in the same direction: output falls and PPI inflation rises. The bond tax is neutral under symmetric calibration: because each country’s net foreign asset position is unchanged (each country reduces its holdings of rival-bloc bonds by exactly as much as it reduces its own issuance), output and inflation are unaffected.

Second, the model is calibrated to four asymmetric regions: the United States (US), US-allied countries including the European Union (WE), the China-Russia-aligned bloc (CR), and a neutral rest of the world (NE). Bloc assignment follows Den Besten et al. (2023), using a political alignment index combining sanctions data, military imports, Belt and Road Initiative participation, and UNGA voting on Russia’s invasion of Ukraine. The US and WE impose all three taxes on CR, and vice versa; NE neither imposes nor receives taxes.

Five main findings emerge from the asymmetric simulation. First, fragmentation predominantly affects CR and WE: both experience substantial declines in consumption and production across all three tax scenarios, with CR most affected when goods or asset taxes are applied. Second, the US is largely insulated: its lower trade and financial exposure to the rival bloc relative to WE limits the pass-through of fragmentation. Third, spillovers to neutral NE are nearly negligible: the expenditure-switching channel (which raises demand for untaxed NE goods) and the global income channel (which reduces demand for all goods as the world becomes poorer) roughly cancel each other out. Fourth, fragmentation is not necessarily inflationary: whether PPI inflation rises or falls depends on the relative weight of commodities in production and the mix of taxes applied — a goods tax lowers PPI inflation, while a commodity tax raises it. Fifth, the bilateral exchange rates most affected are those of the CR bloc, which appreciate under goods and asset taxes and depreciate under commodity taxes.

Sensitivity analyses confirm robustness across higher elasticity of substitution between domestic and foreign goods (eta raised from 1.5 to 5), lower elasticity of substitution between labor and commodities (xi lowered from 0.4 to 0.1), tighter financial market integration (bond transaction costs multiplied by 5), and permanent shocks (persistence rho raised to 1). Under permanent shocks, the goods-tax effect on PPI inflation approaches zero — consistent with the closed-form result — while commodity-tax effects on production become larger and more persistent.

Q: What is the core research question of FraNK? A: The paper asks how geoeconomic fragmentation — modeled as policy-driven increases in taxes on rival countries’ goods, commodities, and bonds — affects output, inflation, exchange rates, and capital flows at both the global and country level. It also asks whether different sources of fragmentation (real versus financial) have distinct macroeconomic implications, and whether neutral countries experience meaningful spillovers.

Q: How does the model depart from the Gali-Monacelli (2005) benchmark? A: Three departures are made. The model is multi-country (N countries) rather than a single small open economy facing the rest of the world. Financial markets are incomplete, so international risk sharing is imperfect — a realistic assumption in a fragmented world. And intermediate-good production uses a CES bundle of labor and a commodity bundle that includes both domestic and imported commodities, which is essential for capturing commodity market disruptions such as those following Russia’s invasion of Ukraine.

Q: What are the three tax instruments and what does each represent? A: The goods import tax (tau_ijt) is a tariff on final goods imports, representing trade barriers. The commodity import tax (tau_O_ijt) is a tariff on imported commodity inputs, representing sanctions or restrictions on energy and raw material trade. The bond tax (theta_ijt) is a capital control discouraging purchases of bonds issued by rival countries, representing financial fragmentation or sanctions on financial assets.

Q: What does the closed-form symmetric-calibration result establish about output? A: Under the symmetric calibration, both the goods import tax and the commodity import tax reduce output unambiguously (Proposition 3.3). The bond tax is neutral for output under symmetry because each country’s net foreign asset position is unchanged — any reduction in holdings of rival-bloc bonds is exactly matched by a reduction in own-bond issuance, leaving net positions and aggregate demand unaffected (Proposition 3.4).

Q: Why does the goods import tax reduce PPI inflation while the commodity import tax raises it? A: The goods import tax operates through two opposing channels: a demand channel (households substitute away from foreign goods, reducing aggregate demand) and a supply channel (import taxes raise firms’ real marginal costs). The closed-form solution establishes that the demand channel dominates, so PPI inflation falls. The commodity import tax operates only through the supply channel — raising the cost of intermediate inputs directly — so PPI inflation rises unambiguously. CPI inflation rises on impact under the goods tax because import prices are directly included in the CPI even as PPI falls.

Q: Under what condition does simultaneous fragmentation (goods and commodity taxes together) produce PPI inflation? A: When both taxes are imposed simultaneously, the net effect on PPI inflation is ambiguous. The paper shows analytically that PPI inflation rises if and only if omega * gamma_O_tilde > gamma_tilde * (phi/sigma), where omega is the commodity weight in production, gamma_O_tilde captures commodity import weights, and gamma_tilde captures goods import weights. That is, fragmentation tends to be stagflationary the larger the weight of commodities in the production function, consistent with the empirical finding in Caldara et al. (2024) of stagflationary effects from elevated geopolitical risk.

Q: Why is the US more shielded from fragmentation than its WE allies? A: The US has relatively lower trade and financial exposure to the CR bloc compared to WE. Because the trade and financial weights calibrated from UN Comtrade, IMF CPIS, BIS LBS, and IMF CDIS data place WE in closer economic relationships with CR countries, a tax on CR imports or assets falls more heavily on WE than on the US. This asymmetry is a direct consequence of the calibration: no structural or strategic advantage of the US is assumed beyond its actual pattern of trade and financial linkages.

Q: What happens to the CR bloc’s exchange rate under each tax scenario? A: Under the goods import tax, the CR exchange rate appreciates: CR’s own tax reduces demand for US/WE goods, increasing domestic demand relative to the rest of the world, and the reduced demand for CR bonds from abroad raises CR interest rates, further attracting capital. Under the commodity import tax, the CR exchange rate depreciates: lower commodity demand reduces CR commodity prices and production, shifting labor toward goods, increasing goods supply, and lowering the CR price level relative to trading partners. Under the bond tax, the CR exchange rate also appreciates, as reduced CR demand for US/WE bonds is interpreted by markets as a shift in capital flows favoring CR assets.

Q: What explains the near-zero spillovers to neutral countries? A: Two forces operate on NE in opposite directions. The expenditure-switching channel raises demand for NE goods and commodities, as taxing countries divert purchases away from taxed rival goods toward untaxed NE products — a positive demand shock for NE. The global income channel reduces demand for all goods, including NE’s, as the taxing and taxed regions become poorer and reduce imports from everywhere. In the calibration these two forces approximately cancel, leaving NE macroeconomic variables nearly unchanged.

Q: How is the commodity sector modeled, and why does this matter for the commodity tax result? A: Each country has a representative commodity firm using a linear production function (Y_iOt = A_iO * H_iOt), where A_iO is interpretable as a per-capita endowment of natural resources. Intermediate-good firms use a CES bundle of labor and commodities (domestic and imported) with elasticity xi=0.4 between the two. When the commodity import tax is imposed, firms face higher commodity input costs, raising real marginal costs and PPI inflation while depressing production. The asymmetry between commodity exporters (CR, NE) and importers (WE) under this tax is the main source of differential regional effects.

Q: How are financial openness differences across country pairs captured, and what effect do they have? A: Bond transaction costs psi_ijF differ across pairs: psi_12F = psi_21F = 0.01 for the US-WE pair (reflecting high financial integration), while all other pairs have psi_ijF = 1 — one hundred times higher — reflecting limited cross-bloc financial integration. The sensitivity analysis multiplies all psi_ijF by 5 (less open financial markets) and finds that bond position volatility falls but qualitative results are unchanged, confirming that the financial openness calibration does not drive the main results.

Q: What are the main caveats acknowledged by the authors? A: The model omits capital accumulation, so investment dynamics are absent. Cross-country production networks (global value chains) are not modeled, which the authors acknowledge limits the richness of the production structure relative to Baqaee-Farhi (2024) style models. Domestic financial markets are assumed frictionless. The model has no role for dollar dominance in the global economy, which may matter for exchange rate and capital flow dynamics in reality. These are flagged as directions for future research.

Q: What is the key result for permanent (rho=1) versus temporary (rho=0.9) fragmentation shocks? A: Under permanent shocks, output reductions become permanent rather than transitory. For the goods import tax, the effect on PPI inflation approaches zero in the permanent case, consistent with the closed-form prediction that the demand channel effect on PPI vanishes when the tax persists indefinitely (households no longer have an intertemporal substitution motive). The commodity tax permanent shock induces a larger and more persistent fall (rise) in production for commodity importers (exporters). Bond tax permanent shock has larger magnitude effects but is otherwise qualitatively similar to the temporary case.

Q: How does FraNK relate to the existing DSGE literature on sanctions and trade wars? A: The paper positions FraNK as providing a unified framework covering all three forms of fragmentation (goods, commodity, and financial) simultaneously, with nominal rigidities allowing for inflation analysis, closed-form analytical results for transparency, and a multi-country setup rather than small-open-economy. Ghironi et al. (2024) study sanctions in a three-country model but without nominal rigidities. Itskhoki and Mukhin (2022) analyze sanctions on Russia but in a small-open-economy. Attinasi et al. (2023) and Conteduca et al. (2024b) use richer production networks (Baqaee-Farhi) but are static and exclude financial fragmentation. FraNK trades production network richness for dynamics, nominal rigidities, financial fragmentation, and analytical tractability.

Geoeconomic fragmentation: A policy-driven reversal of economic integration, often guided by strategic or geopolitical considerations, operationalized in FraNK as simultaneous increases in taxes on rival countries’ goods imports, commodity imports, and bond purchases.

Fragmentation shock: A simultaneous increase in three tax rates — goods import tax (tau), commodity import tax (tau_O), and bond tax (theta) — applied by each bloc against the other, representing the policy instruments through which integration is reversed.

Demand channel (goods tax): The mechanism by which a goods import tax reduces aggregate demand, as households substitute away from now-more-expensive foreign goods, reducing output and — because this channel dominates the supply channel — lowering PPI inflation.

Supply channel (commodity tax): The mechanism by which a commodity import tax raises intermediate input costs for firms, increasing real marginal costs and PPI inflation while reducing output — a purely cost-push effect with no offsetting demand-side force.

Bond tax neutrality: Under symmetric calibration, capital controls on rival-bloc bonds are macroeconomically neutral because each country’s net foreign asset position is unchanged: the reduction in holdings of rival bonds is exactly matched by a reduction in own-bond issuance, leaving the IS curve and Phillips curve unaffected.

Expenditure-switching channel: The force by which fragmentation between two blocs diverts import demand toward untaxed third-country (neutral) goods, generating a positive demand spillover for NE countries that roughly offsets the global income channel.

Global income channel: The negative spillover to neutral countries arising from the reduction in world income caused by fragmentation between the taxing blocs, which reduces demand for all goods including those of neutral producers, approximately canceling the expenditure-switching channel.

Hedge funds and the Treasury cash-futures basis trade

Mon, 01 Jan 0001 00:00:00 +0000

The U.S. Treasury market is the deepest and most liquid fixed-income market in the world, yet in March 2020 it experienced unprecedented dysfunction—widening bid-ask spreads, skyrocketing repo rates, and diverging arbitrage spreads that prompted massive Federal Reserve intervention. This paper documents the rise and near-collapse of the Treasury cash-futures basis trade—an arbitrage strategy among hedge funds exploiting a persistent disconnect between cash Treasury prices and futures prices—as a central feature of that episode. Using regulatory datasets on hedge fund exposures and repo transactions, the authors show that at its peak the basis trade accounted for an estimated $400–$500 billion in positions, constituting more than 60% of total hedge fund Treasury exposure, more than 70% of hedge fund repo borrowing, and more than 25% of primary dealers’ repo lending. A model and empirical evidence link the trade’s growth after 2016 to broader Treasury market developments, and show how the trade’s reliance on short-term repo financing creates both margin risk and rollover risk. In March 2020 many of these risks materialized, though the unwinding of basis positions was likely a consequence rather than the primary cause of the stress; prompt Federal Reserve intervention may have prevented a liquidity spiral.

In depth

Q1. What is the Treasury cash-futures basis trade and why did it become popular?

The basis trade exploits the arbitrage relationship Pₜ,τ = ΣBₜ,ₛcₛ + Bₜ,T Fₜ,τ,T: when futures prices are too high relative to the present value of the deliverable bond, traders go “long the basis” by buying the cash bond and shorting the futures, financing the long position in the overnight repo market. The trade became popular following 2016 as demand for long Treasury futures positions grew (from institutional investors seeking leveraged duration exposure) while the supply of warehousing capacity from dealers contracted under post-crisis regulatory constraints. Hedge funds stepped in as the marginal warehouser, exploiting the resulting premium embedded in futures prices. The trade is nearly zero net-cash but requires continuous repo rollover.

Q2. How large did the trade become and how was its size estimated?

Using regulatory data—specifically CFTC Form 40 (hedge fund futures positions), SEC Form PF (AUM and derivatives exposures), and FR 2004 (primary dealer repo data)—the authors estimate basis trade positions peaked at $400–$500 billion, comprising more than 60% of hedge fund Treasury exposure, more than 70% of hedge fund repo borrowing, and more than 25% of primary dealer repo lending to hedge funds. The data allow the authors to identify basis positions directly, distinguishing them from outright long Treasury positions, by matching the simultaneous long cash / short futures pattern that defines the trade. The estimates underscore that hedge funds had become systemically important participants in Treasury market intermediation.

Q3. What financial stability risks does the basis trade create?

The basis trade creates two interrelated risks: margin risk (variation margin calls on futures positions can force immediate liquidation) and rollover risk (if repo lenders withdraw funding, the cash Treasury position must be sold). The paper’s model formalizes how limits to arbitrage—specifically repo market illiquidity and margin requirements—impair risk-sharing between dealers and holders of long futures positions. These constraints mean that even a moderate adverse price move can trigger a self-reinforcing cycle: higher basis volatility → margin calls → forced sales → further basis widening → further margin calls.

Q4. What happened in March 2020 and what was the Federal Reserve’s role?

Beginning in early March 2020, the COVID-19 pandemic triggered a “dash for cash” that disrupted Treasury market functioning: bid-ask spreads widened dramatically, repo rates spiked, and the cash-futures basis moved sharply against basis traders, generating large margin calls. The authors find that while Treasury market disruptions spurred hedge funds to sell Treasuries, the unwinding of the basis trade was likely a consequence rather than a primary cause of the stress. The Federal Reserve intervened by dramatically expanding Treasury purchases from dealers and offering unlimited repo and reverse repo facilities, which likely prevented a liquidity spiral by removing the constraint on dealer intermediation capacity. The paper argues this episode highlights structural vulnerabilities in Treasury market intermediation arising from the shift of warehousing capacity to hedge funds.

Key concepts

Treasury cash-futures basis trade : an arbitrage strategy in which a trader simultaneously holds a long position in cash Treasury bonds (funded via repo) and a short position in Treasury futures, profiting from the convergence of cash and futures prices at delivery.

warehousing role of hedge funds : the function of holding Treasury bonds on behalf of institutional investors who want long futures exposure, financed in the repo market; this creates a link between Treasury, futures, and repo markets and exposes the system to repo rollover and margin risk.

rollover risk : the risk that short-term repo lenders decline to roll over funding at maturity, forcing the borrower to sell the collateral asset (Treasury bonds) at potentially distressed prices.

Heterogeneous innovations and growth under imperfect technology spillovers

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question. Jo and Kim ask two related questions: (1) How do firms use different types of innovation when learning others’ technology takes time? (2) How does this process alter the aggregate implications of firm innovation, particularly in the context of increasing competition?

Model. The paper develops a discrete-time infinite-horizon endogenous growth model with multi-product firms pursuing two types of innovation — “own-innovation” (improving existing product quality) and “creative destruction” (entering new product markets by displacing incumbents) — subject to a novel friction called “imperfect technology spillovers.” The friction takes the specific form of lagged learning: creative destruction builds on the one-period-lagged technology of the target market’s incumbent, while only the incumbent can observe the current frontier technology level. This one-period lag creates a technology gap (Δ = q_t / q_{t−1}) between the incumbent’s frontier and the level available to rivals. Four possible technology gap values arise in equilibrium: Δ₁ = 1 (no gap), Δ₂ = λ (one successful own-innovation), Δ₃ = η (one successful creative destruction), and Δ₄ = η/λ. The step sizes satisfy λ² > η > λ, meaning a single creative destruction improves quality more than a single own-innovation, but two consecutive own-innovations dominate a single creative destruction.

Key Mechanisms. The learning friction generates two novel mechanisms. First, the “market-protection effect”: incumbents with a technology advantage (Δ > 1) intensify own-innovation to widen the gap and protect their product lines when competitive pressure rises. Formally, own-innovation probability is highest for Δ₂ products and declines monotonically (z₂ > z₃ > z₄ > z₁), and ∂z₂/∂x > ∂z₃/∂x > 0 while ∂z₁/∂x < 0, conditional on value coefficients. Second, the “technological barrier effect”: higher overall own-innovation and creative destruction intensity widens the average technology gap across products, reducing rivals’ conditional probability of successfully taking over a product market. This is distinct from the standard Schumpeterian effect (lower expected future profits) and from the escape-competition effect in step-by-step models (which apply only to neck-and-neck, single-product firms).

Data and Empirical Strategy. The empirical analysis combines the USPTO PatentsView database, the Longitudinal Business Database (LBD), the Longitudinal Firm Trade Transactions Database (LFTTD), the Census of Manufactures (CMF), Compustat, and NBER-CES data, covering the universe of U.S. patenting firms from 1976 to 2016, with main analyses from 1982 to 2007. Own-innovation is proxied by the self-citation ratio of patents (the ratio of self-citations to total backward citations); creative destruction by new products added and low-self-citation patents. Exogenous competitive pressure comes from China’s WTO accession in 2001, instrumented by the industry-level NTR tariff gap (the gap between non-NTR and NTR rates in 1999) following Pierce and Schott (2016).

Empirical Findings. Pre-shock (1982–1999): patents with lower self-citation ratios (closer to creative destruction) have significantly longer backward citation gaps (coefficient −2.29 to −2.59, p < 0.01 across specifications), confirming that learning others’ technology takes more time. Creative-destruction-type patents also have higher market value (Kogan et al. stock return measure) and scientific value (forward citations), with self-citation ratio negatively associated with both (e.g., coefficient on self-citation for market value: −0.289 without firm FE; −0.110 with firm FE, p < 0.01). Conditional on patenting, higher self-citation ratios are negatively associated with employment growth (coefficient −0.256, p < 0.05), number of industries added (−0.158, p < 0.05), and products added (−0.274, p < 0.01).

Post-shock (DID): foreign competition had no statistically significant effect on overall patent counts, but firms with above-average innovation intensity in industries with high NTR gaps significantly increased their self-citation ratio — indicating a shift toward own-innovation. The triple-interaction coefficient is 0.795 (p < 0.01) with baseline controls. For a firm with average lagged innovation intensity (0.18) in an industry with an average NTR gap (0.291), this corresponds to a 4.2 percentage point increase in the seven-year growth rate of the self-citation ratio, representing a 15.0% increase relative to the average growth rate of 28.2 percentage points. Consistent with the technological barrier effect, firm entry rates are lower in industries with higher TFPR-skewness-based technological barriers (coefficient −0.012 to −0.016, p < 0.05).

Quantitative Analysis. Calibrated to the U.S. manufacturing sector in 1992, the model matches six target moments including average number of products (2.3), products added (0.3), firm entry rate (7.6%), average productivity growth (1.9%), high-growth-firm employment growth (22.5%), and import penetration (15.3%). Creative destruction contributes approximately 1.88 times more to growth per unit than own-innovation (step size ratio 0.075/0.04). The aggregate R&D-to-sales ratio (untargeted) is 4.6% in the model vs. 4.1% in data.

A counterfactual increasing outside entrants by 83% (matching the rise in import penetration from 15.3% to 25.1% between 1992 and 2007) generates a 1.51% increase in aggregate creative destruction arrival rate x, but firm-level creative destruction probability falls 1.33% and startup creative destruction also falls 1.33%. The aggregate R&D-to-sales ratio falls 1.6% and creative destruction R&D intensity falls 1.2%. Average domestic productivity growth declines 11.0%, with growth from creative destruction falling 13.0% and growth from domestic startups falling 1.7%. The total mass of domestic firms falls 6.4%.

In economies with creative destruction costs 80 times higher than the U.S. baseline, the same competitive pressure shock raises rather than lowers total R&D (by 1.0%), but domestic growth still falls 9.7%, because the marginal decline in creative destruction impedes the growth contribution and firm entry even when aggregate innovation spending rises.

In depth

Q1. What is the key friction that distinguishes this model from the existing multi-product firm literature (e.g., Klette and Kortum 2004; Akcigit and Kerr 2018)?

A: The key friction is “imperfect technology spillovers,” modeled as lagged learning: creative destruction can only build on the one-period-lagged technology of the target product (q_{j,t−1}), while the product’s current owner observes the frontier technology (q_{j,t}). In models without this friction — such as Akcigit and Kerr (2018) — rivals can instantly learn and copy frontier technology, so firms have no technological advantage and cannot protect their markets. In the current model, own-innovation by the incumbent widens the gap between q_{j,t} and q_{j,t−1}, creating a barrier that a rival must overcome even after successful creative destruction. This makes own-innovation an endogenous function of the technology gap, a feature absent from existing multi-product firm frameworks.

Q2. Why does the model predict that own-innovation increases with the technology gap up to a point, then decreases?

A: From Corollary 1, the ordering z₂ > z₃ > z₄ > z₁ reflects competing forces. Products with gap Δ₂ = λ gain the most from additional own-innovation in terms of reducing the probability of losing the product line (equation 2), so own-innovation is highest there. Products with Δ₃ = η or Δ₄ = η/λ already have substantial technological advantages from prior creative destruction, so the marginal value of own-innovation in reducing market loss probability is lower. Products with Δ₁ = 1 have no advantage at all: if a rival succeeds in creative destruction, the incumbent loses the product regardless of own-innovation (equation 1), so z₁ is lowest. Beyond a certain gap level, the incumbent is sufficiently protected that additional own-innovation has diminishing returns in deterrence.

Q3. What is the market-protection effect formally, and for which products is it strongest?

A: The market-protection effect (Corollary 2) is the positive response of a firm’s own-innovation to an increase in the aggregate creative destruction arrival rate x, conditional on the value coefficients A₁ and A₂ being fixed. It is strongest for products with Δ₂ = λ (∂z₂/∂x is the largest and positive), positive but weaker for Δ₃ = η (∂z₃/∂x > 0), of ambiguous sign for Δ₄ = η/λ, and negative for Δ₁ = 1 (∂z₁/∂x < 0). The asymmetry reflects the asymmetric payoff to own-innovation across gap levels: for Δ₂ products, successful own-innovation can turn a losing situation into a winning one because it shifts the technology gap from Δ₁ to Δ₂ from the rival’s perspective, effectively defeating the rival’s creative destruction attempt. This mechanism provides a micro-foundation for why frontier firms (like Google or NVIDIA) keep innovating intensely despite their technological leads, a pattern the standard step-by-step model cannot explain.

Q4. What is the technological barrier effect and how does it differ from the Schumpeterian effect?

A: The technological barrier effect refers to the reduction in rivals’ incentive for creative destruction caused by an increase in the average technology gap across product lines. When incumbents do more own-innovation or when outside firms do more creative destruction, the distribution of technology gaps shifts rightward (density at Δ₁ falls; density at Δ₂, Δ₃, Δ₄ rises). This raises the average technology barrier rivals must overcome to successfully take over a product market, reducing the conditional takeover probability x^{takeover} and the expected value of creative destruction B. In the U.S. counterfactual, the technological barrier effect accounts for 17.0% of the total change in the aggregate creative destruction rate x and 15.0% of the change in startup creative destruction x_e. In contrast, the Schumpeterian effect refers to the reduction in expected future profits from owning a product due to increased displacement risk (through the value coefficient A₂), a mechanism present in standard quality-ladder models. Both operate simultaneously but the technological barrier effect is a novel feature of this framework.

Q5. How is own-innovation vs. creative destruction measured empirically, and what validates this measure?

A: The self-citation ratio (the share of a patent’s backward citations that cite the same assignee’s earlier patents) is used as the primary measure: a higher ratio indicates greater reliance on the firm’s own prior knowledge, hence a higher probability that the innovation improves an existing product line (own-innovation). This is validated empirically in three ways. First, patents with lower self-citation ratios have significantly larger backward citation gaps (coefficient −2.29 to −2.59 across fixed-effect specifications on 728,721 observations), consistent with creative destruction requiring more time to learn others’ technology. Second, lower self-citation patents have higher market value and scientific value (forward citations), consistent with η > λ (creative destruction contributes more per event to quality). Third, firm-level regressions show that lower self-citation ratios are associated with higher employment growth, more products added, and more industries entered, consistent with creative destruction contributing more to firm expansion.

Q6. How does the DID identification strategy work, and what are the main results?

A: The identification exploits the removal of trade policy uncertainty (TPU) after China’s WTO accession in 2001. The treatment variable is the industry-level NTR gap (the gap between non-NTR and NTR tariff rates in 1999): industries with larger gaps experienced a larger reduction in uncertainty and thus a greater increase in Chinese import competition. The DID compares patenting firms across periods (1992–1999 vs. 2000–2007) and across high- vs. low-NTR-gap industries, with a triple interaction for firm-level innovation intensity (lagged five-year average patents per employee, normalized within two-digit NAICS). The main finding (Table 4): the NTR gap × Post interaction has no significant effect on overall patent counts (coefficient 0.238 without controls, standard error 0.237), but the triple interaction (NTR gap × Post × innovation intensity) has a positive and significant effect on the growth rate of the self-citation ratio (0.732 without controls, p < 0.05; 0.795 with baseline controls, p < 0.01). This implies that innovation-intensive firms in high-competition industries shifted their composition toward own-innovation, while overall patenting was unchanged — consistent with an offsetting rise in own-innovation and fall in creative destruction.

Q7. What are the aggregate growth effects of increasing competitive pressure in the calibrated model?

A: Using an 83% increase in outside entrants (matching the 1992–2007 rise in import penetration from 15.3% to 25.1%), average domestic productivity growth falls 11.0%. Decomposing: growth from domestic own-innovation falls 11.4%, growth from domestic creative destruction falls 13.0%, and growth from domestic startups falls 1.7% (Table 9). The aggregate R&D-to-sales ratio falls 1.6% and the creative destruction R&D intensity falls 1.2%, indicating that the decline in creative destruction R&D outweighs the rise in own-innovation R&D. The total mass of domestic firms falls 6.4% and the average number of products per firm falls 5.5%.

Q8. How do results differ in economies with high creative destruction costs vs. the U.S.?

A: When creative destruction costs (χ̃) are set 80 times higher than the U.S. baseline, the initial equilibrium has much lower creative destruction: R&D-to-sales ratio is 1.39% (vs. 4.58% in U.S.), creative destruction R&D intensity is 8.6% (vs. 63.9%), average number of products is 1.0 (vs. 2.3), and average domestic productivity growth is 1.4% (vs. 1.9%). Under the same competition shock, total R&D actually rises by 1.0% in this high-CD-cost economy (because own-innovation increases more than creative destruction falls, given the already low baseline of creative destruction), in contrast to the −1.6% in the U.S. However, domestic growth still falls 9.7% even in this economy, driven by reductions in creative destruction by incumbents and startups combined with a decline in the mass of domestic incumbents. This result holds even with a fixed firm mass (Table E5), confirming the mechanism is not solely due to entry/exit dynamics.

Q9. What is the technological barrier effect’s quantitative contribution to the decline in creative destruction?

A: In the U.S. counterfactual (Table 8 and associated decomposition), 17.0% of the total change in the aggregate creative destruction arrival rate x and 15.0% of the total change in startup creative destruction x_e are attributable specifically to the technological barrier effect — that is, to the shift in the technology gap distribution µ(Δℓ) holding all else equal. The conditional takeover probability x^{takeover} declines from 73.2% to 73.0%. The density at Δ₁ (the easiest gap to overcome) falls 0.4%, while densities at Δ₃ and Δ₄ rise 1.1% and 1.4% respectively, driven by increased creative destruction by outside firms and intensified own-innovation by incumbents.

Q10. What are the policy implications the paper draws from its framework?

A: The paper argues that policies evaluating innovation should account for composition, not just aggregate R&D levels or patent counts. Increased overall innovation driven by defensive own-innovation contributes less to economic growth than creative destruction and restricts firm entry — so it is less beneficial than it appears. In low-creativity economies (e.g., European economies with high regulatory barriers to creative destruction), increased foreign competition may raise aggregate R&D while still lowering domestic growth, misleading policymakers who track only total innovation spending. The model also suggests that the mixed empirical findings in the competition-innovation literature (Aghion et al. 2005; Bloom et al. 2016; Autor et al. 2020) can be reconciled by accounting for compositional shifts: the net effect of competition on total innovation is ambiguous because it raises own-innovation for technologically advantaged firms while reducing creative destruction for all firms.

Key Concepts

Imperfect Technology Spillovers: The novel friction introduced in this paper, modeled as lagged learning: firms attempting creative destruction can only access the one-period-lagged technology of the target product market (q_{j,t−1}), while the incumbent product owner observes and can improve from the current frontier (q_{j,t}). This asymmetry creates a persistent technological advantage for incumbents and enables strategic defensive innovation.

Own-Innovation: R&D investment by a firm to improve the quality of its existing product lines. Successful own-innovation raises product quality by a step size λ > 1. Own-innovation does not require learning others’ technology and, in the model, constitutes the incumbents’ defensive margin against creative destruction. At the aggregate level, it contributes more to total growth than creative destruction because it succeeds more frequently, but per successful event it contributes less (λ < η).

Creative Destruction: R&D investment enabling a firm to enter a new product market by displacing the incumbent. Successful creative destruction improves the lagged quality of the target product by a step size η > λ, where λ² > η > λ. It requires learning the incumbent’s one-period-lagged technology, takes longer to develop (evidenced empirically by longer backward citation gaps), and contributes more to firm growth and product expansion per event than own-innovation.

Technology Gap (Δ): The ratio of a product’s current-period technology to its previous-period technology (Δ_{j,t} = q_{j,t}/q_{j,t−1}). This gap summarizes the technological advantage the incumbent holds in a product market under imperfect spillovers. Four values are possible in equilibrium: Δ₁ = 1, Δ₂ = λ, Δ₃ = η, Δ₄ = η/λ. The gap determines both the incumbent’s own-innovation incentive and the rival’s probability of successfully completing a product takeover conditional on creative destruction.

Market-Protection Effect: The mechanism by which incumbents with a technological advantage (Δ > 1) increase own-innovation in response to heightened competitive pressure (an increase in the aggregate creative destruction arrival rate x). This effect is maximized for products with Δ₂ = λ and positive but diminishing for Δ₃. It is absent for Δ₁ = 1 products (where own-innovation cannot prevent displacement) and is formally distinct from the escape-competition effect in step-by-step innovation models, which applies only to neck-and-neck single-product firms.

Technological Barrier Effect: The reduction in rivals’ incentive for creative destruction caused by an increase in the average technology gap across the economy’s product lines. When incumbents intensify own-innovation and/or when outside creative destruction increases, the distribution of technology gaps shifts toward higher Δ values, reducing the conditional probability that a rival successfully takes over any given product market. This feedback mechanism endogenously suppresses creative destruction and firm entry beyond what the Schumpeterian effect alone would predict.

Self-Citation Ratio: The share of a patent’s backward citations that cite patents previously owned by the same firm. Used in the paper as a continuous proxy for the likelihood that a patent represents own-innovation vs. creative destruction: a ratio of 1 (100% self-citations) implies 100% probability of own-innovation; a ratio of 0 implies 100% probability of creative destruction. This measure follows Akcigit and Kerr (2018) and is validated in the paper against learning time, quality, and firm growth outcomes.

NTR Gap (Trade Policy Uncertainty Shock): The industry-level difference between non-NTR (column 2) and NTR (column 1) U.S. tariff rates in 1999, used as an instrument for the exogenous increase in Chinese competitive pressure following China’s WTO accession and the U.S. granting of Permanent Normal Trade Relations (PNTR) in 2002. Industries with larger NTR gaps experienced a greater reduction in trade policy uncertainty and thus a larger increase in competitive pressure from foreign firms.

Inequality and asset prices during Sudden Stops

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper studies the cross-sectional dimension of Fisher’s (1933) debt-deflation mechanism as it operates during Sudden Stop crises — episodes characterized by large, abrupt reversals in the current account. The central question is how the distribution of wealth and leverage across households shapes the macroeconomic dynamics of financial crises, and whether greater inequality makes Sudden Stops more or less severe.

Data and Methodology

The empirical analysis uses panel microdata from the Mexican Family Life Survey (MxFLS) across three waves (2002, 2005, 2009), covering a representative sample of approximately 8,400 households in 150 localities. The 2009 wave captures a Sudden Stop in which Mexico’s current account reversed by 1.5 percentage points of GDP, per capita consumption fell 7 percent, and housing prices fell 4 percent below pre-crisis trend by 2010. Households are sorted by net wealth and leverage ratio — defined as total debt divided by total assets — to identify how balance sheet heterogeneity drove differentiated asset-holding dynamics during the crisis.

The theoretical framework is a Bewley small open economy model with heterogeneous agents, incomplete markets, aggregate risk (simultaneous shocks to the international interest rate and total factor productivity), and an occasionally-binding loan-to-value (LtV) collateral constraint. Households hold two assets: a one-period risk-free international bond and a risky domestic collateralizable asset (land). Households face persistent non-insurable idiosyncratic risk in both labor income and dividend returns; the latter creates an endogenous risk-wealth tradeoff, since larger asset holdings raise future income volatility while simultaneously expanding debt capacity. The model is calibrated to Mexican data — matching the leverage ratio distribution in 2005 (10 percent of households financially constrained) and a net foreign asset position of −35 percent of GDP — and solved using the FiPIt algorithm combined with the Krusell-Smith stochastic-simulation approach.

Main Findings with Quantitative Magnitudes

The empirical evidence from Mexico’s 2009 crisis reveals sharply divergent asset dynamics across the household balance sheet distribution. Wealthy households (top net-wealth decile) with low leverage increased their real estate holdings by 61.4 percent (annualized, relative to the average) between 2005 and 2009, consistent with a crisis-dampening effect whereby unconstrained agents absorb fire-sales. Wealthy households in the top decile of both net wealth and leverage ratio — financially constrained — reduced their real estate holdings by 36.6 percent, consistent with a crisis-amplifying effect. Cross-country descriptive evidence shows that Sudden Stop episodes are associated with significantly larger contractions in consumption and GDP in more unequal economies (Gini index, World Bank data, 58 Sudden Stop episodes identified by Bianchi and Mendoza 2020).

In the calibrated model, the crisis-dampening effect dominates relative to the representative agent baseline: the heterogeneous-agents economy produces a smaller decline in asset prices (−0.99 percent vs. −2.57 percent in the representative agent model during crisis episodes), but a larger and more persistent consumption decline (−2.97 percent vs. −1.17 percent) and current account reversals (1.56 percentage points vs. 0.09 percentage points). The wealth Gini index generated by the calibrated model is 0.61, close to the untargeted 2005 Mexican estimate of 0.73. The aggregate equity premium generated is 5.1 percent, close to the data estimate of 6.5 percent; of this, 55.3 percent is attributable to the risk component, 35.9 percent to the persistence effect, and 8.6 percent to the constraint effect.

When comparing the baseline emerging economy (wealth Gini 0.61) to an advanced economy calibration in which idiosyncratic dividend risk is set to zero (wealth Gini 0.29), crises are milder and less frequent in the more equal economy: consumption drops 1.0 percentage point less, asset prices drop 0.2 percentage points less, and the net foreign debt position is 6.2 percentage points larger relative to GDP. The implied slope coefficient from the model relating consumption declines during Sudden Stops to the income Gini (−11.1) closely matches the cross-country empirical estimate (−11.5). An economy with an income Gini index 0.10 points lower experiences a decline in consumption 1.1 percentage points smaller during a crisis.

An impulse response to a two-standard-deviation aggregate shock confirms that, conditional on starting from a perfectly equal (symmetric) initial distribution via complete redistribution, declines in consumption and asset prices are approximately 0.5 percentage points smaller than in the baseline economy with the stationary ergodic distribution as initial condition.

Redistributive Dividend Tax

A flat 30 percent dividend income tax, redistributed as lump-sum transfers, reduces Sudden Stop severity by lowering average asset prices by 9.6 percent relative to the benchmark, which shrinks effective debt capacity and limits bond adjustment during crises. The average current account reversal during a crisis falls by 0.54 percentage points, and aggregate consumption falls by 0.63 percentage points less than in the benchmark. Crisis probability under the benchmark threshold falls from 4.3 to 1.83 percent (less than half). Average welfare improves by a gain equivalent to 2.8 percent of consumption. However, 26.7 percent of households — those more leveraged and three times wealthier than the beneficiaries — experience welfare losses averaging 6.8 percent of consumption, due to asset price declines and tighter financial conditions.

Overall Conclusion

Both the empirical evidence and the model suggest that economies with lower inequality, whether due to reduced idiosyncratic risk (as in advanced versus emerging economy calibrations) or wealth redistribution across agents with identical idiosyncratic risk processes, experience less severe Sudden Stop crises.

In depth

Q1. What are the two cross-sectional channels through which household heterogeneity affects the debt-deflation mechanism, and in which direction do they move asset prices?

A1: The dampening effect operates when unconstrained wealthy households — who hold diversified portfolios and have precautionary savings in bonds — purchase fire-sold assets from constrained households, relieving downward pressure on asset prices. The amplifying effect operates when highly leveraged households, once pushed into binding credit constraints by declining asset prices, must further liquidate asset positions, deepening the price decline and tightening the collateral constraint for additional households via the pecuniary externality. These two effects move in opposite directions, so the net effect of inequality on crisis severity is theoretically ambiguous and depends on calibration.

Q2. What specific empirical evidence from Mexico’s 2009 Sudden Stop supports both cross-sectional effects?

A2: Using MxFLS microdata, Table 1 in the paper shows that wealthy households (top net-wealth decile) with low leverage (deciles I–VII of leverage) increased their real estate holdings by 61.4 percent between 2005 and 2009 — evidence for the dampening effect. Wealthy households in the top decile of both net wealth and leverage reduced their real estate holdings by 36.6 percent — evidence for the amplifying effect. Between 2005 and 2009, the share of financially constrained households (leverage ratio above 0.168, the 90th percentile) increased by 1.7 percentage points, while the share of financial savers dropped by 5.0 percentage points. The pre-crisis period (2002–2005) shows no comparable divergence, ruling out a mechanical mean-reversion explanation.

Q3. What is the risk-wealth tradeoff, and why is it central to generating a realistic wealth and leverage distribution in the model?

A3: The risk-wealth tradeoff arises because idiosyncratic dividend risk is endogenous to asset holdings: holding more risky domestic assets increases debt capacity (relaxing borrowing constraints) but also raises future income volatility, since the variance of household flow income is convex in asset holdings. For households earning high dividend realizations, there exists a threshold beyond which precautionary savings motives — driven by rising income risk — dominate the benefit from expanded debt capacity, causing these households to begin accumulating bonds and eventually become net savers. This mechanism generates an empirically plausible distribution in which some households are financially constrained at the LtV limit, others are unconstrained borrowers, and a fraction are net savers holding both domestic assets and positive international bonds.

Q4. How does the model calibration match the stationary distribution of Mexican households?

A4: Three parameters governing the dividend income risk process (average dividend yield, autocorrelation, and standard deviation) are jointly calibrated to match three statistics from the MxFLS 2005 distribution of households: 14.1 percent financial savers (data: 14.2 percent), 75.9 percent unconstrained indebted (data: 75.8 percent), and 10.0 percent financially constrained (data: 10.0 percent). The collateral fraction κ = 0.168 is set equal to the 90th percentile of the leverage ratio distribution in 2005, reflecting that the average delinquency rate for commercial bank household credit was 10.3 percent between 2004 and 2008. The discount factor β = 0.90 matches the average net foreign asset position relative to GDP of −35 percent for Mexico.

Q5. How does the heterogeneous-agents model compare to the representative agent model in terms of crisis dynamics?

A5: In the heterogeneous-agents benchmark, the average current account reversal during a Sudden Stop is 1.56 percentage points, consumption falls 2.97 percent, and asset prices fall 0.99 percent below the steady state. In the representative agent model with the same average leverage ratio (κ = 0.12), the current account reversal is only 0.09 percentage points, consumption falls 1.17 percent, and asset prices fall 2.57 percent. The crisis-dampening effect in the heterogeneous economy produces a smaller asset price drop but a larger consumption decline, because leveraged households must make larger consumption adjustments when hit by negative idiosyncratic shocks in addition to the aggregate shock. Impulse response analysis shows the heterogeneous-agents economy generates current account reversals 1.9 percentage points larger than the representative agent, and consumption responses approximately four times larger.

Q6. What is the mechanism by which comparing emerging and advanced economy calibrations shows that lower inequality leads to less severe crises?

A6: The advanced economy calibration sets idiosyncratic dividend risk to zero, eliminating the risk-wealth tradeoff and resulting in a wealth Gini of 0.29 (compared to 0.61 in the baseline). Without dividend risk, households have weaker incentives to accumulate assets as a precautionary buffer against income volatility, so they hold less debt on average and the long-run net foreign debt relative to GDP is 6.2 percentage points larger (i.e., less debt). During a Sudden Stop under this calibration, consumption drops 1.0 percentage point less, asset prices drop 0.2 percentage points less, and the economy is less frequently in crisis. The model-implied slope of consumption decline on income Gini is −11.1, matching the cross-country empirical estimate of −11.5.

Q7. What does the impulse response analysis reveal about the effect of wealth redistribution on crisis severity, holding idiosyncratic risk constant?

A7: The impulse response analysis compares the baseline heterogeneous-agents economy (with the stationary ergodic distribution as the initial condition) against a version in which all households are given a perfectly symmetric initial distribution — identical bond and asset holdings equal to long-run averages — while retaining the same idiosyncratic risk processes. The symmetric initial condition corresponds to a complete redistribution of wealth without changing fundamentals. In the first three periods after a two-standard-deviation aggregate shock, the symmetric economy shows declines in consumption and asset prices approximately 0.5 percentage points smaller than the baseline. This demonstrates that even holding the risk environment constant, reducing wealth dispersion mitigates crisis severity.

Q8. How does the equity premium decomposition work in the heterogeneous-agents model, and which components are quantitatively most important?

A8: The aggregate equity premium is decomposed into five components (Equation 7 in the paper): a constraint effect (positive, increasing in the measure and intensity of constrained households), a risk effect (positive, from the negative covariance between the individual stochastic discount factor and individual equity return, weighted more heavily on constrained households), a persistence effect (positive, from the covariance between idiosyncratic dividend return and asset holdings, since high-dividend households accumulate more assets), a trading cost effect (approximately zero in aggregate), and a no-short-sales effect (negative, since households at the short-sales constraint add to asset demand without increasing the marginal benefit of saving). In the calibrated model, the equity premium is 5.1 percent; the risk effect accounts for 55.3 percent, the persistence effect for 35.9 percent, and the constraint effect for 8.6 percent.

Q9. What is the mechanism by which the dividend income tax reduces crisis severity?

A9: A flat 30 percent dividend income tax lowers average after-tax dividend returns, reducing households’ incentive for precautionary accumulation of domestic assets and weakening the risk-wealth tradeoff. As a result, households demand fewer domestic assets and fewer international bonds in normal times. The reduced demand for the domestic asset lowers the equilibrium asset price by 9.6 percent on average relative to the benchmark, which — through the pecuniary externality embedded in the LtV constraint — tightens borrowing constraints, raising the share of financially constrained households from 5.6 to 7.8 percent. Nevertheless, the reduction in equilibrium debt positions means that during a crisis, bond adjustments and consumption drops are more limited: the average current account reversal during crises falls by 0.54 percentage points, and aggregate consumption falls by 0.63 percentage points less than in the benchmark. Crisis probability under the benchmark threshold falls from 4.3 to 1.83 percent.

Q10. Who benefits and who loses from the dividend income tax, and by how much?

A10: Among the simulated population, 73.3 percent of households experience welfare gains averaging 6.2 percent of consumption in consumption-equivalent terms, while 26.7 percent experience welfare losses averaging 6.8 percent of consumption. The average welfare gain across all households is equivalent to 2.8 percent of consumption. The households experiencing losses are more leveraged and three times wealthier on average than those that benefit; the policy reduces their net worth through lower asset prices and tightens their financial constraints. The welfare analysis accounts for the transition to the new tax policy.

Q11. Why does the representative agent model miss the cross-sectional effects that are central to the paper’s mechanism?

A11: In the representative agent model, all households behave identically and either collectively want to buy or sell assets, but since there is no one to trade with domestically, actual asset holdings remain unchanged by cross-sectional forces. Additionally, the average debt constraint multiplier in the representative agent equals the single household’s multiplier, whereas in the heterogeneous model a small fraction of highly constrained households can have much larger individual multipliers, amplifying the aggregate debt-deflation effect. In the calibrated stationary model, 10 percent of constrained households own 7.7 percent of assets and have a consumption share of 9.0 percent, while 75.9 percent of unconstrained indebted households hold 88.1 percent of assets with a consumption share of 78.1 percent — distributional features invisible to a representative agent.

Q12. What robustness does the model validation provide for the quantitative results?

A12: The model reproduces the untargeted net wealth and asset distributions across deciles from MxFLS 2005 closely, with slight underestimation at the top deciles; the exception is the bottom decile of debt (where the model cannot generate households with negative net wealth since default is not modeled). The aggregate law of motion for the Krusell-Smith algorithm fits with R² = 0.99 for bond position and R² = 0.93 for asset price, and Den Haan (2010) accuracy checks show maximum forecast errors of 2.8 (current account) and 1.1 (asset price). The model replicates the untargeted magnitude of current account reversals observed in Mexican Sudden Stops. The wealth Gini of 0.61 is close to the untargeted 2005 Mexican estimate of 0.73, and the equity premium of 5.1 percent is close to the data estimate of 6.5 percent.

Key Concepts

Sudden Stop: An episode characterized by a large, abrupt reversal in the current account, typically triggered by a sudden halt in foreign capital inflows. In this paper, Sudden Stops are modeled as endogenous crises that arise from the interaction of a negative aggregate shock (simultaneous rise in the international interest rate and decline in total factor productivity) with an occasionally-binding LtV collateral constraint. The paper follows Bianchi and Mendoza (2020) in identifying 58 such episodes over the past four decades.

Debt-deflation mechanism (cross-sectional dimension): The paper studies Fisher’s (1933) debt-deflation spiral — in which declining asset prices tighten credit constraints, forcing further asset sales, further depressing prices — through the lens of household heterogeneity. The cross-sectional dimension refers to the fact that different households (wealthy unconstrained vs. highly leveraged constrained) respond differently to price declines, generating two opposing effects: dampening (wealthy buyers absorb fire-sales) and amplifying (constrained households fire-sell additional assets).

Risk-wealth tradeoff: A novel feature of the model in which holding more risky domestic assets simultaneously (a) expands debt capacity by relaxing the LtV constraint and (b) increases future income volatility through higher exposure to idiosyncratic dividend risk, since the variance of household flow income is convex in asset holdings. This tradeoff generates the endogenous transition of households from indebted to net-saver status and gives rise to the empirically plausible distribution of savers, unconstrained borrowers, and constrained households.

Loan-to-value (LtV) collateral constraint: A borrowing limit requiring that households’ international debt (negative bond holdings) cannot exceed a fixed fraction κ of the market value of their domestic asset holdings. In the paper, κ = 0.168 (the 90th percentile of the Mexican leverage ratio distribution in 2005). The constraint is occasionally binding and generates a pecuniary externality: households fail to internalize that their individual portfolio choices affect the aggregate asset price, which in turn determines the borrowing limits of all other households.

Pecuniary externality: The externality arising from the LtV constraint in which each household’s choice of asset holdings affects the equilibrium asset price, thereby changing the borrowing limits of all households simultaneously. This externality drives the debt-deflation spiral and is the source of Sudden Stop crises in the model: no single household internalizes the aggregate impact of its fire-sales on credit conditions.

Fire-sale: In the context of this paper, the forced liquidation of domestic asset holdings by financially constrained households during a crisis. Fire-sales are triggered when the LtV constraint becomes binding, forcing households to sell assets to reduce debt; the resulting price decline tightens the constraint further, producing additional fire-sales. The paper documents that, during Mexico’s 2009 Sudden Stop, wealthy constrained households (top decile of both net wealth and leverage) reduced real estate holdings by 36.6 percent, while wealthy unconstrained households increased holdings by 61.4 percent.

Dampening and amplifying effects: Two opposing cross-sectional effects on asset prices during a crisis. The dampening effect: unconstrained wealthy households purchase depressed assets fire-sold by constrained households, relieving downward pressure on prices and weakening the debt-deflation spiral. The amplifying effect: highly leveraged households that are pushed into binding constraints by falling prices must also fire-sell assets, further depressing prices and tightening financial conditions. The net impact on crisis severity depends on which effect dominates, which the paper establishes empirically and quantitatively is inequality-dependent.

Equity premium decomposition: A decomposition derived in the paper (Equation 7) that expresses the aggregate excess return on the risky domestic asset as the sum of five components: a constraint effect (positive, from the measure and intensity of binding LtV constraints), a risk effect (positive, from the covariance of individual stochastic discount factors with individual equity returns), a persistence effect (positive, from the covariance of idiosyncratic dividend returns with asset holdings due to return persistence), a trading cost effect (approximately zero in aggregate), and a no-short-sales effect (negative). In the calibrated model, the risk and persistence effects account for 91 percent of the 5.1 percent equity premium.

International trade and macroeconomic dynamics with sanctions

Mon, 01 Jan 0001 00:00:00 +0000

Sanctions are increasingly used as an instrument of economic statecraft, yet their macroeconomic consequences—especially the transitional dynamics and their effects on business cycles—are poorly understood. This paper develops a micro-founded framework combining the intertemporal general-equilibrium structure of standard open-economy macro models with the rich trade-theoretic microfoundations of modern trade theory to study sanctions systematically. In a two-country, two-sector model where Home specializes in differentiated consumption goods (heterogeneous firms, endogenous entry, Melitz-style) and Foreign specializes in homogeneous intermediate goods (Cournot oligopoly in extraction), sanctions—modeled as trade bans and financial restrictions excluding particular Foreign agents—reallocate resources across and within countries, affect production, exchange rates, and welfare, and are shown to inflict larger welfare losses when they target sectors of comparative disadvantage. A central finding is that focusing only on long-run outcomes and overlooking initial transitional dynamics substantially misdirects welfare assessments; sanctions weaken international comovement and fragment markets but, contrary to some claims, leave the structure of business cycles largely intact.

In depth

Q1. What is the model structure and what types of sanctions does it capture?

The model is a two-country, two-sector economy: Home has a comparative advantage in differentiated consumption goods (produced by heterogeneous firms with endogenous entry under monopolistic competition, as in Melitz 2003), while Foreign specializes in homogeneous intermediate goods (produced via Cournot competition among a fixed number of upstream firms and processed by a representative distributor). This structure is motivated by the pattern in which Western economies specialize in high-value, firm-entry-intensive industries while sanctioned countries often specialize in commodity production (energy, natural gas). Sanctions are modeled as two distinct instruments: trade bans (restrictions on commerce in goods) and financial restrictions (excluding particular Foreign agents from capital markets). The model accommodates both Ricardian and Melitz-type comparative advantage.

Q2. What are the key results on welfare effects and the role of transitional dynamics?

Sanctions reallocate resources across and within countries, with welfare losses larger when sanctions target sectors of comparative disadvantage rather than sectors of comparative advantage; and focusing only on long-run welfare ignores significant transitional costs that substantially change the total welfare assessment. The model implies that initial transitional dynamics—disruptions to trade flows, entry and exit of firms, exchange rate movements, and adjustment of resource allocation—can be quantitatively important and even dominate long-run effects in welfare calculations. Assessments based solely on steady-state comparisons may therefore produce seriously misleading conclusions about whether and how severely sanctions harm the imposing or target economy.

Q3. How do sanctions affect international comovement and business cycles?

Sanctions weaken international business cycle comovement and fragment markets—reducing the degree to which shocks in one country transmit to the other—but leave the structural properties of business cycles within each country largely intact, in the sense that the cyclical dynamics of output, consumption, and investment retain their qualitative features. This result has policy implications: sanctions can reduce the interdependence of the sanctioned country’s business cycle from the rest of the world (which could be either beneficial or harmful depending on the source of shocks), but cannot fundamentally restructure the domestic cycle.

Q4. What is the baseline application and what general lessons emerge?

While the model’s comparative advantage structure is explicitly motivated by the 2022 Western sanctions against Russia—with intermediate goods interpretable as energy—the framework is designed to be more broadly applicable to other geopolitical conflicts involving sanctioned commodity producers facing differentiated-goods exporters, such as US-China trade tensions. The general lessons are: (1) the sector targeted by sanctions matters greatly for their welfare costs; (2) transitional dynamics are not second-order; (3) financial sanctions operate through different channels than trade bans and should be modeled separately.

Key concepts

comparative disadvantage in sanctions : the paper’s finding that sanctions are more costly when they target goods in which the targeted country has a comparative disadvantage—sectors the country cannot efficiently produce domestically—because those are the sectors where trade provides the highest value and substitution is hardest.

financial restrictions : one of the two types of sanctions modeled, in which particular Foreign agents (firms or sovereign entities) are excluded from international capital markets, distinct from trade bans that restrict commerce in goods.

Is it AI or data that drives firm market power?

Mon, 01 Jan 0001 00:00:00 +0000

Labor Market Shocks and Monetary Policy

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Research question. The paper asks two related questions: (1) How much, and through which channels, do employer-to-employer (EE) worker transitions affect macroeconomic outcomes — particularly inflation? (2) What is the optimal monetary policy within a class of Taylor rules when EE flows are taken explicitly into account?

Motivation. Standard monetary policy frameworks condition on the unemployment rate as the primary labor market slack measure and underemphasize the “quality” dimension of employment. The paper documents a striking empirical pattern: the 2016–2019 recovery and the 2021–2022 recovery from COVID-19 featured nearly identical declines in the unemployment rate, yet exhibited dramatically different EE rate dynamics and inflation outcomes. During 2016–2019, the EE rate remained flat despite a roughly 25 percent decline in the unemployment rate from trend. During 2021–2022, the EE rate rose by around 8 percent above trend over a comparable unemployment decline. Correspondingly, unit labor cost (ULC) growth reached approximately 6 percent during the COVID-19 recovery when unemployment fell below 4 percent, compared with only about 2 percent ULC growth in the 2016–2019 period at similar unemployment levels.

Methodology. The authors develop a Heterogeneous Agent New Keynesian (HANK) model with a frictional labor market featuring on-the-job search (OJS). Workers are heterogeneous in wealth (mutual fund shares), human capital, match-specific productivity, and endogenous piece-rate wages. Human capital stochastically appreciates when employed and depreciates when unemployed, capturing scarring effects and job-stayer wage growth. Wage determination follows a Bertrand competition protocol based on flow output: workers switch to higher-productivity matches and extract the full surplus from the new firm, while outside offers from lower-productivity firms can still trigger rebargaining with the incumbent firm and raise the piece rate without a job switch. Three vertically integrated sectors — labor services, intermediate goods, and final goods — are linked so that the real price of labor services pl is the real marginal cost for intermediate firms and the sole driver of inflation in the New Keynesian Phillips curve (absent aggregate productivity shocks). The economy is subject to AR(1) shocks to the discount rate β (demand), aggregate labor productivity z (supply), and OJS efficiency ν (the relative search efficiency of employed workers). The model is solved using the Sequence-Space Jacobian (SSJ) method, extended to handle discretized worker distributions as direct inputs to equilibrium conditions.

The model is calibrated to U.S. pre-Great Recession data (2004–2006), targeting the fraction of hand-to-mouth individuals (16 percent of SIPP sample), unemployment rate (5.1 percent), EU separation rate (3.8 percent quarterly), EE rate (2 percent quarterly from LEHD), earnings drop upon job loss (35 percent), wage growth of job switchers (9 percent), and the labor share (0.67). Shock processes are estimated by minimizing deviations from empirical correlations and standard deviations of output, unemployment, EE rate, and inflation over 1995:Q3–2008:Q4.

Main findings — positive analysis. Shocks to OJS efficiency account for 43.1 percent of fluctuations in inflation in the variance decomposition, and 78.7 percent of fluctuations in the EE rate. The mechanism: a higher OJS efficiency lowers the expected match value EJ for labor services firms through three channels — (i) a compositional shift toward employed job seekers who extract the entire match surplus, (ii) shorter expected match duration as workers face higher poaching probabilities, and (iii) more frequent wage rebargaining where outside offers bid up wages without accompanying productivity gains. To maintain the free-entry condition, the real price of labor services pl must rise, increasing the real marginal cost and inflation. This direct labor market effect explains 139 percent of the total increase in pl; general equilibrium effects through reduced tightness θ — which raises expected match values by making vacancies easier to fill and workers less likely to be poached — offset −42 percent; the remainder (3 percent) comes from real rate changes driven by the monetary policy reaction.

In two historical simulations, muted OJS efficiency during 2016–2019 generated approximately 0.23 percentage points lower annualized inflation at the peak relative to a counterfactual economy with the same unemployment path but an endogenously rising EE rate. Conversely, elevated OJS efficiency during 2021–2022 generated approximately 0.56 percentage points higher annualized inflation compared to the flat-EE-rate counterfactual. The paper notes that strong worker mobility accounts for roughly 10 percent of the approximately 6 percentage point total rise in annual inflation during the COVID-19 recovery episode.

An important cross-model comparison shows that the Representative Agent New Keynesian (RANK) version of the model overestimates the decline in demand, output, and labor market tightness upon a positive OJS shock, and underestimates the rise in real rate, marginal cost, and inflation. Household heterogeneity is therefore quantitatively important: hand-to-mouth households’ demand responds directly to labor income increases from job switches, mitigating the demand decline and amplifying inflation.

Main findings — normative analysis. The optimal monetary policy within an augmented Taylor rule — adding an EE gap term ΦEE(EEt − EE*) alongside the standard inflation and unemployment gap terms — prescribes Φ*_u = −3.18 and Φ*_EE = 2.22 (with Φπ fixed at 1.5). This yields a 78.7 percent reduction in the central bank loss relative to the baseline Taylor rule. A policy that ignores EE dynamics and optimizes only the unemployment gap coefficient (finding Φu = −2.71, ΦEE = 0) produces a 12 percent larger central bank loss than the full optimal policy. In terms of welfare, the optimal policy delivers 0.16 percent additional lifetime consumption equivalent in the aggregate. Workers at the bottom of the match quality distribution gain the most (0.24 percent), as do the unemployed (0.20 percent), while those at the top of the wealth distribution gain the least due to larger share price fluctuations under the more aggressive policy.

Scope conditions. Results are derived conditional on a dual-mandate central bank objective (variance of inflation and output gaps), within a class of Taylor-type rules (not fully optimal Ramsey policy), under first-order approximation around a non-stochastic steady state. The historical simulations abstract from supply shocks active in the normative exercises and assume the economy starts from steady state in 2016.

In depth

Q1. What is the OJS efficiency shock, and how does it differ from a standard demand or supply shock?

An OJS efficiency shock is modeled as a time-varying shift in νt, the relative job search efficiency of employed workers compared with unemployed workers. Unlike demand shocks (discount rate β innovations) and productivity shocks (aggregate z innovations), which move inflation and unemployment in opposite directions under standard New Keynesian logic (divine coincidence), OJS efficiency shocks move inflation and unemployment in the same direction: a positive OJS shock raises inflation while also raising unemployment (because the higher real rate induced by the central bank’s reaction reduces demand and employment). This makes OJS shocks behave like cost-push shocks and introduces a genuine policy trade-off for a dual-mandate central bank.

Q2. What are the three mechanisms through which higher OJS efficiency raises the real price of labor services, and what is the quantitative contribution of each?

The decomposition (Figure 8) shows that the direct effect of ν on EJ — encompassing the composition channel (more employed job seekers who extract the full surplus), the match-duration channel (shorter expected match lives), and the wage rebargaining channel (outside offers raise wages without productivity gains) — explains 139 percent of the total increase in pl. The general equilibrium reduction in labor market tightness θ, which raises EJ and partially offsets the cost increase, explains −42 percent in total: −18 percent through increased supply of labor services L (productivity-enhancing job switches improve the match distribution) and −24 percent through reduced output Y (lower aggregate demand). Real rate effects account for the remaining 3 percent net (8 percent from the inflation channel and −5 percent from the unemployment channel). Labor market effects in total therefore explain 97 percent of the marginal cost increase.

Q3. Does the positive relationship between EE rates and inflation require wage increases upon job switches?

No. The paper demonstrates (Section 2.4.2, Figure 3) that even when the piece rate for workers hired from unemployment is set to α = 0.95 (so that outside offers have negligible wage effects), a positive OJS efficiency shock still generates a decline in output and a rise in inflation in both the RANK and TANK models. Quantitatively, the inflation response is similar across the baseline and near-zero composition-channel specifications, confirming that the shorter expected match duration is the primary driver of the increase in the real price of labor services. The match duration channel operates independently of wage increases: firms anticipate shorter matches and require a higher flow price to break even on vacancy costs.

Q4. How does household heterogeneity change the quantitative effects of OJS shocks relative to the RANK benchmark?

Under a constant real rate, in the RANK model a higher OJS efficiency increases the real price of labor services and inflation but has no effect on aggregate demand or output (because higher labor income for the PIH household is exactly offset by lower firm profits). In the TANK model, hand-to-mouth households consume their entire labor income, so the rise in labor income from job switches directly boosts their demand, raising output and tightness and further amplifying inflation. Under an endogenous real rate, the RANK model overestimates the decline in demand and output, and underestimates the rise in real rate and inflation, compared with the TANK model. The TANK model requires a substantially larger equilibrium real rate increase to contain inflation because HtM households’ demand is less elastic to the real rate than PIH households'.

The six AR(1) parameters governing β, z, and ν (three persistence parameters ρj and three standard deviations σj) are estimated by minimizing the sum of squared deviations between model-generated and empirical moments: the autocorrelation of output; correlations of the unemployment rate, EE rate, and inflation with output; and standard deviations of output, unemployment rate, EE rate, and inflation. Data cover 1995:Q3–2008:Q4. Estimated values are ρβ = 0.909, ρz = 0.332, ρν = 0.936 and σβ = 0.001, σz = 0.002, σν = 0.003. The variance decomposition (Table 4) assigns 43.1 percent of inflation variance to OJS efficiency shocks ν, 52.0 percent to demand shocks β, and 4.9 percent to productivity shocks z.

Q6. How is the “missing inflation” during 2016–2019 quantified, and what is the counterfactual?

The exercise simulates two economies both replicating the same unemployment path — a 15 percent decline in unemployment relative to its 5.2 percent steady state, spread linearly over 16 quarters, followed by mean reversion. The first economy uses only positive demand shocks, which generate an endogenously rising EE rate consistent with the historical unemployment-EE correlation. The second economy additionally introduces negative OJS efficiency shocks to keep the EE rate unchanged, as observed in the data during 2016–2019. Annualized inflation in the second economy is 0.23 percentage points lower at the peak (16 quarters after the shock), implying that had the EE rate risen normally, inflation would have been around 2 percent in 2019 rather than the observed 1.8 percent.

Q7. How is the inflationary role of elevated EE transitions during 2021–2022 quantified?

Using the same unemployment path as the 2016–2019 exercise, the COVID-19 recovery economy combines positive demand shocks with positive OJS efficiency shocks to replicate the observed 0.16 percentage point (8 percent above trend) increase in the EE rate. Comparing this economy to the flat-EE-rate economy from the prior exercise, the elevated EE rate generates 0.56 percentage points higher annualized inflation. Because annual inflation rose approximately 6 percentage points in the data during this episode, the model attributes roughly 10 percent of the total inflation increase to strong worker mobility.

Q8. What are the optimal Taylor rule coefficients when EE dynamics are included, and what is the welfare cost of ignoring them?

The optimal policy over the augmented Taylor rule it = i* + Φπ(πt − π*) + Φu(ut − u*) + ΦEE(EEt − EE*), with Φπ fixed at 1.5 and a dual-mandate loss function W = var(πt − π*) + 0.25·var(Yt − Y*), prescribes Φ*_u = −3.18 and Φ*_EE = 2.22. This reduces the central bank loss by 78.7 percent relative to the baseline rule (Φu = −0.25, ΦEE = 0). If the EE gap term is excluded and only the unemployment gap coefficient is re-optimized (finding Φu = −2.71), the central bank loss is 12 percent higher than under the full optimal policy.

Q9. How does the optimal policy affect macroeconomic volatility, and who gains most from it?

Table 5 shows that the optimal policy substantially reduces volatility of inflation (standard deviation falls from 0.0013 to 0.0011), output (0.0059 to 0.0020), consumption (0.0059 to 0.0020), unemployment (0.0047 to 0.0013), labor market tightness (0.0600 to 0.0175), and the real marginal cost pl (0.0203 to 0.0081), at the cost of higher real rate volatility (0.0019 to 0.0033) and share price volatility (0.1975 to 0.3051). In terms of welfare (Table 6), the unemployed gain 0.20 percent in lifetime consumption equivalents (versus 0.15 percent for the employed), workers at the bottom quintile of match quality gain 0.24 percent (versus 0.16 percent at the top), and wealth-poor individuals in the bottom share quintile gain 0.23 percent (versus 0.11 percent at the top, whose gains are eroded by larger share price fluctuations).

Q10. How does the model extend the SSJ computational method, and why is this extension necessary?

The standard SSJ method of Auclert, Bardoczy, Rognlie, and Straub (2021) handles settings where only scalar aggregates enter equilibrium conditions in sequence space. In this model, the discretized distributions of employed workers µE(h, x) and unemployed workers µU(h) at the job search stage enter directly into the expected match value EJ (because human capital and current match productivity determine output and wage levels upon new contacts), and the distribution λE(h, x, α) at the production stage enters into labor services firm profits ΓS. The authors treat worker distributions as histograms and compute Jacobians for each mass point, combining the SSJ method with Reiter (2009)-style projection. This substantially increases computation time but remains feasible, extending the SSJ method to multi-stage models with search frictions where endogenous distributions are state variables.

Q11. What are the three sources of wage growth in the HANK model, and what is their relevance for inflation dynamics?

First, human capital h stochastically appreciates during employment (at rate πE = 0.018 per quarter, calibrated to annual job-stayer wage growth of approximately 2 percent), raising wages through a higher piece-rate base. Second, job switches to higher-productivity matches yield wage increases as the worker extracts the full surplus from the new firm (the new piece rate equals x/x’, the ratio of old to new match productivity). Third, outside offers with productivity x’ satisfying αx < x’ < x — not good enough to trigger a switch but better than the current bargaining threat — cause the incumbent firm to raise the piece rate to x’/x via rebargaining, increasing wages without a job change. The second and third channels are the ones directly affected by OJS efficiency shocks and are inflationary: they raise labor costs beyond productivity gains.

Q12. Why do OJS shocks have a shorter match duration channel even without wage increases?

When OJS efficiency ν rises, each employed worker faces a higher probability νtf(θt) of contacting another firm each period. Even if wages do not change upon contact (as in the α = 0.95 robustness exercise), a labor services firm posting a vacancy expects that any match it forms will be shorter-lived: the worker is more likely to be poached in the future. This shortens the expected present discounted value of the match for the firm, reducing EJ. To satisfy the free-entry condition (expected profit = vacancy cost κ), the price of labor services pl must rise, increasing the real marginal cost and inflation. Figure 3 confirms a nearly identical inflationary response under α = 0.95 as under the baseline, isolating this match-duration mechanism.

Key Concepts

OJS efficiency shock (νt shock). A time-varying shift in the relative job search efficiency of employed workers compared with unemployed workers. Modeled as an AR(1) process for νt (estimated persistence ρν = 0.936). An increase in νt raises the probability that employed workers contact outside firms each period, boosting the EE rate. In the model, this acts as a cost-push shock: it raises inflation and unemployment simultaneously, breaking divine coincidence and creating a policy trade-off for a dual-mandate central bank.

Expected match value (EJt). The ex-ante expected value to a labor services firm of a filled vacancy, conditional on contacting a worker, defined as a weighted average of match values J across the pool of job seekers (unemployed and employed). The free-entry condition Vt = κ/q(θt) = EJt pins down the real price of labor services pl: when EJt declines (due to shorter match durations or compositional shifts toward high-surplus-extracting workers), pl must rise to maintain zero expected profit for vacancy posters.

Composition channel. The mechanism by which a rise in OJS efficiency shifts the composition of the job-seeker pool toward employed workers, who (under Bertrand competition) extract the entire flow surplus of a new match and receive wage equal to plF(h,x). Since firms receive zero rent from poached workers, an increase in the fraction of employed in the applicant pool lowers EJt and requires a compensatory increase in pl.

Match duration channel. When OJS efficiency ν rises, each existing match faces a higher probability of dissolution because the worker is more likely to be poached. The reduced expected match duration lowers the present discounted value of a match for the firm (even holding wages fixed), reducing EJt and raising pl. Demonstrated as the primary driver of inflation in the α = 0.95 robustness exercise where wage increases upon job switches are near zero.

Piece-rate α (endogenous). The share of match output F(h,x) that the worker receives as wage, determined through Bertrand competition on flow output following Postel-Vinay and Robin (2002). A worker hired from unemployment starts at α = x̄/x’ (where x̄ is the lowest match productivity). Job switches to higher-x’ firms reset α = x/x’. Rebargaining upon a credible outside offer from a firm with αx < x̃ < x raises α to x̃/x. The piece rate endogenizes wage dynamics for switchers, stayers, and job losers, allowing the model to discipline these moments in the data.

Divine coincidence (and its breakdown under OJS shocks). In standard New Keynesian models, demand and productivity shocks move inflation and unemployment gaps in opposite directions, so stabilizing inflation also stabilizes the output gap. OJS efficiency shocks break this property: they generate simultaneous increases in inflation and unemployment, introducing a genuine trade-off between the two mandates and making EE-augmented Taylor rules welfare-improving relative to rules that respond only to unemployment.

Sequence-Space Jacobian (SSJ) method with distributed worker states. An extension of the Auclert, Bardoczy, Rognlie, and Straub (2021) computational method to settings where discretized distributions of workers (µE(h,x) and µU(h)) enter directly into equilibrium conditions — specifically into the free-entry condition via EJt and into firm profits. The authors treat distributions as histograms and compute Jacobians for each mass point, combining SSJ with Reiter (2009)-style projection to efficiently solve for transitional dynamics under aggregate uncertainty.

Lender concentration of external debts and sudden stops

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper studies how the lender structure of external debt — specifically, the degree to which a borrowing country’s external debt is concentrated among a small number of large lenders — affects open economies’ credit conditions, borrowing behavior, and the severity of sudden stops.

Core Mechanism

The paper argues that the pecuniary externality arising from collateral foreclosure can be internalized not only by borrowers (as in the standard Bianchi 2011 framework) but also by lenders. When a large lender holds a substantial share of total loans, it has an incentive to foreclose only partially on seized collateral. Selling foreclosed collateral injects asset supply and depresses the collateral price; a sufficiently large lender internalizes this price impact and therefore restrains foreclosure. Atomistic lenders, by contrast, take the collateral price as given and sell all seized collateral (foreclosure rate = 1). Consequently, concentrating external debt in fewer, larger lenders supports a higher collateral price during financial downturns. This higher collateral price raises borrowing capacity, weakens borrowers’ precautionary saving motive, and causes them to overborrow relative to the social optimum.

Empirical Evidence

Using FFIEC 009a data — quarterly exposure of individual U.S. banks to the external debts of other countries, covering 2003Q1–2022Q2 — the paper documents two new empirical facts. First, lender concentration of emerging countries’ external debt has been considerably higher than that of advanced countries since the Global Financial Crisis. The average difference in the mean top-3 lender concentration (LTop3) between emerging and advanced economies is 0.11 (= 0.93 − 0.82), with a t-statistic of 13.87. Second, higher lender concentration alleviates sudden stop events in terms of both current account reversal and the decline in asset price proxies. In a difference-in-differences specification interacting sudden stop indicators with lagged lender concentration, the coefficient on the interaction term is negative and statistically significant across all concentration measures. A one-standard-deviation increase in LTop3 (7.2 percentage points) results in a 2.6 percentage point reduction in current account-to-GDP reversal during sudden stops, constituting 7.5% of the overall sudden stop increase. Lender concentration also mitigates real effective exchange rate depreciation during sudden stops, consistent with the mechanism operating through the collateral price channel. Results hold when controlling for rollover risk motives.

Model

The model extends a standard small open economy DSGE framework (Bianchi 2011) by introducing one large lender who holds share eta of total loans and internalizes the pecuniary externality of collateral foreclosure, alongside atomistic lenders who hold share (1 − eta) and take the collateral price as given. When tradable endowment falls short of debt obligations (foreclosure state), lenders optimally choose their foreclosure rate: atomistic lenders set foreclosure rate = 1 (sell all seized collateral), while the large lender sets foreclosure rate < 1 (partial foreclosure to maintain the collateral price). Higher lender concentration (larger eta) leads to lower aggregate foreclosure, less collateral sold, a higher nontradable goods price, a higher borrowing capacity, more tradable consumption, and a weaker precautionary saving motive — generating overborrowing relative to the social planner’s allocation.

Two channels through which concentration affects overborrowing are identified: (1) a debt capacity channel, whereby concentration raises the nontradable price in foreclosure states and thereby increases borrowing capacity; and (2) an amplification channel, whereby concentration steepens the decline in nontradable price per unit fall in tradable consumption, amplifying the pecuniary externality that the social planner internalizes.

Quantitative Results (Calibrated to Argentina)

In the competitive equilibrium, agents encounter foreclosure with probability 2%, and the large lender sells two-thirds of seized collateral. The social planner’s allocation eliminates foreclosure entirely. The social planner’s allocation can be implemented via a state-dependent debt tax; the implied consumption-equivalent welfare gain is 0.78%. The pecuniary externality internalized by lenders is estimated to equal two-thirds of the externality internalized by borrowers. Overborrowing is increasing in lender concentration.

Optimal Lender Structure

When lender countries optimally choose their lender structure, they select further concentration relative to the baseline in order to gain higher foreclosure repayment. Under optimal lender structure, domestic agents consume and borrow more and encounter sudden stops with higher probability, but completely avoid foreclosure events. Borrower welfare improves by 0.1% in consumption-equivalent terms relative to the baseline competitive equilibrium. The paper concludes that managing lender structure benefits both sides of the international credit market, and notes that policies targeting creditor coordination — such as collective action clauses — may be insufficient to fully correct the efficiency implications of lender structure.

Key Implication

Because lender concentration alleviates crisis severity, emerging economies (which are documented to have substantially more concentrated lender structures than advanced economies) face a reduced precautionary saving motive and therefore tend to overborrow more than advanced economies, compounding their vulnerability to sudden stops.

In depth

Q1. What is the paper’s central departure from the Bianchi (2011) sudden stops framework?

The standard Bianchi (2011) model features atomistic lenders who take the collateral price as given, so the pecuniary externality of collateral fire-sales is internalized only by the borrower’s social planner. This paper introduces a large lender who holds a non-trivial share eta of total loans and therefore internalizes the price impact of selling foreclosed collateral. This creates a second source of pecuniary externality internalization — on the lender side — that is absent from the canonical framework.

Q2. Why do atomistic lenders sell all seized collateral, while the large lender does not?

Atomistic lenders take the collateral price as given and therefore face no downside from selling their entire share of seized collateral — they cannot individually affect the price. The large lender, holding share eta of total loans, recognizes that selling a large quantity of collateral depresses the nontradable goods price, which reduces the value of any remaining collateral claims. It therefore optimally sets foreclosure rate < 1, retaining some seized collateral to support the equilibrium price.

Q3. What are the two channels through which lender concentration amplifies overborrowing, and how do they differ?

The debt capacity channel operates in foreclosure states: higher concentration reduces foreclosure, raises the nontradable price, and increases the collateral value that backs borrowing. This directly expands the borrowing capacity available to agents and weakens their precautionary saving motive. The amplification channel operates through the slope of the nontradable price response: greater concentration steepens the decline in the nontradable price per unit fall in tradable consumption, which amplifies the pecuniary externality that the social planner internalizes. The two channels reinforce each other in driving overborrowing.

Q4. What empirical dataset is used, and what does it measure?

The paper uses FFIEC 009a data, which records the quarterly exposure of individual U.S. banks to the external debts of other countries, covering 2003Q1–2022Q2. From these data, the paper constructs lender concentration measures — including LTop3, the combined share of the top three lenders — at the borrowing-country level for each quarter.

Q5. What is the quantitative magnitude of the lender concentration gap between emerging and advanced economies?

The average difference in mean top-3 lender concentration (LTop3) between emerging countries and advanced countries is 0.11 (= 0.93 − 0.82), and this difference is highly statistically significant, with a t-statistic of 13.87. This gap emerged and persisted notably since the Global Financial Crisis.

Q6. How does lender concentration affect sudden stop severity in the empirical specification, and how large is the effect?

The paper estimates a difference-in-differences specification in which current account reversal (and other sudden stop outcome variables) is regressed on a sudden stop indicator, lagged lender concentration, and their interaction, with country and time fixed effects. The coefficient on the interaction term is negative and statistically significant across all concentration measures. A one-standard-deviation increase in LTop3 (7.2 percentage points) reduces current account-to-GDP reversal by 2.6 percentage points, which corresponds to 7.5% of the overall increase in the current account during a sudden stop episode.

Q7. Does higher lender concentration also mitigate exchange rate and asset price pressures during sudden stops?

Yes. Lender concentration is also found to mitigate real effective exchange rate depreciation during sudden stops, which is consistent with the model’s proposed mechanism: higher concentration supports the collateral (nontradable goods) price, which in turn limits the depreciation of the real exchange rate. The paper reports results on asset price proxy declines as well.

Q8. What is the welfare cost of overborrowing under the baseline calibration to Argentina?

The social planner’s allocation, implemented by a state-dependent debt tax, delivers a consumption-equivalent welfare gain of 0.78% relative to the competitive equilibrium. This measures the efficiency cost of overborrowing under the calibrated model in which the large lender sells two-thirds of seized collateral and competitive equilibrium agents encounter foreclosure with probability 2%.

Q9. How large is the lender-side pecuniary externality relative to the borrower-side externality?

Under the baseline calibration, the pecuniary externality internalized by lenders is estimated to be two-thirds of the externality internalized by borrowers. This is described as a “plausible parameterization,” meaning that lender-side internalization of the externality is quantitatively substantial relative to the classic borrower-side effect.

Q10. What does the optimal lender structure exercise find, and what does it imply for welfare?

When lender countries are allowed to optimally choose lender structure, they select a more concentrated structure than the baseline in order to maximize foreclosure repayment. Under this optimal structure, domestic (borrowing-country) agents consume and borrow more, face sudden stops with higher probability, but completely avoid foreclosure events. Borrower welfare improves by 0.1% in consumption-equivalent terms relative to the baseline competitive equilibrium. This implies that concentrating lender structure can be mutually beneficial for both sides of the international credit market.

Q11. Why might collective action clauses be insufficient to correct the efficiency implications of lender structure?

Collective action clauses are policies designed to improve creditor coordination in sovereign debt restructuring. The paper argues that the efficiency distortions arising from lender structure go beyond pure coordination failures: because a concentrated lender structure generates welfare-relevant pecuniary externalities through the collateral price channel — affecting overborrowing and crisis severity — addressing creditor coordination alone is insufficient to fully resolve these inefficiencies.

Key Concepts

Lender concentration (LTop3): The combined loan share held by the top three lenders in a borrowing country’s external debt. Measured using FFIEC 009a data. Used as the primary empirical proxy for the degree to which external debt is concentrated in a few large creditors rather than dispersed among many atomistic lenders.

Pecuniary externality (lender-side): The price impact that a large lender imposes on the collateral market when selling foreclosed assets. Unlike in the standard Bianchi (2011) framework where only borrowers (via the social planner) internalize this externality, a sufficiently large lender also internalizes it by restraining collateral sales to support the collateral price.

Foreclosure rate (zeta): The fraction of seized collateral that a lender sells after foreclosure. Atomistic lenders set zeta = 1 (sell everything); the large lender sets zeta < 1 (partial foreclosure) to prevent collateral price depression. The aggregate foreclosure rate is a weighted average across lender types.

Overborrowing: Borrowing in excess of the social planner’s optimal level, arising because competitive equilibrium agents do not internalize the pecuniary externality of their borrowing on the collateral price. In this model, overborrowing is increasing in lender concentration because a more concentrated lender structure supports a higher collateral price, reducing precautionary saving.

Sudden stop: An abrupt reversal of capital inflows to an emerging economy, typically associated with a sharp current account reversal, real exchange rate depreciation, and a decline in asset prices. In the model, sudden stops are associated with foreclosure states in which tradable endowment falls short of debt obligations.

Debt capacity channel: The mechanism by which higher lender concentration raises the nontradable goods price in foreclosure states, thereby increasing the collateral value and expanding agents’ borrowing capacity, which weakens the precautionary saving motive.

Amplification channel: The mechanism by which higher lender concentration steepens the slope of the nontradable price response to a fall in tradable consumption, amplifying the magnitude of the pecuniary externality that the social planner internalizes and thus increasing the social planner’s incentive to restrict borrowing.

Life-cycle worker flows and cross-country differences in aggregate employment

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research question. The paper asks: what are the sources of cross-country differences in aggregate employment across European economies, and which types of worker flows — between employment (E), unemployment (U), and nonparticipation (N) — drive those differences? The authors pay particular attention to heterogeneity by gender and age, motivated by the observation that cross-country employment dispersion is concentrated among women, youth, and older workers, and that a large portion of the dispersion is traceable to differences in labor force participation rather than unemployment rates alone.

Data. The empirical analysis draws on microdata from the EU Statistics on Income and Living Conditions (EU-SILC), an annual survey covering 32 European countries for 2004–2019. Germany is covered using the German Socio-Economic Panel (GSOEP, 2003–2018) because GSOEP longitudinal coverage begins earlier. The combined sample contains 7,064,306 individual-year observations for 2,221,672 individuals. Labor force status is recorded monthly via a retrospective calendar; transition probabilities are estimated at the quarterly frequency after correcting for measurement error (a “de-NUN-ification” procedure following Elsby et al. [2015]) and time-aggregation bias (Shimer [2012]).

Methodology — empirical. Six quarterly transition probabilities among E, U, and N are estimated by gender and single year of age (16–65). The life-cycle profile of each probability is extracted nonparametrically by regressing age-time cells on age and time dummies, removing business-cycle variation. To decompose cross-country employment differences into contributions of the six transition rates while handling the path-dependence of the decomposition (6! = 720 possible orderings), the authors apply the Shapley-Owen decomposition, which assigns to each transition rate its average marginal contribution across all orderings. An initial first-pass decomposition allocates the aggregate employment gap between any two countries into three parts: demographics, initial conditions (distribution across E, U, N at age 16), and transition probabilities. Transition probabilities account for 93–105% of the cross-country variance in aggregate employment, while demographics and initial conditions together explain less than 10%.

Methodology — structural model. The authors build a life-cycle Diamond-Mortensen-Pissarides (DMP) model with three labor market states, calibrated separately by gender and country for France, Germany, Italy, Spain, and the U.K. — the five largest economies in the sample. A key feature is that all primitives (technology, search and matching) are age-independent; life-cycle variation in worker flows arises endogenously from the finite retirement horizon and from two search margins: (i) an intensive margin — variable search intensity s in [0,1] chosen optimally each period — and (ii) an extensive margin — the endogenous labor force participation decision modeled as a discrete choice with i.i.d. extreme-value utility shocks. The model also incorporates permanent match quality (an experience good revealed stochastically with probability alpha per period following Jovanovic [1979]), transitory match-quality shocks (persistent AR(1) process), exogenous job-destruction shocks (per-period probability delta), a two-tier UI system, a two-tier EPL system capturing temporary vs. permanent contracts, and proportional value-added and social-security taxes.

Main empirical findings.

For male workers, employment-to-unemployment (EU) transitions account for approximately half of the cross-country variance in aggregate male employment across all 32 countries, rising to about three-quarters when looking at the five largest economies, and exceeding 85% for prime-age males (ages 25–54). Transitions in the reverse direction (UE) explain less than 30% of the variance across all 32 countries and play almost no role among the five largest economies. The labor force participation margin (combining NE and EN transitions) explains a non-negligible 25–30% of the aggregate male employment gap.
For female workers, at least half of the cross-country variance in employment is explained by participation-related flows, primarily transitions from nonparticipation to employment (NE). In the full 32-country sample, NE alone explains 65% of the variance in female employment rates across all ages (16–65). Its role is somewhat smaller in the five largest economies, where EN transitions also play a larger role. Crucially, the sum of NE and EN variance contributions for women is at least as large as the sum of UE and EU contributions, underlining the indispensability of a three-state model.

Main quantitative (model-based) findings. The model decomposes cross-country employment differences into technology (the distribution of permanent match quality, job-separation risk delta, and information frictions alpha), search parameters (vacancy costs, non-work utility, search-cost parameters), and policies (UI generosity, firing costs, taxes). The total employment variance across the five economies and two gender groups is 0.36 percentage points squared. Technology differences over-explain this variance (contribution of 0.65), while policies play almost no role (contribution of -0.04) and search frictions have a negative variance contribution (-0.25). The negative sign of search and policy contributions reflects the negative cross-country correlation between these factors and technology: countries with high employment rates (e.g., France) tend to have more generous UI and higher taxes, which the model attributes to compensating technology advantages. For individual countries: France is about 4.4 percentage points above the cross-country benchmark, driven by technology and partly offset by the highest replacement ratios and labor tax rates in the sample (67% and 56%, respectively). Spain is about 7 percentage points below the benchmark, driven by the lowest measured labor productivity (78% of Germany’s level) and the highest employment outflow rates (~4–5% per quarter vs. ~2% in France).

The channels through which technology affects employment are predominantly the employment inflows, not outflows. The exogenous job-separation risk delta affects aggregate employment mostly through its impact on expected duration of future employment spells, which reduces search incentives and job-finding rates from both unemployment and nonparticipation, and lowers labor force attachment. Similarly, mean permanent match quality (mu_x) and labor taxes (tau_ss) operate mainly through the inflow margin. Technology effects are amplified by search effort margins, particularly for women and youth: women face higher non-work utility (interpreted as labor-market frictions or opportunity costs), implying a lower employment surplus and therefore a higher surplus elasticity; for young workers, the long remaining horizon amplifies the effect of technology variations on discounted lifetime earnings, generating relatively higher search-effort responses.

Scope conditions. The analysis is confined to European countries. The structural decomposition covers only the five largest European economies. The authors acknowledge that parameters labeled as “job-separation risk” may also capture employment protection and temporary contracts not explicitly modeled, or non-monetary quit motives, so the attribution to “technology” should be interpreted with that caveat in mind. The model operates in a complete-markets, no-savings environment without on-the-job search.

In depth

Q1. What fraction of cross-country employment variance is explained by transition probabilities vs. demographics and initial conditions?

A: In the full 32-country sample, transition probabilities account for 94.7% of the cross-country variance in aggregate male employment and 99.9% for female employment. In the five largest economies, the corresponding figures are 93.5% (men) and 104.9% (women) — the slight excess above 100% reflects the negative contribution of initial conditions for women. Demographics and initial conditions together explain less than 10% of the variance, with somewhat larger demographic effects in Baltic and Eastern European countries, plausibly due to emigration-driven changes in age composition.

Q2. For male workers, which specific transition probability dominates the cross-country employment variance, and how does this vary by age and across country groupings?

A: EU (employment-to-unemployment) transitions account for approximately 51% of the cross-country variance in aggregate male employment (ages 16–65) across all 32 countries, rising to 77% in the five largest economies, and to 89% for prime-age males (ages 25–54) in the same group. By contrast, UE (job-finding from unemployment) explains at most 29% across all 32 countries and virtually nothing in the five largest economies. For prime-age men, EU remains dominant throughout; toward the end of the working life, EN (employment-to-nonparticipation) transitions become the main driver as workers move into retirement.

Q3. For female workers, what is the primary driver of cross-country employment variance, and does the pattern differ from men?

A: For women, transitions from nonparticipation to employment (NE) explain 65% of the cross-country variance in female employment across all ages in the 32-country sample. This dominance is more concentrated at ages 20–30, when participation entry is particularly heterogeneous across countries, likely reflecting fertility and child-rearing patterns. The sum of NE and EN contributions for women equals or exceeds the combined UE and EU contributions in both country groupings, demonstrating a fundamentally different demographic structure of employment differences for women relative to men.

Q4. How does the model generate life-cycle variation in transition rates despite having age-independent primitives?

A: The model produces age-varying transition rates through two mechanisms operating on age-independent fundamentals. First, variable search intensity declines as workers age because the remaining time to retirement shortens, reducing the expected lifetime returns to job search — the “horizon effect” (Cheron et al. [2011, 2013]). This mechanism explains virtually all of the life-cycle variation in the NE job-finding rate and an overwhelmingly large share of the variation in the UE rate, as shown by counterfactual exercises that fix search intensity at its life-cycle average. Second, information frictions about permanent match quality generate declining separation rates over the working life: young workers disproportionately hold matches with unrevealed quality and thus face higher reallocation risk upon quality revelation; as workers age, their employment share shifts toward matches with revealed quality, which have lower separation rates due to sorting.

Q5. What does the structural decomposition (Table 7) reveal about the role of technology vs. policies in explaining cross-country employment differences?

A: The variance decomposition in Table 7 shows that technology parameters (permanent match-quality distribution, job-separation risk delta, and match-quality revelation probability alpha) account for a variance contribution of 0.65 (against total employment variance of 0.36), over-explaining the cross-country dispersion. Labor market policies (UI benefits, firing costs, taxes) have a near-zero variance contribution of -0.04. Search parameters contribute -0.25. The result that policies explain little does not mean they have no level effect: in simple comparative statics, the model predicts that more generous UI and higher labor taxes lower employment. However, in the cross-country calibration, countries with higher employment rates tend to have more interventionist policies, so the cross-country correlation between policies and technology masks individual policy effects at the variance level.

Q6. How do technology effects propagate to employment differences through worker flows, and why is the inflow channel dominant?

A: Table 8 decomposes employment elasticities with respect to delta (job-separation risk), mu_x (mean log permanent match quality), and tau_ss (social security tax rate) into contributions from (i) the NE job-finding rate, (ii) the share of nonemployed in the labor force (labor force attachment, u-tilde), (iii) the differential between UE and NE rates, and (iv) the employment outflow rate (pEO). At the aggregate level, the separation risk delta has an employment elasticity of -0.28, of which the outflow contribution (dpEO = -0.08) is smaller in absolute magnitude than the sum of inflow contributions (dpNE = -0.06, du-tilde = -0.07, dpDelta = -0.06). Mean match quality mu_x has an employment elasticity of 0.53, primarily mediated through inflows. The mechanism is that changes in delta or mu_x alter expected lifetime earnings, which in turn change search incentives and participation decisions, generating correlated movements in job-finding rates and labor force attachment that amplify the employment impact beyond what a simple outflow change would imply.

Q7. Why do women and youth show larger search-effort responses to technology variations?

A: For women, the calibrated non-work utility yo is higher in all five countries than for men (interpreting this as extra costs and wedges on the returns to working), which implies a smaller employment surplus. A smaller surplus generates a higher elasticity of surplus with respect to parameter changes, and since search intensity and participation decisions depend on expected surplus, women exhibit larger employment elasticities to technology variations. The aggregate employment elasticity of delta is -0.39 for women vs. -0.19 for men; for mu_x, it is 0.78 for women vs. 0.33 for men. For youth (ages 20–29), the long remaining horizon amplifies the effect of technology changes on discounted expected lifetime earnings, which in turn amplifies participation incentives: the labor force attachment channel (du-tilde) contributes -0.13 for youth compared to -0.07 at the aggregate, while dE = -0.31 for youth vs. -0.28 aggregate for delta.

Q8. What is the quantitative role of individual technology sub-components (match quality, job-separation risk, information frictions)?

A: Panel B of Table 7 breaks down technology into three sub-components. Match quality (mean mu_x and variance sigma^2_x) and job-separation risk (delta) are the key drivers; the match-quality revelation probability (alpha, “match revelation”) plays almost no independent role (variance contribution approximately 0.00). For France, the primary positive technology contributor is mean match quality (consistent with France’s labor productivity slightly above the German benchmark). For Germany and the U.K., the low job-separation risk is the primary positive contributor. For Spain, the high job-separation risk — calibrated to match Spain’s employment outflow rate of around 4–5% per quarter versus 2% in France — is the main negative contributor, reflecting the widespread prevalence of temporary contracts.

Q9. What role do labor market policies play at the country-specific level, even though they explain little cross-country variance?

A: Panel C of Table 7 shows that employment protection legislation plays almost no role for any country. Labor taxes are quantitatively important: they explain the relatively high employment rate in the U.K. (the country with the lowest social security contribution rate, about 20%), contributing positively. In France, where labor taxes exceed 50% of the average wage, the policy contribution is strongly negative, roughly offsetting the large positive technology contribution. UI benefits lower aggregate employment — Italy, with calibrated UI benefits lower than France’s, has a smaller employment gap vis-a-vis the benchmark partly because of this. The finding that policies explain little variance while having large individual-country effects is explained by the negative cross-country correlation: countries with generous policies also tend to have favorable technology, so policy and technology contributions partially offset each other in the variance decomposition.

Q10. How does the model fit untargeted moments, particularly the empirical Shapley-Owen variance decomposition?

A: The model is calibrated to aggregate transition rates by gender, and to moments describing labor productivity, vacancy rates, and policy targets. Despite having age-independent primitives, the calibrated model captures the empirical life-cycle profiles of transition rates as untargeted moments: declining NE and UE rates with age, rising EN rates near retirement, and the hump-shaped patterns. More stringently, the model replicates the empirical Shapley-Owen variance decomposition: it correctly predicts that EU separations account for most of the employment variance for men, and that NE inflows are relatively more important for women and youth. A notable limitation is that the model overshoots the UN (unemployment-to-nonparticipation) transition rate for a significant share of data points — but the authors note that flows between U and N play almost no role in cross-country employment variance.

Q11. What is the “horizon effect” and how does it operate in this model?

A: The horizon effect, coined by Cheron et al. [2011, 2013] in a two-state (E/U) DMP model, refers to the phenomenon that as workers approach retirement, the expected returns to job search fall because the remaining period of employment is shorter. This reduces search intensity from both unemployment and nonparticipation, lowering job-finding rates, and in the present model also affects the match-acceptance probability: workers near retirement find it optimal to remain in unemployment to collect UI benefits rather than accept a job offer, further reducing the UE rate. The current paper generalizes this effect to a three-state setting by incorporating the labor force participation margin alongside search intensity, generating plausible declining job-finding rates and increasing EN rates at older ages from age-independent parameters.

Q12. How does the paper handle the gender dimension in the model calibration?

A: The model assumes that men and women share the same production and matching technology parameters within a country (A, cv, delta, alpha, mu_x, sigma^2_x, sigma^2_z), but allows the search-cost and non-work-utility parameters (ceu, cnu, cu, kappa_u, kappa_n, yo) to differ by gender. The gender-specific search parameters are identified from the gender-specific transition rates: for example, kappa_u (marginal search cost in unemployment) for women is inferred from the female UE transition rate, relative to the normalization for men. The non-work utility yo is consistently higher for women in all five countries, rationalizing lower female employment through a lower employment surplus. This generates a higher surplus elasticity for women, which in turn explains why women’s employment is more responsive to technology variations across countries.

Key Concepts

Shapley-Owen Decomposition. A method from cooperative game theory (Shapley [1953], Owen [1977]) used here to decompose cross-country differences in employment into contributions of individual worker-flow transition rates (or structural parameters). It computes the marginal contribution of each component averaged over all 6! = 720 orderings of the six transition rates, yielding a unique, symmetric, exact decomposition that sums to the total employment gap. Unlike sequential decompositions, it is path-independent.

Extensive Margin of Search Effort. The binary labor force participation decision: whether a nonemployed worker enters the unemployment state (and thus accesses the superior search technology at a flow cost) or remains in nonparticipation. In the paper’s model, this is captured as a discrete choice between states U and N, governed by i.i.d. extreme-value utility shocks, yielding a closed-form logit participation probability.

Intensive Margin of Search Effort. The continuous choice of search intensity s in [0,1] by nonemployed workers (both unemployed and nonparticipants), which scales the probability of meeting a vacancy per period. The optimal intensity equates the marginal cost of search (convex in s) to the marginal benefit (the expected surplus from meeting a firm times the contact rate). Search intensity declines with age because the remaining working life shortens, reducing the discounted value of a job.

Permanent Match Quality (x). A time-invariant, match-specific productivity component drawn from a log-normal distribution upon meeting a firm, but initially unobserved by both worker and firm (an experience good). With per-period probability alpha, the quality is revealed; prior to revelation, the parties form expectations over the distribution. Revelation triggers reallocation of bad matches, generating a negative relation between job tenure and separation probability (following Jovanovic [1979]).

Horizon Effect. The mechanism by which workers reduce search effort as they approach retirement because the expected present value of future employment spells shortens. In this paper the concept, coined by Cheron et al. [2011, 2013] in a two-state DMP setting, is extended to include the labor force participation margin: near-retirement workers not only search less intensively but also become more likely to choose nonparticipation (or to remain unemployed to collect benefits rather than accept a job), generating the observed life-cycle decline in job-finding rates from age-independent parameters.

Technology Parameters (theta). In the paper’s structural decomposition, “technology” refers specifically to the vector (mu_x, sigma^2_x, alpha, delta) — the mean and variance of log permanent match quality, the match-quality revelation probability, and the exogenous job-destruction probability. These are contrasted with search-cost parameters (phi) and policy parameters (psi). The label “technology” is acknowledged to potentially also capture employment protection and quit motives not explicitly modeled.

Life-Cycle DMP Model. A finite-horizon version of the Diamond-Mortensen-Pissarides search-and-matching framework in which workers live for J periods, all primitives are age-independent, and life-cycle variation in worker flows arises endogenously from the interaction of the finite horizon with search intensity, labor force participation, and match-learning mechanisms. The model distinguishes three labor market states (E, U, N) and uses Nash bargaining to split the employment surplus.

Monetary policy in open economies with production networks

Mon, 01 Jan 0001 00:00:00 +0000

This paper studies the design of monetary policy in a multi-sector small open economy with domestic input-output linkages and cross-border production networks, under nominal price rigidities in domestic sectors. The main result is that the monetary policy that closes the domestic output gap is nearly optimal, and it is implemented by stabilizing an aggregate inflation index that weights each sector’s inflation by its role as a supplier of inputs and a net exporter within the international production network. Sectors with small direct or indirect import shares receive large weight in the index; ignoring cross-border linkages leads monetary policy to overemphasize inflation in sectors that are intensive exporters directly or indirectly through downstream sectors. Three channels link sectoral markup wedges to the aggregate output gap: the CPI channel (present in closed economies too) and the net export income and net profit income channels (unique to open economies with cross-border linkages). Using the World Input-Output Database, the output-gap-closing policy is shown to outperform alternatives that abstract from economic openness or input-output linkages.

In depth

Q1. What is the output gap monetary policy and how is it implemented?

The output gap (OG) monetary policy stabilizes the aggregate inflation index proportional to the aggregate output gap—defined as the difference between output in the sticky-price equilibrium and in the efficient flexible-price equilibrium—by weighting each sector’s inflation according to the product of its price rigidity and its OG weight. The price rigidity component maps positive sectoral inflation into a negative sectoral markup wedge under nominal rigidities; the OG weight measures the sector’s contribution to the aggregate output gap through domestic and cross-border network linkages. This policy eliminates first-order aggregate distortions and is shown to be nearly optimal.

Q2. What are the CPI, net export income, and net profit income channels?

Three channels link a negative sectoral markup wedge to a positive aggregate output gap: the CPI channel (lower domestic prices raise real factor prices and stimulate supply), the net export income channel (lower domestic prices increase net exports and domestic labor income), and the net profit income channel (two opposing effects: lower prices increase net export profits but also raise the cost of imported inputs). The CPI channel operates in closed economies as well, while the net export income and net profit income channels are unique to open economies with cross-border input-output linkages.

Q3. Why does ignoring cross-border linkages lead monetary policy to overweight intensive exporters?

Failing to account for cross-border production networks causes monetary policy to overemphasize inflation in sectors that export intensively directly and indirectly—because the net profit income channel, which reduces the OG contribution of intensive exporters by raising the cost of their imported inputs, is omitted when the economy is treated as closed. Without the cross-border linkages, intensive direct or indirect exporting sectors appear to have larger aggregate output gap contributions through domestic channels alone, causing the aggregate inflation index to over-weight those sectors.

Q4. How do the results relate to existing monetary policy frameworks?

The paper bridges the multi-sector closed-economy result that optimal policy targets a Domar-weighted aggregate inflation index and the one-sector open-economy result that optimal policy trades off domestic inflation against terms-of-trade distortions, showing that cross-border input-output linkages modify the Domar weights through the net export income and net profit income channels. In the limit where all sectors have no cross-border linkages, the OG weights reduce to Domar weights; the one-sector open economy policy prescription is a special case of the general framework.

Q5. What is the empirical validation?

Using the World Input-Output Database, the paper computes the theoretical sectoral OG weights for actual economies and shows that the OG monetary policy outperforms alternative policies that ignore either economic openness or input-output linkages. The database provides cross-country cross-sector data on intermediate input flows that allow computation of the model’s OG weight formulas for real economies.

Key concepts

output gap (OG) monetary policy : the monetary policy that closes the aggregate output gap (difference between sticky-price and efficient flexible-price output), implemented by stabilizing the network-weighted aggregate inflation index; shown to be nearly optimal in the open-economy production network framework.

sectoral OG weight : the weight assigned to a sector’s inflation in the aggregate inflation index under OG monetary policy; measures the sector’s contribution to the aggregate output gap through the CPI, net export income, and net profit income channels; differs from the Domar weight in open economies due to cross-border linkages.

Domar weight : the ratio of a sector’s gross output to GDP; the weight used in the closed-economy multi-sector optimal inflation index literature; coincides with the OG weight when there are no cross-border production linkages.

labor wedge : a weighted average of sectoral markup wedges proportional to the aggregate output gap; the monetary policy target in the OG framework.

efficiency wedge : a weighted average of exogenous sectoral shocks; determines the efficient flexible-price equilibrium; independent of sectoral markup wedges at first order, so the OG policy can separately close the aggregate distortions caused by markup wedges.

Monetary policy trade-offs amid global supply chain disruptions

Mon, 01 Jan 0001 00:00:00 +0000

This paper employs a proxy structural VAR model to examine the effects of global supply chain (GSC) shocks on U.S. macroeconomic variables and the Federal Reserve’s historical response, and evaluates two counterfactual monetary policy rules using the COVID-19 episode. Large fiscal stimulus amplifies inflation while cushioning the output downturn from GSC shocks. Historically, the Fed adopted a loose stance, looking through price surges from supply chain disruptions. The first counterfactual—which stabilizes inflation—entails less accommodation and yields a more favorable inflation-output trade-off, reflecting greater price flexibility and limited output losses. The second counterfactual—which minimizes a dual-mandate loss function—calls for greater initial easing; under inflation targeting (IT) this involves moderate accommodation, while under average inflation targeting (AIT) the looser initial policy generates more persistent inflation and ultimately requires a contractionary response, worsening the trade-off.

In depth

Q1. What is the empirical strategy?

The paper estimates a proxy structural VAR model that identifies GSC shocks using the news-based Supply Bottleneck Index (SBI) of Burriel et al. (2024) as a proxy, then evaluates the Fed’s historical response to those shocks and two counterfactual policy rules that substitute for the historical stance. The proxy SVAR approach identifies the GSC shock’s impulse response function and then traces the macroeconomic dynamics that would have obtained under alternative policy rules, holding the non-policy shocks at their historical values. The SBI captures sudden decreases in supply chain functioning from natural disasters, geopolitical events, strikes, and pandemics.

Q2. What is the role of fiscal stimulus in amplifying GSC shock effects?

Large fiscal stimulus—such as the U.S. transfers and spending during COVID-19—amplifies the inflationary impact of GSC shocks while cushioning the output downturn; the interaction between supply disruptions and fiscal expansion is thus an important determinant of the inflation-output dynamics. Without the large fiscal stimulus, GSC shocks would generate the standard supply-shock trade-off with less amplified inflation. With stimulus, the combination of higher aggregate demand (from fiscal transfers) and reduced aggregate supply (from GSC disruptions) creates a strongly inflationary environment.

Q3. What does the first counterfactual (inflation-stabilizing policy) show?

The counterfactual that stabilizes inflation requires less monetary accommodation than the historical stance and yields a more favorable inflation-output trade-off, suggesting that the Fed’s historical ’look-through’ approach was suboptimal given the interaction with fiscal stimulus. The intuition is that earlier and firmer monetary tightening in response to GSC-driven inflation would have reduced inflation expectations pass-through and prevented a larger buildup of price pressures, while the output cost of that tighter stance was limited by the greater price flexibility the model identifies in this environment.

Q4. What is the comparison between IT and AIT in the second counterfactual?

The second counterfactual calls for greater initial easing than the historical stance; under inflation targeting (IT) this involves moderate accommodation, while average inflation targeting (AIT) implies an even looser initial policy that generates more persistent inflation and ultimately requires a contractionary response, worsening the inflation-output trade-off relative to IT. The AIT result reflects the design of that framework: making up for periods of below-target inflation with above-target periods creates a commitment to easy policy even when supply-side inflationary pressures are elevated, producing a worse outcome when supply shocks drive inflation above target.

Key concepts

proxy structural VAR : a structural VAR identified using an external instrument (the proxy variable) that is correlated with the structural shock of interest but uncorrelated with other shocks; used here to identify GSC shocks using the Supply Bottleneck Index. global supply chain (GSC) shock : a sudden decrease in the supply provision or functioning of supply chains stemming from adverse events (natural disasters, pandemics, geopolitical events); identified in this paper as acting like supply shocks, lowering output and raising prices. average inflation targeting (AIT) : a monetary policy framework in which the central bank targets the average rate of inflation over time, implying accommodation of below-target periods with above-target periods; shown here to imply looser initial policy and more persistent inflation in response to supply shocks, worsening the trade-off relative to standard IT.

Motivating banks to lend? Credit spillover effects of the Main Street Lending Program

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Research Question. Minoiu, Zarutskie, and Zlate ask whether participation in the Main Street Lending Program (MSLP)—a Federal Reserve emergency facility launched in mid-2020 to channel credit to small and mid-sized firms during the COVID-19 pandemic—caused banks to lend more outside the program. The authors focus on credit spillover effects: did MSLP-participating banks ease standards and expand volumes on their general commercial and industrial (C&I) loan books, beyond the direct loans originated under the program itself?

Institutional Context. The MSLP opened for lender registration on June 15, 2020 and began accepting loan submissions on July 6, 2020, expiring December 31, 2020. Of $600 billion in available SPV capacity, only $16.05 billion was actually deployed, making overall take-up approximately 2.7% of capacity. Despite this, the program required participating banks to retain 5% of each loan’s credit risk while offloading 95% to the SPV, and charged borrowers LIBOR plus 300 bps. Registration rate among all Call Report banks was 11.7% (614 out of 5,242 banks), with participation rising steeply with bank size: from 6.5% of banks in the below-$1-billion asset group to 63.8% of banks with assets above $50 billion.

Data and Methodology. The analysis draws on multiple data sources: (a) supervisory Y-14Q H1 loan-level data covering C&I loans above $1 million commitments, reported by 32 bank holding companies (BHCs) that account for roughly three-quarters of total U.S. C&I loans; (b) Y-14Q A9 loan portfolio segment data for small business C&I loans (below $1 million commitments) from 22 BHCs; (c) quarterly Senior Loan Officer Opinion Survey (SLOOS) microdata for April, July, and October 2020, providing bank-level assessments of lending standard changes, loan terms, demand shifts, and stated reasons for tightening; (d) Dealscan syndicated loan originations for 262 banks (51 MSLP participants); and (e) bank balance sheet data from Call Reports, including the Ellul-Yerramilli risk management index (RMI) for 16 BHCs. The core empirical design is a difference-in-differences (DiD) comparing MSLP-participating vs. non-participating banks before (2020:Q1–Q2) and after (2020:Q3) program implementation. To address nonrandom selection, the authors instrument MSLP participation with three variables: (i) a dummy for banks that cited registration as “too burdensome” in the September 2020 supplementary SLOOS; (ii) a dummy for banks with prior experience pledging loan collateral at the Fed’s discount window; and (iii) a dummy for banks with prior experience pledging securities collateral at the discount window. Firm×quarter fixed effects absorb time-varying credit demand at the borrower level (Khwaja-Mian design), and bank×borrower fixed effects further control for relationship-specific lending patterns.

Main Findings — Extensive Margin (Large Business Loans). In the Y-14Q H1 data, MSLP banks were 30–32% more likely to renew existing loans than non-MSLP banks in 2020:Q3, with the probability of renewal 1.6–1.7 percentage points higher (against a sample average renewal rate of 5.3%). New loan originations were 22–27% more likely at MSLP banks, or 1.1–1.4 percentage points higher (against a sample average origination rate of 5.1%). 2SLS estimates are similar in magnitude to OLS, indicating selection bias is modest.

Main Findings — Extensive Margin (Small Business Loans and Survey Data). In the A9 small business segment data, MSLP lenders had 17.3% more small business loan accounts outstanding in 2020:Q3 than non-MSLP banks. In SLOOS microdata, MSLP banks were approximately 15 percentage points less likely to report tightening C&I lending standards in 2020:Q3 (conditional on demand controls), compared to an actual tightening rate of 37.5%. This effect is larger for small (more financially constrained) firms (16–17 percentage points) than for large firms (13–14 percentage points).

Main Findings — Intensive Margin. On loan terms, MSLP banks charged spreads that were approximately 9 basis points lower on renewed/originated C&I loans in the Y-14Q data, and 13.5 basis points lower in the Dealscan syndicated loan sample, compared to non-MSLP banks in 2020:Q3. 2SLS estimates are somewhat larger (19–30 bps). In the Dealscan sample, MSLP banks also extended syndicated loans that were 11.2% larger (about $2.4 million more given a $22 million average loan size). Survey data confirm MSLP banks were less likely to tighten most individual loan terms.

Aggregate Magnitude. The authors estimate that, in the absence of the MSLP, total loan renewals and originations at Y-14Q reporting banks in 2020:Q3 would have been approximately 10% lower. Scaling to the broader banking sector, the estimated credit spillover effect is approximately $44.8 billion in C&I lending—nearly three times the $16.05 billion in direct MSLP loan purchases.

Mechanism. Survey and objective evidence both point to reduced risk aversion as the primary channel, rather than immediate balance sheet constraint relief. MSLP banks were significantly less likely to cite “reduced tolerance for risk” as a reason for tightening lending standards after the program’s introduction, while showing no differential propensity to cite capital or liquidity deterioration. Banks with higher risk management index scores (more risk-averse institutions) exhibited larger spillover effects on two of three lending margins. Indicators of immediate balance sheet tightness (excess capital cushions, cost of capital, core deposit reliance) do not predict larger spillovers, with a partial exception for lower excess capital and higher loan loss reserves — suggesting future rather than current balance sheet constraints may have played some role.

Scope Conditions and Robustness. The backstop mechanism is explicitly tied to the program’s credibility period: the spillover effects are smaller in 2020:Q4, consistent with the Treasury’s November 19, 2020 announcement that the program would not be extended, which diminished its backstop role. Placebo regressions using 2018 and 2019 data find no differential lending behavior between MSLP and non-MSLP banks before the program, supporting parallel trends. Results are robust to controls for PPP participation, credit line drawdown exposure, loan loss provisioning, and bank-level loan portfolio cyclicality.

In depth

Q1. What precisely is the “spillover effect” that the paper measures, and how does it differ from the direct effect of the MSLP?

A: The direct effect is the $16.05 billion in MSLP loans purchased by the SPV — credit extended specifically through the program. The spillover effect refers to changes in banks’ general C&I lending behavior outside the program: renewals and originations of non-MSLP loans, changes in lending standards and terms for all business borrowers, and changes in small business loan volumes. The sample in the Y-14Q regression explicitly excludes MSLP loans themselves, so the estimates reflect only the indirect, broader credit effects.

Q2. What instruments does the paper use for MSLP participation, and why are they plausibly exogenous?

A: Three IVs are employed: (1) a dummy for banks that cited program registration as “too burdensome” as a very important reason for not joining (from the September 2020 supplementary SLOOS); (2) a dummy for banks that pledged loan collateral at the Fed’s discount window in December 2019; and (3) a dummy for banks that pledged securities collateral at the discount window in the same period. The exclusion restriction argument is that (1) reflects banks’ administrative capacity and prior Fed engagement rather than underlying balance sheet strength or lending appetite, and that (2) and (3) reflect familiarity with Fed collateral processes in ways that made a loan-based program easier to understand and join — without independently affecting lending standards or volumes in 2020:Q3.

Q3. How large are the spillover effects on the extensive margin of large corporate lending?

A: In the Y-14Q H1 data across 32 BHCs, MSLP banks renewed loans 1.6–1.7 percentage points more frequently and originated new loans 1.1–1.4 percentage points more frequently in 2020:Q3, relative to non-MSLP banks. Against sample averages of 5.3% renewal rate and 5.1% origination rate, these translate to MSLP banks being 30–32% more likely to renew and 22–27% more likely to originate loans. The 2SLS estimates are broadly similar in magnitude, suggesting that self-selection bias in OLS is limited.

Q4. What are the estimated aggregate dollar spillovers from the MSLP?

A: The paper calculates that, in the absence of the program, total loan renewals and originations at Y-14Q H1 MSLP banks in 2020:Q3 would have been lower by approximately $33.6 billion (derived from 44,274 bank-borrower pairs × 1.38 existing loans per pair × 3.06 percentage points of extra loan activity × $17.98 million average loan size). Scaling to all Y-14Q banks (MSLP and non-MSLP alike), the shortfall would represent roughly a 10% reduction in total 2020:Q3 loan renewals and originations. Extrapolating to the full banking sector (since Y-14Q banks cover about 75% of total C&I lending), and assuming similar spillover magnitudes for banks outside the sample, total MSLP spillovers amount to roughly $44.8 billion — approximately three times the $16.05 billion in direct MSLP loan purchases.

Q5. What is the estimated effect on C&I lending standards using survey data?

A: Using SLOOS microdata, the paper estimates that MSLP banks were approximately 15 percentage points less likely to tighten C&I lending standards in 2020:Q3 compared to non-MSLP banks, after controlling for demand conditions. The actual tightening rate in 2020:Q3 was 37.5%, meaning the counterfactual tightening rate absent the program would have been approximately 5 percentage points higher. In a further hypothetical where all SLOOS sample banks had participated, the counterfactual tightening rate would have been nearly 10 percentage points higher than actual.

Q6. Are spillover effects larger for small or large borrowers, and what does this imply?

A: The SLOOS-based estimates show that MSLP banks were 16–17 percentage points less likely to tighten lending standards for small firms (annual sales below $50 million), compared to 13–14 percentage points less likely for large and middle-market firms — a statistically significant difference. The authors interpret this as consistent with the MSLP reducing risk aversion broadly, with the largest effect on borrowers facing greater credit constraints where uncertainty about creditworthiness was highest.

Q7. What evidence supports the risk aversion (psychological backstop) mechanism over the balance sheet constraint mechanism?

A: From SLOOS data, MSLP banks were significantly less likely (at the 1% level) to cite “reduced tolerance for risk” as a reason for tightening lending standards after the program’s introduction, while showing no differential likelihood of citing deteriorating capital or liquidity positions as reasons. Furthermore, splitting banks by the risk management index (RMI), the spillover effects are stronger for high-RMI (more risk-averse) banks on two of three lending outcomes. Conversely, proxies for immediate balance sheet constraints — excess capital cushions, core deposit ratios, equity issuance, and cost of capital — do not yield consistently stronger spillover effects for more constrained banks. The only partial exception is lower excess capital and higher loan loss reserves, which are associated with more loan renewals, suggesting future rather than current balance sheet constraints may have contributed.

Q8. What is the risk management index (RMI), and how is it used here?

A: The RMI is an index developed by Ellul and Yerramilli (2013) that captures the strength of a bank’s internal risk management function, constructed from variables including whether the bank has a chief risk officer (CRO), the CRO’s executive status and relative compensation, risk committee member experience, and meeting frequency. Available for 61 BHCs over 2011–2013, it is matched to 16 BHCs in the Y-14Q H1 sample and used as a pre-COVID proxy for institutional risk aversion. Banks above the median RMI show larger MSLP spillover effects on loan renewals and tightening standards, consistent with the interpretation that the MSLP reduced effective risk aversion more for banks that had higher baseline risk-consciousness.

Q9. How do the authors address the concern that PPP participation — not MSLP participation — might drive the results?

A: First, they test directly that MSLP participation does not predict outstanding PPP/federally-guaranteed loan balances (in Q2 or Q3 2020) in the A9 loan segment data, finding no correlation. Second, they add an interaction of PPP loan balances (divided by total assets) × Post to the baseline regression in Table A10 and find that while PPP lending is positively associated with loan renewals and originations, the MSLP bank × Post coefficient remains statistically significant and similar in magnitude to the baseline, ruling out PPP participation as the driver of the baseline results.

Q10. What explains the low take-up of the MSLP despite its large designed capacity?

A: Survey responses from the September 2020 supplementary SLOOS indicate several demand- and supply-side constraints: banks reported they could generally meet credit demand outside the program; borrower leverage limits (capped at 4–6× EBITDA depending on facility) were seen as too restrictive; the LIBOR plus 300 bps interest rate was high relative to historical pricing for eligible firms; and registration and loss-sharing arrangements were viewed as burdensome and uncertain. The paper interprets these findings as consistent with banks treating the MSLP primarily as a backstop — a facility they would activate only if economic conditions deteriorated significantly — rather than a primary lending channel.

Q11. How does the paper address the threat that MSLP participation reflects bank-level cyclicality in loan portfolios?

A: Table 10 controls for bank-specific C&I loan portfolio cyclicality, measured as the correlation between each bank’s C&I loan growth and aggregate banking-sector C&I loan growth estimated over 1985:Q1–2021:Q2 using two functional forms. The MSLP bank × Post coefficient estimates remain very similar to the baseline after including these controls, ruling out the concern that MSLP participants were simply banks with naturally more procyclical or countercyclical lending patterns.

Q12. What happens to the estimated spillover effects in 2020:Q4, and what does this reveal?

A: The paper shows (Table A6) that extending the sample to include 2020:Q4 yields somewhat smaller estimated spillover effects than in the baseline 2020:Q3 period. The authors attribute this to the November 19, 2020 announcement by Treasury Secretary Mnuchin that the MSLP would not be extended beyond year-end, which effectively ended the program’s backstop role and — consistent with the psychological backstop mechanism — reduced banks’ confidence in the program’s future availability and thus the spillover motivation.

Q13. Does the paper find spillover effects on intensive margin loan terms, and how large are they?

A: On loan spreads, MSLP banks charged approximately 9 basis points lower spreads on floating-rate C&I loans renewed or originated in 2020:Q3 in the Y-14Q data (2SLS: 19 bps), and approximately 13.5 bps lower spreads in the Dealscan syndicated loan sample (2SLS: 30 bps). The 9 bps OLS estimate implies the average spread across all LIBOR-indexed C&I loans in 2020:Q3 would have been approximately 4 bps higher absent the program (i.e., 0.43 × 9 bps), relative to an actual average spread of 235 bps — an effect the authors characterize as economically small. On loan size, the Dealscan evidence indicates MSLP banks extended syndicated loans that were 11.2% larger (2SLS: 25% larger).

Key Concepts

Credit Spillover Effects: As used in this paper, spillover effects refer to the impact of MSLP participation on participating banks’ lending behavior outside and beyond the program itself — specifically, changes in loan renewal rates, new loan origination rates, lending standards, and loan terms for non-MSLP C&I loans. This is distinct from the direct effect (i.e., loans originated through the MSLP proper).

Psychological Backstop: The paper’s term for the mechanism by which the MSLP reduced participating banks’ effective risk aversion without necessarily easing their immediate balance sheet constraints. By committing to provide lending support if conditions deteriorated, the program built banks’ confidence to lend ex ante, functioning as “insurance” against bad outcomes rather than a direct funding facility. The mechanism is distinguished from balance sheet easing by the fact that constrained and unconstrained banks exhibited similar spillover effects.

Extensive Margin of Lending: The binary dimension of lending activity — specifically, whether a bank renews an existing loan or originates a new loan within a bank-borrower pair. In this paper, measured as the share of existing loan commitments within each bank-borrower pair that are renewed or newly originated each quarter. Contrasted with the intensive margin.

Intensive Margin of Lending: The quantitative dimension of existing lending relationships — specifically, the average loan size and average spread on loans renewed or originated in a given period, conditional on a loan being extended.

Senior Loan Officer Opinion Survey (SLOOS): A quarterly Federal Reserve survey of senior lending officers at large U.S. banks covering self-reported changes in C&I lending standards, terms (including spreads, maximum loan size, maturity, covenants, collateral requirements), demand conditions, and — in supplementary editions — reasons for changing standards. Used in this paper both as an outcome variable (tightening standards) and as a control variable (changes in loan demand) and as a source of IV variation (burden of MSLP registration).

Risk Management Index (RMI): An index developed by Ellul and Yerramilli (2013) measuring the strength of a bank’s internal risk management function, combining information on the presence and compensation of a chief risk officer, risk committee composition, and meeting frequency. Used in this paper as a pre-pandemic proxy for institutional risk aversion to test whether the MSLP disproportionately reduced risk aversion in banks with stronger risk controls.

Difference-in-Differences with Granular Fixed Effects: The primary identification strategy, comparing changes in lending outcomes between MSLP-participating and non-participating banks before (2020:Q1–Q2) and after (2020:Q3) program implementation. The paper uses firm×quarter fixed effects following Khwaja and Mian (2008) to absorb borrower-level credit demand, and bank×borrower fixed effects following Chodorow-Reich (2013) to absorb relationship-specific supply factors — isolating the bank credit supply effect attributable to MSLP participation.

Originate-and-Distribute Feature (of MSLP): The MSLP’s design in which banks originate MSLP loans but sell 95% of the credit exposure to the SPV, retaining only 5%. This feature was intended to free up balance sheet capacity for further lending. The paper tests whether this channel (easing current balance sheet constraints) explains the observed spillovers, finding limited support relative to the risk aversion reduction channel.

Multinational production and global shock propagation during the great recession

Mon, 01 Jan 0001 00:00:00 +0000

Oil price fluctuations, US banks, and macroprudential policy

Mon, 01 Jan 0001 00:00:00 +0000

This paper estimates the effect of oil price fluctuations on US banking variables using a Bayesian SVAR with sign restrictions following Baumeister and Hamilton (2019). Oil market shocks that lead to a contraction in world economic activity are found to unambiguously lower the amount of bank credit to the US economy, tend to decrease US banks’ net worth, and tend to increase the US credit spread. The effects can be strong and long-lasting or more modest and short-lived, depending on the source of the oil price fluctuation. The effects are found to be stronger for smaller and lower-leveraged banks.

In depth

Q1. What is the empirical strategy?

The paper extends the state-of-the-art oil market SVAR of Baumeister and Hamilton (2019) to incorporate three US banking variables—banks’ net worth, the US credit spread, and the amount of bank credit extended—estimated with monthly data over January 1974 through December 2019. An agnostic approach is taken on sign restrictions for the US banking block: no restrictions are imposed on banking variables beyond those already imposed by Baumeister and Hamilton (2019) on the oil block, so the results for banking variables are driven primarily by data rather than prior restrictions. This extends earlier work that studied oil prices and credit spreads (Abbritti et al., 2020) or oil prices and stock markets (Kilian and Park, 2009) in isolation.

Q2. What is the main finding regarding the effect of oil shocks on banks?

Oil market shocks that lead to a contraction in world economic activity are found to unambiguously lower the amount of bank credit to the US economy, tend to decrease US banks’ net worth, and tend to increase the US credit spread. “Unambiguously” reflects that the sign restrictions impose no prior on the direction of credit’s response, so the finding that credit falls is driven entirely by data. The paper is the first to characterize the effect of oil market shocks on banks’ net worth and to estimate the credit effect within the SVAR framework.

Q3. How do the effects differ by the source of oil price fluctuations?

The effects on banking variables can be strong and long-lasting or more modest and short-lived, depending on the underlying source of the oil price change—reflecting the SVAR framework’s decomposition of oil price movements into distinct structural shocks. The distinction between oil supply shocks, demand shocks driven by global activity, and demand shocks driven by speculative factors implies that shocks of the same sign in the oil price may have different magnitudes and durations of effects on banks, consistent with Kilian (2009)’s decomposition.

Q4. Which banks are most affected?

The effects of oil market shocks on banking variables are found to be stronger for smaller and lower-leveraged banks. Smaller banks may be more exposed to oil-related regional economic downturns through concentrated loan portfolios, while lower-leveraged banks may face different collateral and risk dynamics relative to more highly leveraged peers.

Key concepts

oil market Bayesian SVAR : a structural vector autoregression that uses a Bayesian prior over sign restrictions to identify oil supply shocks, oil demand shocks related to global real activity, and oil-specific demand shocks, following Baumeister and Hamilton (2019); extended here to include US banking variables. credit spread : the difference between yields on corporate bonds or loans and a risk-free reference rate; used as a measure of the credit risk premium and financial conditions in US credit markets.

Optimal monetary policy with uncertain private sector foresight

Mon, 01 Jan 0001 00:00:00 +0000

Central banks must set policy under uncertainty about how private-sector expectations form, which changes how monetary policy transmits to output and inflation. This paper studies optimal time-consistent monetary policy using a New Keynesian finite-horizon planning (NK-FHP) model in which households and firms have limited foresight: they solve structural problems only up to a finite horizon, and update their beliefs about longer-run inflation by averaging over past data. In this setting—unlike in standard New Keynesian models—an “inflation scares” problem can arise: agents’ longer-run inflation expectations can deviate persistently from the central bank’s target, generating costly and prolonged disinflations. The authors formally characterize optimal policy when the planning horizons of private-sector agents are uncertain and a risk of inflation scares is present, showing that risk-management considerations modify the standard “leaning against the wind” principle with a novel preemptive motive: the optimal policy responds more aggressively to the risk of unanchoring to prevent inflation scares from materializing. An estimated version of the model is used to quantify how much this preemptive motive mattered during the post-pandemic inflation surge.

In depth

Q1. What is the NK-FHP model and how does it differ from standard New Keynesian models?

In the NK-FHP model, households and firms are boundedly rational because they evaluate state-contingent paths only up to a finite horizon; beyond that horizon they extrapolate longer-run beliefs by averaging over past data, making those beliefs adaptive rather than anchored at the target. When agents have long planning horizons, the model approximates rational expectations: inflation expectations are well anchored, disinflations are relatively costless, and policy transmits quickly. When planning horizons are short, longer-run inflation expectations can become unanchored, disinflations are costly, and policy transmission lags lengthen. The NK-FHP model thus nests both extremes and provides micro-foundations for the “inflation scares” discussed by Goodfriend (1993).

Q2. What is the “inflation scares problem” and why does it matter for optimal policy?

An inflation scare occurs when agents’ longer-run inflation expectations deviate persistently from the central bank’s target because agents with short planning horizons update beliefs adaptively, and past high inflation feeds forward into current expectations. This creates a welfare-relevant asymmetry: once expectations become unanchored, a disinflation is costly in output because the central bank must build credibility against backward-looking expectations. The standard NK model with rational expectations does not generate this problem—rational agents’ inflation expectations are pinned to the target irrespective of history—so it cannot address the design of policy specifically to prevent scares from materializing.

Q3. What is the “preemptive motive” and how does it modify the leaning-against-the-wind principle?

Optimal time-consistent policy under uncertain private-sector foresight adds a preemptive motive to the standard leaning-against-the-wind (LATW) principle: the central bank contracts demand not just in response to current output-gap and inflation deviations, but also to prevent expectations from becoming unanchored. Under the standard NK LATW result (Clarida, Galí, and Gertler 1999), the policymaker responds to the means of output and inflation. Under uncertain and potentially short-horizon foresight, optimal policy also depends on the distribution of output and inflation, as well as agents’ beliefs about future inflation—specifically, whether those beliefs risk drifting away from target. The preemptive motive implies a more aggressive policy response to the risk of an inflation scare even before the scare has fully materialized.

Q4. How does the paper relate to the post-pandemic inflation experience?

Using parameter estimates from an estimated version of the NK-FHP model, the paper applies the optimal policy framework to quantify how much the preemptive motive matters during the recent post-pandemic inflation surge. The model—which has been shown in related work (Gust, Herbst, and López-Salido 2022, 2024) to fit macroeconomic time series substantially better than hybrid NK models and to account for initial underreaction and subsequent overreaction of inflation forecasts—is well suited to analyze an episode where longer-run inflation expectations initially remained anchored but later showed signs of drift. The paper’s quantification indicates that risk-management considerations, including the preemptive motive, significantly affect the optimal policy path.

Key concepts

finite-horizon planning (NK-FHP) : a bounded-rationality framework (Woodford 2018) in which agents evaluate only those state-contingent paths within a finite planning horizon, updating beliefs about events beyond the horizon adaptively from past data.

inflation scares : episodes (Goodfriend 1993) in which agents’ longer-run inflation expectations deviate persistently from the central bank’s target, making disinflation costly; the NK-FHP model provides micro-foundations for such scares.

preemptive motive : the additional incentive for a policymaker to tighten beyond what current output-gap and inflation deviations alone would prescribe, specifically to prevent longer-run inflation expectations from becoming unanchored.

time-consistent policy under uncertainty : optimal policy that does not rely on commitment and hence accounts for future re-optimization; in this model it must also account for the non-additive uncertainty arising from a distribution of planning horizons.

Professional survey forecasts and expectations in DSGE models

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks whether Survey of Professional Forecasters (SPF) data can be efficiently integrated into medium-scale DSGE models, and whether models with imperfectly rational expectations based on Adaptive Learning (AL) outperform the standard Rational Expectations (RE) hypothesis when survey forecasts are used as observables. The authors work with quarterly US data spanning 1981q2–2019q2, using the Philadelphia Fed Real-Time Data Set (first and second releases) alongside SPF nowcasts for inflation, consumption, investment, and output growth. The SPF nowcast is defined as a prediction formed in the middle of period t+1 for period t+1 given information for period t, making it a suitable proxy for the model-based expectation E_t y_{t+1}.

The core methodological contribution is a re-specification of structural shocks into persistent (AR) and transitory (i.i.d.) components. For the risk premium, investment-specific technology, government spending, and markup shocks, each shock is decomposed into two independent innovations, yielding 12 total structural innovations. A reduced-form VAR exercise motivates this: SPF nowcast innovations explain 19–33% of the 5-year forecast error variance of the macro variables and 44–71% of the variance of the nowcasts themselves. The 1-quarter RMSFE of the baseline RE model without SPF is 1.10 for inflation, 1.26 for consumption, 1.19 for investment, and 1.26 for GDP — all significantly exceeding the SPF RMSFEs of 0.21, 0.43, 1.49, and 0.35.

Log marginal likelihood improves monotonically as shocks are progressively re-specified: baseline RE (–577.37), RE with two-component markups (RE_mu, –536.63), adding real shocks stepwise (–473.29, –410.84), and finally all shocks (RE_all, –385.07). RE_all matches or beats SPF 1-quarter forecast accuracy (RMSFE ratio to SPF of 1.00 for inflation and investment; beats SPF for consumption growth), and Diebold-Mariano tests show no significant difference from SPF up to 5 quarters ahead. The paper further shows that once this two-component structure is imposed, exogenous sentiment shocks become unnecessary: RE_all (–385.07) outperforms RES_all (–388.17), and the RE model with all real shocks re-specified but without sentiment decisively dominates.

Three AL belief specifications are then estimated: MSVflex (full RE information set with an independently and rapidly updating constant, posterior autocorrelation 0.9937 — nearly a random walk), RBflex (restricted information set augmented with shock innovations, with meaningful time-variation of belief coefficients at rho_AL = 0.87), and HBflex (agents switch between MSV and RB based on past forecasting performance; average RB weight 0.34, weight sensitivity delta = 4.77). All AL models outperform RE_all: MSVflex (–381.38), HBflex (–355.09), RBflex (–351.59), with RB and HB yielding the largest gains particularly during and after the Great Financial Crisis.

AL models address three specific RE limitations. First, trend breaks: the ALM constant tracks persistent deviations, with ALM constants for consumption and investment successfully picking up rising macroeconomic trends in earlier sub-periods, yielding superior long-term forecasts. Second, time-varying transmission: the RB model generates cyclical volatility that stays lower in normal times and rises during distress, reducing reliance on large persistent investment-technology shocks relative to RE. Third, predictability of forecast errors: the RE model’s investment forecast inherits the SPF underreaction (b-coefficient 0.72, p < 0.001), while RBflex and HBflex reduce this to 0.17 and 0.34 respectively, both statistically insignificant.

On an extended sample including the Covid recession, the RBflex model underperforms because its restricted information set cannot handle abrupt complex dynamics; MSVflex and HBflex continue to perform well, with the MSV regime dominating in the HB model during Covid and post-Covid periods. Scope conditions: the dataset is US, 1981q2–2019q2 for baseline estimation; the predictability (underreaction) problem is confirmed only for investment SPF, not for inflation, consumption, or GDP growth in this sample.

In depth

Q1. What is the SPF nowcast, and why do the authors treat it as a proxy for model-based expectations?

The SPF nowcast is defined as a prediction formed in the middle of quarter t+1 for the value of a variable in quarter t+1, conditional on information available through quarter t. Because agents are assumed to make decisions for period t and form expectations for t+1 based on information through t, this timing aligns precisely with the model-based conditional expectation E_t y_{t+1}. The authors use first-release data (r1) and the SPF nowcast (f0) both published in the course of t+1 as measurement variables, with the Kalman filter recovering implied structural shocks.

Q2. How large is the informational content of SPF nowcasts in reduced-form analysis?

A 7-variable Cholesky VAR places each SPF series last, so the survey innovation is orthogonal to standard macro variables by construction. The 5-year forecast error variance decompositions show SPF nowcast shocks explain 19% of inflation variance, 33% of consumption variance, 33% of investment variance, and 29% of GDP variance (Table 1). The nowcasts themselves are explained 44–71% by their own innovations. SPF nowcasts also substantially outperform the baseline RE model: the RE model without SPF produces RMSFE ratios of 1.10 for inflation, 1.26 for consumption, 1.19 for investment, and 1.26 for GDP relative to SPF (all statistically significant by Diebold-Mariano test).

Q3. What is the shock re-specification, and why is it necessary to exploit survey data?

The Smets-Wouters (2007) ARMA(1,1) shock structure conflates the transitory and persistent innovation into a single disturbance, making it impossible for the Kalman filter to separately attribute high-frequency and low-frequency movements. The re-specification splits each shock b_t into a persistent component b_t^ar (driven by epsilon^bar with persistence rho_b) and an i.i.d. transitory component b_t^iid (driven by epsilon^biid), yielding 12 total structural innovations. This allows survey nowcasts — which are forward-looking — to identify the persistent component separately from the transitory one. Without this, marginal likelihood improvements are far smaller (RE: –577 vs. RE_all: –385).

Q4. Does re-specification of real shocks render exogenous sentiment shocks redundant?

Yes. Models with standard real shock processes but exogenous sentiment shocks (RES: –477.88; RES_mu: –488.96) do fit substantially better than models without sentiment (RE: –577.37; RE_mu: –536.63), confirming Milani’s (2017) result. However, once the two-component real shock structure is introduced, RE_all (–385.07) outperforms RES_all (–388.17) and the estimated sentiment shocks become small and explain little of the business cycle. The fundamental shock re-specification subsumes what sentiment shocks were previously capturing.

Q5. How do AL models compare to RE in terms of model fit?

All three AL models outperform RE_all: MSVflex (–381.38, improvement of 3.69 log-likelihood units), HBflex (–355.09, improvement of 29.98 units), RBflex (–351.59, improvement of 33.48 units). The RB and HB specifications, which assume more severe deviation from RE with restricted information sets and time-varying transmission, achieve the largest gains. The MSV improvement accumulates gradually, concentrating in the late 1990s and 2000s, while RB shows sustained improvement in the 1980s and mid-1990s and performs exceptionally well during and after the GFC.

Q6. How does the AL mechanism handle macroeconomic trend shifts?

Under RE with fixed coefficients, expectations anchor around a constant steady state, so persistent deviations from trend generate systematic forecast errors. Under AL, the ALM constant mu_t in the Actual Law of Motion evolves over the business cycle. In the MSVflex model, the autocorrelation parameter for the constant is estimated at 0.9937 (posterior mean), making it nearly a random walk that can track long-lasting trends. ALM constants for consumption and investment in the MSV setup successfully pick up rising macroeconomic trends in earlier sub-periods, translating into superior longer-term forecast performance relative to RE.

Q7. How does the RB model generate time-varying volatility, and why does this matter for investment dynamics?

In RBflex, as beliefs are revised via the Kalman filter, the sensitivity of expectations and realized variables to shocks changes over the business cycle. The model generates cyclical volatility that remains lower in normal times and rises during distress — a realistic pattern absent from RE models. Consequently, RB does not need to rely as heavily on large persistent risk premium and investment-specific technology shocks: average volatility of these processes in the RB model does not increase in the last sub-period and remains generally lower across the whole sample, in contrast to RE’s behavior during the GFC. The RB model also shows a 3-times-smaller estimated measurement error in the investment SPF equation relative to the AL specification without restricted beliefs.

Q8. What happens to predictability of model-based forecast errors under AL versus RE?

Using the Coibion-Gorodnichenko (2015) regression of forecast errors on forecast revisions, the RE model’s investment forecast shows a b-coefficient of 0.72 (p < 0.001), inheriting the underreaction documented in SPF investment data (b = 0.49, p = 0.006). AL models break this inheritance: RBflex ALM b-coefficient for investment is 0.17 (not statistically significant) and HBflex is 0.34 (not statistically significant). AL models achieve this because they relax the RE constraint of internal consistency between agents’ and model forecasts, allowing the ALM to generate efficient forecasts even when agent PLMs display sluggish adjustment.

Q9. How do the models perform during the Covid recession?

The RBflex model does not perform optimally on the extended sample including the Covid recession. The authors attribute this to the restricted information set in the RB PLM being insufficient to describe the abrupt, complex macroeconomic dynamics of the Covid crisis. The MSVflex and HBflex models continue to perform well. In the HBflex model, the MSV regime naturally dominates during the Covid and post-Covid periods, while the RB regime had been more prominent between recessions in the pre-Covid sample.

Q10. What is the role of heterogeneous beliefs, and how do agents switch between PLMs?

In HBflex, expectations are a weighted average of MSV and RB predictions with weights evolving as a function of past belief forecast errors. The weight sensitivity parameter is estimated at delta = 4.77, indicating weights are relatively sensitive to fitness. The average estimated weight on the RB PLM is 0.34 (MSV receives 0.66 on average). The RB weight tends to increase and reach its highest values between recessions, consistent with the restricted model being more parsimonious and useful in stable periods, while the fuller MSV model dominates in high-volatility episodes such as the Covid recession.

Q11. What are the out-of-sample forecasting results?

The out-of-sample evaluation covers 2008q1–2019q2. The RB model outperforms the RE model in predicting investment and interest rate dynamics, and for investment it also outperforms professional forecasters during this period. At longer horizons (up to 5 quarters ahead), RE model forecasts are generally not statistically significantly different from SPF predictions once SPF nowcasts are included as observables, suggesting that observing the SPF data is sufficient to capture the most informative content from surveys for longer-horizon predictions.

Q12. What is the relationship to Milani (2017) and the prior literature on sentiment shocks?

Milani (2017) found that exogenous sentiment shocks orthogonal to fundamentals were needed to fit SPF forecasts alongside an AL model and explained a significant portion of US business cycle fluctuations. The current paper shows this result is not robust to re-specifying fundamental shocks into persistent and transitory components: once the two-component structure is introduced, sentiment shocks become small and economically unimportant (RES_all at –388.17 versus RE_all at –385.07). What Milani attributed to sentiment was largely capturing the inability of single-innovation shocks to separately account for high-frequency and low-frequency variance.

Key concepts

SPF Nowcast as proxy for model expectations: The Survey of Professional Forecasters’ nowcast is defined as a prediction formed in the middle of quarter t+1 for the value of a variable in that same quarter, conditional on information available through quarter t. This timing makes it directly comparable to the model-based conditional expectation E_t y_{t+1}, so the SPF nowcast can be added to the DSGE model’s observable set with a straightforward measurement equation linking it to model expectations plus i.i.d. measurement error.
Shock re-specification into persistent and transitory components: Each structural shock (risk premium, investment-specific technology, government spending, and markup shocks) is decomposed into an AR(1) persistent component driven by epsilon^bar and an i.i.d. transitory component driven by epsilon^biid, replacing the ARMA(1,1) specification in Smets-Wouters (2007) that conflates both into a single innovation. This decomposition is the key technical device enabling survey data to separately identify low-frequency and high-frequency sources of volatility.
Adaptive Learning (AL): An expectation-formation mechanism in which agents do not know true model parameters and instead estimate linear forecasting models (PLMs) that are updated each period via a Kalman filter algorithm. This produces a time-varying Actual Law of Motion — transmission parameters mu_t, T_t, R_t all evolve with beliefs — enabling endogenous trend drift and time-varying shock responses absent from RE models with fixed coefficients.
Minimum State Variable (MSV) beliefs with flexible constant: An AL specification in which agents use the same endogenous state variables and shocks as in the RE solution but with the constant term updated at an independent, more rapid rate. The constant’s autocorrelation is estimated at 0.9937, making it nearly a random walk capable of tracking persistent macroeconomic trend deviations from the deterministic steady state.
Restricted Beliefs (RB): An AL specification in which each agent’s PLM uses a reduced information set — autoregressive terms of the forward-looking variable augmented with selected shock innovations — rather than the full RE state space. This more severe departure from RE yields the largest marginal-likelihood gain over RE_all, generates realistic cyclical volatility amplification, and produces a 3-times-smaller measurement error for investment SPF, but underperforms during the Covid recession due to the restricted set’s inability to handle abrupt complex dynamics.
Heterogeneous Beliefs (HB): An AL specification in which agents may switch between MSV and RB PLMs as a weighted average, with weights evolving as a function of past belief forecast errors. The average weight on RB is 0.34 and the weight sensitivity delta is estimated at 4.77; the RB weight tends to be highest between recessions and lowest during high-volatility episodes such as the Covid recession when the fuller MSV information set dominates.
FIRE predictability test (Coibion-Gorodnichenko regression): Under Full Information Rational Expectations, the regression of forecast errors on forecast revisions should yield a b-coefficient of zero. A positive and significant b indicates systematic underreaction to news. The paper confirms b = 0.49 (p = 0.006) for investment SPF — but not for inflation, consumption, or GDP — and shows the RE model inherits this inefficiency (b = 0.72, p < 0.001 for investment), while AL models reduce it to insignificance (RBflex: 0.17; HBflex: 0.34).

Quantifying the allocative efficiency of capital: The role of capital utilization

Mon, 01 Jan 0001 00:00:00 +0000

Standard measures of capital allocative efficiency—based on the dispersion of the average revenue product of capital (ARPK)—are severely biased when capital utilization is endogenous. When utilization is flexible, firms can bypass physical adjustment constraints by varying intensity, so that the correct efficiency measure requires the dispersion of average revenue product of capital services (ARPKS), defined as the log difference between revenue and utilized capital, not of ARPK. Contrary to the standard view that higher ARPK dispersion signals lower allocative efficiency, the paper demonstrates that when efficiency improvements arise from greater utilization flexibility, ARPK dispersion can increase alongside efficiency gains. An application to India’s capital market liberalization reform shows that the standard approach (ignoring utilization) predicts allocative efficiency gains of 5.25% (statistically significant), while the corrected approach accounting for utilization finds gains of only 0.04% (not statistically significant).

In depth

Q1. What is wrong with ARPK dispersion as a measure of allocative efficiency?

ARPK dispersion conflates two conceptually distinct quantities—the dispersion of physical factor allocation and the dispersion of utilization intensity—so it is not a monotone proxy for allocative efficiency when utilization is endogenous. In the Hsieh-Klenow (2009) framework, higher ARPK dispersion is interpreted as higher misallocation. But ARPK is simply revenue over capital inputs, so when firms with too little (too much) capital relative to their productivity simply utilize their capital more (less) intensely, the variance of ARPK rises even as the efficiency of factor services allocation improves. The standard interpretation therefore has the causality backwards in economies with flexible utilization.

Q2. What is ARPKS and why does it correctly measure capital allocative efficiency?

ARPKS—the average revenue product of capital services, defined as the log difference between revenue and utilized capital—is the theoretically correct sufficient statistic for capital allocative efficiency when utilization is endogenous, because it measures the dispersion in the productivity of factor services rather than the dispersion of physical factor inputs. The paper embeds endogenous utilization into a neoclassical investment model and shows formally that the variance of log ARPKS is zero in the efficient equilibrium, while the variance of log ARPK is not. ARPK dispersion is a combination of ARPKS dispersion and utilization variation, and the latter is not a sign of misallocation.

Q3. Can higher ARPK dispersion accompany higher allocative efficiency?

Yes: when allocative efficiency improvements arise from greater flexibility in capital utilization, ARPK dispersion increases even though allocative efficiency improves. Greater utilization flexibility generates more variation in how intensively different firms use their capital, raising the ratio of revenue to physical capital input for high-utilization firms. A researcher using ARPK dispersion would therefore mistakenly conclude that allocative efficiency fell when it actually rose. The paper provides counterfactual simulations illustrating this phenomenon.

Q4. What is the empirical application and what do the results show?

An application to Bau and Matray (2023)’s Indian capital market liberalization reform finds that: the standard approach (ignoring utilization) predicts allocative efficiency gains of 5.25% (statistically significant); accounting for utilization, the corrected estimate is only 0.04% (not statistically significant). The analysis uses firm-level panel data for India including capacity utilization rates and capital maintenance expenses. Maintenance expenses serve as a proxy for capital utilization rates in the model, bridging the gap between observed capacity and the theoretically relevant utilization measure.

Key concepts

average revenue product of capital (ARPK) : the ratio of revenue to physical capital input; commonly used as a proxy for firm-level distortions in the Hsieh-Klenow (2009) framework, but shown to be a biased measure of allocative efficiency when capital utilization is endogenous. average revenue product of capital services (ARPKS) : the ratio of revenue to utilized capital; the theoretically correct measure of capital allocative efficiency when utilization is endogenous; its dispersion is zero in the efficient equilibrium. capital utilization : the intensity with which a firm deploys its physical capital stock; endogenous in the model, allowing firms to partially bypass adjustment constraints; the omission of utilization is the source of the bias in standard ARPK-based efficiency estimates.

Racial disparities in crime and wealth

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks whether racial differences in labor income can simultaneously explain both the crime gap and the wealth gap between Black and White individuals in the United States. The authors build a large-scale overlapping generations (OLG) model in which property crime is endogenously determined — agents choose whether to steal alongside their consumption and savings decisions — while drug-related incarcerations are treated as exogenous, reflecting evidence that racial profiling distorts enforcement independently of offending behavior. The model is calibrated to match several well-documented racial disparities: Black individuals comprise 12.36% of the adult population but 33.8% of the incarcerated population; 42.7% of Black individuals fall in the bottom wealth quintile (below $3,400 in assets) versus 15.1% of White individuals; the median Black-White wealth gap is 89.5% (SCF 2019). Data sources include the Survey of Consumer Finances (SCF 2019), Uniform Crime Reports (UCR 1996–2011), NLSY79, PSID (1968–2021), and MORG (2000–2019).

The model incorporates four dimensions of labor market disparity between Black and White agents: educational attainment, unemployment risk and duration, age-earnings profiles, and idiosyncratic income shock processes. It also incorporates race-skill-specific survival probabilities (life expectancy at birth: 73 years for Black, 78 years for White), scarring effects from incarceration on future labor income, a progressive income tax, means-tested transfers, and accidental bequests distributed within race groups.

The benchmark model successfully replicates key data moments. Black individuals constitute 34.3% of the incarcerated population (data: 33.8%). The model-generated median wealth gap is 83.6% (data: 89.5%). The share of Black individuals in the bottom wealth quintile is 37.7% in the model versus 42.7% in the data. The model does not match the average wealth gap: the model-generated gap is 58.9% versus 84.4% in the SCF.

The main counterfactual experiments yield three findings. First, equalizing labor market conditions — particularly age-earnings profiles — is the dominant driver of both racial wealth and crime disparities. When all labor market conditions are equalized, the Black crime rate falls by 66.25% (from 11.97% to 4.04%), the median wealth gap declines by 69.6% (from 83.58% to 25.4%), and the share of Black individuals in the bottom wealth quintile falls from 37.73% to 20.75%. Equalizing age-earnings profiles alone accounts for the largest single-factor effect: the median wealth gap declines from 83.58% to 44.16% and the Black crime rate from 11.97% to 7.59%. The resource cost of equalizing age-earnings profiles is estimated at 3.29% of GDP for the No-HS group and 22.2% of GDP for the HS group.

Second, higher crime and incarceration rates among Black individuals do not significantly contribute to their lower wealth. When crime is entirely eradicated, the share of Black individuals in the bottom quintile barely moves (37.73% to 37.61%), and the median wealth gap falls only from 83.58% to 82.6%. The mechanism is that most crimes are committed by young, already-poor individuals who are not saving in any case; income loss during incarceration is not large enough to affect wealth accumulation meaningfully.

Third, equalizing life expectancy generates a 25.39% reduction in the median wealth gap and a 12.4% decline in the share of Black individuals in the bottom wealth quintile, with negligible effect on crime rates.

The paper also validates the model against Cesarini et al. (2023), who find a small, statistically insignificant effect of lottery wealth on criminal behavior in Sweden. The model replicates this finding: a $150,000 windfall reduces incarceration risk over seven years by 0.81 percentage points. The mechanism is that lottery winnings displace means-tested transfers, winnings gradually dissipate as low income persists, and individuals eventually return to poverty and resume criminal activity.

Q: What is the central research question and why does the paper treat property crime and drug crime differently? A: The paper asks whether racial labor income differences can simultaneously account for both crime and wealth disparities. Property crimes are modeled endogenously because offending behavior responds rationally to economic incentives. Drug crime incarcerations are exogenous to capture evidence that racial profiling in enforcement — rather than differential offending alone — drives racial disparities in drug arrests: Beck and Blumstein (2018) show differential offending explains only about 52% of the drug imprisonment gap, versus over 70% for overall imprisonment.

Q: What are the benchmark model’s key calibration targets and how well does it fit the data? A: The benchmark targets Black individuals as 34.3% of the incarcerated population (data: 33.8%), a median Black-White wealth gap of 83.6% (data: 89.5%), and 37.7% of Black individuals in the bottom wealth quintile (data: 42.7%). The model does not match the average wealth gap: the model-generated gap is 58.9% versus 84.4% in the SCF, which the authors acknowledge explicitly.

Q: What is the quantitative effect of equalizing all labor market conditions? A: Experiment 5 (equalize educational attainment, unemployment risk, and age-earnings profiles jointly) reduces the Black crime rate by 66.25% (from 11.97% to 4.04%), the median wealth gap by 69.6% (from 83.58% to 25.4%), and the share of Black individuals in the bottom quintile from 37.73% to 20.75%. Equalizing all factors including life expectancy drives the median wealth gap to 0%, with the bottom-quintile share for Black individuals at 19.31%.

Q: Which single labor market factor matters most for the wealth gap and crime rate? A: Equalizing age-earnings profiles (Experiment 3) is the single most important factor, reducing the median wealth gap from 83.58% to 44.16% and the Black crime rate from 11.97% to 7.59%. By contrast, equalizing educational attainment or unemployment risk each reduces the median wealth gap only to 76.71%, with smaller crime effects.

Q: Does education-group heterogeneity matter for interpreting the age-earnings equalization effect? A: Yes, substantially. Equalizing age-earnings profiles for the No-HS group reduces the Black crime rate by 21% with little effect on the median wealth gap. Equalizing profiles for the HS group reduces the median wealth gap by approximately 40% with a much smaller effect on crime rates. The earnings channel to crime operates primarily at the bottom of the education distribution, while the earnings channel to wealth accumulation operates more strongly in the high school group.

Q: Why does crime have so little effect on the wealth distribution? A: Criminals are predominantly young and already-poor individuals who are not accumulating savings. Because these individuals have minimal assets and rely heavily on means-tested transfers for consumption, the income loss during incarceration does not reduce their wealth meaningfully. When crime is completely eradicated, the share of Black individuals in the bottom quintile falls only from 37.73% to 37.61% and the median wealth gap declines from 83.58% to only 82.6%.

Q: What is the effect of eliminating drug-related incarcerations on the Black wealth distribution? A: Experiment 4 (eliminating drug crime incarcerations) reduces the share of Black individuals in the bottom quintile only slightly, from 37.73% to 37.30%. Eliminating the scarring effect of all incarcerations likewise has negligible effects on the bottom-quintile share (37.53% versus 37.73% in the benchmark) and the zero-assets share (32.56% versus 33.24%). Neither the direct incarceration penalty nor its labor market scarring meaningfully affects wealth accumulation.

Q: What happens to crime and wealth when the property crime clearance rate changes? A: Doubling the clearance rate from 17.2% to 34.4% reduces the Black crime rate from 11.97% to 1.72% and the White rate from 3.05% to 0.52%, with minimal change in the wealth distribution (Blacks in bottom quintile: 37.83%). Halving the clearance rate to 8.6% more than doubles Black crime to 27.53% and White crime to 9.55%, and increases the share of Black individuals in the bottom quintile by about 11% to 42.01%. This asymmetry — crime reduction barely helps wealth but crime increase does hurt — is consistent with the poverty-trap mechanism.

Q: How does the model validate against the Cesarini et al. (2023) Swedish lottery study? A: Cesarini et al. find a small, statistically insignificant negative effect of a $150,000 lottery windfall on conviction rates. The model replicates this: simulating 34,709 individuals per skill-race group, a $150,000 windfall reduces incarceration risk over the following seven years by 0.81 percentage points. When the authors use model-generated property crime records rather than incarceration records as the dependent variable, they find a statistically significant effect more than twice as large, suggesting incarceration data systematically understates the crime-reducing effect of wealth shocks.

Q: What is the mechanism by which lottery winnings have minimal persistent effects on crime? A: Lottery winners in the model are disproportionately drawn from low-income, low-wealth individuals who also receive means-tested transfers. After winning, these individuals lose transfer eligibility, so winnings substitute for lost transfers rather than being invested. With income levels remaining low, winnings dissipate over time, individuals return to poverty, and resume criminal activity. Larger lottery prizes extend the crime-free interval but do not permanently alter behavior.

Q: What is the role of life expectancy differences in racial wealth and crime gaps? A: Equalizing survival probabilities generates a 25.39% reduction in the median wealth gap and a 12.4% reduction in the share of Black individuals in the bottom quintile, with virtually no change in crime rates. The channel operates through savings incentives: a shorter expected lifetime (73 years for Black versus 78 for White) reduces the return to wealth accumulation independently of income.

Q: What are the fiscal resource requirements implied by the income equalization experiments? A: Implementing equalized age-earnings profiles for the No-HS group would require resources equal to 3.29% of total GDP, while equalization for the HS group would require 22.2% of GDP. These figures reflect the scale of redistribution needed to close earnings profiles and serve as a benchmark for assessing policy feasibility.

Q: How does incarceration scarring affect lifetime income in the benchmark, and how does this validate against external data? A: A Black high school graduate who experiences at least one incarceration earns 16.8% less over his lifetime than one who is never incarcerated; for White high school graduates the gap is 28.7%. Gordon et al. (2023) report corresponding empirical estimates of 18.6% for Black and 32.7% for White high school graduates, closely validating the model’s scarring calibration.

Endogenous property crime: A rational choice by working-age agents who weigh the expected gain from stealing (fraction γ = 6.4% of average labor income y) against the probability of apprehension (clearance rate πa = 17.2%), the loss of means-tested transfers, scarring of future labor income, and the minimum consumption floor in jail. Retired agents face no such choice.

Exogenous drug incarceration: Incarceration for drug possession modeled as an exogenous shock with race-age-specific probabilities, not responsive to individual optimization, capturing the possibility that racial profiling in enforcement generates disparities in drug arrests independently of offending behavior.

Scarring effect: Post-incarceration labor income penalty modeled as a higher probability of drawing a lower idiosyncratic income shock state upon labor market re-entry, calibrated so the model reproduces lifetime income gaps between ever-incarcerated and never-incarcerated individuals by race-skill group (18.6% for Black HS, 32.7% for White HS per Gordon et al. 2023).

Age-earnings profile (ε^{i,ζ}_j): The deterministic, skill-race-age-specific component of labor income estimated from PSID data for each of six race-education groups. The gap between Black and White age-earnings profiles is identified as the dominant driver of both the racial wealth gap and racial crime disparities, accounting for the largest single-factor reduction in both outcomes across all counterfactual experiments.

Means-tested transfer floor: A consumption support program that fills the gap between an agent’s post-tax income plus assets and a minimum threshold κ (5.8% of average net tax income and assets). This transfer is a critical mechanism linking wealth shocks to crime: lottery winnings and other wealth gains displace transfer eligibility, causing winnings to be consumed rather than saved, and eventually exhausted.

Median wealth gap: The percentage difference between median White and median Black wealth — 89.5% in the 2019 SCF, 83.6% in the benchmark model — used as the primary scalar summary of racial wealth disparity, chosen because the model does not match the average wealth gap (model: 58.9%, data: 84.4%).

Victimization probability (πv(Y)): A step-wise decreasing function of taxable income capturing spatial concentration of property crime in low-income neighborhoods; in equilibrium this equals the aggregate property crime rate χp, ensuring market clearing in the crime sector and implying that poorer agents face higher victimization risk.

Robot adoption and inflation dynamics

Mon, 01 Jan 0001 00:00:00 +0000

Robot Adoption and Inflation Dynamics

Research Question

Basso and Rachedi investigate how robot adoption influences inflation dynamics — specifically, whether the surge in automation during the 2000s and 2010s can explain the muted sensitivity of inflation to unemployment (the “flat Phillips curve”) observed in advanced economies prior to the Covid pandemic, and whether the same framework can account for the subsequent resurgence of steep inflation-unemployment co-movement.

Data and Methodology

The empirical analysis uses an annual panel covering 384 U.S. metropolitan statistical areas (MSAs) from 2008 to 2018. The dependent variables are non-tradable goods inflation (log-difference of services prices excluding rents and utilities, from BEA regional price parities) and wage inflation (log-difference of average compensation per job). Robot adoption at the MSA-year level is constructed following Acemoglu and Restrepo (2020a): industry-level robots per employee at the U.S. national level are weighted by industry employment shares in each MSA, yielding an MSA-year robot-per-employee ratio.

The regression specification extends Hazell et al. (2022) by adding an interaction term between the lagged unemployment rate and the (demeaned) robot-per-employee ratio, along with MSA and year fixed effects. Year fixed effects absorb common inflation expectations and the endogenous response of monetary policy to aggregate demand shocks. To address endogeneity, unemployment is instrumented with a Bartik shift-share variable of tradable demand spillovers, and robot adoption is instrumented with average industry-level robot penetration in the five largest European economies — under the identifying assumption that robot demand shocks are weakly correlated across advanced countries.

The theoretical framework is a New Keynesian model augmented with (i) directed search frictions in the labor market, and (ii) producer-level automation decisions in the spirit of Acemoglu and Restrepo (2020a). Producers pay a fixed entry cost, draw idiosyncratic efficiency for employing labor, and then choose between a robot technology (certain output at low efficiency) and a labor technology (uncertain hiring, higher potential efficiency). This generates an automation threshold: low-efficiency producers install robots, displacing low-wage jobs. A Taylor rule closes the model. Quantitative exercises compare two steady states calibrated to robot-per-employee ratios of 0.2% (low automation, targeting the U.S. in the early 2000s) and 0.6% (high automation, calibrated to one standard deviation of robot penetration variation across MSAs).

Main Findings

Empirical. In the baseline IV regression, a one standard deviation increase in robot adoption reduces the sensitivity of price inflation to unemployment by 17%, and the sensitivity of wage inflation to unemployment by 9%, relative to a MSA with the average robot penetration. The larger flattening effect on price inflation than on wage inflation implies that robot adoption also diminishes the pass-through from wages to prices. All three effects are statistically significant at the 5% level, and are robust to controls for demographic structure (age composition, gender/race/education participation rates, MPC heterogeneity), occupational structure (abstract, routine, manual, and offshorable occupations), and import competition exposure (Chinese and Mexican import shares).

Model quantification. Comparing the high-automation to the low-automation steady state, the model generates a 14% reduction in the slope of the price Phillips curve and a 13% reduction in the slope of the wage Phillips curve, conditional on the same-sized demand shocks in both economies. The price Phillips curve result accounts for 82% of the empirical estimate (17%). The model overstates the flattening of the wage Phillips curve (13% vs. 9% in the data), and therefore understates the reduction in the wage-to-price pass-through.

Mechanisms. Automation flattens the Phillips curve through two primary channels. First, the outside option of automating production reduces workers’ bargaining power and dampens the elasticity of wages to unemployment (the “Wage Setting Effect”). Second, a higher share of robot firms reduces the aggregate labor share, muting the pass-through from wages into prices (the “Steady State Effect”). A third channel — firms cyclically substituting workers for machines in response to a shock (the “Cyclical Effect”) — operates during the transition but the Wage Setting Effect accounts for the bulk of the flattening.

Non-linearity and the post-Covid resurgence. When robot-production is subject to convex adjustment costs, the threat of automation that underlies the Wage Setting Effect becomes inoperative during large expansionary shocks. When investment in machines surges, the marginal cost of producing robots rises sharply, raising the price of machines and pushing the automation threshold downward — more firms must use labor. Workers then negotiate higher wages, which pass into prices. Conditional on small demand shocks, the high-automation economy still exhibits a flatter Phillips curve than the low-automation economy. Conditional on large demand shocks (simulated as a 2 percentage point drop in unemployment), there is no difference in the inflation response between the low- and high-automation economies, so the Phillips curve reverts to steep.

In depth

Q1. What is the exact empirical specification and how does it map to a structural object?

The regression is: non-tradable goods inflation = β × lagged unemployment + γ × (lagged unemployment × demeaned robot adoption) + ζ × lagged robot adoption + χ × relative non-tradable price + MSA fixed effects + year fixed effects + error. In a multi-region model without automation, Hazell et al. (2022) show that the coefficient β identifies the aggregate slope of the Phillips curve because year fixed effects absorb both common inflation expectations and the endogenous monetary policy response to aggregate demand shocks. Adding the interaction term extends this logic: γ identifies how robot adoption causally shifts the slope of the local Phillips curve, which maps into changes in the aggregate slope.

Q2. What are the first-stage instruments and why are they valid?

Unemployment is instrumented with local tradable demand spillovers — a Bartik variable weighting national industry value-added growth (excluding each MSA’s own contribution) by each MSA’s average industry value-added shares, so national supply disturbances uncorrelated with MSA-level heterogeneity generate plausibly exogenous unemployment variation. Robot adoption is instrumented with the implied robot-per-employee ratio obtained by replacing U.S. industry robot installations with the average across the five largest European economies, weighted by U.S. industry employment shares; this isolates the supply-side efficiency improvements in robot technology that drove global adoption, conditional on robot demand shocks being weakly correlated across countries. The correlation between the two instruments in the sample is 0.2, ensuring they do not strongly co-move.

Q3. What are the point estimates and their magnitudes in the baseline IV regression?

For price inflation (Panel A, Column 4), the base sensitivity β = −0.5069 (SE 0.1381, significant at 1%), and the interaction coefficient γ = 0.0066 (SE 0.0030, significant at 5%). For wage inflation (Panel B, Column 4), β = −0.9580 (SE 0.2450, significant at 1%), and γ = 0.0049 (SE 0.0024, significant at 5%). A one standard deviation increase in robot adoption reduces price inflation sensitivity by 17% and wage inflation sensitivity by 9% relative to the average-automation MSA.

Q4. What does the difference in flattening magnitudes (17% for prices vs. 9% for wages) imply about the wage-price pass-through?

Because automation reduces the price Phillips curve slope by proportionally more than the wage Phillips curve slope, each percentage-point change in wages translates into a smaller percentage-point change in prices in higher-automation areas. This indicates that robot adoption diminishes the influence of wage changes on price changes — i.e., it reduces the wage-to-price pass-through. In the model, this operates through the Steady State Effect: a larger share of production carried out by robot firms means that a given change in average wages applies to a smaller portion of total marginal costs, weakening the price response.

Q5. How is the automation threshold determined in the theoretical model, and what economic forces govern it?

A producer opts for the labor technology if and only if the expected value of a labor firm (= job-filling probability × (producer price × labor efficiency − posted wage) − entry cost) exceeds the value of a robot firm (= producer price × robot efficiency − machine price − entry cost). Since the value of a labor firm increases in labor efficiency, there is a unique cut-off efficiency level γ* at which a producer is indifferent. Producers with labor efficiency above γ* post vacancies; those below γ* install robots. The cut-off rises (more automation) when wages rise relative to machine prices, and falls (less automation) when machine prices rise due to costly robot production during large expansionary shocks.

Q6. How does the wage-posting equilibrium under directed search generate the Wage Setting Effect of automation?

Under directed search, each labor firm posts a wage to maximize its expected value, and workers sort into sub-markets offering higher wages but lower job-finding probabilities. The equilibrium posted wage for a firm with labor efficiency γj is Wγj,t = PP,t × γj × (1 − η), where η is the elasticity of matches to vacancies. The option to install a robot — available at any time — limits how much any individual firm needs to offer workers. When automation increases, the outside option becomes more attractive to more firms, which constrains wage offers industry-wide, reducing the elasticity of average wages to unemployment fluctuations.

Q7. How is the slope of the price Phillips curve characterized analytically?

Log-linearizing the model around the steady state and substituting labor market and wholesaler equilibrium conditions into the pricing equation yields: inflation = −[(ε−1)/φ] × Ψ(γ*; Θ) × unemployment gap + β × expected future inflation, where Ψ(γ*; Θ) is a function of the automation cut-off γ*, the elasticity of substitution ε, the matching function elasticity η, the efficiency bounds γM and γH, and the distribution shape parameter α. In contrast to standard New Keynesian models where the slope depends only on markup and nominal rigidity parameters, this expression depends directly on the degree of automation through the steady-state threshold γ*.

Q8. Across different structural parameter configurations, does automation always flatten the Phillips curve?

Yes. Numerical analysis of the closed-form Phillips curve expression (Figure 1) shows that robot adoption unambiguously decreases the slope of the price Phillips curve across all combinations of the key structural parameters — the distribution shape parameter α, the matching elasticity η, the upper bound of labor efficiency γH, and the steady-state unemployment rate ū. The flattening effect is more pronounced when η is low, when α implies a larger fraction of low-efficiency producers, and when the steady-state unemployment rate is low.

Q9. How do the three mechanism channels (Cyclical, Wage Setting, Steady State) compare quantitatively?

The paper isolates channels by comparing alternative model specifications: (i) Baseline directed search with endogenous automation, (ii) Directed search with fixed automation (removing Cyclical and Wage Setting Effects, leaving only the Steady State Effect), (iii) Random search with τ = 0.5 (efficient bargaining, retaining both the Cyclical and Wage Setting Effects), (iv) Random search with τ = 0.01 (near-zero worker bargaining power, removing the Wage Setting Effect but retaining the Cyclical Effect). Figure 5 shows that the Steady State Effect alone accounts for only a small portion of the total inflation differential between low- and high-automation economies. The Wage Setting Effect — isolated by comparing τ = 0.01 and τ = 0.5 economies with endogenous automation — accounts for the bulk of the flattening. The Cyclical Effect (isolated by comparing fixed and endogenous automation with τ = 0.01) contributes an intermediate amount.

Q10. What is the quantitative exercise comparing low- and high-automation steady states?

The low-automation economy targets the U.S. robot-per-employee ratio of 0.2% in the early 2000s (Acemoglu and Restrepo, 2020a), calibrated with robot-specific technological change ζ = 2. The high-automation economy features a 200% higher robot-per-employee ratio of 0.6%, calibrated to replicate one standard deviation of cross-MSA dispersion in robot penetration in the data. Both economies are simulated with 10,000 realizations of preference shocks, and the slopes of the price and wage Phillips curves are estimated from simulated inflation and unemployment outcomes. The price Phillips curve flattens by 14% and the wage Phillips curve by 13% moving from low to high automation, conditional on the same-sized shock in both economies.

Q11. How does the model account for the Covid-era resurgence of high inflation despite high automation?

The paper extends the machine manufacturer’s production function to include an asymmetric convex adjustment cost that activates when investment deviates more than 5% from its steady-state level (parameterized with δ = 0.0015 and ϱ = 100). Under a small expansionary shock (0.25 percentage point decrease in unemployment), inflation rises less in the high-automation economy, consistent with a flat Phillips curve. Under a large expansionary shock (2 percentage point decrease in unemployment), the surge in robot investment triggers sharply rising machine prices, eliminating the automation outside option for marginal producers and fully restoring workers’ bargaining power — so the inflation response is identical in the low- and high-automation economies, consistent with a steep Phillips curve. The paper interprets this as a proof-of-concept consistent with post-Covid wage compression evidence for low-wage workers documented by Autor, Dube, and McGrew (2023).

Q12. What do the robustness checks establish regarding alternative explanations?

The interaction of unemployment and robot adoption remains statistically significant at the 5% level across all the robustness checks (Appendix A). These include controlling for: (i) demographic heterogeneity — shares of young (below 30) and old (above 60) individuals, female/Black/Asian labor market participation, low-education attainment shares, overall participation, and MSA-level average marginal propensity to consume (MPC); (ii) occupational structure — shares of abstract, routine, manual, and offshorable occupations; and (iii) import competition — MSA exposure to Chinese and Mexican import competition. The coefficient on the robot-unemployment interaction term is stable across specifications, with the magnitude remaining close to that in the baseline (approximately 0.0140 across all demographic robustness columns in Table A.1).

Key Concepts

Automation threshold (γ):* The paper-specific level of idiosyncratic labor efficiency at which a producer is indifferent between installing a robot and posting a vacancy. Producers with labor efficiency below γ* choose the machine technology; those above choose the labor technology. The threshold is determined by the relative profitability of the two technologies, and it shifts endogenously with wages, machine prices, and job-filling probabilities. A higher γ* means more of the production sector is automated.

Wage Setting Effect of automation: The channel through which the existence of the outside option to install robots reduces workers’ bargaining power and dampens the elasticity of wages to unemployment fluctuations. Under directed search, firms’ ability to substitute machines for labor at a lower cost constrains the wage offers they need to post, so that a given decline in unemployment generates a smaller increase in average wages in higher-automation economies.

Steady State Effect of automation: The channel through which a larger steady-state fraction of robot firms reduces the aggregate labor share, so that even a given change in wages translates into a smaller change in aggregate marginal costs and prices. This channel operates even when automation cannot change upon a shock (fixed automation baseline).

Cyclical Effect of automation: The channel through which firms actively replace workers with machines in response to expansionary shocks that raise wages, generating an endogenous dampening of labor demand and putting downward pressure on the wage increase itself. This channel requires endogenous automation choices at business-cycle frequencies.

Robot-specific technological change (ζ): In the paper’s model, the parameter governing the efficiency with which machine manufacturers transform final goods into robots. A higher ζ reduces the relative price of machines (PM/P = 1/ζ), making automation more attractive to lower-efficiency producers and raising the automation threshold γ*. In quantitative exercises, variation in ζ across steady states drives differences in the degree of automation.

Price Phillips curve slope (Ψ): In the paper’s log-linearized model, the structural coefficient linking inflation to the unemployment gap. Unlike in standard New Keynesian models — where the slope depends only on the markup and nominal rigidity — Ψ is a function of the automation threshold γ*, the matching elasticity η, the efficiency distribution parameters (γM, γH, α), and the elasticity of substitution ε. Robot adoption shifts γ* and thereby changes Ψ.

Asymmetric investment adjustment cost: An extension of the machine manufacturer’s production function that imposes convex costs when robot investment deviates above 5% from its steady-state level (parameterized by δ and ϱ). This specification makes it increasingly costly to rapidly scale up automation in response to large demand shocks, causing the machine price to spike and the automation outside option to cease being effective for marginal producers, thereby restoring workers’ bargaining power and steepening the Phillips curve during large expansionary episodes.

Skilled immigration frictions as a barrier for young firms

Mon, 01 Jan 0001 00:00:00 +0000

High-skilled immigration policy frictions—particularly the H-1B visa lottery, fixed annual cap, and associated compliance costs—impose well-known burdens on firms, but their disproportionate impact on young, technology-intensive companies has received less attention. This paper provides the first study combining firm-level panel data on H-1B outcomes with a general equilibrium model of firm dynamics to quantify these effects. Using the random allocation of H-1B visas in the FY 2014 and FY 2015 lotteries as quasi-random variation, the authors find that lower H-1B visa win rates significantly reduce the survival of young firms (aged 0–5) in technology-intensive sectors, while the impact for older firms is not statistically significant. A general equilibrium model with endogenous firm entry and exit, skilled foreign labor, and H-1B-style policy frictions matches the age distribution of high-tech firms and shows that eliminating major immigration policy frictions would increase average productivity in the high-tech sector primarily by enabling more young firms to enter and survive, which in turn drives the exit of older, less productive firms.

In depth

Q1. What is the quasi-random identification strategy, and what does it identify?

The paper uses H-1B visa lottery win rates in fiscal years 2014 and 2015 as quasi-random variation in access to skilled foreign workers, combining National Establishment Time Series (NETS) data on firm survival with Labor Condition Application (LCA) and H-1B petition data. Because the lottery randomly allocates visas among firms that applied (when the cap is binding), the fraction of applications that result in approvals is plausibly exogenous to firm characteristics, conditional on applying. The empirical finding—that lower lottery win rates significantly reduce survival of young firms (0–5 years old) in tech-intensive sectors but not of older firms—is identified off this lottery variation. The age-heterogeneity result is central: large incumbent firms have alternative channels (offshore hiring, internal labor markets, H-1B cap-exempt hires) that small, young firms lack.

Q2. Why are young high-tech firms more exposed to H-1B frictions than older firms?

Young firms in high-tech sectors depend heavily on specialized skilled foreign workers because they compete in rapidly changing technology fields where the domestic talent pool may not supply the precise skills needed at the pace required; they cannot easily substitute with a second-choice candidate or offshore to a foreign affiliate as large multinationals can. The paper cites GAO (2011) survey evidence that in years when the H-1B cap bound, most large firms found alternative (often costly) ways to hire their preferred candidates, while small firms were more likely to fill positions with different candidates, incurring delays and economic losses.

Q3. What does the general equilibrium model predict about aggregate productivity?

The model shows that eliminating major H-1B-style immigration policy frictions would increase average productivity in the high-tech sector through the entry and survival channel: fewer frictions allow more young firms to enter and survive, which raises competitive pressure and leads to the exit of older, less productive firms (a selection effect via creative destruction). This mechanism implies that the productivity gain from liberalizing skilled immigration comes not primarily from incumbent firms hiring more foreign workers, but from the change in the firm age and productivity distribution—a general equilibrium effect that partial-equilibrium analyses based on incumbent firms would miss.

Q4. How does the model match the data on firm dynamics?

The model is calibrated to match the age distribution of firms in high-technology sectors in the data, including the stylized fact that the share of young (0–5 year old) high-tech firms has declined since the early 2000s concurrent with a period of more restrictive skilled immigration policy (the H-1B cap fell from 195,000 in 2003 to 85,000 in 2005 and has remained constant). The model also captures the pattern—documented in the data—that the entry of younger firms leads to a greater exit of older firms, consistent with the Hopenhayn-Rogerson (1993) model of firm dynamics.

Key concepts

H-1B visa frictions : the set of costs and constraints associated with the H-1B temporary skilled worker visa program in the US, including per-firm application costs, a fixed aggregate cap of 85,000 visas for private firms per year, and random lottery allocation when applications exceed the cap.

firm survival channel : the mechanism through which immigration policy frictions reduce the probability that young high-tech firms survive to maturity, as distinct from the hiring channel (whether incumbent firms hire foreign workers); the paper argues the former is the quantitatively relevant margin.

Soft landing and inflation scares

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

Why did the 2021–2023 US inflation surge end in a soft landing — disinflation without a major recession — while the Volcker disinflation of 1979–1987 required substantial output losses? And was the timing and strength of the Federal Reserve’s reaction to the inflation surge decisive in achieving this outcome?

Methodology and Model

The paper develops and estimates a micro-founded Heterogeneous-Expectation New Keynesian (HENK) model in which agents hold idiosyncratic, dispersed beliefs about the long-run (steady-state) level of inflation. The key departure from full-information rational expectations (FIRE) is that information about the long-run value of inflation is dispersed and sticky: agents update their beliefs through pairwise social learning (SL), adopting the forecasting model of the agent whose belief produced lower recent inflation forecast errors. This tournament process — inspired by genetic algorithms — generates a time-varying cross-sectional distribution of subjective inflation beliefs.

The model admits a closed-form solution that retains the entire time-varying distribution of beliefs and can be estimated with standard full-information Bayesian methods using the inversion filter (Cuba-Borda et al. 2019). The FIRE benchmark is nested as the special case in which the average belief deviation from the target is zero at all times.

Estimation uses four US macroeconomic observables (output gap, CPI inflation, one-quarter-ahead average SPF inflation expectation, and the proxy funds rate of Choi et al. 2022 that captures both conventional and unconventional monetary policy) over 1985Q1–2023Q4. A formal model comparison rejects the RE null hypothesis (p < 0.0001) in favor of the HENK specification.

Main Findings With Quantitative Magnitudes

Inflation scares are endogenous: In the model, inflation scares arise whenever repeated above-target inflation outcomes validate and diffuse above-target beliefs through social interactions. Under the historical scenario, the share of agents holding long-run inflation beliefs between 1 and 3 percent (annualized) falls to 40 percent in mid-2022 before recovering above 90 percent by end-2023, indicating a partial but not complete unanchoring of expectations.
Timing dominates strength: Counterfactual simulations show that the timing — not the strength — of the Fed’s reaction to the inflation surge is the key determinant of inflation expectations management and subsequent macroeconomic outcomes. Varying the Taylor-rule inflation coefficient by +/-10 percent (moving from 1.64 to 2.00) produces negligible differences in inflation and output gap dynamics, with welfare ratios of 1.052 and 0.981 relative to benchmark respectively under the ad-hoc loss function. By contrast, varying the timing via the interest-rate smoothing parameter by +/-10 percent produces much larger divergences.
The Fed fell behind the curve: Under a scenario in which the Fed had strictly followed its estimated Taylor rule (removing the negative monetary policy shocks observed from mid-2020 to mid-2022), inflation would have peaked approximately 3 percentage points lower on a yearly basis. Inflation expectations would have remained lower for almost a year longer, and the subsequent rise in expectations would have been more gradual and lower-peaking. Crucially, the output gap in this preemptive-tightening scenario would have been only briefly negative (in 2022Q2) and not deep enough to trigger a recession.
Further delays would have been highly costly: A delay of the tightening by one, two, four, or eight quarters would have produced successively worse outcomes. A two-year delay generates runaway inflation and 100 percent loss of target credibility (complete unanchoring). A delay of approximately three quarters would have resulted in a sizable, self-reinforcing entrenchment of above-target inflation expectations. The welfare cost of an eight-quarter delay is 5.76 times the benchmark loss under the ad-hoc measure (1.167 under the microfounded measure).
Early rate cuts would have reignited inflation: A counterfactual 100-basis-point cut as early as 2022Q3 would have pushed annual inflation approximately 2 percent above the historical scenario through end-2023, with inflation expectations rebounding by about 1 percent (annualized) immediately after the cut. Under no early-cut scenario would inflation or expectations have converged back to target by end-2023.
Expectation heterogeneity amplifies shocks: Greater initial dispersion in beliefs amplifies and prolongs the impact of all shocks (demand, supply, monetary policy, expectation). After a one-standard-deviation cost-push shock, higher initial belief dispersion produces larger and more persistent deviations in inflation, output, and interest rates. The model-implied interquartile range of beliefs is correlated 0.538 with the SPF interquartile range and the cross-sectional standard deviation is correlated 0.483 (both p < 0.001).
Historical decomposition: Over the 2010s, negative expectation shocks account for a substantial fraction of the persistent below-target inflation (“missing inflation”). From approximately mid-2022 onward, positive expectation shocks account for most of the variance of inflation in the model. The recent disinflation is attributed to a combination of: easing supply pressures, normalization of monetary policy, and re-anchoring of inflation expectations.

Scope Conditions

Results are conditional on the estimated HENK model applied to US data, 1985Q1–2023Q4, using a stylized three-equation NK backbone (no labor market dynamics, no financial sector, no capital). The proxy funds rate is more volatile than the federal funds rate, which affects the welfare comparison for large preemptive tightening scenarios. Counterfactual scenarios are implemented through unexpected monetary policy shocks; anticipated shocks would only strengthen the inflationary effects of delays.

In depth

Q1. What is the core mechanism by which an inflation scare can develop in the HENK model?

A: When inflation repeatedly exceeds the target — whether due to shocks or delayed policy — agents whose beliefs are already above-target incur lower forecast errors than those anchored at the target. During pairwise social interactions (the tournament step of social learning), above-target beliefs spread through the population because they are selected as the “better” forecasting model. The resulting upward shift in the average belief feeds higher inflation through the New Keynesian Phillips Curve, which validates above-target beliefs further, creating a self-reinforcing loop. This mechanism differs from rational-expectations models, where beliefs mean-revert automatically.

A: Two assumptions deliver the closed-form. First, beliefs are private and dispersed (Assumption 1): agents observe only the belief of their matched mate, not the population distribution. Second, a quasi-rational-expectations (quasi-RE) observer treats aggregate beliefs as a random walk in expectations (Assumption 2: a martingale). Under these conditions, the aggregate subjective inflation expectation equals the average subjective belief about steady-state inflation plus the rational-expectations forecast. This augmented minimum-state-variable (MSV) solution can be estimated with full-information methods (the inversion filter) via standard Dynare tooling.

Q3. What data are used and how are observables mapped to model variables?

A: The estimation uses four quarterly US observables from 1985Q1–2023Q4: the output gap (real GDP from FRED, HP-filtered with a one-sided adjusted filter); the CPI inflation rate (CPIAUCSL, FRED); one-quarter-ahead average CPI inflation expectation from the Survey of Professional Forecasters (CPI3); and the proxy funds rate of Choi et al. (2022), which captures both QE and QT so that unconventional monetary policy is reflected in the instrument. Inflation and expectations are demeaned by the sample average to express them as deviations from steady state. The discount factor is calibrated at 0.99; all other parameters are estimated via Bayesian methods with Metropolis-Hastings (8 parallel chains x 100,000 iterations, acceptance rate ~30%).

A: The posterior mean of the decay parameter in the fitness evaluation (discounting of past forecast errors) is 0.775, implying a half-life of past forecast errors of approximately 3 quarters. The frequency of news shocks has a posterior mean of 0.436, meaning approximately 40 percent of agents receive an inflation news shock every quarter. The standard deviations of the aggregate and idiosyncratic news shocks are very small (posterior means of 0.0004 and 0.0006, respectively) but strictly positive. The 95 percent confidence intervals for both exclude zero.

Q5. How does the HENK model outperform the RE benchmark in fitting the data?

A: Formal model comparison rejects the RE null (p < 0.0001) with equal prior model weights (50/50). On second moments, only the HENK model replicates positive autocorrelation in inflation (0.428 vs. 0.162 for RE, against an empirical interval of [0.239; 0.579]), in inflation expectations (0.824 vs. 0.161, empirical interval [0.839; 0.927]), and in inflation forecast errors (0.122 vs. -0.145). Additionally, the HENK model reproduces the untargeted cross-sectional dispersion of beliefs over the business cycle, including the increase during the GFC and the COVID-19 era and the low dispersion during the Great Moderation — with correlations of 0.538 and 0.483 between model and SPF dispersion measures.

Q6. What does the historical shock decomposition reveal about the recent inflation surge?

A: The decomposition (Section 3.3) shows that in the initial phase of the COVID-19 shock (2020Q2-Q3), negative demand and monetary policy shocks drove inflation down. Adverse cost-push (supply) shocks dominate from early 2021 into 2022. Expectation shocks — the contribution of dispersed beliefs — are negative throughout the 2010s (explaining part of the “missing inflation”) and remain briefly negative at the pandemic’s onset before turning sharply positive and driving most of the variance of inflation in the final two years of the sample (2022-2023). The loose monetary policy stance (negative monetary policy shocks from mid-2020 to mid-2022, visible in the Taylor-rule residuals) also contributes substantially to the inflation dynamics.

Q7. What does the Taylor-rule counterfactual show, and why doesn’t preemptive tightening cause a recession in the model?

A: Removing the monetary policy shocks after 2020Q4 so that the proxy rate follows the estimated Taylor rule would have reduced the inflation peak by approximately 0.75 percentage points per quarter (equivalent to about 3 percentage points annualized) and kept expectations lower-anchored for almost a year longer. The output gap under the Taylor-rule scenario is only briefly negative (2022Q2) and does not constitute a recession. This occurs because the preemptive tightening exploits the sluggishness of subjective expectations stemming from information frictions: by raising rates earlier when beliefs are still anchored (or only weakly above target), the CB prevents the social-learning mechanism from diffusing above-target beliefs, which in turn softens the stabilization trade-off between inflation and output.

Q8. What is the U-shaped welfare relationship between preemptive tightening size and welfare?

A: Both the ad-hoc and microfounded welfare measures show a U-shaped relationship as the size of the front-loaded tightening in 2021Q1 increases from 100 bps to 400 bps to 800 bps. At 100 bps, the welfare ratio is 0.336 (ad-hoc, improvement over benchmark at 1.0); at 400 bps it improves further to 0.304; but at 800 bps (front-loading the entire subsequent tightening cycle) the ratio rises to 0.555, reflecting that the output costs of a very large early rate increase become prohibitive amid the series of supply shocks that hit in 2022. The maximum welfare gain in the microfounded criterion occurs at a slightly larger early increase than in the ad-hoc criterion, attributed to the absence of a financial sector and use of the more volatile proxy funds rate.

Q9. Does increasing the hawkishness of the Taylor rule compensate for falling behind the curve?

A: No. Varying the inflation reaction coefficient by +/-10 percent (to 2.00 for “hawk” and 1.64 for “dove”) from the posterior mean of approximately 1.82 produces negligible differences in inflation and output gaps. The hawkish scenario achieves marginally earlier rate increases but does not reduce the inflation gap relative to the historical benchmark. Welfare ratios are 0.960 (hawkish, slight improvement) and 1.057 (dovish, slight deterioration) under the ad-hoc measure, and 0.981 and 1.052 under the microfounded measure. The joint simulations varying both smoothing (timing) and hawkishness (strength) confirm that timing is the dominant factor: the two “earlier reaction” scenarios are clustered together and well-separated from the two “later reaction” scenarios, regardless of the inflation coefficient.

Q10. How does the model handle the role of initial belief dispersion in monetary policy transmission?

A: Impulse response function exercises varying the initial standard deviation of beliefs (as a share of the maximum model-generated standard deviation under the filtered shocks) show that greater initial dispersion uniformly amplifies and prolongs the macroeconomic response to all shock types (demand, cost-push, monetary policy, expectation). The mechanism is: greater dispersion means the population contains more “extreme” (far-from-target) beliefs; a shock that temporarily moves inflation off target temporarily validates extreme beliefs (lower forecast errors), causing them to spread in social interactions and shift the average belief further from target. This raises nominal rates (through the Taylor rule), deepens output losses, and prolongs the return to steady state.

Q11. What are the implications of early interest rate cuts in the counterfactual scenarios?

A: A 100-basis-point cut in any quarter from 2022Q3 through 2023Q2 would have reignited inflation expectations. The 2022Q3 scenario is most severe: expectations rebound approximately 1 percentage point higher (annualized) immediately post-cut, and annual inflation remains on average 2 percent above the historical path through end-2023. Across all early-cut scenarios, neither inflation nor inflation expectations would have returned to target by end-2023; instead, inflation would have been landing approximately 2 percent above the 2 percent target. The welfare ratios for early cuts range from 1.200 (cut in 2022Q3) down to 1.079 (cut in 2023Q2) under the ad-hoc measure — all welfare-worsening.

Key Concepts

Inflation scare (Goodfriend 1993, as used in this paper): A situation in which the public’s long-run inflation expectations become unanchored from the central bank’s target, making beliefs about above-target steady-state inflation self-fulfilling via the New Keynesian Phillips Curve. In the HENK model, a scare arises endogenously when above-target inflation outcomes repeatedly validate above-target beliefs, causing them to spread through social interactions. Measured in the paper by the share of idiosyncratic beliefs falling between 1 and 3 percent (annualized); lower share = more severe scare.

Social learning (SL): The belief-updating mechanism in which agents are paired at random each period and compare their inflation forecasting models; the agent whose model produced lower recent forecast errors (measured by the discounted sum of squared forecast errors with half-life approximately 3 quarters) is adopted by both members of the pair. This evolutionary tournament process — analogous to a genetic algorithm — generates a nonlinear, history-dependent distribution of beliefs that can drift persistently away from the target.

Steady-state learning: The restriction that agents’ heterogeneous beliefs concern only the low-frequency (intercept) component of inflation — i.e., their subjective perception of the steady-state inflation rate — while the rest of their inflation forecast (the effects of transitory shocks and lagged variables) coincides with rational expectations. This assumption, combined with internal rationality, permits a closed-form MSV solution of the HENK model.

Internal rationality: The assumption that each agent uses a perceived law of motion that is consistent with the true MSV solution of the HENK economy (including the effect of heterogeneous beliefs on dynamics), even if their intercept differs from the rational-expectations value. Agents internalize how the aggregate deviation of expectations from RE affects inflation, but they disagree about the long-run level.

Quasi-rational-expectations (quasi-RE) observer: An observer (or central bank) who, lacking information about how individual private beliefs are formed and aggregated, treats aggregate beliefs as a martingale — i.e., the expected future aggregate belief equals its current value. This assumption closes the model and permits estimation with full-information (inversion filter) methods, while preserving consistency between subjective beliefs and the law of motion.

Belief dispersion / expectation heterogeneity: The time-varying cross-sectional standard deviation (or interquartile range) of idiosyncratic beliefs in the population. In the model this is an endogenous, history-dependent outcome of the SL process. Greater dispersion amplifies the response of all macroeconomic variables to any shock by providing more “extreme” beliefs that can gain traction in pairwise tournaments when inflation temporarily deviates from target. Measured empirically by the interquartile range and standard deviation of individual SPF forecasts.

Proxy funds rate (Choi et al. 2022): A summary measure of the US monetary policy stance that incorporates both conventional interest rate policy and the effects of unconventional policies (quantitative easing and tightening), used in the paper in place of the federal funds rate to capture the full stance of monetary policy in the estimation and historical decomposition.

Inversion filter (Cuba-Borda et al. 2019): A computationally efficient estimation algorithm that, rather than the Kalman or particle filter, inverts the observation equation analytically to recover the sequence of structural shocks for a given parameter vector. It enables full-information Bayesian estimation of the nonlinear HENK model by separating the linear part of the solution from the nonlinear social-learning residual.

Spread too thin: The impact of lean inventories

Mon, 01 Jan 0001 00:00:00 +0000

This paper investigates the macroeconomic consequences of widespread just-in-time (JIT) inventory management, documenting a fundamental trade-off: JIT raises firm profitability and reduces micro-level volatility in normal times, but renders the economy significantly more vulnerable to large unanticipated shocks.

The empirical analysis draws on a novel dataset of approximately 200 publicly listed U.S. manufacturing firms for which the author identifies JIT adoption years using narrative records from SEC filings and historical news archives. Firm-level balance sheet data come from Compustat Fundamentals Annual (1980–2018), merged with county-level weather event data from NOAA. Four empirical facts are documented. First, JIT adoption is associated with a 13% decrease in inventory-to-sales ratios and a 9% increase in sales. Second, JIT adopters experience a roughly 7% decline in sales and employment growth volatility. Third, JIT adopters are approximately 25–30% more cyclical than non-adopters: a 1% increase in GDP growth predicts an additional 0.47 percentage point increase in JIT firm sales growth above the non-adopter baseline of roughly 1.6%. Fourth, a weather disaster predicts an additional 3% decline in JIT firm sales and employment relative to non-JIT firms.

To explain and quantify these facts, the author builds and structurally estimates a dynamic general equilibrium model with a distribution of heterogeneous final goods firms that differ in idiosyncratic productivity, inventory holdings, and JIT adoption status. Materials must be drawn from inventory stocks; new orders are subject to stochastic fixed order costs. JIT producers draw from a first-order stochastically dominated order cost distribution relative to non-JIT firms. Adopting JIT requires an upfront sunk cost and a smaller continuation cost thereafter. The model is estimated via simulated method of moments (SMM) targeting 11 moments (adoption frequency, inventory-to-sales ratios, covariances, and spike frequencies for both firm types), with nine parameters to be estimated.

In the estimated model steady state, JIT adoption delivers a 9–10% increase in output, a 40% decline in the aggregate inventory-to-sales ratio (close to the observed 35% decline in nonfarm inventories-to-final-sales from 1980 to 2018), a 1.3% increase in firm value, a 1.3% increase in measured TFP, and a welfare gain of 1.43% in consumption equivalent terms. These gains arise because lower order costs allow firms to better align material input use with realized productivity, smoothing inventory cycles.

The vulnerability side is quantified through an unanticipated supply disruption calibrated to match the 3.4% drop in real U.S. GDP between 2019 and 2020. In response, the JIT economy experiences an approximately 0.40 percentage point excess output contraction relative to the no-JIT counterfactual, amounting to roughly 13–15% more output lost. The mechanisms are stockouts — firms that fully exhaust their inventories and cannot produce — and hoarding behavior, whereby firms that retain some inventory draw stocks down more slowly to preserve buffers, reducing material input use. Both channels reduce production relative to the counterfactual. The excess output loss is estimated at approximately $100 billion, comparable to state and local government allocations under the CARES Act.

JIT nevertheless remains welfare-improving even under this shock. For a social planner to prefer a no-JIT world, the negative productivity shock to the intermediate goods sector would need to be nearly 14% — an order of magnitude larger than the calibrated COVID-19 shock. The trade-off is robust across alternative order cost distributions, parameterizations, partial anticipation scenarios, and stockout cost specifications.

Q: What is the central trade-off identified by the paper? A: JIT adoption reduces fixed order costs, enabling firms to place smaller and more frequent orders, which raises sales, reduces micro-level volatility, and increases firm value and welfare in normal times. However, because JIT firms hold fewer inventories, an unexpected aggregate shock increases the likelihood of stockouts and hoarding behavior, producing a deeper aggregate output contraction relative to an economy without JIT. Firms do not internalize the prospect of large shocks when making their private adoption decisions, generating the externality at the heart of the trade-off.

Q: How does the paper measure JIT adoption, and how large is the sample? A: The author constructs an adoption dummy for approximately 200 publicly listed manufacturing firms by exhaustively reviewing SEC filings and historical news archives for keywords including “JIT,” “just-in-time,” “lean manufacturing,” “pull system,” and “zero inventory.” Each document is individually analyzed to confirm the adoption year and to ensure it refers to the firm itself rather than its suppliers. More than half of observed adopters in the sample adopt prior to 1990, and nearly all adopt before 2000. The final Compustat-linked sample covers about 5,017 unique manufacturing firms from 1980 to 2018.

Q: What are the firm-level efficiency gains from JIT adoption? A: JIT adoption is associated with a 13% decrease in inventory-to-sales ratios and a 9% increase in sales; the corresponding standard deviation changes are –16% and +4%, respectively. Adopters also experience a roughly 7% decline in both sales and employment growth volatility, and a 5% increase in sales per worker relative to non-JIT firms. JIT firms additionally show a roughly 20% standard deviation reduction in squared forecast errors, indicating improved predictability of profitability.

Q: How much more cyclical are JIT firms relative to non-JIT firms? A: A 1% increase in GDP growth is associated with approximately a 1.6% increase in sales growth for non-adopters; JIT adopters experience an additional 0.47 percentage point increase above this baseline, making them roughly 25–30% more cyclical. This elevated cyclicality is estimated from variation external to the firm and reflects the heightened sensitivity of lean producers to aggregate demand fluctuations.

Q: How are JIT firms affected by local weather disasters? A: On average, a weather disaster predicts an additional 3% decline in JIT firm sales and employment relative to non-JIT firms. Using upstream supply chain linkages from Compustat Segment files, a unit increase in the average number of disasters hitting a firm’s suppliers predicts a 7–8% decline in firm sales and employment, with a similar excess decline for JIT firms. These results parallel the strategy in Barrot and Sauvagnat (2016).

Q: What is the model structure, and how does the JIT adoption decision work? A: The model features a representative household, a representative intermediate goods firm producing materials with capital and labor, and a continuum of heterogeneous final goods firms that differ in idiosyncratic productivity (AR(1) in logs), inventory holdings, and JIT adoption status. Each period has three stages: adoption decision, order decision (conditional on stochastic fixed order cost draw), and production decision. JIT producers draw order costs from a distribution first-order stochastically dominated by the non-JIT distribution, meaning JIT firms face systematically lower expected order costs. Adoption requires an upfront sunk cost c_s; maintaining JIT requires a smaller continuation cost c_f (estimated at slightly more than one-third of c_s), generating hysteresis: conditional on being an adopter, the probability of remaining one is estimated at 94%.

Q: What moments are targeted in the SMM estimation, and how well does the model fit? A: Eleven moments are targeted to identify nine parameters: the empirical adoption frequency, plus five moments each for JIT and non-JIT firms (mean inventory-to-sales ratio, the covariance matrix of inventory-to-sales ratios and log sales delivering three moments, and the frequency of positive inventory-to-sales ratio spikes exceeding 0.20). The model successfully fits targeted moments; non-targeted regression coefficients reproduce a quantitatively similar reduction in inventory-to-sales ratios after adoption, a comparable increase in sales among adopters, and reductions in firm volatility of 4–5% versus 6–7% in the data.

Q: What are the estimated key structural parameters? A: The upper support of the order cost distribution among non-adopters is estimated to be an order of magnitude larger than that of adopters, implying JIT firms place orders about 45% smaller than non-JIT firms. The estimated carrying cost is about 20% of inventory value. The estimated share of non-adopters in the model’s steady state implies a mass of JIT establishments of approximately 0.40. The technology parameters for the idiosyncratic productivity process are consistent with prior estimates in the structural firm dynamics literature.

Q: What are the steady-state aggregate gains from JIT adoption in the model? A: Relative to a counterfactual economy with no JIT option, the estimated model delivers a 9–10% increase in output, a 40% decline in the aggregate inventory-to-sales ratio (close to the observed 35% decline from 1980 to 2018), a 1.3% increase in firm value, a 1.3% increase in measured TFP, and a welfare gain of 1.43% in consumption equivalent terms. The TFP gain arises because lower order costs reallocate resources toward high marginal product producers at the aggregate level.

Q: How is the unanticipated disaster calibrated, and what are its effects in the JIT versus no-JIT economies? A: The disaster is an unanticipated negative shock to aggregate productivity in the intermediate goods sector, calibrated to match the 3.4% drop in real U.S. GDP between 2019 and 2020. In response, the JIT economy experiences approximately a 0.40 percentage point excess output contraction relative to the no-JIT counterfactual, amounting to roughly 13–15% more output lost. This excess loss equals approximately $100 billion, comparable to CARES Act allocations to state and local governments.

Q: What are the two mechanisms through which JIT amplifies the disaster shock? A: The first mechanism is stockouts: because JIT firms hold fewer inventories, an unexpected spike in order costs makes them more likely to fully exhaust their existing stocks, leaving them with no material inputs and forcing them to forgo production entirely. The second mechanism is hoarding: firms that do not fully stock out face a higher shadow value of inventories and cut back on material input use to draw inventories down more slowly, reducing output even without a full stockout. Both mechanisms reduce material input utilization in the JIT economy, causing a sharper drop in sales relative to the counterfactual.

Q: Is JIT still welfare-improving when the COVID-19 shock is accounted for? A: Yes. A social planner comparing welfare across steady states would not prefer to eliminate JIT even accounting for the deeper crisis it generates. For the planner to prefer a no-JIT world, the negative productivity shock to the intermediate goods sector would need to be nearly 14% — an order of magnitude larger than the calibrated 3.4% shock. This implies that the welfare gains from JIT in normal times substantially outweigh the welfare costs of the deeper recession under a COVID-19-scale shock.

Q: How does the paper relate to the Great Moderation literature? A: JIT adoption is credited in prior work (McConnell and Perez-Quiros, 2000; Blanchard and Simon, 2001; Kahn et al., 2002) as contributing to the roughly 35% reduction in the aggregate inventory-to-sales ratio between 1980 and 2018 and to the broader decline in macroeconomic volatility. The estimated model is consistent with this: JIT adoption reduces firm-level volatility and, in the steady state, implies a reduction in aggregate inventory-to-sales ratios close to the observed magnitude. However, the paper documents that the same forces that smooth normal-times fluctuations amplify unanticipated large shocks.

Q: What robustness checks does the paper conduct? A: The paper considers alternate parameterizations (all robustly show the micro-macro trade-off), larger disaster sizes calibrated to UK and France 2020 contractions (JIT economy contracts ~10% vs. ~8.7%, a ~15% larger contraction), partial anticipation (a sizable excess output drop persists because the left tail of firm outcomes is truncated at zero profits), stockout costs (trade-off remains with ~1.2% firm value gain and ~10% excess contraction), and an alternative right-skewed beta order cost distribution (firm value gain rises to 1.8%, trade-off remains). An alternative CUSUM-based measure of JIT adoption identifying approximately 560 firms produces qualitatively similar empirical results.

Q: What is the subsample estimation finding on adoption costs over time? A: Comparing 1980–1989 and 1990–2018 subsamples, the upfront sunk cost of JIT adoption estimated from the 1980s sample is about 26% higher than in the later subsample, implying it has become easier to initiate JIT production over time. Steady-state output rises by about 3.4% in the 1990–2018 period relative to 1980–1989, and the excess output contraction under the disaster shock is about 15% relative to the 1980s counterfactual, close to the baseline estimate.

Just-in-Time (JIT) Production: A lean inventory management philosophy that minimizes the time between orders by committing to smaller and more frequent orders from suppliers, reducing costs of managing large material purchases and storing idle stocks; in the model, JIT is operationalized as drawing order costs from a distribution first-order stochastically dominated by the non-JIT distribution.

Stockout: The condition in which a final goods firm enters a period with no inventories (s = 0) and chooses not to place an order, leaving it without any material inputs and forcing it to forgo production entirely for that period.

Hoarding (in the disaster context): The behavior of firms that, facing a higher shadow value of inventories during an unexpected shock, cut back on material input use in order to draw down existing inventory stocks more slowly, preserving buffers at the cost of reduced current production.

Fixed Order Cost: A stochastic, labor-denominated cost that a firm must pay each period in which it places a materials order; JIT adopters face a systematically lower distribution of these costs, enabling more frequent ordering at smaller quantities.

Adoption Sunk Cost: The one-time upfront cost c_s a non-adopter must pay to initiate JIT status, which exceeds the continuation cost c_f paid by existing JIT firms to maintain their status; the gap between these costs generates hysteresis in the adoption decision.

Simulated Method of Moments (SMM): The structural estimation procedure used to identify model parameters by minimizing the weighted distance between model-simulated moments and their empirical counterparts; here applied with 11 targeted moments to identify 9 parameters in an overidentified system.

Micro-Macro Trade-off: The paper’s central finding that individual firms rationally adopt JIT for private profitability gains (1.3% increase in firm value, 1.43% welfare gain), while the aggregate economy becomes more fragile to unanticipated shocks (roughly 13–15% deeper output contraction) because firms do not internalize the systemic vulnerability created by economy-wide lean inventories.

Staffing agencies and in-house bargaining

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks whether a labor market with search-and-matching frictions and firms producing under decreasing returns to labor is better characterized by in-house hiring with intra-firm wage bargaining (Stole-Zwiebel) or by an alternative arrangement in which intermediaries — “staffing agencies” — search for and employ workers and then rent them to producing firms on a frictionless, perfectly competitive market. The paper’s second and central question is what happens when firms can choose their optimal combination of the two arrangements simultaneously.

The model is static. There are Z homogeneous firms with production function F(n) satisfying F’’(n) < 0, N homogeneous workers, and a standard concave constant-returns-to-scale matching function M = m(V, N). Firms can post vacancies, workers search, and Nash bargaining with worker bargaining weight β determines wages. The analysis is conducted with fully general production and matching functions throughout, deviating to specific functional forms (Cobb-Douglas matching, power production function F(n) = An^α) only when needed to illustrate a particular efficiency result. All main results hold for both directed and random search.

Comparing the two polar arrangements (Theorem 3.1). When all hiring is in-house (Stole-Zwiebel), equilibrium firm size n^SZ, aggregate employment Zn^SZ, labor market tightness θ^SZ, and the equilibrium wage w^SZ are all strictly higher than their counterparts under full staffing-agency employment (n^SA, Zn^SA, θ^SA, w^SA). The mechanism is that under in-house hiring with decreasing returns, a worker’s threat to leave raises the marginal product — and hence the wage — of remaining workers, giving workers additional bargaining leverage. Firms respond by over-employing in-house hires to dilute each worker’s marginal product and thus moderate wages. This over-employment raises vacancy posting and tightness, which in general equilibrium bids up wages despite each firm’s individual wage-moderation motive.

Efficiency (Theorem 3.2). Under the standard Hosios condition — worker bargaining weight β equals the elasticity η(θ) of the matching function with respect to vacancies — the staffing-agency equilibrium achieves the social planner’s optimum (θ^SA = θ*), while the in-house equilibrium posts strictly too many vacancies (θ^SZ > θ^SA = θ*). The in-house arrangement can be optimal for some β > η when workers’ bargaining power is sufficiently high (Theorem 3.3, proved for Cobb-Douglas matching and power production function), because the over-employment incentive then counteracts the externality from underprovision of vacancies.

The main result: staffing agencies dominate (Theorem 3.4). When firms choose their profit-maximizing combination of in-house hires n^SZ and rented staffers n^SA, the unique equilibrium has n^SZ = 0 and n^SA > 0 — firms use only staffers. The key is Lemma 3.1: renting one additional staffer reduces the wage paid to in-house workers by more than does hiring one additional in-house worker (formally, ∂w^SZ/∂n^SA < ∂w^SZ/∂n^SZ). This asymmetry arises because staffers cannot leave during intra-firm bargaining breakdowns — they remain regardless — so each additional staffer tightens the firm’s fallback position more effectively than an additional in-house hire. With continuous labor, any positive mass of in-house workers leaves residual scope for further wage moderation through staffers, so the firm always finds it profitable to convert the last in-house hire to a staffer. The corner solution n^SZ = 0 is thus the unique equilibrium. With discrete labor, a firm would be indifferent between exactly one and zero in-house workers.

The paper also notes that this staffing-agency arrangement is formally equivalent to the “labor packer” or intermediate-good setup widely used in applied macroeconomics (e.g., Gertler, Sala, and Trigari 2008) to avoid Stole-Zwiebel complications, providing a micro-foundation for that modeling convention.

Q: Why does in-house hiring with decreasing returns to labor generate higher wages and employment than the staffing-agency arrangement? A: Under decreasing returns, if a worker’s wage negotiation breaks down and the worker leaves, the marginal product of the remaining n−1 workers rises. This gives each in-house worker additional bargaining leverage beyond the standard β parameter. To counteract this, firms over-employ in-house hires to keep the marginal product low. In general equilibrium this raises tightness θ^SZ > θ^SA, which in turn raises wages w^SZ > w^SA even though each individual firm’s motive was wage moderation.

Q: What is the formal basis for the in-house wage equation, and what does it depend on? A: Following Stole and Zwiebel’s stability condition, the continuous-labor wage for a firm with n workers is w(n) = (1−β)b + n^(−1/β) ∫₀ⁿ z^((1−β)/β) F’(z) dz. The wage depends on the entire distribution of marginal products over [0, n], not merely on the marginal product at n. In the special case of a power production function, the integral yields an explicit power function in n.

Q: When is the staffing-agency equilibrium socially efficient? A: Under the standard Hosios condition β = η(θ*), the staffing-agency equilibrium attains exactly the planner’s tightness (θ^SA = θ*), because bargaining in staffing agencies is standard — the worker’s outside option does not affect other workers’ wages and so the usual efficiency characterization applies. The in-house equilibrium then strictly over-posts vacancies (θ^SZ > θ*).

Q: Can the in-house equilibrium ever be socially optimal? A: Yes, but only under specific parameter conditions. Theorem 3.3 shows that with Cobb-Douglas matching (η constant) and a power production function F(n) = An^α, there exists a threshold β̂ ∈ (η, 1) at which θ^SZ = θ*. The intuition is that strong worker bargaining power creates a vacancy-underprovision problem; the over-employment incentive under in-house hiring then partially corrects it. The functional form restriction is made for expositional convenience; the core logic is general.

Q: What is Lemma 3.1 and why is it the key to the main result? A: Lemma 3.1 states that, given any positive number of in-house hires n^SZ > 0, renting one additional staffer reduces the wage paid to in-house workers by more than does hiring one additional in-house worker: ∂w^SZ/∂n^SA < ∂w^SZ/∂n^SZ. This is proved by showing the relevant integral in the difference (∂w^SZ/∂n^SA − ∂w^SZ/∂n^SZ) is negative for n^SZ > 0 given F’’ < 0.

Q: Why does renting an additional staffer moderate in-house wages more than hiring an in-house worker? A: An in-house worker who is hired can, in principle, leave during a bargaining breakdown, triggering renegotiation all the way down to zero in-house workers and driving the firm’s fallback to zero profit. A rented staffer cannot leave; at minimum, all rented staffers remain in production regardless of in-house bargaining outcomes. Each additional staffer thus raises the firm’s floor payoff in bargaining by more than an additional in-house hire does, generating stronger wage moderation.

Q: Why does Theorem 3.4 produce a corner solution rather than an interior mix? A: Because labor is treated as a continuous input, any strictly positive mass n^SZ > 0 of in-house workers leaves the marginal in-house worker with positive bargaining leverage through the threat-to-leave mechanism. The firm can always improve its bargaining position by converting that marginal in-house worker to a staffer. This margin is present no matter how small n^SZ is, so the only equilibrium is n^SZ = 0. In discrete labor the firm would be indifferent between exactly one and zero in-house hires.

Q: What happens to labor market tightness when both arrangements coexist? A: In the mixed equilibrium the tightnesses for in-house and staffer jobs must be equal in equilibrium (θ^SZ = θ^SA). If one tightness were higher, workers would prefer that job type (higher wage and higher probability of finding it), but firms would reduce vacancy posting there (costlier to fill), automatically equalizing tightness. This equilibration occurs even though in equilibrium vacancy posting for in-house jobs goes to zero.

Q: Do the results require directed search or hold under random search as well? A: The results hold under both directed and random search. Appendix 3.C establishes that with random search and a single pooled matching function M = m(V^SZ + V^SA, N), the unique equilibrium also features n^SZ = 0. The directed-search assumption is made without loss of generality.

Q: What does this paper imply for the applied macroeconomics literature’s “labor packer” modeling convention? A: The paper provides a formal micro-foundation for the labor-packer or intermediate-good approach used in New Keynesian DSGE models (e.g., Gertler, Sala, and Trigari 2008) to sidestep Stole-Zwiebel bargaining. In that literature, a “wholesale firm” or “packer” searches for workers and sells their services to final-goods firms under perfect competition — formally identical to the staffing-agency arrangement in this paper. Theorem 3.4 shows this arrangement is the unique equilibrium outcome of rational firm choice, so the shortcut is not merely convenient but theoretically grounded.

Q: What does the empirical literature say about wage differentials between in-house and agency workers? A: Drenik et al. (2023), using Argentine administrative data linking temp agencies to user firms, estimate a significant wage premium for in-house hires relative to temp workers. This is consistent with the paper’s theoretical prediction that w^SZ > w^SA in the polar-case comparison (Theorem 3.1), though the paper itself presents no empirical estimation.

Q: What are the implications of the staffing-agency arrangement for measured labor shares? A: The paper notes that costs for staffers typically appear in firm accounts as intermediate input costs rather than labor costs. A shift from in-house hires to staffers therefore reduces measured labor costs and, because it also reduces value added (by more than the labor-cost reduction), lowers the measured labor share at the firm even when actual labor input and output are unchanged.

Q: What future extensions do the authors identify as priorities? A: The authors flag three main extensions: (i) heterogeneous workers and firms, which could generate predictions about which firms use each hiring mode; (ii) worker effort/loyalty differences between in-house and agency workers that could make in-house hiring attractive ex post; and (iii) a frictional rental market for staffers or heterogeneous tasks within the firm, where insufficient staffer supply in certain sub-markets could restore a role for in-house hiring.

Staffing agency (in this paper’s sense): An intermediary that posts vacancies on the frictional labor market, employs workers through standard Nash bargaining, and rents those workers one-for-one to producing firms on a frictionless, perfectly competitive market. The staffing agency is separated from the firm’s production decisions; its search activity has constant returns to scale.

In-house hiring with Stole-Zwiebel bargaining: A market arrangement in which the producing firm itself posts vacancies, employs workers, and conducts intra-firm Nash bargaining. Under decreasing returns to labor, the bargaining outcome for worker i depends on the firm’s payoff if that worker left, which in turn depends on wages paid to the remaining n−1 workers — generating a system of interdependent bargaining problems captured by the differential equation w(n) = (1−β)b + n^(−1/β) ∫₀ⁿ z^((1−β)/β) F’(z) dz.

Wage-moderation incentive (over-employment): Under in-house hiring, a firm has an incentive to hire more workers than a social planner would recommend, because additional workers reduce each worker’s marginal product and hence the wage the firm must pay. This incentive is present because decreasing returns mean a departing worker raises the marginal product of remaining workers, giving each in-house worker leverage over the firm.

Differential wage-moderation effect (Lemma 3.1): The finding that, given any positive mass of in-house hires, renting one additional staffer reduces in-house wages by more than hiring one additional in-house worker (∂w^SZ/∂n^SA < ∂w^SZ/∂n^SZ). The asymmetry arises because staffers cannot leave during intra-firm bargaining breakdowns, so they provide a more effective floor to the firm’s fallback payoff.

Hosios condition (as applied here): The standard efficiency condition β = η(θ), where β is the worker’s Nash bargaining weight and η(θ) is the elasticity of the job-offer arrival rate with respect to tightness. When this condition holds, the staffing-agency equilibrium is socially optimal (θ^SA = θ*) and the in-house equilibrium is inefficient (θ^SZ > θ*).

Stock market participation and macro-financial trends

Mon, 01 Jan 0001 00:00:00 +0000

This paper documents a puzzle for canonical limited-participation models: when U.S. stock market participation rose from 31.6% to 53% between 1989 and 2007—a period also characterized by the Great Moderation—the equity premium and stock return volatility increased rather than fell as those models would predict. The paper resolves this puzzle using an RBC model with concentrated capital ownership in which capitalists have external habit utility with a habit stock that depends on aggregate per capita consumption. As participation rises, the representative capitalist’s consumption converges to aggregate consumption, shrinking the surplus-consumption ratio and raising endogenous average risk-aversion; this risk-aversion channel dominates the conventional risk-sharing channel (which predicts a lower equity premium under higher participation). The model implies that higher participation generates a sizeable rise in both the equity premium and stock return volatility while reducing the risk-free rate and aggregate consumption volatility—jointly explaining the observed U.S. macro-financial patterns. Household-level data from the Consumption Expenditure Survey (1984–2017) and cross-state variation support the model’s mechanism.

In depth

Q1. What is the puzzle the paper addresses?

Existing limited-participation models predict that higher stock market participation should reduce the equity premium (by improving risk-sharing), yet the U.S. experienced a rising equity premium and higher stock return volatility precisely during the period of sharp participation growth (1989–2007), at the same time as the Great Moderation. The standard channel predicts that as more households access financial markets, the representative capitalist’s risk burden falls and the covariance between capitalists’ consumption and equity returns declines, lowering the equity premium. The data contradict this prediction, motivating the paper’s novel mechanism.

Q2. What is the novel risk-aversion channel?

As stock market participation rises, the representative capitalist’s consumption converges toward aggregate per capita consumption, shrinking the surplus-consumption ratio and thereby raising the endogenous effective risk-aversion of the economy—this risk-aversion channel dominates the conventional risk-sharing channel. The key assumption is that capitalists’ habit stock depends on aggregate per capita consumption. The surplus-consumption ratio (the gap between the capitalist’s consumption and the habit level) determines risk-aversion in the external habit utility framework. As participation rises, the capitalist’s consumption approaches the habit level, increasing risk-aversion and the equity premium, even as aggregate consumption volatility falls.

Q3. What are the model’s predictions for macro-financial variables?

In the model economy, an increase in stock market participation generates a sizeable rise in both the equity premium and the volatility of stock returns, a moderate increase in the price-dividend ratio, and a fall in the average risk-free rate and aggregate consumption volatility—jointly accounting for the U.S. macro-financial experience since the 1980s. The rise in equity premium and stock volatility produced by higher participation substantially counteracts the shrinking effect due to lower aggregate uncertainty from the Great Moderation, providing a unified explanation for the co-movement of these macro-financial trends.

Q4. What is the empirical evidence supporting the mechanism?

Household-level data from the U.S. Consumption Expenditure Survey (1984–2017) show that the model-implied average risk-aversion for the representative stockholder trended upward over time closely tracking the rate of participation, while the stockholder-to-aggregate consumption ratio trended downward; cross-state data document a negative relationship between participation and the stockholder-to-aggregate consumption ratio. Both the time-series and cross-sectional patterns are consistent with the model’s prediction that higher participation compresses the gap between stockholder and aggregate consumption, the key driver of the risk-aversion channel.

Key concepts

participation puzzle : the empirical regularity that only a fraction of the population participates in the stock market; exploited in asset pricing models to explain the equity premium with plausible average risk-aversion; this paper studies the consequences of the upward trend in participation since the 1980s. surplus-consumption ratio : the gap between the capitalist’s consumption and their habit level, normalized by consumption; the key state variable in external habit utility models; determines endogenous risk-aversion so that a shrinking surplus-consumption ratio raises risk-aversion. risk-aversion channel : the novel mechanism introduced in this paper: as stock market participation rises, the capitalist’s consumption converges to aggregate consumption, shrinking the surplus-consumption ratio and raising endogenous risk-aversion and thus the equity premium; dominates the conventional risk-sharing channel in the model. risk-sharing channel : the conventional channel in limited-participation models: higher participation improves risk-sharing, reducing the covariance between stockholder consumption and equity returns and tending to depress the equity premium; present in the model but dominated by the risk-aversion channel.

The crowding-in effects of local government debt in China

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper asks how changes in the composition (not the size) of Chinese local government debt influence bank risk-taking, credit allocation between privately owned enterprises (POEs) and state-owned enterprises (SOEs), and local total factor productivity. The focus is a 2015 debt-to-bond swap program in which local governments were required to convert outstanding implicit debt — primarily bank loans to local government financing vehicles (LGFVs) and LGFV-issued corporate bonds — into explicitly guaranteed local government bonds.

Institutional Context

Following China’s 2008–09 fiscal stimulus, local government debt outstanding rose from 5.8% of GDP in 2006 to 22% by 2013 and reached RMB 15.4 trillion (24% of GDP) by end-2014. The debt was largely held through LGFVs, which are nominally corporate firms but with implicit government backing. Under China’s amended budget law effective early 2015, all outstanding debt had to be converted to provincial government bonds through a three-year swap program. Before the swap, government bonds accounted for only 8% of outstanding local government debt; the remaining 92% (approximately RMB 14.17 trillion) needed to be swapped. Commercial banks hold on average 88% of newly issued local government bonds; the government bond share of commercial bank assets rose from 1.7% in 2014 to 14% in 2019.

Mechanism

Under Basel III capital adequacy ratio (CAR) regulations, Chinese commercial banks — specifically the Big Five systemically important banks using the internal-ratings-based (IRB) approach — assign risk weights above 80% on average to corporate loans, but only 20% (the regulatory approach) to local government bonds. Converting LGFV debt to government bonds therefore reduces banks’ risk-weighted assets, loosening the binding CAR constraint. The paper formalizes this through a partial-equilibrium model of bank portfolio choice: a lower risk weight on government-bond assets (modeled as a fall in ξ_g) loosens an effective capital constraint, inducing banks to shift toward riskier (POE) lending and reducing the POE-SOE loan rate spread. The model predicts this effect is larger in provinces with higher initial outstanding government debt.

Data

The empirical analysis uses: (1) confidential loan-level data from one of the Big Five Chinese commercial banks covering approximately 400,000 unique firm-loan pairs from 2008:Q1 to 2017:Q4 (regression sample 2013:Q1–2017:Q4); (2) province-level outstanding debt data at end-2014 for 25 provinces, constructed from prefectural-level data collected by Qu et al. (2023); and (3) firm-level balance sheet data from China’s Annual Survey of Industrial Firms (ASIF), covering above-scale manufacturing firms.

Main Findings with Quantitative Magnitudes

Using a triple-difference (DDD) identification — interacting POE status, a post-2015 dummy, and provincial initial government debt — the paper finds:

At the average level of provincial government debt, the debt swap program reduced the POE credit spread (loan rate deviation from benchmark rate, relative to SOEs) by approximately 3.18 percentage points (coefficient α = −3.182, significant at p < 0.01).
For provinces with initial outstanding debt one standard deviation above the mean (approximately 0.402 log units above mean), the swap reduced the POE credit spread by an additional 1.15 percentage points (= 0.402 × 2.849; coefficient β = −2.849, significant at p < 0.01), accounting for 10.1% of the standard deviation of loan rates in the sample.
In terms of the raw loan rate gap between SOEs and POEs (averaging 42 basis points in the sample), the program narrowed this spread by approximately 6 basis points in high-debt provinces (one standard deviation above mean), accounting for about 1/7 of the average gap.
On the extensive margin, in provinces with outstanding debt one standard deviation above the mean, the swap raised the probability of bank lending to POE firms by approximately 1.2 percentage points (= 0.402 × 0.0292).
2SLS estimates instrumenting swapped debt by initial outstanding debt interacted with the post-2015 dummy confirm: one standard deviation increase in swapped debt leads to an 11.21% decline in the POE loan rate deviation from benchmark relative to SOEs (= 3.723 × 3.013%), accounting for 0.98 standard deviations of the loan rate variable.
For provincial total factor productivity (TFP), provinces with 1% higher outstanding government debt before the swap experienced a 2.2% larger increase in TFP after 2015. The debt swap amount itself (instrumented) has a positive and significant effect on provincial TFP.

Scope Conditions and Parallel-Trends Validation

Pre-trend tests show that neither the average POE-SOE rate spread (α_τ) nor its interaction with provincial government debt (β_τ) is significantly different from zero in 2014 relative to the base year 2013. Both turn significantly negative only from 2015 onward, validating the parallel-trends assumption. Results are robust to: excluding LGFV firms, excluding large firms (top 10% by assets), restricting to central SOEs as controls (dropping local SOEs), controlling for local debt capacity, GDP growth, FDI/GDP, aged population, total loans, and bank branch fixed effects. A placebo test using the 2016 deleveraging policy shows no significant effect on bank risk-taking, distinguishing the debt-swap mechanism from contemporaneous policy changes.

In depth

Q1. What is the key theoretical channel through which the debt-to-bond swap affects bank lending to POEs?

The channel is the risk-weighting mechanism under Basel III capital adequacy ratio (CAR) regulations. Under the IRB approach used by Big Five banks, corporate loans carry average risk weights above 80%, while local government bonds carry a fixed regulatory weight of 20%. Converting LGFV corporate loans and bonds to local government bonds on the bank’s balance sheet reduces total risk-weighted assets, loosening the binding CAR constraint. The bank responds by adopting a riskier investment policy — lowering the cutoff ω̂ in the model — which increases lending to POE firms and reduces the POE-SOE credit spread.

Q2. Why is the effect of the swap predicted to be larger in provinces with higher initial outstanding government debt?

Proposition 2 of the model shows that the sensitivity of the POE loan rate spread to the debt swap policy (∂²ΔR_loan / ∂ξ_g ∂g) is positive, meaning it increases with the amount of government debt g. Provinces with more outstanding debt at end-2014 have more LGFV loans to swap into lower-risk-weight bonds, implying a larger reduction in risk-weighted assets for banks operating in those provinces and hence a larger relaxation of the CAR constraint. Empirically, the correlation between province-level outstanding debt and the amount of swapped debt from 2015–2017 is 0.85 (p-value < 0.0001), confirming the mechanism.

Q3. How does the empirical specification identify the effect of the debt swap rather than pre-existing trends?

The authors use a triple-difference (DDD) design: the outcome (loan rate deviation from benchmark) is regressed on the interaction POE × Post × GovDebt, where GovDebt is the demeaned log of province-level outstanding debt at end-2014. Pre-trend analysis (Equation 16) estimates year-specific coefficients α_τ and β_τ using 2013 as the reference year. For 2014, both coefficients are statistically indistinguishable from zero. From 2015 onward, both turn significantly negative at the 95% confidence level, consistent with the debt-swap policy triggering the change and inconsistent with pre-existing differential trends by province debt level.

Q4. How do the authors establish that the risk-taking channel rather than a demand-side story drives the results?

Two complementary exercises address demand versus supply. First, the authors add firm × year-quarter fixed effects, which absorb all firm-level time-varying factors (including loan demand). After removing demand effects, the triple-difference coefficient on GovDebt × POE × Post becomes more negative (−23.66, significant at 5%) than the baseline (−2.849), suggesting demand-side movements are not the source of the finding. Second, adding bank-branch × year-quarter fixed effects to remove supply-side heterogeneity makes the triple-difference term insignificant while leaving the POE × Post coefficient at −2.196 (significant at 5%), implying the result is primarily supply-driven and province-specific supply factors captured by the triple interaction absorb into the branch-level controls.

Q5. What heterogeneous effects across firm types provide additional evidence for the risk-taking interpretation?

Three dimensions of heterogeneity all point toward bank risk-taking. (a) Size: the credit-easing effect (coefficient on GovDebt × POE × Post) is larger in magnitude for small POEs (by firm assets or by loan size) than for large POEs, consistent with small firms being riskier borrowers. (b) Credit rating: the effect is larger for low-rating POEs (below AA-) than for high-rating POEs, consistent with banks taking on more risk in response to a loosened CAR constraint. (c) Firm-bank distance: the effect is larger for firms located farther from the lending bank branch, where information asymmetry is more severe, consistent with increased bank risk-taking toward harder-to-monitor borrowers.

Q6. How do the authors confirm that the debt swap program is the operative channel rather than the overall regulation?

Using the Bertrand-Mullainathan (2001) 2SLS approach, the authors treat the amount of swapped debt (ln(1 + Swap_jy)) as the channel variable, instrumented by GovDebt_j × Post_y (and its interaction with POE_i for the intensive-margin regression). The first-stage results are strong (F-statistics of 158–268), confirming that provinces with more initial outstanding debt swap more debt after 2015. The second-stage results show: (a) on the intensive margin, a one-standard-deviation increase in swapped debt leads to an 11.21% decline in the POE loan rate deviation from benchmark relative to SOEs; (b) on the extensive margin, provinces with more swapped debt show significantly higher probability of POE lending. Both second-stage estimates are significant, confirming the debt swap program as the transmission channel.

Q7. What is the effect of the debt swap on provincial total factor productivity, and through what channel?

Provinces with 1% higher outstanding government debt before the swap experienced a 2.2% larger increase in average provincial TFP after 2015 (column 2 of Table 13, coefficient = 0.0220, significant at p < 0.01), with the parallel-trend analysis showing no significant pre-2015 differential effect (the 2014 coefficient is 0.00346, insignificant). 2SLS estimates using swapped debt as the channel variable confirm a positive, significant effect of swapped debt on provincial TFP, with a coefficient of 0.0253 (p < 0.01) in the second stage. The mechanism is credit reallocation from less-productive SOEs to more-productive POEs, consistent with POEs having higher average productivity as documented in Hsieh and Klenow (2009).

Q8. How do the authors rule out that the deleveraging policy (implemented in December 2015) drives the results?

A placebo test replaces the Post_y dummy (equal to 1 from 2015 onward) with DeLevy (equal to 1 from 2016 onward, coinciding with the deleveraging policy). Neither the coefficient on GovDebt × POE × DeLevy nor on POE × DeLevy is statistically significant in the placebo regressions (Table 11). This distinguishes the mechanism from the deleveraging policy and confirms that the debt swap program — not deleveraging — is the source of the credit reallocation to POEs.

Q9. How do the authors confirm results are not driven by the debt capacity channel?

The local government debt reform also regulated debt capacity (the ratio of outstanding debt to a centrally assigned debt limit) for each local government. The authors control for the province-level debt capacity measure (DebtCap_j, the average ratio of local government debt to the debt limit in 2016–2017) alongside the baseline interaction terms. Table 9 shows the baseline results remain valid and significant after including debt capacity controls: the coefficient on GovDebt × POE × Post is −2.210 (p < 0.05) and the POE probability of lending result (coefficient on GovDebt × Post = 0.0277, p < 0.01) both hold, ruling out the debt capacity channel as the driver.

Q10. What does the model predict about the general relationship between capital adequacy requirements and bank risk-taking?

Proposition 1 establishes that tightening the capital adequacy ratio requirement (increasing ψ) leads to a safer investment policy (ω̂ increases, meaning the bank sets a higher cutoff before taking risky projects) and a lower leverage ratio. This is the benchmark: the debt swap effectively softens the constraint by reducing risk-weighted assets, analogous to lowering the effective ψ̃, which induces the opposite effect — riskier investment policy (lower ω̂) and lower POE credit spreads. The IRB approach’s property that risk weights are higher and increasing in project riskiness (ξ’(ω) < 0 and ξ’’(ω) ≤ 0) is essential for these comparative statics to hold.

Key Concepts

Debt-to-Bond Swap Program (2015): China’s central government program requiring local governments to convert all outstanding non-government-bond debt (primarily bank loans to LGFVs and LGFV-issued corporate bonds) into explicitly guaranteed provincial government bonds over three years starting in 2015. The program covered RMB 15.4 trillion in outstanding debt, of which 92% needed to be converted; by end-2018, approximately 90% of non-government-bond debt had been swapped.

Risk-Weighting Channel: The mechanism by which the change in debt composition affects bank lending. Under Basel III’s internal-ratings-based (IRB) approach, Chinese Big Five banks assign risk weights above 80% on average to corporate loans but only 20% (the regulatory approach) to local government bonds. Swapping LGFV debt for government bonds reduces the bank’s total risk-weighted assets without changing the size of assets, loosening the binding capital adequacy ratio constraint and enabling increased lending to riskier (POE) borrowers.

POE Credit Spread: Defined in the paper as the difference between the loan rate for privately owned enterprises (POEs) and that for state-owned enterprises (SOEs), measured as the percentage deviation of each loan’s interest rate from the benchmark rate set by the central bank. SOEs are treated as effectively riskless borrowers due to implicit government guarantees; POEs are the riskier counterparts. The paper tracks the POE credit spread as the primary outcome variable.

Local Government Financing Vehicles (LGFVs): Nominally corporate firms established by Chinese local governments to raise funds for public investment — primarily through bank loans and LGFV-issued corporate bonds (“municipal corporate bonds”). LGFVs are implicitly backed by local governments but not explicitly guaranteed, so the bank loans and bonds they issue carry higher Basel III risk weights (treated as corporate exposures) than formal government bonds.

Capital Adequacy Ratio (CAR) Constraint: The Basel III requirement that a bank’s equity capital exceed a minimum fraction ψ of its risk-weighted assets. For systemically important Big Five banks in China, implemented via the IRB approach for corporate loans and the regulatory approach for government bonds since 2012. In the theoretical model, the CAR constraint is binding and determines the bank’s effective leverage; relaxing it (by reducing risk-weighted assets) permits the bank to shift toward riskier lending.

Internal Ratings-Based (IRB) Approach: The Basel III methodology used by the Big Five Chinese banks to calculate risk-weighted assets for corporate loan portfolios. Under this approach, the risk weight is an increasing function of credit risk (higher-risk loans receive higher weights), so the average weight on corporate loans exceeds 80%, and even high-quality loans carry weights above 50%. This contrasts with the fixed 20% regulatory weight assigned to local government bonds.

Crowding-In Effect: In this paper’s usage, the mechanism by which restructuring local government debt composition — specifically, replacing corporate-form LGFV debt with low-risk-weight government bonds — frees up bank capacity to extend credit to private firms (POEs) that would otherwise face higher credit spreads or loan denial. This is framed as the opposite of the standard crowding-out effect (where more government debt squeezes private credit), arising because it is the composition rather than the size of government debt that changes.

Total Factor Productivity (TFP) Reallocation Effect: The paper measures provincial average TFP (using the Brandt et al. 2013 methodology) and documents that provinces with more government debt outstanding before the swap experienced larger TFP gains after 2015, attributing this to credit reallocation from less-productive SOEs to more-productive POEs. The effect is interpreted as a reduction in credit misallocation rather than within-firm productivity improvement.

The Geography of job creation and job destruction

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks why unemployment rates differ so persistently across local labor markets, and what role job creation and job destruction play in generating those differences. The authors document a comprehensive set of spatial labor market facts using administrative and survey microdata from Germany, the United States, and the United Kingdom, then build and calibrate a quantitative theoretical framework that accounts for all documented regularities.

Data and scope. For Germany, the authors use administrative data from the German employment office (universe of vacancies and unemployed, 1999–2020) and the IAB social security sample (SIAB, 2% of all workers, 2000–2017) aggregated to 194 commuting zones. For the U.S., they use BLS Local Area Unemployment Statistics (2000–2019) at commuting zones, CPS worker flows at metropolitan areas, and JOLTS vacancy data for the 18 largest MSAs (covering roughly 40% of the U.S. labor force). For the UK, they use Nomis data and Jobcentre Plus vacancy records (2004–2006) for 378 Local Authority Districts.

Empirical findings. Spatial unemployment rate differences are large and highly persistent. In Germany, the correlation of local unemployment rates across commuting zones over a 19-year span is 0.84 (West) and 0.77 (East). In the U.S., the correlation between 2000 and 2019 unemployment rates is 0.81; in the UK it is 0.76. In all three countries, local labor markets with lower unemployment are tighter (more vacancies per unemployed worker) and less productive. Firms in low-unemployment markets fill vacancies more slowly — in Germany, vacancy duration ranges from approximately 35 days in high-unemployment locations to approximately 65 days in low-unemployment locations, roughly an 85% difference.

A formal steady-state decomposition reveals that across all three countries, differences in job-separation rates account for approximately two-thirds of the cross-sectional variation in unemployment rates, while differences in job-finding rates account for roughly one-third. Specifically: Germany 62.4% separations / 33.2% job-finding; U.S. 72.0% / 32.8%; UK 64.3% / 35.8%. This primacy of separation rates in the cross-section stands in stark contrast to business-cycle dynamics, where job-finding rates account for 50–60% of unemployment fluctuations (Fujita and Ramey, 2009).

Theory. The authors embed a Diamond-Mortensen-Pissarides (DMP) model with endogenous separations — following Den Haan, Ramey, and Watson (2000) — into a Rosen-Roback spatial equilibrium framework. Locations differ in exogenous productivity; workers and firms are freely mobile; cost-of-living differences sustain the spatial equilibrium. The model is calibrated to the U.S. median-unemployment labor market (separation rate 0.0128, job-finding rate 0.2368, vacancy-filling rate 0.7365) plus the productivity differential between the 5th and 95th percentile unemployment locations (4.8% higher and 3.0% lower productivity than median, respectively). The baseline model, imposing the Hosios condition, matches the spatial patterns of separation rates, job-finding rates, tightness, vacancy duration, wages, and cost of living without targeting most of these. The decomposition in the calibrated baseline model attributes 33.5% of spatial unemployment variation to job-finding rates, compared to 32.8% in the data.

The baseline model generates a counterfactual upward-sloping Beveridge curve and cannot explain why job-finding rates dominate business-cycle fluctuations. Introducing on-the-job search (with 12% of employed workers searching each period, calibrated from Faberman et al., 2017) resolves both problems. In the extended model, job-to-job transition rates are virtually constant across local labor markets (matching the data) but strongly procyclical over the business cycle. This asymmetry amplifies the response of vacancies and job-finding rates to aggregate productivity shocks while muting the cyclical variation in separation rates. The extended model’s business-cycle decomposition attributes 54.4% of unemployment volatility to job-finding rates, within the empirical 50–60% range.

Policy implications. Under the Hosios condition, the decentralized equilibrium is efficient — large spatial differences in unemployment, tightness, and wages are efficient outcomes, not signs of mismatch. The relevant policy benchmark is not deviation of tightness from the national average but deviation from the model’s location-specific prediction conditional on local productivity.

Q: What is the central empirical puzzle the paper addresses? A: Spatial unemployment differences are large and persistent — in Germany, unemployment rates ranged from 1.9% to 11.9% across commuting zones even after 15 years of decline. These differences are not well understood theoretically, and the crucial missing empirical piece was data on job creation and vacancy filling across locations, which this paper provides for three countries.

Q: How large and persistent are cross-sectional unemployment differences in each country? A: In Germany, commuting-zone unemployment ranged from 3.6% to 24.0% in 2000 and persisted with a 19-year correlation of 0.84 (West) and 0.77 (East). In the U.S., the 2000–2019 correlation is 0.81, with unemployment as low as 1.5% and as high as 16.9% in 2000. In the UK, the 2004–2018 correlation is 0.76, with 2004 unemployment ranging from 1.8% to 13.1%.

Q: What do the data show about the relationship between unemployment and labor market tightness across locations? A: In all three countries, lower-unemployment labor markets are tighter — they have more vacancies per unemployed worker. This is documented for Germany using the universe of registered vacancies, for the U.S. using JOLTS data for 18 large MSAs, and for the UK using Jobcentre Plus administrative data. The relationship holds after controlling for local labor market composition (age, gender, education, occupation, industry shares).

Q: What do vacancy-filling rates look like across locations, and how large are the differences? A: Vacancy-filling rates are lower in low-unemployment (tight) labor markets. In Germany, the monthly probability of filling a vacancy is approximately 50% higher in high-unemployment markets than in low-unemployment markets. Completed vacancy duration ranges from about 35 days in high-unemployment locations to about 65 days in low-unemployment locations — a difference of approximately 85%. The UK data show a strikingly similar elasticity of vacancy-filling rates with respect to unemployment rates to Germany.

Q: What does the formal decomposition reveal about the sources of spatial unemployment differences? A: In a steady-state two-state decomposition, separation rates account for 62.4% (Germany), 72.0% (U.S.), and 64.3% (UK) of cross-sectional unemployment variation, while job-finding rates account for 33.2%, 32.8%, and 35.8%, respectively, with small residuals. This consistently assigns primary importance to separation rates across all three countries.

Q: Why is the primacy of separation rates in the cross section surprising, and what literature does it contrast with? A: The business-cycle literature (Fujita and Ramey, 2009; Shimer, 2012) finds that job-finding rate variation accounts for 50–60% of unemployment fluctuations over the cycle, roughly twice the contribution of separation rates. The spatial pattern is the mirror image: separations dominate. Any credible theory of spatial unemployment must rationalize both patterns simultaneously — a challenge the paper explicitly takes up.

Q: How does the baseline DMP model with endogenous separations generate the spatial patterns? A: Higher-productivity locations feature higher match surpluses. Higher surplus induces more vacancy creation and tighter markets, raising job-finding rates and lowering vacancy-filling rates. Crucially, a higher surplus means idiosyncratic shocks must be more negative to make the joint surplus negative, so fewer matches dissolve — separation rates are lower. The calibrated model reproduces the 32.8% job-finding / ~67% separation decomposition without targeting it (model yields 33.5% job-finding).

Q: What are the calibration targets and key parameter values in the baseline model? A: The model is calibrated monthly to the U.S. economy. Median-unemployment-location targets: separation rate 0.0128, job-finding rate 0.2368, vacancy-filling rate 0.7365. Productivity targets: the 5th-percentile-unemployment location is 4.8% more productive than median, and the 95th-percentile-unemployment location is 3.0% less productive. Key calibrated values include matching elasticity alpha = 0.4711 (equal to worker bargaining power under Hosios), matching efficiency m = 0.4371, vacancy posting cost kappa = 0.3070, and flow nonmarket value z = 0.9072.

Q: What are the two shortcomings of the baseline model, and how does on-the-job search resolve them? A: The baseline model generates a counterfactual upward-sloping Beveridge curve and cannot generate the asymmetry between cross-sectional and business-cycle drivers of unemployment. Adding on-the-job search (fraction phi = 0.12 of employed workers searching, calibrated from Faberman et al., 2017) resolves both. It corrects the Beveridge curve by allowing the model to match the spatial vacancy-unemployment relationship, and it introduces procyclical job-to-job mobility that amplifies the cyclical response of job-finding rates while dampening cyclical separation rate variation.

Q: How do job-to-job transition rates differ across space versus over the business cycle, and why does this matter? A: Job-to-job rates are virtually constant across the cross-section of local labor markets (the extended model is calibrated to match this). But they are strongly procyclical — high in booms, low in recessions, about as volatile as job-finding rates over the cycle. In a boom, more employed workers search, spurring vacancy creation, which raises both vacancy-filling probability (making vacancies easier to fill) and job-finding probability for the unemployed, amplifying the cyclical job-finding rate response while muting the cyclical separation rate response.

Q: What does the extended model predict for business-cycle dynamics? A: The model with on-the-job search and aggregate productivity shocks (parameterized following Hagedorn and Manovskii, 2008) generates unemployment and vacancy rates that are an order of magnitude more volatile than productivity — matching the data. Labor market tightness is about twice as volatile as unemployment, as in the data. The Fujita-Ramey decomposition in the model attributes 54.4% of unemployment volatility to job-finding rates, which falls within the empirical range of 50–60%.

Q: What is the paper’s efficiency result and its policy implication? A: Under the Hosios condition (imposed in calibration), the decentralized equilibrium is efficient: job creation and destruction are privately efficient in each market, and free mobility of workers and firms ensures efficient spatial allocation. Therefore, large observed differences in unemployment, tightness, and wages across locations are not evidence of inefficiency. The relevant signal for policy is not deviation from the national average but deviation from the model’s location-specific prediction conditional on productivity. Locations where data deviate from model predictions are candidates for policy intervention.

Q: Do the spatial patterns survive controls for worker and firm composition? A: Yes. The authors regress labor market tightness and vacancy-filling rates on local unemployment rates and a full set of composition controls (age, gender, education, occupation, and industry shares) derived from the IAB microdata for Germany, along with year fixed effects. The relationship between local unemployment and both tightness and job-filling rates remains highly statistically and economically significant after these controls, for both Germany and the U.S.

Q: How does the model handle wages and cost of living, and does it match the data? A: Wages are determined by state-contingent generalized Nash bargaining with worker bargaining power eta. Cost-of-living differences are backed out as the values needed to sustain the spatial equilibrium (Rosen-Roback). Neither wages nor costs of living are calibration targets in the cross section, yet the model closely matches the empirically observed wage gradient across local labor markets and the negative correlation between cost of living and local unemployment (using Economic Policy Institute Family Budget Calculator data).

Labor market tightness: The ratio of vacancies posted in a local labor market to the number of unemployed workers in that market; the paper documents that tightness is systematically higher (more vacancies per unemployed worker) in lower-unemployment locations across all three countries.

Job-separation rate (EU rate): The share of employed workers who transition from employment to unemployment in a period; in the paper’s framework, this is endogenously determined by the idiosyncratic match productivity threshold below which the joint match surplus turns negative, and it is the primary driver of spatial unemployment differences (accounting for roughly two-thirds of cross-sectional variation).

Job-finding rate (UE rate): The share of unemployed workers who transition from unemployment to employment in a period; in the paper’s framework, this is higher in tighter (lower-unemployment) markets, but accounts for only roughly one-third of spatial unemployment variation — the opposite of its dominant role in business-cycle fluctuations.

Spatial Beveridge curve: The cross-sectional relationship between vacancy rates and unemployment rates across local labor markets; in the data it is downward sloping (low-unemployment locations have both high vacancies and low unemployment), which the baseline model fails to capture but the extended model with on-the-job search reproduces.

Endogenous separation threshold: The location-specific minimum idiosyncratic match productivity below which the joint match surplus becomes negative and the worker-firm pair dissolves; this threshold is lower (tolerates a wider range of idiosyncratic shocks) in higher-productivity locations because the average surplus is larger, generating lower separation rates in more productive locations.

Spatial equilibrium (Rosen-Roback): The equilibrium condition in which differences in local costs of living adjust to make workers and firms indifferent across locations, sustaining persistent productivity-driven differences in wages and unemployment as equilibrium outcomes rather than disequilibrium phenomena.

Procyclical on-the-job search: The mechanism by which the fraction of employed workers actively searching — and thus the rate of job-to-job transitions — is approximately constant across the cross-section of local labor markets but strongly procyclical over the business cycle. This asymmetry is the key to reconciling why job-finding rates drive business-cycle unemployment variation while separation rates drive spatial unemployment variation.

Hosios condition: The parametric restriction equating the unemployment elasticity of the matching function (alpha) and the workers’ Nash bargaining weight (eta); when satisfied, job creation is efficient in every local labor market. The paper imposes this condition deliberately to demonstrate that the decentralized equilibrium is efficient despite large spatial differences in outcomes.

The housing wealth effect: Quasi-experimental evidence

Mon, 01 Jan 0001 00:00:00 +0000

This paper estimates a causal housing wealth effect on consumption using a quasi-natural experiment in Stockholm, Sweden. The identification exploits an unanticipated political decision — announced in September 2007 — to renew the operating contract of Bromma Airport through 2038, reversing a long-standing expectation of closure by 2011. Because the decision resulted from opaque political bargaining and was widely characterized as a political coup by opposition parties, the announcement was genuinely unexpected. The negative externality of continued airport operations (primarily aircraft noise exceeding 70 decibels within a mapped contour) capitalized locally into house prices within one quarter of the announcement. Using difference-in-differences on all single-family house transactions in Stockholm Municipality from 2004 to 2012, the authors estimate a house price decline of 19.4 percent for dwellings within 1,000 meters of the noise contour relative to those farther away (t-statistics above 5; robust to control variables and sample period). Co-op apartment prices show no statistically significant response, consistent with greater structural noise insulation in multi-story concrete buildings.

The consumption outcome is new car purchases, observed at quarterly frequency in a registry-based household panel covering all Stockholm residents, with balance sheet information (loan-to-value ratios, bank deposits, mortgage types) and GIS-located residences. The paper focuses on the intensive margin — the log value of new cars purchased conditional on a purchase — since no effect is found on the extensive margin (probability of buying). A two-sample IV approach yields a short-run elasticity of 0.39: homeowners near the noise contour reduce the value of new cars purchased by 7.7–8.5 log points relative to homeowners farther away. Converting to a marginal propensity for expenditures (MPX): conditional on purchasing a new car, the car MPX is 2.5 cents per dollar of housing wealth lost; scaling by the annual new-car purchase rate of 0.049 per household yields an aggregate new-car MPX of 0.12 cents per dollar per year. Including a symmetry assumption for used cars raises the overall car MPX to 0.38 cents per dollar per year.

Heterogeneity analysis reveals that the collateral channel dominates the pure wealth channel. Homeowners with loan-to-value ratios above 50 percent respond almost twice as strongly as those below (elasticities of 0.526 versus 0.269). Homeowners with below-median bank deposits respond with an elasticity of 0.694, roughly five times larger than those with larger deposits. The financing data show that 47 percent of a new car’s value is financed with credit on average, of which 71 percent takes the form of mortgage debt; however, households with high LTV ratios borrow one-third less per dollar of car value, almost entirely through reduced mortgage use.

A calibrated life-cycle model (quarterly, ages 30–85, Cobb-Douglas preferences over non-durables and cars, long-term fixed-rate mortgage, adjustment costs for cars and mortgages, information friction) replicates the empirical findings. In simulation, a 19.4 percent permanent house-price shock reduces new car values purchased by 6.1 log points on average over the first four quarters, implying an elasticity of 0.31 and a new-car MPX of 0.20 cents per dollar — close to the empirical 0.12 cents and within the 95 percent confidence interval. The model decomposes the response: the collateral effect accounts for 93 percent of the car MPX and 83 percent of the total MPX in the first four quarters; the pure wealth effect accounts for the remainder. The model further shows that full information awareness would roughly double the one-year response, and that smaller shock magnitudes, shorter measurement windows, and crisis-era credit conditions (where more households are already at borrowing limits) each amplify estimated MPXs — helping account for the wide range of estimates (0.12 to 2.3 cents per dollar) in prior literature.

The identification is validated by dose-response monotonicity with distance to the noise contour, placebo tests showing no response for apartment owners or renters, and absence of income effects or differential moving behavior in the treatment group.

Q: What is the quasi-experiment and why is it well-suited for identifying housing wealth effects? A: The Stockholm municipality unexpectedly renewed Bromma Airport’s operating contract through 2038 in September 2007, reversing a broadly held expectation that the airport would close by 2011. The decision emerged from closed-door political negotiations and was denounced as a political coup by opposition parties, making it genuinely unanticipated. Because the shock is geographically contained within the airport’s noise contour, it is unrelated to macroeconomic conditions and unlikely to generate general equilibrium feedback. The authors also verify that no differential income effects, tax changes, or other policies affected the treatment versus control groups over the study window.

Q: How large is the estimated house price effect, and how precisely is it measured? A: Dwellings within 1,000 meters of the noise contour experienced a price decline of 19.4 percent relative to dwellings farther away (baseline estimate, longer sample period). The estimate is highly significant with t-statistics above 5 in all specifications and is robust to the inclusion of rich property-level controls; adding controls changes the pre-crisis estimate only trivially (from -21.4 to -21.3 percent). Co-op apartment prices show no statistically significant response across all specifications, consistent with better structural insulation of multi-story concrete buildings.

Q: What is the main consumption response finding? A: Homeowners near the noise contour reduce the log value of new cars purchased by 7.7–8.5 log points relative to homeowners farther away (reduced form, intensive margin). There is no detectable effect on the extensive margin — the probability of purchasing a new car changes by only 0.029 percentage points per quarter against a baseline of approximately 1.2 percent per quarter. Two-sample IV yields an elasticity of 0.39 (statistically significant at 1 percent), meaning a 1 percent decline in house prices leads to a 0.39 percent reduction in new car values among purchasers.

Q: What does the elasticity of 0.39 imply for the marginal propensity to spend on cars? A: Conditional on purchasing a new car, the car MPX is 2.5 cents per dollar of housing wealth lost (calculated as 0.393 × 19.4% × SEK 250,000 average car value, divided by SEK 774,060 housing wealth loss). Scaling by the annual new-car purchase frequency of 0.049 per household yields an aggregate new-car MPX of 0.12 cents per dollar per year. Assuming an equal response for used cars, the overall car MPX is 0.38 cents per dollar per year. These estimates are substantially smaller than Mian et al. (2013)’s 1.8–2.3 cents per dollar, a discrepancy the model helps explain.

Q: What is the role of the loan-to-value ratio in shaping the consumption response? A: Homeowners with LTV ratios above 50 percent respond almost twice as strongly (elasticity 0.526) as those with LTV below 50 percent (elasticity 0.269). The financing data confirm the mechanism: on average 71 percent of car-purchase borrowing takes the form of mortgage debt, but households with high LTV ratios borrow one-third less per dollar of car value, with the difference almost entirely attributable to reduced mortgage use. This pattern is consistent with binding borrowing constraints preventing high-LTV households from extracting home equity for collateral.

Q: What is the role of liquid savings (bank deposits) in the response? A: Homeowners with bank deposits below the median respond with an elasticity of 0.694, roughly five times larger than homeowners with larger deposits (elasticity approximately 0.139). This heterogeneity is consistent with deposits serving as a buffer stock that allows wealthier households to smooth consumption without altering borrowing behavior after a wealth shock.

Q: What does the quantitative model find about the relative importance of the collateral channel versus the pure wealth effect? A: In the first four quarters following the shock, the collateral effect accounts for 93 percent of the car MPX response and 83 percent of the total expenditure MPX; the pure wealth effect accounts for only 7.5 percent of car MPX and 19 percent of total MPX over the same horizon. Over a longer horizon of 20 quarters, the collateral channel remains dominant at 69 percent of the car baseline, while the wealth effect rises to 32 percent. For non-durable consumption, the short-run collateral effect is 81 percent and the wealth effect is 19 percent.

Q: How does the model match the empirical estimates? A: Simulating a permanent 19.4 percent house-price shock for 200,000 household pairs, the model produces a 6.1 log point average reduction in new car values over the first four quarters, corresponding to an elasticity of 0.31 and a new-car MPX of 0.20 cents per dollar. The empirical estimate is 0.12 cents, and the model value falls within the empirical 95 percent confidence interval. The model also replicates the pattern of no extensive-margin response in the short run and a gradual build-up in the non-durable consumption response (maximum elasticity of 0.079 reached only after ten quarters).

Q: Why is the short-run response concentrated in cars rather than non-durables? A: The paper establishes an intertemporal smoothing mechanism for durables analogous to McKay and Wieland (2021): households delay or bring forward lumpy durable purchases in response to shocks to borrowing capacity. Although cars represent only 5.5 percent of total consumption in the model (Cobb-Douglas expenditure share), they account for 45–72 percent of the total expenditure response in the first four quarters after the house-price shock. The non-durable consumption response builds slowly and reaches its maximum after about ten quarters.

Q: What factors does the model identify as explanations for the wide range of MPX estimates across studies? A: Three factors are identified. First, shock magnitude: larger shocks produce smaller partial-equilibrium MPXs because more households hit borrowing constraints; across shock sizes from -30 to +20 percent, car and total MPXs can range from 1 to 2 cents per dollar. Second, measurement period: short-run (1-year) MPXs exceed long-run (3-year) MPXs, especially for durable goods. Third, the state of the economy: in a crisis-era bust following credit-fueled boom, many more households are constrained when prices fall, amplifying MPXs; Guerrieri and Iacoviello (2017) report car elasticities of 0.24 in the boom phase and 0.49 in the bust phase of the US financial crisis.

Q: What is the role of the information friction in the model? A: Because the quasi-experiment occurred in “normal times” just before the global financial crisis became acute, the authors argue that households were not immediately aware of the house-price shock; they only update their perceived housing wealth when they attempt to adjust their mortgage, trade cars, or receive a random information update. Under full information awareness, the one-year MPX would be approximately twice as large, and the one-year total MPX could be as much as three times as large (with a car MPX of 3 cents per dollar and total MPX well above 6 cents per dollar under full information with small positive shocks). The information friction thus attenuates the estimated MPX relative to a world of full information.

Q: What placebo and robustness tests support the identification? A: Co-op apartment owners show no statistically significant price or consumption response, consistent with their structural insulation from aircraft noise. Renters also show no consumption response. The dose-response test confirms a monotone relationship between distance to the noise contour and both house price and car expenditure effects. Income effects are absent (Figure B.2), and there is no differential probability of moving in either the short or long run. Tax reforms benefited both groups equally and had already been announced before the quasi-experiment.

Q: How does this study’s identification strategy compare to instrumental variable approaches using housing supply elasticity? A: Supply elasticity IV approaches (Mian et al. 2013; Aladangady 2017; Kaplan et al. 2020) rely on regional variation in construction constraints and must assume that consumption demand factors are either observed or uncorrelated with supply elasticity — an assumption critiqued by Davidoff (2016). This paper’s identification exploits an exogenous change in a local negative externality, yielding a geographically granular shock unrelated to macroeconomic conditions and free from general equilibrium feedback. The result is interpretable as a partial equilibrium housing wealth effect in the sense of Berger et al. (2018) and Guren et al. (2020).

Housing wealth effect: The causal effect of a change in housing wealth on household consumption expenditure, decomposed in this paper into a pure wealth channel (change in lifetime resources) and a collateral channel (change in borrowing capacity via home equity).

Marginal propensity for expenditures (MPX): The change in spending per dollar change in housing wealth; distinct from the marginal propensity to consume (MPC) because spending on durables may be lumpy and differ from the flow of consumption services. The paper distinguishes the car MPX conditional on purchase (2.5 cents per dollar), the aggregate new-car MPX (0.12 cents per dollar per year), and the total expenditure MPX.

Collateral channel: The mechanism by which a decline in house prices reduces homeowners’ borrowing capacity — because the house serves as collateral for mortgage debt — thereby tightening credit constraints and reducing spending, independent of any change in permanent income. The model assigns 93 percent of the short-run car MPX to this channel.

Two-sample instrumental variable (TSIV): The empirical strategy of Angrist and Krueger (1992) used here to estimate the consumption elasticity: the house-price first stage is estimated in one sample (transaction data), and the reduced-form consumption effect is estimated in a second sample (household panel), with the IV elasticity computed as the ratio.

Information friction: The assumption in the model that households do not immediately observe the spatial divergence in house prices; they update their perceived housing wealth only when they attempt to adjust their mortgage, trade a durable good, or receive a random information shock. This friction attenuates the short-run consumption response and is calibrated to “normal times” conditions.

Noise contour: The geographic boundary around Bromma Airport within which properties are regularly exposed to noise levels of at least 70 decibels, as adjudicated by the Swedish Land and Environment Court. Properties within 1,000 meters of this contour define the treatment group.

Intertemporal smoothing of durables: The pattern, documented in the model and complementary to McKay and Wieland (2021), whereby households adjust lumpy durable purchases (cars) rapidly in response to changes in borrowing capacity, so that durables account for a disproportionately large share of the total expenditure response in the short run (45–72 percent in the first four quarters despite a 5.5 percent Cobb-Douglas expenditure share).

The price of intelligence: How should socially-minded firms price and deploy AI?

Mon, 01 Jan 0001 00:00:00 +0000

Leading AI firms such as OpenAI and Anthropic publicly claim dual mandates of profit and social welfare, raising the question of whether—and how—a social mandate should change their pricing and deployment decisions. This paper provides a framework to answer this question, deriving a Modified Lerner Rule for socially minded AI firms that extends the standard profit-maximizing Lerner Rule to incorporate incentives for aggregate efficiency, distributional concerns, and labor market stability. Using U.S. data on 525 detailed occupations, the paper evaluates optimal pricing and deployment paths for an AI capable of replacing human labor in each job at 50% of the cost. The main finding is that a welfarist firm (one that values profits and social welfare) should price closer to marginal cost because, for the jobs considered, efficiency gains outweigh distributional concerns—AI does not primarily displace low-income workers. A conservative firm focused on labor market stability should price above the profit-maximizing level in the short run, but not in the long run. The paper concludes that the most pro-social course of action for AI firms with market power is to refrain from exercising that power, and that proposals to tax AI to protect labor markets miss the counteracting role of market power.

In depth

Q1. What is the Modified Lerner Rule and what motives does it capture?

The Modified Lerner Rule states (P − MC)/P = M/ε, where ε is the demand elasticity and M is a modifier that summarizes the motives of the socially minded firm; M = 1 corresponds to the standard profit-maximizing Lerner Rule. The modifier M reflects four distinct considerations: (1) profit motives push M toward 1; (2) aggregate efficiency considerations push M toward 0 (marginal-cost pricing, which maximizes the “size of the pie”); (3) distributional concerns (who benefits from AI) can be positive or negative depending on whether AI substitutes for high- or low-income workers; and (4) the incentive to minimize labor market disruptions pushes M above 1 in the short run, because the cost of labor disruption is higher while workers are still adjusting, but not in the long run. The formula is derived in a general equilibrium model where the AI firm has a monopoly over an AI capable of replicating human skills.

Q2. What does the welfarist case imply for pricing?

A firm that values both profits and aggregate social welfare should price closer to marginal cost than the profit-maximizing firm, because for all 525 occupations considered, the aggregate efficiency gains from AI adoption outweigh the distributional costs. This finding reflects the structure of AI’s labor market effects: since AI does not primarily displace low-income workers in the US occupational data used, distributional concerns do not push toward restricting AI access. The welfarist firm therefore faces a dominant efficiency motive to expand access by pricing down toward marginal cost, accepting lower profits in exchange for greater welfare gains from AI adoption.

Q3. What does the conservative case imply?

A firm focused solely on labor market stability should price above the profit-maximizing level in the short run, because restricting AI deployment reduces the speed of worker displacement; but this above-profit-maximizing pricing is optimal only temporarily, and converges toward profit-maximizing pricing in the long run as workers adjust. The intuition is that the cost of disrupting the labor market is highest when workers have not yet adjusted—their human capital is not yet redeployed—so a conservative firm acts as a gradual deployer. This conservative pricing is distinct from the welfarist case: the conservative motive restricts access more than a welfarist mandate, since it is willing to sacrifice efficiency to slow disruption.

Q4. Why does the paper argue against taxing AI?

The paper argues that proposals to tax AI firms to protect workers from displacement overlook the fact that AI firms may already exercise significant market power, which protects workers by restricting AI supply below the efficient level. Adding a tax on top of an already-restricted supply would harm consumers (who face high AI prices and limited access) without providing meaningful additional protection for workers (since output is already suppressed by market power). The paper’s analysis implies that the first-order social priority is to have AI firms refrain from exercising their market power—by pricing closer to marginal cost—rather than further restricting supply through taxation.

Key concepts

Modified Lerner Rule : (P − MC)/P = M/ε, where M captures a socially minded firm’s weighting of profit, aggregate efficiency, distributional, and stability motives; the paper’s key pricing formula, derived from a GE model with a monopoly AI firm.

welfarist vs. conservative firm : two polar cases: the welfarist firm maximizes a weighted sum of profits and aggregate welfare (implying near-marginal-cost pricing); the conservative firm prioritizes labor market stability (implying above-profit-maximizing pricing in the short run to slow displacement).

labor disruption cost : the welfare cost to workers of being displaced by AI, which is higher in the short run when workers must reallocate across jobs or sectors and lower in the long run after adjustment; the paper’s formal treatment of this cost motivates the conservative firm’s gradual deployment strategy.

The role of wage expectations in the labor market

Mon, 01 Jan 0001 00:00:00 +0000

This paper develops a Mortensen-Pissarides (DMP) search and matching model with internally rational (IR) agents who hold subjective beliefs about wages rather than perfect knowledge of the Nash bargaining outcome. The standard DMP model struggles with two empirical regularities: high volatility of U.S. labor market variables relative to productivity, and a near-zero correlation between labor market tightness and productivity post-1989. The IR model significantly improves alignment with U.S. labor market data relative to the standard rational expectations benchmark, by generating a self-referential belief mechanism: shifts in beliefs about the future returns to labor affect current wages, which agents use to update beliefs. Wage expectations in the model are consistent with European Commission professional forecasters data, and an econometric test rejects the rational expectations null hypothesis for survey real wage expectations.

In depth

Q1. What is internal rationality and how does it differ from standard rational expectations?

Internal rationality (IR) means agents know all internal aspects of their optimization problem and maximize their objectives given their knowledge, but lack perfect information about the equilibrium wage function that emerges from Nash bargaining; they therefore hold subjective beliefs about wages. Under standard rational expectations, workers and firms know the exact wage function from Nash bargaining. Under IR, they have limited foresight about the outcome of wage negotiations and use a subjective model to form wage expectations. This is a small but disciplined departure from RE: the paper considers belief systems implying only a small deviation from rational expectations that match aspects of survey wage expectations.

Q2. What is the empirical failure of the standard DMP model that motivates the paper?

The standard DMP model fails on two counts: it cannot reproduce the high observed volatility of unemployment, vacancies, and market tightness relative to productivity, and it cannot generate the near-zero post-1989 correlation between productivity and labor market tightness. The first failure—the Shimer (2005) puzzle—has attracted extensive research, but the near-zero tightness-productivity correlation has been largely neglected. The paper shows that allowing for small deviations from rational expectations in the form of internal rationality resolves both puzzles simultaneously.

Q3. What is the self-referential belief mechanism and how does it generate extra dynamics?

The model has a self-referential mechanism: shifts in beliefs about future returns to labor affect current wages, and agents use realized wages to update their beliefs about future wages; this creates an additional dynamic source beyond technology shocks that helps match the data. When firms and workers revise beliefs about future wages upward, current wages rise through the Nash bargaining outcome (since reservation values of both parties shift); this realization then feeds back into updating beliefs, generating wage and employment dynamics not tied to current productivity. This mechanism provides a microfoundation for previous adaptive learning models of unemployment.

Q4. What is the empirical validation of the model’s wage expectations?

Wage expectations in the IR model are validated against survey data from European Commission professional forecasters, and an econometric test rejects the rational expectations null hypothesis for real wage expectations from survey data. The consistency between model-implied and surveyed wage expectations provides external validation for the IR departure from RE, showing that the subjective beliefs assumed in the model correspond to beliefs actually held by professional forecasters rather than to arbitrary deviations.

Key concepts

internal rationality (IR) : a bounded rationality concept in which agents fully optimize given their beliefs and knowledge of their own decision problem, but lack perfect knowledge of equilibrium objects (here, the wage function emerging from Nash bargaining); allows small, disciplined deviations from rational expectations. DMP model : the Mortensen-Pissarides-Diamond search and matching model; the standard theory of equilibrium unemployment; criticized for generating insufficient labor market volatility relative to productivity (the Shimer puzzle) and for counterfactual positive tightness-productivity correlation. belief shock : an exogenous shift in agents’ subjective beliefs about future wages; generates employment and wage dynamics independently of current productivity shocks via the self-referential mechanism; introduced as an additional structural shock in the IR-DMP model.

Tokenomics: Optimal monetary and fee policies

Mon, 01 Jan 0001 00:00:00 +0000

The rapid proliferation of cryptocurrency tokens—roughly 10,000 outstanding with a total market capitalization around $3 trillion as of early 2024—raises new questions about the design of token monetary policy and fee structures. This paper makes two contributions. Empirically, using supply histories for approximately 2,000 tokens, it documents three systematic patterns: average token money growth rates decline with age and stabilize at about 0.2% per month; long-run money growth rates and convergence speeds are positively correlated across tokens in the cross-section; and tokens more widely held by retail investors have relatively lower long-run money growth rates and convergence speeds. Theoretically, the paper derives optimal issuance and fee policies for a profit-maximizing issuer in a dynamic model where commitment matters, showing that a fully committed (Ramsey) issuer who maximizes profits after the initial period makes choices that maximize the total utility value of all tokens, that without any commitment no equilibrium with a positive token price exists unless fees are charged, and that under partial commitment issuers with higher commitment credibility optimally choose lower long-run money growth rates and fee ratios.

In depth

Q1. What are the three empirical facts about crypto monetary policies?

Fact 1: the average money growth rate across the ~2,000 tokens declines with cohort age and stabilizes at approximately 0.2% per month, with more recent cohorts converging faster to their long-run growth rates. Fact 2: in the cross-section of tokens, the estimated long-run money growth rate and the speed of convergence to it are positively correlated—tokens that will eventually have higher money growth also converge more quickly to that level. Fact 3: tokens whose circulating supply is widely distributed among retail investors (measured by the proportion of wallet addresses holding less than 0.1% of total supply) have both lower long-run money growth rates and lower convergence speeds. Together these facts suggest that the degree of decentralization of token ownership systematically influences the choice of monetary policy.

Q2. What are the main theoretical results about commitment?

Without any commitment, no equilibrium with a positive token price can be sustained if the issuer cannot charge user fees; fees create credibility by giving a Markov-perfect issuer an incentive to restrict future token issuance (to collect fees on legacy token holders), which supports a positive price. At the other extreme, with full commitment the Ramsey issuer maximizes profits subject to the full sequence of resource constraints, and a central analytical result is that at steady state the Ramsey issuer’s profit-maximizing choices are equivalent to maximizing the total utility value of all tokens outstanding. This equivalence—profit maximization = welfare maximization for token holders—holds because commitment prevents the issuer from diluting legacy holders; under full commitment, the issuer has no incentive to deviate from the policy that maximizes total token value.

Q3. What does partial commitment imply for policy design?

Under partial commitment (modeled as a probability of sticking to a given policy rather than re-optimizing), issuers with higher commitment probability optimally choose lower long-run money growth rates and reduce both the money growth rate and the fee ratio more slowly over time. This is because higher commitment credibility raises the present value of legacy tokens (users expect the issuer to honor its policy), which makes it optimal to extract less seigniorage and fewer fees in each period while sustaining a higher token price. The model is analytically solvable under partial commitment despite rich economic mechanisms, and the results help interpret Fact 3: tokens with more decentralized ownership (higher effective commitment due to governance constraints) exhibit lower money growth.

Q4. How do the model’s predictions compare with the Bitcoin and Ethereum cases?

Bitcoin exemplifies near-full commitment: its supply schedule is essentially deterministic and hard-coded, resembling the Ramsey policy, though the paper notes a non-zero probability of a fork that could alter the policy. Ethereum exemplifies frequent policy changes (the transition from proof-of-work to proof-of-stake altered issuance and burn rules significantly). Discretionary platforms like MakerDAO, which allow issuer discretion over token supply, more closely resemble the Markov-perfect benchmark. The paper’s framework covers this entire spectrum and predicts that tokens with more commitment (closer to Bitcoin) should have lower long-run money growth and slower convergence—consistent with the empirical facts.

Key concepts

token monetary policy : the issuer’s choice of the rate at which new tokens are minted over time (the money growth rate) and the fees charged per transaction; the paper shows these jointly determine the value of a token and the issuer’s profit.

Ramsey policy for tokens : the full-commitment profit-maximizing policy for a token issuer; a key result is that the Ramsey issuer’s profit-maximizing choices, after the initial period, are equivalent to maximizing the total utility value of all tokens.

partial commitment : a probabilistic commitment technology in which the issuer maintains a given policy with some probability and re-optimizes with the complementary probability; the paper uses this to model the spectrum between Bitcoin (high commitment) and more discretionary platforms.

Turbulent business cycles

Mon, 01 Jan 0001 00:00:00 +0000

Firm-level evidence shows that recessions are characterized not just by aggregate downturns but by a sharp rise in turbulence—a reshuffling of firms’ productivity rankings in which high-productivity firms are less likely to maintain their relative standing. This paper documents four stylized facts about the macroeconomic and cross-sectional effects of turbulence (measured as one minus the Spearman rank correlation of firm-level TFP between adjacent years in Compustat data): turbulence is countercyclical; increases in turbulence reallocate labor and capital from high- to low-productivity firms; turbulence is negatively correlated with aggregate manufacturing TFP and the aggregate stock market; and an increase in turbulence is associated with persistent declines in real GDP, consumption, investment, and employment. To explain the mechanism, the authors build a real business cycle model with heterogeneous firms and financial frictions: when turbulence rises, high-productivity firms’ expected equity values fall because their productivity is less likely to persist, which tightens their borrowing constraints relative to low-productivity firms, inducing reallocation that reduces aggregate TFP. Crucially, turbulence differs from uncertainty shocks because it changes both the conditional mean and variance of the firm productivity distribution, enabling it to generate synchronized recessions with declining aggregate activity.

In depth

Q1. How is turbulence measured and how does it differ from uncertainty?

Turbulence is measured as one minus the Spearman rank correlation (ρₜ) of firm-level total factor productivity between adjacent years using Compustat data; a low correlation indicates more churning of productivity rankings, so 1 − ρₜ rises in recessions. The authors use an instrumental variable approach to correct for attenuation bias from measurement error in firm-level TFP, following Bloom et al. (2018) for the baseline construction. The conceptual distinction from uncertainty is that uncertainty shocks only raise the conditional variance of the productivity distribution while leaving the conditional mean unchanged. A turbulence shock changes both: it makes the conditional mean of future productivity lower for currently high-productivity firms and higher for currently low-productivity firms, thereby inducing reallocation from high to low producers and generating first-moment effects on aggregate output that pure uncertainty shocks cannot produce.

Q2. What are the empirical facts about turbulence, and how are they established?

The paper documents four facts using a vector autoregression with turbulence orthogonalized against uncertainty and other aggregate shocks: (1) turbulence is countercyclical, rising sharply in recessions; (2) an increase in turbulence reallocates labor and capital from high- to low-productivity firms, an effect that is amplified by financing constraints; (3) turbulence is negatively correlated with aggregate manufacturing TFP and aggregate stock market value; and (4) turbulence shocks generate persistent declines in GDP, consumption, investment, and employment. The reallocation effects in fact (2) remain significant after controlling for the confounding effects of recessions and uncertainty, and the amplification by financing constraints is separately identified.

Q3. What is the model mechanism through which turbulence drives recessions?

In the model, firms produce using capital and labor subject to idiosyncratic productivity and borrowing constraints tied to expected equity value; when turbulence rises, high-productivity firms are less likely to remain productive, reducing their expected equity value and tightening their borrowing constraints relative to low-productivity firms. This differential tightening induces reallocation of labor and capital toward low-productivity firms, reducing aggregate TFP. The feedback through equity values and collateral constraints amplifies the reallocation and generates aggregate-level recessions with synchronized declines in activity. The mechanism is distinct from models in which all firms face symmetric uncertainty shocks: turbulence creates differential effects by firm productivity level.

Q4. How does the model match the observed macroeconomic dynamics?

The calibrated model replicates the empirical dynamics: it generates the observed reallocation from high- to low-productivity firms, declines in aggregate TFP and stock market value, and persistent contractions in GDP, consumption, investment, and employment following a turbulence shock. The financial frictions play a quantitatively important role in amplifying the reallocation effects, consistent with the empirical finding that financing constraints amplify the cross-sectional reallocation documented in fact (2).

Key concepts

turbulence : the rate of churning in firms’ productivity rankings, measured as one minus the Spearman rank correlation of firm-level TFP between adjacent years; distinct from uncertainty in that it changes both the conditional mean and variance of the productivity distribution.

reallocation channel : the mechanism through which turbulence depresses aggregate TFP by shifting labor and capital from high- to low-productivity firms, amplified by tighter credit constraints on high-productivity firms whose expected equity value falls when productivity persistence declines.

Unconventional monetary policy spillovers and the (in)convenience of Treasuries

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

The paper asks why unconventional monetary policy (UMP) spillovers from the European Central Bank (ECB) to the U.S. Treasury yield curve vary so substantially over time, and whether the time-varying “convenience” of Treasuries — their non-pecuniary premium as the world’s preeminent safe asset — can explain that variation. The core claim is that a declining convenience yield on Treasuries makes them more substitutable with other safe sovereign bonds, thereby amplifying the portfolio-balance channel through which foreign large-scale asset purchases (LSAPs) depress U.S. term premia.

Data and Methodology

The authors use high-frequency identification of ECB monetary policy surprises following Altavilla et al. (2019), defined as the first principal component of intraday changes in 1-, 3-, 6-, 12-, and 24-month euro OIS rates plus 5- and 10-year German and French bond yields, measured in the 10-20 minute window bracketing each ECB decision press conference. Surprises are normalized so that one unit raises the 24-month euro OIS by 10 basis points. The sample runs from March 2001 to December 2023, covering approximately 265-268 ECB announcement dates. U.S. zero-coupon Treasury yields come from Gürkaynak et al. (2007); the yield is decomposed into an expected short-rate path and a term premium using the shadow-rate term structure model (SRTSM) of Wu and Xia (2016). The convenience yield on Treasuries is proxied by the spread between the 10-year Treasury yield and the maturity-matched overnight index swap (OIS) rate, so that a positive (and rising) spread indicates declining convenience. Structural breaks in the convenience yield are identified via the Bai-Perron test.

The empirical strategy has three main components: (i) 700-business-day rolling regressions of Treasury yields and their decomposition on ECB surprises to document time variation; (ii) interaction regressions (following equation 5/9) that condition the ECB shock effect on lagged convenience-yield proxies, net Treasury supply, intermediary balance-sheet constraints (proxied by G10 covered-interest-parity deviations), and inflation-anchoring indicators; and (iii) a policy decomposition following Swanson (2021) that decomposes ECB surprises into “target,” “forward guidance,” and “LSAP” components. These empirical findings are rationalized in a two-country preferred-habitat model, extending Gourinchas, Ray, and Vayanos (in press) (GRV) by allowing the demand-slope parameter governing investor price elasticity to vary with the convenience yield. Functional derivatives and Malliavin calculus are used to characterize dynamic impulse responses to elasticity shifts.

Main Findings with Quantitative Magnitudes

Rising spillovers post-GFC, concentrated at long maturities. Rolling regressions show that ECB-to-U.S. spillovers were statistically indistinguishable from zero during the conventional-policy era but grew significantly after 2010, well before the ECB’s Expanded Asset Purchase Programme (EAPP) launched in 2015 and before “whatever it takes” (summer 2012). Spillovers began to dissipate not when ECB purchases ended (March 2022) but when the Fed announced tapering in November 2021 — consistent with the convenience channel rather than mere co-movement in LSAP volumes. A Bai-Perron test detects five structural breaks in the relationship between ECB surprises and 10-year Treasury yields.
Term-premium dominance, amplified by inconvenient Treasuries. At average convenience-yield levels, a one-standard-deviation ECB loosening shock (lowering the 24-month euro OIS by 10 basis points) reduces the 10-year Treasury yield by approximately 4.4 basis points (column 5, Table 2). When the Treasury convenience yield is one standard deviation below its historical average (i.e., Treasuries are less convenient), the spillover increases by 1.64 basis points, making the total effect approximately 6.1 basis points — a shift from the bottom 20th to below the 12th percentile of the unconditional distribution of daily Treasury yield changes. This amplification operates entirely through the term premium; the expected path of short rates shows no statistically significant sensitivity to the convenience yield interacted with ECB shocks.
Net Treasury supply amplification. Conditional on the net publicly available U.S. debt stock (Treasury debt less Fed holdings, as a percent of GDP), a one-standard-deviation ECB shock at average supply reduces the 10-year yield by approximately 3.9 basis points; when net supply is one standard deviation above its historical average (approximately 7.6 percentage points of GDP), the same shock generates a 5.35 basis-point decline — a 50-percent amplification (Table 5, column 5).
Intermediary constraints amplification. Conditioning on the first principal component of G10 CIP deviations against the dollar (a proxy for intermediary balance-sheet tightness), a CIP deviation one standard deviation above average amplifies the ECB spillover from approximately 3.9 basis points to 6.2 basis points (Table 7).
Inflation anchoring. Periods when inflation expectations lie outside the interquartile range of the historical distribution are associated with larger spillovers to 10-year Treasury yields, an effect that is statistically significant both above the 75th and below the 25th percentile of expectations, with point estimates of the interaction coefficient reaching approximately 5.0-5.3 basis points (Table 6).
Policy asynchronicity. Spillovers are especially pronounced when the Federal Reserve is tightening while the ECB is easing. The rolling regressions show term-premium spillovers become dominant (relative to expected-path spillovers) post-2014, coinciding with U.S. normalization. The calibrated model shows that, during policy asynchronicity combined with lower convenience, the home short-rate tightening is partially offset by capital inflows induced by foreign QE, with the attenuation especially pronounced at intermediate and long maturities and persistent across multiple periods.
Alternative channels ruled out. Horse-race regressions against the VIX, MOVE index, Economic Policy Uncertainty (EPU) index, Monetary Policy Uncertainty (MPU) index, and 30-day EUR/USD spot variance show none of these candidates displaces the convenience channel. Short-rate-risk decompositions (Bundick et al. 2017) and equity-orthogonal risk premium shocks (Leombroni et al. 2021) cannot explain the post-Taper Tantrum timing pattern of rising term-premium spillovers.

Scope Conditions

All empirical results apply to ECB-to-U.S. spillovers; the paper explicitly leaves Bank of England-to-U.K. Gilt spillovers for future work.
The portfolio-balance amplification through convenience is specific to unconventional monetary policy (LSAP shocks); target and forward-guidance components drive spillovers through different channels (expected short-rate path) and do not exhibit the same convenience-contingent amplification.
The mechanism operates through preferred-habitat investors demanding sovereign-grade credit; the Bund convenience yield does not amplify U.S. spillovers, consistent with Bunds being an imperfect representation of the full portfolio requiring substitution under ECB capital-key-based purchases.

In depth

Q1. How do the authors measure ECB monetary policy surprises, and why do they prefer this measure?

A1: Surprises are the first principal component of intraday changes in 1-, 3-, 6-, 12-, and 24-month euro OIS rates plus 5- and 10-year German and French bond yields, measured from 10-20 minutes pre-announcement to 10-20 minutes post-press conference. This cross-section of yields is preferred because it summarizes shocks to the overall stance of policy both at and away from the effective lower bound, including effects on different parts of the yield curve. The composite measure therefore subsumes both conventional rate actions and unconventional (LSAP, forward guidance) dimensions. Surprises are normalized so one unit raises the 24-month euro OIS by 10 basis points.

Q2. What is the key empirical fact about the timing of spillover emergence and dissipation?

A2: Rolling regressions show ECB spillovers to U.S. Treasury yields became statistically significant when the rolling window began integrating observations starting in approximately 2010 — substantially before the ECB’s EAPP (2015) and even before “whatever it takes” (summer 2012). Moreover, spillovers began to dissipate not when the ECB’s Pandemic Emergency Purchase Programme ended (March 2022) but when the Fed announced tapering in November 2021. This timing pattern is inconsistent with a simple “both central banks doing QE simultaneously” explanation and instead points to the importance of Federal Reserve balance sheet behavior for the convenience of Treasuries.

Q3. How do the authors decompose the Treasury yield, and what does the decomposition reveal about the channel of transmission?

A3: Following standard term-structure decomposition, the n-year yield equals the expected path of short-term rates over the maturity plus a maturity-specific term premium. Rolling regressions on this decomposition show that term-premium spillovers dominate expected-path spillovers, especially post-2014 when the Federal Reserve is out of sync with other advanced economies. Early ECB UMP spillovers showed a more even mix of expected-path and term-premium effects; later spillovers loaded much more heavily on the term premium. This is consistent with the portfolio balance channel — LSAPs remove duration risk and compress term premia, and this effect transmits internationally.

Q4. How is the convenience yield proxied, and why does the paper use this proxy in particular?

A4: The authors use the spread between the sovereign bond yield and the maturity-matched overnight index swap rate (Y − OIS), expressed so that a larger spread (sovereign yield higher than OIS) reflects less convenience. Prior to the GFC, Treasury yields ran below swap rates (negative spread, high convenience); post-GFC, the spread reversed and turned positive, reflecting deterioration in Treasury specialness. This proxy is preferred because it captures the relative convenience as priced by the marginal investors the model focuses on — those with sovereign credit quality preferences and arbitrageurs — rather than broader measures such as the Treasury-to-corporate spread.

Q5. What is the quantitative impact of convenience yield variation on the size of ECB spillovers to U.S. yields?

A5: In the most conservative specification (Table 2, column 5), an ECB loosening shock that lowers 24-month euro OIS by 10 basis points reduces the 10-year Treasury yield by 4.4 basis points when the convenience yield is at its historical average. When the convenience yield falls one standard deviation below average (Treasuries are less convenient), the spillover increases by 1.64 basis points to approximately 6.1 basis points. A one-standard-deviation change in 10-year Treasury yields in the sample is 5.86 basis points; the 4.4 bp response falls in the bottom 20th percentile of unconditional daily yield changes, while the 6.1 bp response falls below the 12th percentile.

Q6. Does the amplification of spillovers from ECB shocks by Treasury inconvenience operate through the term premium or the expected short-rate path?

A6: The amplification operates entirely through the term premium. In Table 2, columns 7 and 8, the interaction coefficient between the ECB shock and the convenience yield proxy is positive and statistically significant for the 10-year term premium but is not statistically different from zero for the expected path of short rates. The authors interpret this as confirming the portfolio balance channel: displaced Bund investors substitute into Treasuries, raising Treasury prices and compressing term premia, with no mechanical connection to market participants’ updating of expected future Federal Reserve policy rates.

Q7. How does net Treasury supply interact with the size of ECB spillovers?

A7: Net U.S. Treasury supply (debt outstanding as a percent of GDP, less Fed holdings) is strongly positively correlated with the swap spread, confirming the link between supply and convenience. Interaction regressions (Table 5) show that a one-standard-deviation ECB shock at average net supply reduces 10-year yields by 3.9 basis points. When net supply is one standard deviation above average (approximately 7.6 percentage points of GDP), the same shock generates a 5.35 basis-point decline — roughly a 50 percent amplification. The point estimates suggest this operates primarily through term premia, though those interaction coefficients are statistically insignificant in the term premium specification.

Q8. How do intermediary balance-sheet constraints relate to Treasury convenience and ECB spillover amplification?

A8: The authors follow Du, Hébert, and Huber (2023) in using deviations from covered interest parity (CIP) among G10 currencies against the dollar as a proxy for the shadow cost of intermediary balance-sheet constraints. When CIP deviations are at historical average, the ECB spillover to 10-year Treasury yields is approximately 3.9 basis points; when CIP deviations are one standard deviation above average, the spillover rises to approximately 6.2 basis points. The authors also use the plausibly exogenous variation from quarter-end “window dressing” (per Correa, Du, and Liao 2020): LSAP-type ECB surprises landing near quarter-end generate larger spillovers to the term premium, and the further into the quarter an announcement occurs, the larger the LSAP shock’s effect on the term premium — consistent with balance-sheet constraints amplifying the portfolio balance channel.

Q9. What is the theoretical model, and what is the key innovation relative to the baseline GRV framework?

A9: The paper extends the two-country preferred-habitat model of Gourinchas, Ray, and Vayanos (in press), in which segmented investors demand bonds of specific maturities and currencies while capital-constrained global arbitrageurs partially bridge the segmentation. The key innovation is allowing the demand-slope parameter α_j(τ) — which in GRV is fixed and governs how inelastic investors are with respect to price — to vary over time as a function of the convenience yield. When Treasuries are special (high convenience), α_H(τ) is large, demand is inelastic, and foreign shocks have limited pass-through. When convenience falls, α_H(τ) shrinks, demand becomes more elastic, investors reallocate more aggressively in response to yield differentials, and U.S. term premia respond more strongly to ECB purchases. Functional derivatives and Malliavin calculus are used to characterize both instantaneous and dynamic amplification effects.

Q10. What does the calibrated model predict about the maturity structure of spillover amplification?

A10: In the calibration exercise (Figure 4), the elasticity perturbation is modeled as a smooth function (transformed Cauchy distribution) centered at the 10-year maturity, and the ECB QE shock is a purchase concentrated at the 5-year maturity amounting to 10 percent of euro-area GDP. The marginal change in the home yield impulse response (the quantity ∂²_{α_H,b} log P^τ_{Hs}) is positive across nearly all maturities and horizons, but is most pronounced around the 5-year maturity and during the first few periods after the shock — where the ECB purchase profile and the demand perturbation are most closely aligned in tenor. Amplification effects are persistent across horizons due to the dynamic multiplier in Theorem 3.1.

Q11. How does the model rationalize the 2019 yield curve inversion?

A11: In August 2019, the 10-year Treasury yield fell below short-term rates despite a robust domestic labor market, while the Fed was raising rates and the ECB remained accommodative. The model’s asynchronicity exercise (Section 3.3) shows that combining a home short-rate increase with ongoing foreign QE and a contemporaneous decline in Treasury convenience produces attenuated or even reversed yield curve responses. More elastic investors facing a flatter demand curve shift into longer-term Treasuries — whose relative yields remain attractive globally — resulting in a yield-curve inversion driven not by recession expectations but by asymmetric monetary policy and a time-varying convenience premium.

Q12. Do alternative explanations — risk sentiment, policy uncertainty, exchange rate volatility — explain the time variation in ECB spillovers?

A12: No. Horse-race regressions in Table 9 condition the ECB shock on lagged VIX, MOVE index, Economic Policy Uncertainty (Baker et al. 2016), Monetary Policy Uncertainty (Husted et al. 2020), and 30-day EUR/USD spot variance. None of these measures displaces the baseline convenience-yield interaction, which remains statistically significant across all specifications. Elevated EPU is associated with smaller spillovers (consistent with uncertainty impairing substitution), but this does not reduce the magnitude or significance of the convenience-yield interaction. Exchange-rate variance does not alter spillover size. A rolling regression decomposing the term premium into a short-rate-uncertainty component (Bundick et al. 2017) and a residual shows the empirical pattern is more consistent with the residual — not the short-rate-volatility channel. An equity-orthogonal risk premium shock (Leombroni et al. 2021) explains some term premium effects in the early GFC period (2008-2012) but cannot rationalize the post-Taper Tantrum pattern of growing term-premium spillovers.

Q13. How does the Swanson (2021) decomposition confirm the portfolio balance channel?

A13: Following Swanson (2021), the authors decompose ECB surprises into a “target surprise” (change in 3-month OIS futures), a “forward guidance surprise” (residual from projecting 24-month futures onto the target surprise), and an “LSAP surprise” (residual from projecting French and German 10-year bond yields onto target and forward guidance). In the full sample (Table 3), LSAP shocks drive spillovers to U.S. yields exclusively at higher maturities and exclusively through the term premium; they have no statistically significant impact on the expected path of short rates. Conditioning LSAP shocks on the convenience yield (Table 4, panel c) shows that it is specifically LSAP-type announcements combined with Treasury inconvenience that generate larger medium- and long-term term-premium spillovers, confirming the portfolio balance mechanism.

Q14. What are the implications for fiscal and monetary policy?

A14: The paper argues that the persistently low long-term rates and yield curve inversions observed between the GFC and the COVID-19 pandemic were driven partly by ECB LSAPs amplified by U.S. quantitative tightening, which increased net Treasury supply, reduced Fed absorption, constrained dealer balance sheets, and lowered Treasury convenience. Simultaneously, U.S. monetary tightening raised short-term rates while ongoing ECB easing depressed long rates, reshaping the yield curve in a manner consistent with the model. More broadly, the effectiveness of conventional domestic monetary policy tightening is attenuated when the convenience yield is compressed and foreign QE is ongoing — not because the short rate fails to move, but because more elastic investors reallocate around it. This suggests policy asynchronicity, combined with declining convenience, creates a constraint on monetary independence that may require more forceful or coordinated policy action.

Key Concepts

Convenience yield (Treasury convenience premium) The non-pecuniary value that investors derive from holding U.S. Treasury securities over and above cash flows and credit risk — arising from their deep and liquid markets, broad regulatory compatibility, high-quality collateral function, and reserve-currency status. Operationalized in this paper as the spread between the n-year Treasury yield and the maturity-matched overnight index swap (OIS) rate; a positive and rising spread indicates declining convenience, not increasing yield risk.

Portfolio balance channel (of unconventional monetary policy transmission) The mechanism by which large-scale asset purchases by one central bank displace investors from their target allocations, inducing them to substitute into other assets — including foreign sovereign bonds — thereby compressing yields and term premia in those markets. Distinguished from the signaling/expected-path channel in that it operates through changes in duration risk (term premia) rather than revisions to expected future short rates, and is unique to UMP because it targets long-duration assets.

Preferred habitat investors Investors with persistent, institutionally determined demand for bonds of specific maturities and issuers (e.g., insurance companies, pension funds), arising from regulatory constraints, risk management practices, or balance sheet matching. Their demand is modeled as relatively price-inelastic when assets command a convenience premium, and more elastic when that premium erodes.

Demand-slope parameter α_j(τ) In the extended GRV preferred-habitat model, the parameter governing the price elasticity of preferred-habitat investor demand for country-j bonds of maturity τ. Large values imply inelastic demand (strong habitat preferences), small values imply elastic demand and greater cross-border substitutability. The paper’s key innovation is treating this parameter as time-varying — specifically, as a function of the observed Treasury convenience yield rather than a fixed structural constant.

Policy asynchronicity The condition in which the Federal Reserve is tightening monetary policy (raising rates or conducting quantitative tightening) while other advanced-economy central banks (specifically the ECB) are simultaneously easing through LSAPs. The paper argues that asynchronicity interacts with a declining convenience yield to amplify ECB spillovers to U.S. term premia and attenuate the effectiveness of Federal Reserve tightening at the long end of the yield curve.

Swap spread (as inconvenience proxy) The spread of the sovereign bond yield over the maturity-matched OIS rate (Y − OIS). Expressed so that a larger positive value indicates greater Treasury inconvenience. Prior to the GFC, 10-year Treasury yields ran below swap rates (negative spread); post-GFC, this relationship reversed, with the spread turning persistently positive and exhibiting structural breaks consistent with Bai-Perron tests.

Exorbitant privilege The benefit the United States accrues from the global dominance of its sovereign debt and currency, which structurally insulates U.S. financial markets from foreign monetary policy shocks through inelastic global demand for Treasuries. The paper argues this insulation is not structural but endogenous and state-dependent: erosion of exorbitant privilege — operationalized as a declining convenience yield — substantially increases U.S. vulnerability to foreign monetary shocks.

Gâteaux/Malliavin functional derivative (as used in the model) Mathematical tools used to characterize how the impulse response function of the yield curve to policy shocks changes when the demand-slope parameter α_k(τ) is perturbed. The mixed Gâteaux differential ∂²_{α_k,b} log P^(τ)_{js} captures both the instantaneous amplification (direct pass-through increase) and the intertemporal propagation (dynamic multiplier) of a foreign policy shock under lower convenience, enabling a tractable decomposition of state-contingent spillover magnitudes across maturities and horizons.

Wage growth and labor market tightness

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question. Which measures of labor market tightness best predict nominal wage inflation, and do standard measures such as the unemployment rate and the vacancy-to-unemployment ratio capture the relevant slack? The paper also asks whether transitory productivity shocks affect wage growth, and whether the wage Phillips curve is nonlinear.

Motivation and Model. Standard measures of labor market tightness have had mixed performance since the COVID-19 pandemic: unemployment quickly returned to pre-pandemic levels while wage growth remained persistently elevated, motivating a search for superior indicators. The paper builds on the theoretical framework of Bloesch, Lee, and Weber (2024), a tractable New Keynesian DSGE model in which firms set wages and workers search on the job. In this model, labor market tightness is well-summarized by either (a) the quits rate or (b) vacancies per effective searcher (V/ES), where effective searchers include both employed and unemployed job seekers. Unemployment enters the model’s wage Phillips curve but with a coefficient close to zero, because changes in the unemployment share do not substantially shift the composition of searchers in a way that alters firms’ wage incentives. Transitory TFP shocks have theoretically ambiguous effects on nominal wage growth because the outcome depends on the central bank’s policy response.

Data and Methods. The main analysis uses quarterly U.S. data from 1990:Q2 to 2024:Q2. Wage growth is measured as the 3-month log change in the Employment Cost Index (ECI) for wages and salaries of private industry workers. Quits and vacancies are drawn from JOLTS (2001:Q1 forward) and extended back to 1990:Q2 using the Davis-Faberman-Haltiwanger series and Barnichon’s composite Help Wanted Index, respectively. The authors run a “horse race” of OLS univariate regressions of wage growth on thirteen separately normalized tightness indicators. They then run bivariate regressions pairing the quits rate with each other indicator to test whether any alternative provides independent predictive power. Robustness is assessed using 12-month ECI changes. An industry-level panel with time and industry fixed effects covering 11 broad sectors from JOLTS for 2001:Q1–2024:Q2 tests whether the same ranking holds within industries. Forecasting exercises use 1-, 2-, and 4-quarter-ahead in-sample regressions plus rolling out-of-sample one-quarter-ahead predictions beginning in 2004:Q1. Nonlinearity is evaluated via threshold regressions at the 25th percentile (unemployment) or 75th percentile (other measures) and via quadratic specifications.

Main Findings with Quantitative Magnitudes.

Horse race (aggregate, contemporaneous): The quits rate explains 55 percent of variation in 3-month ECI wage growth (R² = 0.55), and V/ES explains 52 percent (R² = 0.52), the two highest among all indicators tested. A one standard deviation increase in either quits (0.39 percentage points) or V/ES (0.08) is associated with 0.20 percentage points higher 3-month wage growth. By contrast, the vacancy-to-unemployment ratio (V/U) explains only 41 percent of wage growth and the unemployment rate only 34 percent. Together, quits and V/ES explain nearly two-thirds of wage growth since 1994 and 78 percent since 2020:Q2.

Bivariate regressions: Conditional on the quits rate, the coefficient on every other tightness indicator drops to near zero, with the sole exception of V/ES, which retains a coefficient of 0.08 (significant) while the quits coefficient remains at 0.14. This result is consistent with the model’s prediction that quits and V/ES are close to sufficient statistics for labor market tightness.

12-month ECI results: The ranking is preserved at longer horizons; quits and V/ES each explain approximately two-thirds of 12-month wage growth.

Productivity: Regressions of 3-month ECI wage growth on 3-month changes in labor productivity, TFP, and utilization-adjusted TFP all yield small, negative, and statistically indistinguishable from zero coefficients, consistent with the model’s prediction of an ambiguous effect of transitory productivity shocks on nominal wages.

Industry-level panel: Quits and V/ES remain the strongest predictors of within-industry wage growth after absorbing industry and time fixed effects. A one standard deviation increase in the industry quits rate (0.93 percentage points) is associated with 0.23 percentage points higher quarterly wage growth; a one standard deviation increase in industry V/ES (0.11) is associated with 0.13 percentage points higher wage growth.

HPW Composite Index: The Heise-Pearce-Weber (HPW) Index, constructed as an OLS-weighted average of quits and V/ES, achieves a correlation of 0.9 with standardized 3-month ECI wage growth. In-sample forecasting R² for the HPW Index at 1, 2, and 4 quarters ahead is 0.62, 0.74, and 0.77, respectively — the highest of all indicators at each horizon.

Out-of-sample forecasting: Only the quits rate and the HPW Index consistently outperform a simple AR(1) benchmark throughout the out-of-sample period from 2004:Q1 to 2024:Q1. The forecasting performance of vacancy-based measures (V/U and V/ES) deteriorated steadily after 2015, consistent with evidence of structural shifts in vacancy measurement documented by Mongey and Horwich (2023).

Nonlinearity: Threshold regressions and quadratic specifications provide little evidence of meaningful nonlinearity in the wage-tightness relationship for quits, V/ES, or the HPW Index over 1990–2024. The fit improvement from adding threshold terms is marginal, and slope coefficients are broadly stable across the full range of tightness, including the extreme tightness observed after COVID.

In depth

Q1. What theoretical mechanism links quits and V/ES to nominal wage growth, in contrast to unemployment?

In the Bloesch-Lee-Weber (2024) model incorporated in the paper, firms use both wages and vacancies to attract and retain workers from unemployment and from other firms, conditional on the overall mass of effective searchers. Labor market tightness is defined as V/S (vacancies over total searchers), not V/U, because employed workers also search on the job. When tightness is high, workers are harder to recruit and more likely to be poached, pressuring firms to raise wages. Quits are the endogenous component of separations and rise mechanically with tightness, making them a near-equivalent sufficient statistic for V/ES. Unemployment enters the wage Phillips curve in principle because the composition of searchers (employed vs. unemployed) matters for firms’ wage-setting incentives, but the coefficient on unemployment is calibrated and estimated to be approximately zero.

Q2. How do the authors extend the quits and vacancies data back to 1990 to cover the full sample period?

JOLTS data on quits and job openings begin in 2001:Q1. The authors extend the quits rate backward to 1990:Q2 using the Davis, Faberman, and Haltiwanger (2012) series, taking a simple average of the two in overlapping quarters (2001:Q1–2010:Q2). Vacancies are extended back to 1990:Q2 using the composite Help Wanted Index constructed by Barnichon (2010), with a similar overlapping average for 2000:Q4–2021:Q3. The effective-searcher measure (V/ES) is available only from 1994:Q1 because the CPS marginally attached worker series begins then.

Q3. How is the V/ES measure constructed, and why does it differ from the standard V/U ratio?

Effective searchers are constructed as ES = U_s + 0.48·U_l + 0.40·Z_want + 0.09·Z_do-not-want + 0.07·N, where U_s is short-term unemployed (less than 27 weeks), U_l is long-term unemployed (27+ weeks), Z_want is marginally attached workers not in the labor force, Z_do-not-want is non-participants not marginally attached, and N is employment. The weights reflect relative search intensities estimated by Abraham, Haltiwanger, and Rendell (2020) and translated to publicly available CPS data by Sahin (2020). Because employed workers constitute a far larger share of the population than the unemployed, including them — even at the low weight of 0.07 — substantially increases the total effective searcher count relative to V/U. This matters because the model predicts that firms’ wage decisions depend on the full pool of potential recruits and retention risk, not just the unemployed.

Q4. What are the results of the bivariate “horse race” pairing quits with each other tightness measure?

In bivariate OLS regressions of 3-month ECI wage growth on the quits rate plus one other indicator, the coefficient on quits remains approximately 0.14–0.22 percentage points per standard deviation regardless of which other variable is included, while all competing indicators’ coefficients fall to near zero. The sole partial exception is V/ES, which retains a coefficient of 0.08 (significant at 5%) alongside a quits coefficient of 0.14; the combined fit is 0.60. For all other measures — including V/U (coefficient drops to 0.04), unemployment (0.00), jobs-workers gap (0.02), Conference Board availability (−0.01), and NFIB difficulty hiring (0.01) — the incremental contribution beyond quits is negligible. This result is consistent with the model’s prediction that quits and V/ES are jointly near-sufficient statistics for wage growth.

Q5. Do the industry-level panel regressions replicate the aggregate ranking, and why is this an important test?

Yes. In panel regressions with industry and time fixed effects covering 11 JOLTS sectors from 2001:Q1 to 2024:Q2, the quits rate has the highest within-industry R² (0.019) and V/ES the second highest (0.010); all other indicators rank below. This within-industry test is important because it removes the possibility that the aggregate correlations are driven by unobserved macro variables that happen to co-move with quits and V/ES. The bivariate industry panel confirms that, conditional on quits, only V/ES adds substantially to the within-industry fit; all other indicators add negligible explanatory power.

Q6. Why might industry-level TFP shocks have a modest positive effect on wages even though aggregate TFP shocks do not?

At the industry level, the central bank does not respond to industry-specific TFP shocks. When a particular industry’s productivity rises and firms lower prices, consumer demand for that industry’s output rises. If demand rises by enough, firms must hire more workers to meet demand despite higher productivity per worker, leading them to post more vacancies and raise wages. At the aggregate level, the central bank does respond to the disinflation associated with positive TFP shocks (following a Taylor rule), which can raise overall consumption enough to require more aggregate hiring and generate a positive TFP-wage correlation — but the direction depends on monetary policy responsiveness, making the aggregate relationship ambiguous and empirically insignificant. The industry regressions find that a 1 percent increase in annual labor productivity is associated with 0.15 percent higher industry annual wage growth, significant at the 10 percent level.

Q7. How is the HPW Index constructed, and what is its in-sample fit with wage growth?

The HPW Index is constructed as a weighted average of the standardized quits rate and V/ES, where the weights are the OLS coefficients from a bivariate regression of 3-month ECI wage growth on both variables simultaneously (estimated over 1994:Q1–2024:Q2). The index is then normalized to have mean zero and standard deviation of one. The HPW Index achieves a correlation of 0.9 with standardized 3-month ECI wage growth. At the peak of post-pandemic inflation, the index predicted wage growth of approximately 2.6 standard deviations above the mean, corresponding to a quarterly wage growth rate of about 1.3 percent, close to realized values.

Q8. How do the out-of-sample forecasting results compare across indicators, and what accounts for the deterioration of vacancy-based measures?

Rolling out-of-sample one-quarter-ahead predictions from 2004:Q1 to 2024:Q1 show that only the quits rate and the HPW Index consistently outperform an AR(1) benchmark across the full period. V/U performed relatively well until 2015 but then deteriorated steadily, and V/ES similarly weakened after 2015, consistent with the finding by Mongey and Horwich (2023) that the relationship between job vacancies and other labor market indicators has persistently shifted since approximately 2010. The forecasting performance of the unemployment rate and several other standard measures deteriorated sharply in the post-COVID period when wage inflation surged, but quits and HPW maintained their performance throughout.

Q9. Is there evidence of nonlinearity in the wage Phillips curve, particularly in the extreme tightness of the post-COVID period?

The paper finds little evidence of meaningful nonlinearity. Threshold regressions at the 25th percentile for unemployment and 75th percentile for other measures yield marginal fit improvements: the R² for unemployment rises from 0.34 to 0.36 (a level shift rather than a slope change), and fit improvements for HPW, quits, and V/ES are essentially zero. Quadratic specifications confirm this: the coefficient on the squared term is insignificant in all specifications. The authors conclude that the relationship between labor market tightness (as measured by quits or the HPW Index) and nominal wage growth is approximately linear, including during the extreme tightness of the COVID aftermath.

Q10. Why does the paper argue that the slope of the wage Phillips curve can be estimated more cleanly than the price Phillips curve?

In the model’s price Phillips curve, monetary policy endogenously responds to TFP shocks, creating an omitted variable problem that biases the estimated slope toward zero. In the wage Phillips curve, TFP and monetary policy shocks affect wages only through their general equilibrium effects on labor market tightness — they do not appear directly on the right-hand side. Consequently, the tightness variable is a sufficient statistic for wage inflation in the model, and the slope coefficient can be estimated consistently from reduced-form regressions without the identification problems that plague the price Phillips curve.

Key Concepts

Vacancies per Effective Searcher (V/ES). The paper’s preferred tightness measure, defined as job openings divided by effective searchers, where effective searchers are ES = U_s + 0.48·U_l + 0.40·Z_want + 0.09·Z_do-not-want + 0.07·N. This differs from the standard V/U ratio by including employed workers (at a weight of 0.07 reflecting their search intensity) and distinguishing between short-term and long-term unemployed and non-participants. It is the theoretically correct tightness measure in the on-the-job-search model, where the full pool of potential recruits — not only the unemployed — determines wage pressure.

On-the-Job Search. The mechanism by which employed workers actively search for and receive job offers from other firms. In the Bloesch-Lee-Weber (2024) model underpinning the paper, on-the-job search implies that firms must set wages not only to attract unemployed workers but also to retain employed workers who may be poached. This changes the relevant measure of tightness from V/U to V/S and makes quits — which are the endogenous separations triggered when workers accept outside offers — a near-sufficient statistic for wage growth.

Quits Rate. The ratio of voluntary separations (quits) to total employment in private sector, sourced from JOLTS (extended to 1990 using Davis et al. 2012). In the model, quits are the endogenous component of the separation rate and are tightly linked to vacancies per effective searcher because workers quit more frequently when labor market tightness is high and outside offers are plentiful. The paper establishes quits as the single best individual predictor of 3-month ECI wage growth (R² = 0.55) and the best out-of-sample forecaster along with HPW.

HPW Tightness Index (Heise-Pearce-Weber Index). A composite indicator of labor market tightness constructed as the OLS-coefficient-weighted average of the quits rate and V/ES, estimated by regressing 3-month ECI wage growth on both variables simultaneously. The index is normalized to mean zero and standard deviation of one. The HPW Index achieves the highest in-sample forecasting fit at 1, 2, and 4 quarters ahead (R² of 0.62, 0.74, and 0.77, respectively) and consistently outperforms the AR(1) benchmark out of sample, unlike most other indicators.

Wage Phillips Curve. The reduced-form relationship between nominal wage inflation and labor market tightness, derived in the paper from first-order conditions of the firm’s optimization problem. In the model’s representation (equation 3), wage inflation is a function of deviations of V/ES and unemployment from steady state plus expected future wage inflation. The paper argues this relationship can be estimated more cleanly than the price Phillips curve because TFP and monetary policy shocks affect wages only through the tightness term, avoiding the omitted-variable bias that flattens price Phillips curve estimates.

Sufficient Statistic for Wage Inflation. As used in the paper’s model, a variable (or pair of variables) such that once it is included in the wage Phillips curve, no other labor market indicator provides additional explanatory power for wage growth. The model predicts, and the empirical horse race confirms, that quits or V/ES are individually near-sufficient statistics: conditional on the quits rate, the coefficients on all other tightness measures (including unemployment, V/U, jobs-workers gap, and survey measures) fall to approximately zero.

Transitory TFP Shocks and Wage Growth. The paper defines these as short-lived, positive shocks to total factor or labor productivity, as measured by 3-month changes in Fernald et al. (2012) series. The theoretical prediction is that their effect on nominal wage growth is ambiguous: if the central bank’s policy response lowers real rates enough, aggregate demand rises sufficiently to require more hiring, generating positive wage effects; if the policy response is limited, lower marginal costs reduce vacancies and wages. In the data, the sign is negative across all three productivity measures but statistically indistinguishable from zero in all specifications.

What's driving the decline in entrepreneurship?

Mon, 01 Jan 0001 00:00:00 +0000

The entrepreneurship rate in the United States—defined as the share of the labor force who own and actively manage a business with at least ten employees—declined by 26% between 1987 and 2015, a decline mirrored in the firm entry rate and not explained by compositional changes in the economy or driven by a small number of sectors. This paper addresses what caused this broad-based decline using Current Population Survey data, two new empirical facts, and a dynamic general equilibrium model of occupational choice. The first new fact is that the decline was larger for higher-education groups (35% for those with more than a college degree versus 2.4% for those without a high-school diploma), indicating that the driving force is not skill-neutral. The second new fact is that the size distribution of entrepreneur firms has been stable, so the entrepreneurship decline represents a shrinkage of the entrepreneurial sector relative to the economy. Estimating the contribution of four candidate explanations—skill-biased technical change (SBTC), increasing regulation, technology-driven increases in fixed and entry costs, and technology-driven productivity advantages for large firms—the paper finds that increasing entry costs account for most of the decline in both the entrepreneurship share and the firm entry rate, with empirical evidence pointing to both regulation and technology as sources of these higher costs.

In depth

Q1. What does the model of occupational choice capture, and how are the explanations identified?

The dynamic general equilibrium model allows individuals to choose between working as an employee (earning wages) and being an entrepreneur (paying fixed and entry costs, then operating a firm); the model generates predictions about the entrepreneurship rate, firm entry rate, and the distribution of entrepreneur firm sizes across groups, which the data discipline. By requiring the model to match changes in entrepreneurship along multiple dimensions—including the education-gradient fact and the stable size distribution—the author can separately identify the contribution of each candidate mechanism. SBTC operates through wages (raising opportunity cost of entrepreneurship for skilled workers); entry-cost increases reduce the number of new entrepreneurs regardless of skill; productivity advantages for large firms shift the size distribution; and regulation/technology-driven fixed-cost increases reduce incumbent-entrepreneur survival.

Q2. Why does skill-biased technical change fail to explain the level decline?

SBTC raises wages for high-skill workers, which could in principle explain why fewer of them choose entrepreneurship; and indeed SBTC is found to have tilted entrepreneurship toward less-educated people. However, SBTC cannot explain the decline in the aggregate entrepreneurship rate because: it does not reduce the incentive to be an entrepreneur for lower-skill workers (who are relatively unaffected), and the stable size distribution of entrepreneur firms is inconsistent with SBTC (which would tend to shift composition rather than reduce overall entrepreneurship). The model confirms that SBTC explains the education gradient but contributes little to the overall level decline.

Q3. What is the role of entry costs, and what drives them?

Increasing entry costs are found to explain most of the decline in the share of people who are entrepreneurs and most of the decline in the firm entry rate; the data also reject the hypothesis that entry-cost increases were accompanied by large changes in entrepreneur firm size, consistent with the observed stability of the size distribution. Empirical evidence suggests two sources of higher entry costs: increasing regulation (occupational licensing, tax-code complexity, zoning restrictions) and technology changes that increase the fixed investments required to operate (e.g., adoption of IT systems). The paper does not fully separate these two sources but presents evidence consistent with both operating simultaneously.

Q4. What is the role of increasing productivity of large firms?

Increasing productivity of large, non-entrepreneurial (e.g., publicly listed) firms matters little for the entrepreneurship rate or the firm entry rate, but has driven most of the reallocation of labor away from entrepreneur businesses. This is because the productivity advantage of large firms shifts the scale of production without necessarily changing who becomes an entrepreneur, largely leaving the extensive margin of entrepreneurship intact while reducing the share of aggregate economic activity attributable to the entrepreneurial sector.

Key concepts

entrepreneurship rate : the share of the labor force who own and actively manage a business with at least ten employees, the paper’s main measure of entrepreneurship, which declined 26% from 1987 to 2015 in the CPS data.

entry costs : the one-time costs required to establish a new entrepreneurial business; the paper finds these rose over the sample period due to both regulation and technology, and identifies them as the primary driver of the entrepreneurship decline.

Journal of Monetary Economics | Macro Paper Warehouse

Payment data, information disclosure, and privacy

Layer 1: Overview

In depth

Q1. What is the modeling/identification strategy, and what are the main threats to it?

Q2. What are the two main channels, and how are they distinguished?

Q3. How does the welfare effect depend on monetary policy stance?

Q4. How does the Bayesian persuasion / noisy-message result work?

Q5. Why do buyers and sellers always want to buy the forecast even when disclosure can lower welfare, and what is the market failure?

Q6. What is the selective-disclosure result?

Q7. How does forecast precision affect outcomes?

Q8. How are privacy and cash modeled, and what is the effect on welfare?

Q9. What are the equilibrium-multiplicity and underinvestment results in the benchmark?

Q10. How does the paper relate to and differ from closely related work?

Q11. What are the CBDC and privacy-protection implications and their scope conditions?

Q12. What extensions and robustness checks are reported?

Key Concepts

Merger guidelines for the labor market

Layer 1: Overview

In depth

Q1. What is the identification/estimation strategy for the key parameters, and what are the threats to it?

Q2. How is the model validated out of sample?

Q3. What is the central welfare metric and policy quantity?

Q4. What are the main mechanisms, and what is downward wage pressure specifically?

Q5. What heterogeneity is documented?

Q6. What do the confidence/threshold figures show?

Q7. How sensitive are results to the assumed efficiency gain?

Q8. How does this paper differ from closely related prior work?

Q9. What are the policy implications and their scope conditions?

Q10. Are there internal inconsistencies a reader should note?

Key Concepts

Monetary Policy, Firm Heterogeneity, and the Distribution of Investment Rates

Layer 1: Overview

In depth

Q1. What is the identification strategy and what are the main threats to it?

Q2. What are the main mechanisms and how are they distinguished empirically?

Q3. What heterogeneity is documented?

Q4. How does the model decompose the heterogeneous extensive-margin effect, and what is the ‘heterogeneous size effect’?

Q5. What role do the different adjustment costs play, and how is the model calibrated?

Q6. What untargeted moments validate the model?

Q7. What robustness checks are run?

Q8. How does this paper relate to and differ from closely related prior work?

Q9. What are the policy implications and their scope conditions?

Q10. What are the main caveats and open questions?

Key Concepts

Policy transition risk, carbon premiums, and asset prices

Layer 1: Overview

In depth

Q1. What is the identification strategy, and what are the main threats to it?

Q2. What are the main mechanisms, and how are they distinguished?

Q3. What heterogeneity is documented?

Q4. What robustness checks and extensions are run?

Q5. How does this paper relate to and differ from closely related prior work?

Q6. What are the policy implications and their scope conditions?

Q7. What happens to asset prices at the moment of each type of tipping?

Q8. What drives the risk-free rate dynamics?

Key Concepts

Macro and micro of external finance premium and monetary policy transmission

Layer 1: Overview

In depth

Q1. What is the empirical strategy for decomposing the EFP, and why does the order of fixed-effect extraction matter?

Q2. What is the variance decomposition result, and what is its headline interpretation?

Q3. Why is the euro-area average sovereign spread, not the country-specific spread, the relevant covariate at the country level?

Q4. What evidence supports the bank lending channel at the bank level?

Q5. What evidence supports the firm balance-sheet channel at the firm level?

Q6. What is found at the contract level?

Q7. What is the identification strategy for monetary policy transmission, and what are its limits?

Q8. What are the main asymmetries in monetary policy transmission to the EFP?

Q9. Why does QT leave the EFP unchanged while QE moves it, and how is this tested?

Q10. How is the bank/firm channel split corroborated via cross-sectional interactions?

Q11. What robustness checks are run on the country-level results?

Q12. How does this paper relate to and differ from prior work?

Q13. What are the policy implications and their scope conditions?

Q14. What significant caveats and unexplained findings does the paper itself flag?

Key Concepts

The Credit Channel of Public Procurement

Layer 1: Overview

In depth

Q1. What is the identification strategy and what are the main threats to it?

Q2. What is the credit channel mechanism and how is it distinguished from a demand story?