Journal of Money, Credit and Banking | Macro Paper Warehouse

A Model of Post-2008 Monetary Policy

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

Layer 1: Overview

Research question and motivation: Since 2008 the US economy has gone through two zero-lower-bound (ZLB) episodes (Dec 2008–Dec 2015 and Mar 2020–Mar 2022). Standard New Keynesian (NK) and monetarist models struggle with three broad facts about US inflation during these episodes, emphasized by Cochrane (2018): (1) no significant deflation, (2) little inflation volatility, and (3) no significant inflation following large quantitative-easing (QE) balance-sheet expansions. A fourth challenge is that money-market rates (federal funds, T-bills) were often below the interest rate on reserves (IOR rate), which many read as evidence of full satiation of reserve demand — undercutting any model relying on a monetary friction. Diba and Loisel build a model that can qualitatively account for all four facts and then draw out implications for policy normalization and the operational framework (floor system).

Model setup: They add banks and bank reserves to the basic NK model. Monopolistically competitive firms must borrow a fraction phi in (0,1] of their nominal wage bill from banks before producing (a cost channel); calibration uses phi=1. Households contain production workers and bankers; bankers produce real loans using their own labor and real reserves via a production function homogeneous of degree d in (0,1], so holding reserves reduces banking (labor) costs — i.e., reserves carry a convenience yield. The central bank sets TWO instruments directly: the IOR rate (I^m) and the nominal stock of reserves (M). A ZLB on the net IOR rate arises because non-interest vault cash is a perfect substitute for reserves. Calvo price rigidity (theta) is assumed.

Key analytical results: Under a permanent IOR-rate peg with an exogenous (or QE-rule) money supply, the model delivers a UNIQUE steady state and local-equilibrium determinacy, provided 1 <= I^m < I = 1/beta. Setting the IOR rate pins down real reserve demand, and given the exogenous nominal stock this pins down the price level; steady-state inflation equals the money growth rate. This rules out the Benhabib-Schmitt-Grohe-Uribe deflationary equilibria. The log-linearized model yields an IS equation, a modified Phillips curve (output enters net of real reserves, with delta_m and slope kappa depending on banking-cost cross-derivatives), and a reserves-demand equation. The characteristic roots satisfy 0 < rho < 1 < omega_1 < omega_2, so anticipated shocks decay exponentially with horizon — the opposite of the basic NK model (where 0<omega_1<1<omega_2 makes effects grow exponentially with ZLB duration). Hence deflation converges to a finite value kappa·z*/[beta·sigma·(omega_1-1)(omega_2-1)] rather than exploding, explaining no severe deflation and low inflation volatility. (In the basic NK model under their calibration, deflation reaches about 21% per year for an expected ZLB duration of two years.)

QE simulations (calibrated to US data, November 2010, start of QE2): Calibration: sigma=1 (log utility), eta=1 (unit Frisch), alpha=0.67, epsilon=6, theta=0.67, phi=1, net IOR rate = 25 bps p.a., benchmark net shadow-rate-minus-IOR spread (I - I^m) = 10 bps p.a. (alternatives 5 and 20 bps), beta=0.999 quarterly, reserves/loans ratio m/ell = 1/9, loan rate I^ell-1 = 3.25% p.a.; derived ical=0.0039, V_b=0.019. Two conditions make QE nearly non-inflationary: demand close to satiation (I^m close to I, Gamma_m near 0) and the expansion perceived as temporary. Results (Figure 1, 5-year expected duration): a single QE2 expansion ($1T to $1.6T over 3 quarters) lowers the I_t - I^m_t spread from 10 to 6.2 bps and raises annualized inflation by only 18 bps on impact. Double/triple/quadruple QE2 lower the spread to 4.5/3.5/2.9 bps and raise inflation by only 27/32/35 bps — strongly decreasing returns to QE. With a 5-bps steady-state spread the single-QE2 impact falls to 9 bps; with 20 bps it rises to 37 bps (inflation impact moves roughly one-for-one with the spread). Inflation impact scales roughly one-for-one with expected duration: single QE2 raises inflation 18 bps (5 yrs), 40 bps (10 yrs), 84 bps (20 yrs); up to 32xQE2 reaches 48/104/212 bps for 5/10/20 yrs (Table 1). The calibration makes omega_1 = 1.0003 (very close to 1) and omega_2 = 1.42.

Implications: A permanent reserve expansion would be fully inflationary (proportional long-run price rise) unless accompanied by a rise in money demand (e.g., a higher IOR rate). The 2021-22 inflation surge may partly reflect expansions coming to be seen as permanent plus adverse supply shocks raising the shadow rate I via a Fisher effect. Forward guidance about expansion duration is a powerful inflation-control tool. An extension with liquid government bonds reconciles non-satiation with T-bill rates below the IOR rate without changing any inflation implications. Normalization (IOR hikes and balance-sheet contraction) is always deflationary — no Neo-Fisherian effect. Under a floor system, determinacy holds for any non-negative IOR response to inflation (Taylor principle not required) and for a wide range of output responses (threshold 15.7 on the output coefficient under their calibration).

In depth

Q1. What is the core modeling innovation relative to the basic New Keynesian model?

They introduce banks and bank reserves with a convenience yield: holding reserves reduces banks’ labor cost of making loans (banker production function f^b homogeneous of degree d in (0,1] in banker labor and reserves), and firms must prepay a fraction phi of their wage bill via bank loans (a cost channel). Crucially the central bank sets BOTH the IOR rate and the nominal stock of reserves, two instruments the Fed controls directly. This gives the model a ‘monetarist element’ while keeping NK price rigidity (Calvo theta).

Q2. Why does the model deliver determinacy and avoid the NK ZLB pathologies?

Because the central bank sets the money supply (exogenously or via a QE rule), the model has a unique steady state provided 1 <= I^m < 1/beta: setting the IOR rate pins down real reserve demand, and the exogenous nominal stock then pins down the price level. The third-order price-level dynamic equation has roots 0<rho<1<omega_1<omega_2, satisfying Blanchard-Kahn for one predetermined variable, so there is a unique bounded solution. Anticipated future shocks decay exponentially (weights omega_1^{-k}, omega_2^{-k} both <1), so deflation stays bounded and inflation volatility stays low. In the basic NK model the analogous roots are 0<omega_1<1<omega_2, so weights grow exponentially with ZLB duration, producing explosive deflation and volatility.

Q3. What exactly are the three (four) facts the model targets, and which mechanism handles each?

(1) No significant deflation and (2) little inflation volatility at the ZLB — handled by determinacy under a money-supply-setting central bank, giving bounded, duration-insensitive deflation. (3) No significant inflation after QE — handled by near-satiation (Gamma_m near 0, small steady-state spread) plus the expansion being temporary, so a large nominal-reserve increase is absorbed by a tiny fall in the IOR-vs-shadow-rate spread rather than by higher prices. (4) Money-market/T-bill rates below the IOR rate — handled by an extension where government bonds provide liquidity services to non-bank entities, generating T-bill returns below the IOR rate without requiring full reserve satiation.

Q4. What are the two key conditions for QE to be nearly non-inflationary, and how sensitive are the results?

Condition 1: demand for reserves is close to satiation, meaning I^m close to I (Gamma_m near 0) so the semi-elasticity of reserve demand is large and a flat Gamma_m absorbs large supply changes through small spread movements. Condition 2: the expansion is perceived as temporary. Sensitivity: the inflation impact moves roughly one-for-one with the steady-state I - I^m spread (single QE2 impact = 9, 18, 37 bps for spreads of 5, 10, 20 bps) and roughly one-for-one with expected duration (18, 40, 84 bps for 5, 10, 20 years). A permanent expansion would be fully (proportionally) inflationary in the long run.

Q5. How is the central spread calibrated given the shadow rate is unobservable, and why is that a limitation?

The shadow bond rate I is a rate on hypothetical bonds with no non-pecuniary services in zero net supply, hence unobservable. Using Nagel (2016) and the repo-T-bill spread (8 bps in Nov 2010), assuming the convenience yield of borrowed Treasuries is half that of T-bills held outright, they back out a net shadow rate I-1 of about 30-35 bps and an I - I^m spread of about 5 bps; to be conservative they set the benchmark spread to 10 bps (alternatives 5 and 20). The authors flag the unobservability of the relevant spread as a genuine limitation of the model’s quantitative QE implications and call for future work with observable spreads.

Q6. How does the liquid-government-bond extension reconcile non-satiation with T-bill rates below the IOR rate?

Workers derive utility from holding government bonds (a proxy for pension/money-market funds that hold bonds and supply financial services). Banks could use bonds instead of reserves for liquidity but choose not to in equilibrium, so the extended model’s equilibrium coincides with the benchmark for all common endogenous variables except the lump-sum transfer T_t. This lets the bond/T-bill return fall below the IOR rate (driven by strong non-bank demand, e.g., collateral or international reserve use) while reserve demand remains unsatiated, leaving all inflation results from Sections 3-4 intact.

Q7. What does the model imply for monetary-policy normalization and Neo-Fisherian effects?

In the log-linearized model under exogenous instruments, current and expected future IOR-rate hikes and balance-sheet contractions ALWAYS exert deflationary pressure: in the inflation solution (Equation 25), the coefficient on i^m_{t+k} is negative and on reserve growth mu_{t+k} is positive, because the unstable eigenvalues omega_1, omega_2 are positive real numbers >1 and delta_m·chi_y < 1. So the model has no Neo-Fisherian region (unlike some NK equilibria in Schmitt-Grohe-Uribe 2017 and Bilbiie 2022). The authors stress this hinges on the eigenvalues being positive reals; with complex or negative eigenvalues (as in MIU models) the sign could flip by horizon.

Q8. What does the model say about the floor system and the Taylor principle?

Under a floor system (nominal reserves exogenous, IOR rate set by a Taylor rule I^m = R(Pi, y)), local-equilibrium determinacy holds for ANY non-negative IOR response to current inflation (r_pi >= 0) — the Taylor principle is not required; even an IOR-rate peg works. If the rule also responds to output, a sufficient condition is r_y < (1 - delta_m·chi_y)/(delta_m·chi_i), whose right-hand side equals 15.7 under their calibration — comfortably above typical output coefficients (about an order of magnitude smaller), so determinacy is likely to prevail.

Q9. What robustness checks support the determinacy result?

Appendix C replaces the exogenous nominal reserve stock with a QE rule (reserves react to output and the price level): determinacy no longer holds for all parameter values but holds for all reasonable calibrations. Appendix D adds household cash via a cash-in-advance constraint: determinacy still holds under an exogenous IOR rate and exogenous monetary base, except for implausible calibrations. The QE simulation results are also stated to be insensitive to most parameters (e.g., raising theta to 0.75 only makes inflation impacts smaller) and to plausible variations in the loan-rate and reserves/loans targets.

It builds on Diba and Loisel (2021), which showed a small monetary friction resolves NK puzzles/paradoxes under an IOR peg. Reserve/banking-cost modeling is close to Curdia and Woodford (2011) and Ireland (2014), but with new analytical results (determinacy proof, closed-form inflation/output solution) and three differences: banking costs tied to time spent on banking, borrowers are firms borrowing the wage bill, and reserve demand is not satiated. It complements asset-side QE models (Gertler-Karadi 2011, Sims et al. 2023) by focusing on the liability side. Versus Andolfatto (2015), which links low inflation to full satiation, this paper generates low inflation WITHOUT full satiation. The determinacy analysis overlaps most with Piazzesi, Rogers, Schneider (2022).

Q11. What are notable caveats the authors themselves raise?

They state the model cannot explain why QE1 (starting from about $45 billion of reserves in 2008) was non-inflationary, since Gamma_m was unlikely to be flat at such low reserve levels; they attribute QE1’s non-inflationary effect to a rise in reserve demand (interbank-market collapse, IOR introduction Oct 2008, later Basel III liquidity-coverage and stress-test requirements). The unobservable shadow rate limits quantitative precision. Results are qualitative for the inflation facts. The Discussion subsection explicitly notes some views ‘go beyond the formal results.’

Key Concepts

Banks of a Feather: The Informational Advantage of Being Alike

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

Layer 1: Overview

Research question and motivation: Can banks effectively monitor their peers under asymmetric information? Effective peer monitoring matters for functioning interbank markets and, by implication, financial markets and the transmission of monetary policy. If banks monitor effectively, central banks can stay in a “night-watchman” role (Goodfriend and King 1988); if they systematically fail to identify solvent counterparties, central banks should be more active (Freixas and Jorge 2008). The paper argues that PORTFOLIO SIMILARITY between two banks is the key to their reciprocal monitoring ability: a lender uses private information about its own loan portfolio to assess the quality of a peer’s portfolio, so it is better informed the more similar the two exposures.

Data and setup: Quarterly bilateral bank-to-bank and bank-to-firm exposures from the German credit register, 2009-2018, covering 2,054 lending and 2,035 borrowing banks, balanced into 2,644,640 lender-borrower-quarter combinations; 701,533 true credit relations (102,044 within the same banking network, 2,087 within the same holding company). Interbank exposure represents 21% of German banks’ total borrowing and 20% of total lending; ~1.4 trillion euros average quarterly exposure by end-2018. The authors build three novel measures: (1) Portfolio quality = 1 minus the exposure-weighted average probability of default (PD) from proprietary supervisory filings (a forward-looking, private quality proxy); (2) Portfolio opacity = exposure-weighted standard deviation of PDs different banks assign to the same borrower (peers’ disagreement); (3) Portfolio similarity = cosine similarity of two banks’ exposure vectors across 10 industries (WZ 73 one-digit) and 9 regions (first zip digit). Estimation uses a Heckman (1977) two-step sample selection model: a Probit selection equation for the extensive margin (whether a credit relation exists) and an OLS outcome equation for the intensive margin (percentage change in bilateral exposure), with lagged credit relation as exclusion restriction, plus lender, borrower and quarter-year fixed effects. Independent variables are standardized.

Main findings (signs, magnitudes, scope): Portfolio quality validation - it negatively and significantly predicts next-quarter NPL ratios up to 2 years ahead, explaining 16-17% of cross-sectional NPL variation and 71-77% with fixed effects. For the AVERAGE bank, lending does NOT respond to borrower Portfolio quality (coefficients negative, mostly insignificant), but DOES respond to the backward-looking NPL ratio: a one-SD higher borrower NPL ratio lowers the probability of receiving a loan by 118 basis points (vs. unconditional 26.53%) and reduces amounts by 133-236 bp (avg. quarterly change 1.46%). Higher borrower Portfolio opacity reduces lending (extensive -38 bp; intensive -57 to -111 bp). The key result: interacting similarity with quality reverses this for similar pairs. For HIGH-similarity pairs (3 SD above mean), a one-SD increase in borrower Portfolio quality raises matching probability by 50 bp and lending by 408 bp; a deterioration cuts lending by 348-368 bp (avg. change between similar banks 10.95%). For LOW-similarity pairs, higher Portfolio quality LOWERS lending (matching -80 bp; amount -563 bp), and lending rises after quality deteriorates (370/342 bp), which Section 6 shows is a demand effect. The NPL-ratio response vanishes for similar pairs. Portfolio similarity itself raises lending: one-SD more sectoral similarity raises intensive-margin lending ~100-259 bp, regional similarity ~84-114 bp - jointly comparable in magnitude to relationship lending, the strongest known predictor. For opaque borrowers, high-similarity lenders lend MORE (extensive +23 bp; intensive +129 to +162 bp). A variance decomposition (Lemmon et al. 2008 ANCOVA) finds common/bank-pair characteristics explain 98.0% of extensive-margin variation and 18.9% of intensive-margin variation; lender, borrower and market characteristics explain only 1.2/0.8/0.1% (extensive) and 35.6/44.2/9.1% (intensive). Implication: peer monitoring works, but only among similar banks; this raises interbank efficiency at the cost of higher systemic risk and too-interconnected-to-fail concerns.

In depth

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

The core estimation is a Heckman (1977) two-step sample selection model: a first-stage Probit for the extensive margin (existence of a bilateral credit relation) and a second-stage OLS for the intensive margin (log change in bilateral exposure), with the inverse Mills ratio carried into the second stage. The exclusion restriction is the lagged existence of a credit relation (Credit relation_{i,j,t-1}), which strongly predicts a current relation (first-stage t-statistic 335; t=293 in the similarity specification) because German interbank exposures are long-lived, yet carries no information on whether exposure will rise or fall next quarter. The chief threats are: (1) demand vs. supply confounding - observed lending is equilibrium, so a negative quality-lending link could reflect borrowers’ demand rather than lenders’ screening; addressed in Section 6. (2) Correlated portfolio quality of similar banks - a lender cutting lending in response to its OWN deteriorating portfolio could be misread as a reaction to a similar borrower’s portfolio; addressed via a matched sample in Section 7. The paper also notes both Portfolio quality and NPL series are persistent, so the predictive regressions should be read as ‘gentle evidence,’ not strict causal proof.

Q2. How do the authors separate supply effects from demand effects?

They adapt Degryse et al. (2019). They define an adjusted exposure change bounded in [-2,2] (Chodorow-Reich 2014; Davis-Haltiwanger 1992) that captures both margins, then regress it on lending-bank-time fixed effects (proxying supply) and borrowing-bank-class x industry x region x time fixed effects (proxying demand, assuming homogeneous demand across lenders). The estimated lender-time fixed effects, demeaned and aggregated to the borrowing-bank level, give a borrower-specific liquidity-supply shock. Regressing this on borrower Portfolio quality, NPL ratio and opacity shows supply is restricted when quality deteriorates, NPL rises, or opacity increases. This confirms the puzzling positive lending-to-low-quality result for dissimilar pairs is a DEMAND effect: low-quality borrowers, shunned by similar lenders, demand more liquidity and turn to dissimilar lenders. The authors stress this borrower-level approach supports but cannot replace the bank-pair analysis, since it cannot include pair characteristics like similarity.

Q3. How do they rule out that lenders are just reacting to their own correlated portfolio quality?

In the full sample, the correlation of Portfolio quality between two above-average-similarity banks is 0.0499 versus only 0.0150 for below-average-similarity pairs. They build a matched subsample (nearest-neighbour matching, assigning each ‘similar’ pair - both similarities above the 75th percentile in 2009Q1 - three ‘dissimilar’ pairs below the 25th percentile with the closest Portfolio-quality correlation) so that within-pair quality correlation is the same for similar and dissimilar pairs, and redefine similarity as binary. If lenders only reacted to their own portfolio, the similarity x quality interaction should vanish in this sample. Instead, the interaction stays positive and mostly significant (and NPL x similarity too); weaker significance in some fixed-effect models reflects the smaller sample, since coefficient sizes are comparable to the main results.

Q4. What are the main mechanisms, and how are they distinguished empirically?

Mechanism: information on a peer’s asset quality is private and costly to obtain; a lender proxies a peer’s portfolio quality by the average quality of the industries/regions it lends to, and can do this more cheaply when it already lends to the same industries/regions (similar portfolio). So similar lenders are better informed. Empirically distinguished by: (a) the average bank reacts to the public NPL ratio but not to private Portfolio quality, while similar pairs react strongly to Portfolio quality and barely to NPL - showing similar lenders access private information; (b) the similarity x quality and similarity x opacity interactions; (c) the supply-shock decomposition separating screening from demand; (d) the matched sample ruling out own-portfolio reactions. A competing mechanism, risk shifting (Elliott et al. 2018) - banks deliberately courting correlated counterparties to raise bailout probability - cannot be ruled out and may co-drive preferential lending between similar peers.

Q5. What heterogeneity is documented?

(1) By similarity: similar pairs (3 SD above mean) react to forward-looking Portfolio quality and lend more to higher-quality and more-opaque peers; dissimilar pairs (3 SD below mean) react only to the backward-looking NPL ratio and end up lending more to low-quality borrowers via demand. (2) By opacity: lending between similar banks is especially important for opaque borrowers, who otherwise struggle to refinance; opaque banks are shunned by dissimilar lenders and turn to similar ones, while low-quality banks are shunned by similar lenders and turn to dissimilar ones. (3) Sectoral vs. regional similarity: both matter; sectoral similarity tends to have larger intensive-margin effects (e.g., 259 vs. 94 bp in Model 3). (4) Lender’s own quality: lenders cut lending when their own Portfolio quality falls (one-SD drop reduces amounts by 215-226 bp within-bank), consistent with prior work (Acharya-Merrouche 2013).

Q6. What robustness checks and additional analyses are run?

(1) Multiple fixed-effect layers: cross-section, lender/borrower fixed effects, and added quarter-year fixed effects (Models 1-4 across tables). (2) Control set: lagged Capital ratio, Liquidity ratio, ROA, Loans-to-assets, Size, relationship lending and reverse relationship lending over an 8-quarter window, difference in liquidity surplus, same-network and same-holding-company dummies. (3) Supply-vs-demand decomposition (Section 6). (4) Matched-sample analysis breaking the quality correlation (Section 7). (5) Validation of Portfolio quality via NPL-predictive regressions and a panel Granger causality test (Juodis et al. 2021; Half-Panel Jackknife Wald > 300; Dumitrescu-Hurlin Z < -50), significant 5-50 quarters ahead. (6) Two-digit WZ 73 industry classification (100 industries) in Appendix B. (7) Variance decomposition (ANCOVA, Type III sums of squares) quantifying explanatory power.

It extends peer-monitoring literature (Goodfriend-King 1988; Rochet-Tirole 1996; Flannery-Sorescu 1996; Furfine 2001) by showing that even among banks, the more similar the lender, the better its monitoring - identifying Perignon et al. (2018)’s ‘informed lenders’ as similar-portfolio banks. Versus relationship-lending work (Affinito 2012; Braeuning-Fecht 2017; Cocco et al. 2009), it shows that with a similar portfolio NO long-standing relationship is needed to obtain quality information, and that similarity mitigates opaque banks’ hampered access on top of relationships. It augments lender/borrower/market-characteristic studies by adding dyadic (common) covariates. Unlike prior work using aggregate bank-level ratios, CDS spreads, or rating-agency disagreement, it uses granular real-exposure data and proprietary supervisory PDs to measure private quality and peer-perceived opacity directly. It links to systemic-risk/contagion literature (Allen-Gale 2000; Fecht et al. 2011; Elliott et al. 2018), showing banks over-expose to similar counterparties despite indirect-contagion risk, surfacing an efficiency-vs-systemic-risk trade-off akin to focus-vs-diversification in Acharya et al. (2006).

Q8. What are the policy implications and their scope conditions?

Peer monitoring is real but partial: only similar banks effectively screen on private, forward-looking quality, while others fall back on inferior public proxies (NPL ratios). This bears on the central-bank ’night-watchman vs. active’ debate - because monitoring fails for dissimilar pairs, a purely hands-off stance may be insufficient. The headline trade-off: stronger lending between similar banks raises interbank informational efficiency and monitoring, but the above-average direct exposure between similar (correlated) banks multiplies systemic risk and too-interconnected-to-fail concerns, and reflects a lack of diversification. Scope conditions: results are specific to the German banking system (2009-2018), a tiered market dominated by private, savings, and cooperative banks with mostly long-term interbank loans (45% over a year, only 15% overnight); the data lack interest rates, so the analysis covers quantities/existence of lending, not prices; effects are estimated on bank-pairs that lent at least once; and the supply-identification assumes homogeneous borrower demand across lenders.

Q9. What are the key caveats the authors themselves flag?

(1) No interest-rate data, so price effects of similarity, quality and opacity are untested. (2) Portfolio quality and NPL series are persistent, so the forward-looking predictive evidence is ‘gentle,’ not definitive. (3) The supply-shock approach gives borrower-level (not pair-level) shocks and cannot incorporate similarity. (4) Risk shifting cannot be ruled out as a co-driver of preferential lending between similar peers. (5) Portfolio quality is built using the median PD across IRB banks, excluding borrowers exposed only to Standardised-Approach banks. (6) The balanced sample includes only pairs that lent at least once, ignoring pairs that could theoretically but realistically would not lend (consistent with tiered-market evidence).

Key Concepts

CBDC as Imperfect Substitute to Bank Deposits: A Macroeconomic Perspective

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

Layer 1: Overview

Research question and motivation: As central banks worldwide explore retail central bank digital currency (CBDC), the macroeconomic consequences depend heavily on how CBDC interacts with bank deposits. Prior work spans a wide range of conclusions — from “no effect” (Brunnermeier and Niepelt 2019) to disintermediation that reduces lending and output (Keister and Sanches 2022; Chiu et al. 2022) to large output gains (Barrdear and Kumhof 2021, +3% GDP). Bacchetta and Perazzi argue these differences hinge on (i) how substitutable CBDC is with checking deposits, (ii) how easily banks replace lost deposits with other funding, (iii) the interest rate on CBDC, and (iv) the competitive structure of banking. The paper provides quantitative welfare estimates in a model where CBDC and deposits are imperfect substitutes and banks are in monopolistic competition.

Model setup: A closed-economy steady-state model (akin to Gali 2015 and Del Negro-Sims 2015) with households, “bank owners,” firms, banks, government, and central bank. Money reduces a transaction cost on consumption (Schmitt-Grohe-Uribe 2004 style). Deposits and CBDC combine via a CES composite liquid asset characterized by three CBDC design dimensions: its interest rate (rc), its relative liquidity (alpha_c/alpha_b, the CES weight), and its substitutability with deposits (elasticity epsilon_cb). Crucially, with monopolistic competition each bank takes the average deposit rate as given, so the equilibrium deposit rate is unaffected by CBDC (Lemma 1); and because firms can fund at the risk-free rate, bank credit extension and loan rates are also unaffected by CBDC in steady state. Calibration (US-based): risk-free rate 4%, deposit spread 2%, loan spread 1%, reserve ratio 5%, deposit management cost 25 bps, interest semi-elasticity of money demand -0.05, inverse Frisch elasticity gamma=1, wealth/consumption=4. The two extreme ownership cases are zeta=1 (“case a,” households fully own banks) and zeta=0 (“case b,” a zero-measure set of bankers receives all profits).

Main findings (welfare in consumption-equivalent basis points): Welfare can improve via three channels — (1) seigniorage allowing lower distortionary labor taxes, (2) a lower opportunity cost of holding money (raising money holdings, cutting transaction costs, stimulating labor and consumption), and (3) redistribution of bank deposit rents from bankers to the general population. The optimal CBDC rate trades off seigniorage versus opportunity-cost reduction and is decreasing in the labor tax rate and decreasing in the share of banks owned by households (Proposition 3). The first two channels alone yield only modest gains: +9 bps at a 25% labor tax and +20 bps at 45%. Adding the redistribution channel (“case b”) raises non-bankers’ welfare to +54 bps (25% tax) and +59 bps (45% tax); the headline maximum is about 60 bps. From Table 2 (epsilon_cb=20, equal liquidity): consumption rises +27 bps (case a) / +54 bps (case b) at 25% tax, and +41 / +62 bps at 45% tax. All benefits require historically normal interest rates (baseline 4%); near the zero lower bound seigniorage, money’s opportunity cost, and deposit rents all vanish, so the welfare gain falls roughly linearly to zero with the deposit spread.

Policy/theoretical implications: CBDC is a tool to mitigate two distortions — distortionary taxation and the gap between the opportunity cost and the (low) production cost of money — plus a redistributive lever against the concentration of bank rents. The pure efficiency gains are modest; the larger gains come from redistribution and are larger where labor taxes (e.g., EU-14 averaging >40% vs. US ~25%), the Frisch elasticity, or the interest semi-elasticity of money demand are higher.

In depth

Q1. What is the model’s identification/derivation strategy, since this is a theoretical paper rather than an empirical one?

There is no econometric identification; results come from a calibrated closed-economy steady-state general equilibrium model. The ‘identification’ of the welfare channels is analytical: three propositions (proved in an online appendix) characterize how seigniorage and the optimal CBDC rate depend on CBDC liquidity (alpha_c), substitutability (epsilon_cb), and the labor tax rate, and numerical experiments on a US-calibrated economy quantify the welfare changes. The key structural assumption enabling the results is monopolistic competition in banking plus a financial-market funding alternative for banks at the risk-free rate.

Q2. Why does the introduction of CBDC leave the deposit rate and bank lending unchanged in this model?

Lemma 1: under monopolistic competition each individual bank takes the aggregate deposit rate as given and does not internalize how aggregate deposit demand shifts with CBDC, so its optimal deposit rate (eq. 30) is invariant to CBDC’s interest rate or liquidity. CBDC lowers aggregate deposit demand, so banks simply rely more on other liabilities (bonds/equity). Lending is unaffected because the marginal cost of bank funding remains the risk-free rate (banks can borrow from the market), so the loan rate (eq. 32) and quantity of loans do not change. This contrasts with monopoly/Cournot banking (Andolfatto 2021; Chiu et al. 2022) where CBDC moves the deposit rate.

Q3. What are the three welfare channels and how is each maximized?

(1) Seigniorage: higher central-bank seigniorage finances lower distortionary labor taxes; maximized by setting rc to raise seigniorage revenue (peak occurs at rc < rb in the cases analyzed). (2) Opportunity cost of money: paying high interest on CBDC raises money holdings and cuts the transaction cost, stimulating labor and consumption; maximized by setting rc equal to the risk-free rate so households drop deposits entirely and drive the transaction cost toward zero. (3) Redistribution: CBDC lets non-bankers capture deposit rents previously held by bankers (via tax cuts or interest on CBDC), maximal when zeta=0 and rc near the risk-free rate. Channels (1) and (2) conflict, generating the optimal-rate tradeoff.

Q4. What does seigniorage look like as a function of the CBDC rate, and what do Propositions 1-2 say?

Seigniorage is non-monotonic in rc: a higher rc lowers seigniorage per unit of CBDC but raises CBDC demand. Proposition 1 (under alpha_b^{epsilon_cb}*epsilon_cb > 1 and negligible CBDC management cost): the seigniorage-maximizing rc exceeds the deposit rate rb; if epsilon_cb>1.5 the optimal rc decreases in CBDC liquidity alpha_c; and the peak seigniorage rises with both alpha_c and epsilon_cb. Proposition 2: within that parameter region, maximum seigniorage is achieved as epsilon_cb to infinity (perfect substitutes) with rc set infinitesimally above rb — i.e., outcompete deposits. In the numerical cases shown, the seigniorage peak occurs at rc < rb, moving closer to rb as CBDC liquidity rises.

Q5. What heterogeneity / cross-country variation does the paper document?

Two dimensions. (i) Labor tax level: US ~25% vs EU-14 averaging >40% (Trabandt-Uhlig 2011). Higher taxes raise the value of the seigniorage/tax-cut channel, lower the optimal CBDC rate, and raise welfare gains (efficiency gains +9 bps at 25% to +20 bps at 45%). (ii) Bank ownership (zeta): ‘case a’ (households own banks) gives small gains (7-8 bps at 20% tax to 18-20 bps at 45%); ‘case b’ (bankers own banks) gives large gains (52-53 bps at 20% to 58-60 bps at 45%) via redistribution. The optimal CBDC rate is higher in case b than case a and rises with the tax rate (Proposition 3 / Figure 3).

Q6. What robustness / alternative-parameter checks are run (Table 3)?

Frisch elasticity (gamma=0.25 i.e. Frisch=4, and gamma=4 i.e. Frisch=0.25): higher Frisch raises case-a gains (e.g., +28 bps at 25% tax) but case-b gains are roughly independent of Frisch. Interest semi-elasticity of money demand set to -0.12 (Benati et al. 2021 for Switzerland): with 45% taxes, gains reach +35 bps (case a) and +85 bps (case b) — this parameter has the biggest impact. Other variations with small effects: deposit/loan management costs, reserve ratio (0% vs 10%), bank-profit tax tau_b (15% vs 35%; lower tau_b means more inequality and larger CBDC gain), loan elasticity epsilon_l, working-capital share phi, wealth/consumption ratio (2 vs 4). Loan-side parameters and household wealth essentially do not matter because lending is unaffected by CBDC. With lump-sum (non-distortionary) taxes, case-a gains shrink (the seigniorage-tax channel is inactive) while case-b gains are essentially unchanged. At the zero lower bound the welfare gain is approximately linear in the deposit spread and zero when the spread (net of management cost) is zero.

Q7. How does this paper relate to and differ from the closest prior work?

Versus Barrdear and Kumhof (2021): shares the transaction-cost money-demand approach but estimates a much smaller welfare benefit; their large +3% GDP gain comes mainly from the central bank buying public debt and lowering the government bond rate — a channel absent here. Versus Brunnermeier-Niepelt (2019): they get equivalence (no effect) under specific funding conditions; here CBDC does affect outcomes through seigniorage, opportunity cost, and redistribution. Versus Andolfatto (2021, monopoly bank) and Chiu et al. (2022, Cournot): in those the CBDC rate moves the deposit rate, whereas monopolistic competition here insulates the deposit rate (Lemma 1). Versus Chiu-Davoodalhosseini (2021): the opportunity-cost channel is shared. The paper abstracts from cyclical issues (cf. Burlon et al. 2022 DSGE; Piazzesi et al. 2022 monetary-policy use of rc) by focusing on steady state.

Q8. What are the main caveats and scope conditions on the welfare results?

(1) Steady-state only — no transitional or cyclical analysis. (2) Requires historically normal interest rates; near the ZLB all three channels are inert. (3) Liquidity and substitutability are treated as fixed design constraints in the welfare optimization, with only rc as the policy lever, because they may be technologically hard to set. (4) The headline ~60 bps gain relies on the extreme ‘case b’ (zero-measure bankers own all banks) and on the welfare function ignoring bankers — i.e., it is largely a redistribution result, not a pure efficiency result. (5) The model deliberately shuts down CBDC effects on bank lending (banks fund at the risk-free rate), so disintermediation-of-credit channels stressed elsewhere are absent by construction. (6) Bank profits in the model equal net interest income (~1.5-2% of consumption), comparable to US bank NII but higher than actual bank profits.

Q9. Is cash incorporated, and does it change the conclusions?

The baseline model excludes cash, but an appendix adds cash as a third zero-interest money in a nested CES (cash and CBDC combine, then that composite substitutes for deposits). The paper shows that if the ‘composite interest’ of cash-plus-CBDC equals the rc of the two-instrument baseline, economic outcomes are unchanged: households rebalance across the three instruments so the equilibrium transaction cost and total cost of holding money are the same.

Key Concepts

Does the Phillips Curve Lie Down as We Age?

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

Layer 1: Overview

Research question and motivation: The paper asks whether population aging flattens the Phillips curve through a previously unexplored channel — age-related differences in the elasticity of substitution across product varieties. Existing work on demographics and monetary policy emphasizes wealth, liquidity, and life-cycle savings channels. The authors instead argue that if older consumers are less willing to substitute across varieties of goods (i.e., they have a lower elasticity of substitution), then firms selling to them have more market power, adjust prices less responsively to marginal cost, and the slope of the Phillips curve falls. Because advanced economies are simultaneously aging and exhibiting a flattening Phillips curve, this offers a structural, demographically-driven explanation.

Data and empirical strategy: The empirical analysis uses barcode (UPC) level retail purchase data from the NielsenIQ Homescan Consumer Panel, 2004-2019. The panel is rotating and nationally representative, surveying between 40,000 and 60,000 households per year (average 57,355 households/year), capturing over 900 million transactions and 1,117 product modules. Purchases are aggregated into five age groups (25-34, 35-44, 45-54, 55-64, 65+) within more than 1,000 disaggregated product modules. The elasticity of substitution within modules is estimated by age using the Feenstra (1994) / Broda and Weinstein (2006) supply-and-demand identification (applied as in Jaravel 2019), with Equation (4) estimated by weighted least squares and aggregate elasticities formed as expenditure-share-weighted averages of module elasticities. Each module must have at least 20 purchasing households.

Main quantitative findings: The youngest cohort (25-34) consistently has the highest elasticity and the oldest (65+) the lowest; the middle groups (35-64) are non-monotonic. Median elasticity is 5.73 for the oldest and 7.02 for the youngest, in line with prior estimates (Broda-Weinstein 2010, Hottman et al. 2016). The maximum gap (oldest vs. youngest) is 1.29 for medians and 1.55 for means — larger than the 0.375 difference Faber and Fally (2022) find between richest and poorest income quintiles. A decomposition (Table 1) attributes the 65+ vs. 25-34 gap to one-third lower within-module elasticities and two-thirds a composition effect (older baskets weighted toward lower-elasticity products); for other age groups vs. 65+, 55-60% comes from the within-module elasticity term. The age pattern survives income controls and is most pronounced in the top two income quartiles (over 70% of expenditure share), so the authors conclude the age gradient is not driven by income.

Mechanism and theory: They extend a Rotemberg (1982) price-adjustment model to multiple consumer types. The log-linearized Phillips curve slope (Eq. 7/19) is the population-weighted average elasticity, sum_a (sigma_a - 1) s_a / phi. A lower share-weighted average elasticity flattens the curve: firms facing less price-sensitive (older) demand have more market power, can delay price changes, so inflation responds less to marginal cost. They note this does not hold in a first-order Calvo approximation with constant returns, but show in an Online Appendix menu-cost model that for empirically relevant parameters a lower elasticity reduces the probability of price adjustment, extending the result.

Quantitative exercise: Calibrating phi = 122 to match a 2022 Phillips-curve slope of 0.055 (the Gagliardone et al. 2023 midpoint of an estimated 0.05-0.06 range), then feeding in 1984 consumption shares yields a slope of 0.056 — a 2.3% reduction over 1984-2022. Benchmarked against the literature’s roughly 50% (halving) decline in the slope (Furlanetto and Lepetit 2024), the demographic channel accounts for about 4.5% of the observed flattening (2.3/50 = 4.5). The authors describe this as not large but a genuine contributing factor.

In depth

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

They use the Feenstra (1994) and Broda-Weinstein (2006) double-difference approach. For each product module they specify a CES demand equation relating changes in expenditure shares to changes in prices (slope -(sigma_m - 1)) and an inverse supply equation. Differencing both relative to a reference barcode k eliminates the time-varying intercepts (alpha_mt, phi_mt). Assuming the differenced demand and supply errors are uncorrelated, the two are combined into a single moment condition (Eq. 4) involving squared and cross-product terms of differenced prices and shares, estimated by weighted least squares; sigma_m and the inverse supply elasticity omega_m are backed out from the estimated theta coefficients subject to sigma_m > 1 and omega_m > 0. The key identifying assumption is the orthogonality of demand and supply shocks (changes in unobserved quality vs. supply-side shocks). A second threat the authors directly address is that age correlates with income, so age differences in elasticity could reflect income; they rebut this by re-estimating within income halves. They use only continuing barcodes (present in t and t-1) to measure period-to-period changes, and exclude non-UPC ‘magnet’ items like fresh produce.

Q2. How is the age effect distinguished from an income effect?

Income in the Homescan data is reported in discrete bins with a two-year lag, so the authors instead construct per-capita expenditure as an income proxy (following Faber and Fally 2022), regressing log total expenditure on household-size dummies and household attributes and netting out size effects; an appendix table shows this proxy is monotonically increasing in reported income bins. Re-estimating elasticities within the lower and upper 50% of the (expenditure-proxied) income distribution (Table 2), the falling-with-age pattern remains apparent conditional on being high income — indeed the gap across ages is even starker at higher incomes. Since upper-income households account for the large majority of expenditure within each age group, the pooled estimates track the upper-income pattern. The authors conclude the age gradient stems from a factor of age unrelated to income.

Q3. What are the two channels behind the age-elasticity gap, and how are they separated?

A decomposition (Table 1) splits the overall elasticity gap between each younger group and the 65+ group into (i) a ‘difference from sigma’ term that varies module elasticities while holding expenditure weights fixed (older people have lower elasticities within the same modules), and (ii) a ‘composition’ term that holds module elasticities at the 65+ values and varies expenditure weights (older baskets tilt toward lower-elasticity modules). For the largest gap (65+ vs. 25-34), about one-third is the within-module elasticity effect and two-thirds is composition; for the other age groups vs. 65+, 55-60% is the within-module elasticity effect.

Q4. Why does a lower elasticity flatten the Phillips curve mechanically in the model?

In the multi-type Rotemberg model the non-linear pricing FOC (Eq. 5) scales marginal cost by consumption weighted by each cohort’s elasticity. Log-linearizing around zero-inflation steady state gives a slope equal to the share-weighted average (sigma-bar - 1)/phi. A lower sigma means products are less substitutable, firms have more market power and are less sensitive to marginal-cost changes, so they can absorb cost changes or delay passing them through without losing demand — making larger but less frequent price changes. Marginal cost must move relatively more to generate the same inflationary pressure, hence a flatter curve. As the old (lower sigma) consume a rising share of output, sigma-bar falls and the curve flattens.

Q5. Doesn’t the Calvo model undercut the result, since elasticity doesn’t enter its Phillips-curve slope?

To a first-order approximation around zero-inflation steady state with constant returns to scale, the elasticity of substitution does not affect the Calvo Phillips-curve slope, because the price-adjustment probability is exogenous and independent of pricing power. The authors address this two ways. First, with decreasing returns the Calvo slope does depend on elasticity (a higher elasticity flattens it via marginal-cost dispersion), an effect absent under Rotemberg because there is no price/cost dispersion. Second, and more importantly, in a one-period menu-cost model (Online Appendix B) they show the firm’s willingness to pay the fixed cost and update prices is increasing in sigma for empirically relevant parameters (6 < sigma < 11, phi around 0.5 implying a 5-10% profit share). Since Calvo is a special case of dynamic menu costs, a lower elasticity maps to a lower adjustment probability and thus a flatter curve, so the result extends beyond Rotemberg.

Q6. What does the quantitative exercise actually compute, and what are its limits?

It is explicitly not a full-scale evaluation — it was added at a reviewer’s suggestion. They write the five-group slope (Eq. 8), calibrate phi = 122 so that 2022 elasticities and consumption shares reproduce a slope of 0.055 (Gagliardone et al. 2023 midpoint of 0.05-0.06, estimated from Danish firm-level marginal-cost data 1999-2019), then substitute 1984 consumption shares (holding elasticities fixed) to get 0.056. The resulting 2.3% slope decline, divided by the roughly 50% decline the literature reports (Furlanetto-Lepetit 2024 survey, with large uncertainty), gives about 4.5% of the observed flattening. The exercise varies only consumption shares, not the estimated elasticities themselves, over time, and the literature’s 50% benchmark is itself uncertain.

Q7. What heterogeneity is documented beyond the age gradient?

By income (Table 2): at lower income, mean elasticities rise slightly until 55-64 and are lowest for 65+; at higher income the age differences are starker than pooled. Median elasticities across income but within age are similar for ages 45+, but below 45 the lower-income group has smaller elasticities than the upper-income group. By year (Appendix Table 6): elasticities by age and year are reported for 2004-2019, with the oldest group lowest in essentially every year. The number of estimable modules differs across groups (e.g., Age 25-34: 378; 35-44: 632; 45-54: 743; 55-64: 768; 65+: 742), with fewer modules at younger and lower-income groups due to the 20-household threshold.

It departs from the wealth/liquidity HANK literature (Kaplan-Violante 2018, McKay-Wolf 2023) and from age-and-monetary-policy work that runs through wealth and savings: Eggertsson et al. (2019) on aging savers pushing down the natural rate, Berg et al. (2021) on age-dependent interest-rate sensitivity via wealth, Leahy-Thapar (2022) on the age structure of entrepreneurs, and Juselius-Takats (2021) on demographics affecting the level of inflation. Closest is Mangiante (2023), who shows older households’ baskets are weighted toward higher-price-rigidity products; this paper instead emphasizes that older households are themselves intrinsically less price-sensitive (lower within-module elasticity), a distinct price channel. It is consistent with Bornstein (2021) (older consumption more persistent) and Aguiar-Hurst (2007) (older households shop more, pay lower prices). It also speaks to the structural-stability literature (Rubio-Ramirez and Fernandez-Villaverde 2007): the aggregate elasticity is not a fixed structural parameter but depends on demographic composition.

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

Because the monetary-policy transmission mechanism depends on the Phillips-curve slope, ignoring the age distribution can bias the conduct and assessment of monetary policy efficacy; transmission will also have heterogeneous effects across age groups; and, all else equal, aging advanced economies should expect a flattening Phillips curve. Scope conditions: the channel is qualitatively important but quantitatively modest (about 4.5% of the observed flattening); the estimate covers retail/UPC purchases only and excludes services (where older households spend more and where price rigidities are higher per Cravino et al. 2022 and Mangiante 2023, so the composition effect may be understated); the flattening result is model-dependent (clean under Rotemberg, requiring the menu-cost argument to extend to Calvo); and the normative implications for optimal monetary policy are left as an open question.

Q10. What robustness checks and caveats does the paper provide?

Income re-estimation within income halves; per-capita expenditure validated as an income proxy against reported bins; a 20-household-per-module threshold; use of continuing barcodes only; exclusion of magnet items; year-by-year elasticity estimates (Appendix Table 6) showing stability of the ranking; the menu-cost extension to address Calvo; and explicit acknowledgment that services are missing from the data and that the quantitative benchmark (50% slope decline) is uncertain. The authors note the middle age groups are non-monotonic, so the result is a young-vs-old contrast rather than a strictly monotone age gradient.

Key Concepts

Estimating the Interest Rate Trend in a Shadow Rate Term Structure Model

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

This paper proposes a shadow rate no-arbitrage dynamic term structure model (SDTSM) with drifting trends to estimate the long-run trend of the real interest rate using yield curve data from the U.S., U.K., and Germany from January 1972 to April/March 2022. The model combines the shadow rate approach of Wu and Xia (2016) to handle the zero lower bound with the shifting endpoint of Bauer and Rudebusch (2020) to capture low-frequency movements. Interest rate trends in all three countries have declined since the 1990s, with strong co-movement among them. The model provides better yield forecasts than existing models. Term premium estimates from the model are stationary and positively correlated with inflation uncertainty measures, corroborating Wright (2011). Under the convention that all permanent shocks to real interest rates are derived from real shocks, the model’s trend estimate also serves as a measure of the natural rate of real interest.

In depth

Q1. What are the two key modeling innovations?

The model combines two innovations: (1) a shadow rate approach following Wu and Xia (2016) to handle the zero lower bound (ZLB)—defining the policy rate as max(shadow rate, lower bound) so that the model remains valid when rates are near zero; and (2) a drifting trend (shifting endpoint) following Bauer and Rudebusch (2020) to capture the slow downward movement of the interest rate trend since the 1990s. Combining these two features is the paper’s key contribution: existing shadow rate models (Wu-Xia) do not model the low-frequency trend; existing shifting-endpoint models (Bauer-Rudebusch) do not account for the ZLB. The combination produces better-identified trend estimates because the shadow rate summarizes financial conditions including the effects of unconventional monetary policy.

Q2. Why use the full yield curve rather than a few selected maturities?

Using the full yield curve with no-arbitrage restrictions allows the model to exploit all information in the Treasury bond market and impose internally consistent restrictions on how maturities are related, improving estimation efficiency relative to models that select a few yields and do not impose no-arbitrage restrictions (e.g., Del Negro et al. 2017; Johannsen and Mertens 2021). The failure of the pure expectations hypothesis implies that a model handling term premiums coherently and flexibly is necessary to correctly extract interest rate trends from long-term yields; the no-arbitrage DTSM provides this structure while also being free of the liquidity premium complications in TIPS-based models.

Q3. What are the main empirical findings about the interest rate trend?

Interest rate trends in the U.S., U.K., and Germany have all declined since the 1990s, with strong co-movement among them; under the convention that all permanent shocks to real interest rates are derived from real shocks, the paper’s trend estimate can be interpreted as a trend estimate of the natural rate of real interest. The strong international co-movement is consistent with global factors—such as declining trend output growth, rising savings, and global safe asset demand—driving the secular decline in real interest rates rather than purely country-specific factors.

Q4. What is the relationship between term premiums and inflation uncertainty?

Term premium estimates from the model are stationary (rather than trending downward as in some models where the trend and the term premium are not well separated) and are positively correlated with inflation uncertainty measures, corroborating Wright (2011)’s finding that term premiums are driven partly by inflation risk. The stationarity of term premiums is a desirable property that results from properly separating the trend component (modeled via the shifting endpoint) from the cyclical component; models that do not include a shifting endpoint may attribute some of the trend to the term premium, producing non-stationary term premium estimates.

Key concepts

shadow rate dynamic term structure model (SDTSM) : a term structure model in which the policy rate is defined as the maximum of a latent shadow rate and the effective lower bound, following Wu and Xia (2016); allows the model to be estimated without modification when short-term rates are near zero. drifting trend (shifting endpoint) : a slow-moving unconditional mean of interest rates that evolves over time, following Bauer and Rudebusch (2020); captures the secular decline in interest rates since the 1990s and separates trend from cyclical variation and term premiums. natural rate of real interest : the long-run equilibrium real interest rate consistent with stable inflation and output at potential; under the assumption that all permanent shocks to real rates are real shocks, the paper’s trend estimate provides a measure of this rate. Beveridge-Nelson trend : the long-run forecast of the shadow rate derived from the model; used here as the operational definition of the interest rate trend; transforms the information in the entire yield curve into a single macroeconomic equilibrium measure.

Financial Fragility and the Fiscal Multiplier

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

Layer 1: Overview

Research question and motivation: Does fiscal stimulus still work when it is financed through a banking system that is undercapitalized and holds large quantities of risky domestic government bonds? This was a first-order policy question in Southern Europe (Spain, Italy, Portugal — “SIP”) during the 2011–2013 European sovereign debt crisis, and the authors argue it is relevant again as central banks raise rates after the Zero Lower Bound. Motivating stylized facts: Spanish banks held domestic sovereign debt equal to more than 150% of Tier-1 capital (Italian banks ~200%, Greek banks ~250% at end-2011); CDS spreads on Italian and Spanish sovereign debt rose from ~100 bps in January 2010 to above 400 bps in 2012–2013 (Portugal exceeded 1000 bps at end-2011); VAR evidence shows sovereign-spread pass-through to corporate lending rates is nearly complete within six months. Gennaioli et al. (2018) document that 12.7% of emerging-market commercial bank assets are (mostly domestic) government bonds, extending relevance beyond Europe.

Model setup: The authors first build a tractable two-period general-equilibrium model with leverage-constrained banks (Gertler-Karadi 2011 incentive-compatibility constraint), long-term debt, and endogenous sovereign default risk to derive analytical propositions. They then build and Bayesian-estimate an infinite-horizon New Keynesian DSGE model of a small open economy in a monetary union (in the spirit of Burriel et al. 2010), calibrated/estimated to Spain. Default risk is modeled as a non-strategic default driven by a stochastic maximum feasible level of taxation (Schabert-van Wijnbergen; Corsetti et al. 2013); the default probability draws from a generalized beta distribution. Long-term bonds use the Woodford (2001) decaying-coupon structure. Estimation uses quarterly Spanish data for 2003Q1–2010Q4 (10 observable series including real GDP, consumption, government spending, exports, imports, inflation, real wage, hours, deposit rate, and the NFC loan rate). The model is estimated WITHOUT sovereign risk because risk was minor over the estimation window. Key calibrated/estimated parameters: weighted steady-state leverage ratio phi-bar = 6.48; lambda_b/lambda_k = 0.5; posterior-mean corporate-loan diversion rate lambda_k-bar = 0.64 (implying lambda_b-bar = 0.32), both higher than the literature’s typical values (below 0.4 and 0.2), indicating financial frictions are relatively important for Spain. Steady-state default probability set to 50 quarterly basis points (~2% per year); default elasticity of 0.003 (small relative to Schabert-van Wijnbergen’s 0.01).

Main quantitative findings: Simulating a financial crisis (a one-off 5% “MIT” increase in the corporate-loan diversion rate, persistence 0.7, output recovering after ~20 quarters) followed by a deficit-financed stimulus of 0.5% of quarterly GDP, the discounted cumulative multiplier is: +0.25 with short-term debt and no sovereign risk (row 1); +0.15 with long-term debt (20-quarter duration) and no sovereign risk (row 2); and -0.65 with both long-term debt and sovereign default risk (row 3). Adding long-term debt explains ~11% of the 90-bp decline; adding sovereign risk explains ~89%. Combining both ingredients lowers the multiplier by at least 0.60 percentage points versus including only one. Nonlinearities: the multiplier falls with stimulus size — for a delayed (4-quarter lag) stimulus, going from 0.5% to 4% of quarterly GDP lowers the multiplier by 0.58 pp (-0.65 to -1.23); for an immediate stimulus by 0.29 pp (-0.14 to -0.43). It falls only mildly with crisis size (delayed: -0.63 to -0.70 as the shock rises from 2% to 15%). Implementation timing: an immediate stimulus has multiplier -0.14 versus -0.65 for a 4-quarter delay, a 0.51-pp gap (the paper states “at least 0.30 pp” lower for a 4-quarter lag). Policy implications: implement stimuli fast after announcement, clean up bank balance sheets before stimulating, and keep stimuli small when banks are undercapitalized.

In depth

Q1. What is the new mechanism (“channel”) the paper identifies, and how does it differ from prior crowding-out stories?

A new credit-availability/crowding-out channel running through bank balance sheets. A deficit-financed stimulus raises the bond supply and (via higher debt) sovereign default risk, depressing bond prices. Undercapitalized, leverage-constrained banks holding existing government bonds suffer capital losses, which reduce net worth and tighten the incentive-compatibility (leverage) constraint, forcing them to cut corporate lending and crowding out private investment. The novelty versus prior bank-sovereign-nexus work (e.g., Corsetti et al. 2012, where banks do not hold government debt and causality runs only from sovereign problems to lending rates) is the feedback loop / ‘doom loop’: capital losses on existing bonds raise rates on newly issued bonds, aggravating the sovereign problem, causing further capital losses and further lending contraction. This amplification cycle requires both long-term debt and endogenous default risk to be quantitatively important.

Q2. What are the three terms in the analytical decomposition of the lending response (equation 9)?

In the two-period model, the change in corporate lending dk0/dg0 decomposes into: (1) direct crowding out by new spending (-lambda_b) — lending must fall to free balance-sheet capacity to absorb newly issued bonds (Kirchner-van Wijnbergen 2016); (2) a funding-cost effect — higher deposit/funding costs raise the required return on loans, reducing loan demand (zero under the small-open-economy assumption); and (3) the key innovation — capital losses on existing long-term bond holdings b_{-1} from the bond-price drop (dq/dg0 < 0) reduce net worth, tightening the constraint and contracting lending further. The third term exists only with multi-period bonds and grows with maturity.

Q3. How is the contribution of each ingredient (maturity vs. sovereign risk) quantified?

By trimming the model stepwise (Table 1). Moving from short-term/no-risk (mu_D = 0.25) to long-term/no-risk (mu_D = 0.15) explains 11% of the total 90-bp decline. Adding sovereign default risk (mu_D = -0.65) explains the remaining ~89%. Thus sovereign risk is the dominant driver, but it bites significantly only in the presence of longer-maturity debt — at short maturities both with- and without-risk multipliers equal 0.25 (Figure 8).

Q4. Why does implementation timing matter, and what is the mechanism?

A financial crisis lowers domestic prices relative to foreign (Eurozone) prices, improving competitiveness/terms of trade. A stimulus raises domestic prices, causing expenditure switching toward foreign goods and lower exports. An immediate stimulus is implemented while domestic goods are still cheap (crisis-induced), partially offsetting the loss; a delayed stimulus arrives after domestic prices have recovered, so the relative-price deterioration is larger and more persistent. Additionally, forward-looking banks anticipate the future debt issue, so the bond price falls (by almost 0.5% extra) and net worth contracts before implementation, producing negative output effects in the pre-implementation period. The cumulative multiplier falls from -0.14 (immediate) to -0.65 (4-quarter delay).

Q5. What heterogeneity / dimensions of variation are documented?

(1) Debt maturity: the multiplier declines with average duration (Figure 8), more steeply with sovereign risk present. (2) Stimulus size: the multiplier falls substantially with size (Table 4), more for delayed stimuli (-0.58 pp) than immediate (-0.29 pp). (3) Financial-crisis size: the multiplier falls only mildly as the lambda_k shock rises from 2% to 15% (delayed: -0.63 to -0.70; immediate: -0.13 to -0.19) — quantitatively small. (4) Implementation lag: monotonically lower multiplier with longer lag (Figure 10). Heterogeneity across SIP countries is documented descriptively in the stylized facts (sovereign exposures and CDS spreads).

Q6. What is the identification/estimation strategy, and what are its limitations?

Two-stage: first partial calibration (standard literature values plus first-moment targets such as steady-state labor supply and the leverage ratio phi-bar = 6.48 from Bank of Spain OMFI assets-over-capital, halved per Gertler-Karadi 2013); second, Bayesian estimation of remaining deep parameters via first-order approximation on 2003Q1–2010Q4 Spanish data. The NFC loan-rate series identifies the corporate-loan diversion rate (posterior mean 0.64). A key limitation acknowledged by the authors: the model is estimated WITHOUT sovereign default risk (because risk was minor in the estimation window, following Bocola 2016), and sovereign-risk parameters are calibrated rather than estimated. Statistical significance of the sovereign-risk effect is assessed by checking whether with-risk IRFs (bond prices, investment, output) lie outside the 90% HPD bands of the no-risk model — they do (Figure 7).

Q7. How is sovereign default modeled, and does default actually hit bank net worth in equilibrium?

Default is non-strategic (Aguiar-Amador 2013 language): each period a stochastic fiscal limit (max feasible taxation) is drawn from a generalized beta distribution; if required taxes exceed it, the government applies a haircut (1 - theta_t) on outstanding liabilities. Notably, the default gains are rebated to unconstrained households via lower lump-sum taxes and used to recapitalize banks in randomized fashion, so aggregate bank net worth is unaffected ex post by realized default (a modeling choice to avoid a discontinuity). The economically active channel is therefore ex ante: anticipated default risk lowers the bond price q_t, which lowers the market value of banks’ existing holdings and tightens the leverage constraint.

Q8. What robustness checks are run (Appendix E)?

The multiplier is recomputed for alternative values of: the steady-state corporate-loan diversion rate, the ratio of government bonds to corporate loans, the steady-state leverage ratio, the household bond-adjustment-cost coefficient, and the fraction of constrained households. Without sovereign risk the multiplier changes very little (for both short- and long-term debt), though it decreases when the fraction of constrained households is reduced. Alternative calibrations of the default-probability function change the multiplier more when debt is long-term and risky. The central conclusion — the multiplier falls substantially once sovereign default risk is added — holds across all alternative parameterizations.

Versus Gornicka et al. (2020): both find a positive multiplier absent sovereign risk or long-term debt; the difference (negative multiplier) arises because Gornicka et al.’s sample pools all excessive-deficit-procedure countries regardless of whether they were in a sovereign crisis, whereas this paper focuses on a crisis country (Spain almost lost bond-market access in May 2012). Versus Corsetti et al. (2012/2013): those have one-directional causality (sovereign problems -> lending rates) and banks do not hold government debt, so the doom-loop feedback is absent. Versus Gertler-Karadi (2013), Bocola (2016), Kirchner-van Wijnbergen (2016), Kollmann et al. (2013): these let banks hold government bonds but treat sovereign risk as absent or exogenous; this paper endogenizes default probability via the fiscal-limit model, creating the amplification cycle. Versus van der Kwaak-van Wijnbergen (2014): that paper studies recapitalizations, not fiscal-policy effectiveness. Empirical support: Homar-van Wijnbergen (2017) find fiscal policy has no significant recovery effect when banks are not recapitalized.

Q10. What are the three main policy recommendations and their scope conditions?

(i) Implement stimuli as soon as possible after announcement (minimize the announcement-implementation lag), because effectiveness deteriorates with delay; (ii) clean up / recapitalize commercial bank balance sheets early in a crisis BEFORE embarking on fiscal stimulus; (iii) keep stimuli small when banks are undercapitalized, since the multiplier declines with size. Scope conditions: these apply specifically to economies where banks are undercapitalized AND hold large quantities of long-term domestic sovereign debt subject to (endogenous) default risk — i.e., a combined banking-sovereign crisis (Spain/Southern Europe 2011–2013, and emerging markets with large domestic bond holdings). Absent sovereign risk or long-term debt, the multiplier is positive and standard.

Q11. Why can the cumulative multiplier be negative even though the direct spending effect is positive?

The impulse-response (Figure 6) shows the output effect is negative before implementation (anticipation tightens bank balance sheets), turns positive at implementation, then turns negative again within a year as the balance-sheet/crowding-out channels dominate, fizzling to zero by ~40 quarters. When the negative areas (discounted) outweigh the positive, the cumulative discounted multiplier (Mountford-Uhlig 2009 definition, equation 32) turns negative (-0.65 in the base case), meaning the stimulus is self-defeating.

Key Concepts

Financial Stability with Fire Sale Externalities

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

Layer 1: Overview

Research question and motivation: Asset fire sales were a defining feature of the 2007-08 crisis, and post-crisis reforms (Basel III liquidity requirements, Money Market Mutual Fund reforms) were introduced to mitigate fire sale externalities by reducing distressed debt obligations and forcing larger liquidity buffers. The paper asks whether policies that successfully mitigate fire sale externalities actually improve financial stability, since it is not obvious how banks re-optimize in response.

Model setup (no empirical data — this is a theoretical paper): The authors build a three-period (t = 0,1,2) Diamond-Dybvig (1983) model of financial intermediation augmented with (i) cash-in-the-market pricing in a financial market as in Allen and Gale (1998), and (ii) limited commitment as in Ennis and Keister (2009), following Li (2017). A unit continuum of ex ante identical depositors have CRRA preferences with relative risk aversion γ > 1. Each depositor is impatient with known probability π. There are two assets: a short-term storage asset (1 unit yields 1 next period) and a long-term asset (1 unit at t=0 yields R > 1 at t=2). The bank invests fraction x in the long-term asset and 1−x short. Long-term assets can be sold at t=1 at an endogenous price p to risk-neutral investors who receive endowment ws (market liquidity) and have outside return R* > 0. Runs are introduced via a sunspot s ∈ {α, β} with run probability q; runs are partial (stop after fraction π is served), following Ennis and Keister. The authors assume R* = R, which implies p ≤ 1 in equilibrium. Financial fragility is measured by q-bar, the maximum run probability q for which the run strategy is an equilibrium (run condition c1 ≥ c2β).

Main analytical findings: (1) Without intervention, banks over-invest in long-term assets relative to the socially efficient level because each competitive bank takes p as given and does not internalize that selling long-term assets in a run depresses p (the fire sale externality); the equilibrium price is inefficiently low. (2) The bank’s best response is in Case I (no excess liquidity, fire sale occurs) when 0 < q < q_l, and Case II (excess liquidity held) when q_l ≤ q < 1 (Lemma 1). There is a unique q_c at which the market-clearing price p* turns from decreasing to increasing in q (Lemma 3). (3) Comparative statics on market liquidity ws (Proposition 1): when the relevant q-bar lies in Case II (low ws), q-bar is strictly increasing in ws, so a small rise in market liquidity raises fragility; when q-bar lies in Case I (high ws), q-bar is strictly decreasing in ws. The mechanism (Lemmas 4-5) is that a higher p* raises c1 via intertemporal substitution; the c2α/c2β effect is always dominant, flipping the sign of dq-bar/dws between cases. (4) The intervention: a regulator controls (x, c1), internalizing the effect on p, while the bank still chooses (c2α, c1β, c2β) taking p as given. The regulator chooses lower x and higher c1 than the bank in Case I (Lemma 6: c1 ≤ c1R, x ≥ xR), raising the market-clearing price (Proposition 2: p* ≤ pR* in Case I). (5) Key result (Proposition 3): q-bar_R ≥ q-bar when both solutions are in Case I (intervention always raises fragility); ambiguous otherwise. When ws (or R) is high, intervention raises fragility (q-bar_R > q-bar); when ws or R is low, intervention involves excess liquidity and lowers fragility (q-bar_R < q-bar). Proposition 4 gives a sufficient condition for q-bar_R > q-bar via four thresholds ws1≤ws≤ws2 and ws3<ws<ws4. When ws is sufficiently high, p = pR = 1, the externality vanishes, and q-bar = q-bar_R. (6) Welfare (Proposition 5): WR(q-bar) ≤ W(q-bar) when both in Case I, and for some parameter values otherwise — intervention does not always improve welfare and can worsen it when market liquidity is large.

Policy implication: Mitigating fire sale externalities does not necessarily increase stability. Because the regulator takes q as given, it ignores that its own intervention can raise q-bar. Policymakers must internalize the fragility effect and balance externality mitigation against increased fragility, especially when market liquidity is high.

In depth

Q1. Is there an identification strategy or empirical data? What are the threats?

No. This is a purely theoretical paper with no data, sample period, or estimation. The quantitative content consists of analytical comparative-statics results (Lemmas 1-6, Propositions 1-5) and numerical illustrations rendered as figures (Figures 4-9) for specific parameter combinations of (ws, R, q, γ, π). There is no econometric identification; the analog of robustness is the set of modeling assumptions and the parameter regions over which results hold.

Q2. What is the core economic mechanism, and how does intervention raise fragility?

The regulator internalizes the fire sale externality by reducing the bank’s long-term holdings x and holding more short-term assets, which reduces asset supply in a crisis and raises the market value p of each long-term asset (this mitigates the externality and is the intended benefit). But two competing effects act on long-term payments c2β: the higher price raises the value of remaining long-term assets, while there are fewer long-term assets left for c2β (whose period-2 return R is fixed, so the price increase does not help c2β as it does c1β). The net effect on c2β is ambiguous. Simultaneously, reducing x lowers the relative cost of t=1 consumption, optimally pushing the regulator to raise short-term payment c1. Since the run condition is c1 ≥ c2β, raising c1 while c2β may fall makes early withdrawal more attractive, raising q-bar. When market liquidity is high, the net effect always increases fragility.

Q3. What is the role of ’excess liquidity’ and how does it reverse the result at low market liquidity?

Excess liquidity (Case II: πc1 < 1−x, holding more short-term assets than needed for the first π payments) is the bank’s/regulator’s hedge against runs. When ws is low, the anticipated fire sale price is low, so the regulator chooses to hold more excess liquidity than the bank. Excess liquidity supplies additional resources to pay c1β and further reduces asset supply (raising p), leaving more resources for c2β. This makes the net effect on c2β favorable enough that q-bar falls. Thus at low market liquidity the regulator can simultaneously mitigate the externality and reduce fragility; at high market liquidity, excess liquidity is small or zero and the fragility-increasing channel dominates.

Q4. What heterogeneity / regime dependence is documented?

Results depend critically on the regime (Case I = no excess liquidity / fire sale; Case II = excess liquidity; Case III = excess liquidity, no fire sale, which never arises in equilibrium). The sign of dq-bar/dws flips between Case I (decreasing) and Case II (increasing). The intervention’s effect on fragility flips with market liquidity ws and long-term return R: low ws or low R → intervention reduces fragility; high ws or high R → intervention raises fragility; very high ws → externality vanishes (p = pR = 1) and intervention is neutral (q-bar = q-bar_R). The switch from Case I to Case II is governed by thresholds q_l (bank) and q_l,R (regulator), with q_l,R < q_l because the regulator internalizes the price and is more inclined to hold excess liquidity.

Q5. What robustness / generality checks are discussed?

Several modeling-assumption relaxations are argued not to change results qualitatively: (i) the assumption R* = R (giving p ≤ 1) can be generalized to allow p > 1, which does not undermine findings in the p < 1 range; (ii) partial runs can be generalized to multiple waves via a richer sunspot space without changing mechanisms; (iii) depositors not observing the bank’s portfolio can be replaced by observing it only after the withdrawal decision, with identical results; (iv) the simultaneous-move game is shown equivalent to a dynamic game in which the regulator moves first, as long as depositors cannot observe regulator choices; (v) the assumption that interventions convey no information to depositors can be relaxed (justified by the complexity of post-crisis regulation, e.g., the 848-page Dodd-Frank Act) without undermining the structure.

Q6. How does this paper relate to and differ from prior work?

It builds on the fire sale externality literature (Lorenzoni 2008; Gale and Gottardi 2015; He and Kondor 2016; Davila and Korinek 2018 on over/under-investment; Acharya et al. 2011 and Gale and Yorulmazer 2020 on distorted portfolios; Perotti and Suarez 2011, Walther 2016, Kara and Ozsoy 2019 on optimal capital/liquidity regulation). It also builds on the bank-run literature (Bryant 1980; Diamond-Dybvig 1983) and on general-equilibrium / endogenous-portfolio extensions (Allen-Gale 2004; Farhi et al. 2009; Eisenbach-Phelan 2021; Cooper-Ross 1998; Ennis-Keister 2006; Li 2017). The stated novel contribution is being the first to show that policies designed to correct fire sale externalities can worsen financial fragility, achieved by jointly endogenizing the portfolio choice, the general-equilibrium asset price, and the equilibrium probability of a run.

Q7. What are the policy implications and their scope conditions?

Macroprudential interventions that regulate short-term liabilities and portfolio choice to curb fire sale externalities can increase the equilibrium probability of runs. The scope condition is market liquidity: the harmful trade-off (mitigate externality but raise fragility, and sometimes lower welfare) arises specifically when market liquidity ws is high (and/or R high); when ws is low, the regulator’s optimal excess-liquidity holding lets intervention both mitigate the externality and reduce fragility. A central caveat is that the regulator takes q as given and so does not perceive that its policy raises q-bar; the prescriptive takeaway is that policymakers must internalize q-bar (the endogenous run probability) when designing such policies, balancing externality mitigation against fragility.

Q8. Are the quantitative results exact magnitudes or signs?

The paper’s results are predominantly signs and ordinal comparisons (e.g., x ≥ xR, p* ≤ pR*, q-bar_R ≥ q-bar, monotonicity in ws and p) plus closed-form threshold expressions (q_l, p_l, p_u, the four ws thresholds in Proposition 4) given in the text and appendices. Specific numeric magnitudes appear only as illustrative figure values (e.g., the example in Figure 9 where intervention raises fragility when ws is near 0.2); the paper does not report calibrated point estimates beyond such illustrative figures.

Key Concepts

Fire sale externality: In this model, the inefficiency arising because each competitive bank takes the t=1 asset price p as given and does not internalize that its long-term holdings and crisis-time asset sales depress p, harming other banks. It leads banks to over-invest in long-term assets and sell more than the efficient amount, pushing the equilibrium price below its efficient level.

Cash-in-the-market pricing: The price of long-term assets at t=1 is set by the limited cash (endowment ws) that risk-neutral investors bring to the market rather than by fundamental value; when banks must sell, scarce market liquidity forces the price down (p ≤ 1 under the R*=R assumption).

Financial fragility (q-bar): Measured as q-bar, the maximum run probability q for which the partial-run strategy profile is part of an equilibrium, i.e., the largest q satisfying the run condition c1 ≥ c2β. Higher q-bar means the banking system is more fragile.

Excess liquidity: Short-term asset holdings beyond what is needed to pay the first π withdrawals (πc1 < 1−x; Case II). It is a precautionary buffer that supplies resources for crisis payments c1β, reduces asset supply, and raises the fire sale price; the regulator holds more of it than the bank when market liquidity is low.

Case I vs Case II vs Case III: Regimes of the bank’s best response: Case I = no excess liquidity, fire sale occurs (small q, high ws); Case II = excess liquidity held with fire sale (large q, low ws); Case III = excess liquidity so large that no fire sale occurs — shown never to be an equilibrium because it implies c2β > c2α > c1 (no run condition).

Regulator/intervention: A planner that chooses (x, c1) internalizing the effect of these choices on the asset price p, while the bank still chooses (c2α, c1β, c2β) taking p as given and the regulator cannot direct depositors’ withdrawal decisions; it represents the two policy instruments of regulating short-term liabilities and portfolio choice.

Fiscal Distress and Banking Performance: The Role of Macroprudential Regulation

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

Layer 1: Overview

This paper studies a transmission channel from sovereign fiscal weakness to banking performance that the literature has largely overlooked: government-provided deposit insurance, rather than banks’ holdings of sovereign bonds. The motivation comes from the Eurozone crisis (especially Greece), where doubts about a government’s ability to honor its deposit-insurance pledge made bank deposits risky and weakened the banking system. The central question is whether allowing macroprudential policy (bank capital requirements) to adjust optimally to the degree of fiscal stress can sever the standard positive co-movement between sovereign and bank credit risk.

The authors build a quarterly DSGE model based on Clerc et al. (2015) and Mendicino et al. (2018), featuring a rich financial sector with multiple agency problems, capital regulation, government deposit insurance, and endogenous bank default from idiosyncratic and aggregate loan-portfolio shocks. Their novel ingredient is that the Deposit Insurance Agency may honor only a fraction p of insured deposits when government finances are fragile; the unhonored portion is bailed in and becomes a junior claim on the failed bank’s repossessed assets. The key fiscal-robustness measure is gamma = p*k (fraction of deposits effectively insured), with robustness rising in gamma. The model is calibrated to Greece using Eurostat and Bank of Greece data over 2000-2010 (pre-crisis, to keep the steady state well behaved). Baseline calibration: gamma0 = 0.34 (set to match the average bank-deposit-vs-German-bund spread); capital requirements of 8% for corporate and 4% for mortgage loans; repossession cost mu = 0.3 (30% asset-value loss); idiosyncratic shock SDs sigma_m = 0.11 (households) and sigma_e = 0.487 (entrepreneurs); bank risk-shock SDs sigma_F = 0.0331 and sigma_H = 0.0163 set so steady-state bank default = 2%. Given the low default rate, the steady-state expected depositor bail-in is only 0.155% and the annualized deposit risk premium is 0.41%.

Main findings: (1) Holding capital requirements fixed, greater fiscal frailty (lower gamma) raises the deposit spread, bank and corporate default rates, and lowers credit and GDP; welfare is a monotone decreasing function of fiscal frailty (1 - gamma). (2) The optimal level of corporate capital requirements rises uniformly as deposits become riskier — from phi_F = 0.1048 at gamma = 0.34 to phi_F = 0.1075 at gamma = 0.05. (3) Crucially, implementing this optimal increase lowers the bank default rate, producing a NEGATIVE correlation between sovereign and financial credit risk — reversing the standard positive correlation in the literature — while also making the output and credit contraction milder than under fixed requirements; the indirect (credit) channel is the bigger contributor to the output gain, not just direct default-cost savings. (4) Fiscal frailty exacerbates the effects of other risk shocks, but optimal macroprudential adjustment mitigates the response, and this insulation is more pronounced when financial uncertainty (risk-shock variance) is high; optimal requirements rise at an increasing rate with risk-shock variance. (5) A bankruptcy-law reform lowering repossession costs (illustrated as 30% to 10%) unambiguously raises welfare, supports LOWER optimal capital requirements, raises credit and output, lowers bank default, and improves insulation to risk shocks. Policy implication: under a banking union with pooled (weighted-average) fiscal capacity, fiscally weak countries see lower optimal requirements (benefit) and fiscally strong countries higher requirements (lose) — rationalizing why southern EU countries favored banking union and northern ones resisted.

In depth

Q1. What is the core mechanism linking fiscal distress to banking performance, and how does it differ from the existing literature?

The mechanism operates through the LIABILITY side of bank balance sheets via deposit insurance, not the asset side (banks holding sovereign bonds). When government finances are fragile, the Deposit Insurance Agency honors only a fraction p of insured deposits; the rest is bailed in and reclassified as a junior claim on the failed bank’s repossessed assets. This raises the riskiness of insured deposits, increases banks’ cost of funding, reduces lending, raises borrowers’ and hence banks’ default probability. The extant literature (Bocola 2016; Broner et al.) focuses exclusively on the asset-side channel (bond prices weakening bank balance sheets) or fiscal-to-bank crowding out; this paper studies the deposit-insurance/liability channel, which played a real role in the Greek crisis.

Q2. How is fiscal robustness modeled formally?

Fiscal robustness is gamma = pk, where k is the (fixed, non-choice) fraction of nominally insured deposits and p is the fraction of the insurance pledge actually honored. The realized return on total bank debt is R-tilde_D = R_D minus (1 - gamma)Omega, where Omega is the default loss per unit of bank debt. gamma can follow a feedback rule gamma_t = gamma0 + gamma1(RB_t - RB) + gamma2*(b_t - b*) + epsilon_t, with gamma1 < 0 (more public-debt repayment lowers fiscal space) and gamma2 > 0; in the baseline these feedback terms are switched off (gamma1 = gamma2 = epsilon = 0) so the analysis isolates differences in gamma0. Because taxation is lump-sum, the true optimal p is always unity; the authors treat reductions in fiscal capacity as exogenous rather than micro-founding the constraint.

Q3. What is the key qualitative result that overturns a standard assumption in the literature?

The literature treats the positive correlation between sovereign credit risk and bank (financial) credit risk as a robust feature. This paper shows that if capital requirements adjust optimally to rising fiscal frailty, the optimal requirement RISES, which lowers the bank default rate, thereby generating a NEGATIVE correlation between sovereign and financial credit risk. So the standard positive co-movement is an artifact of holding macroprudential policy fixed.

Q4. Why do higher capital requirements support, rather than depress, output here?

One might fear that higher requirements reduce bank lending and depress output. In the model’s general equilibrium, however, higher requirements make banks safer, which mitigates the rise in the deposit spread and the decline in deposits and bank credit. The net effect is that the recession is less severe than without policy adjustment. The authors find the INDIRECT effect (supporting a higher level of financial intermediation/credit) is a bigger contributor to the output gain than the DIRECT effect (saving on default costs).

Q5. What does the steady-state welfare analysis show?

Welfare is a negative, monotone function of fiscal frailty (1 - gamma): more fragility is socially detrimental. The reason for monotonicity is that deposit insurance is cheap to provide (funded by lump-sum taxes, so optimal gamma = 1) and there is no good substitute because depositors do not monitor banks. Under optimal capital requirements, welfare is higher for any given gamma, and the welfare benefit of adjusting requirements grows as fiscal frailty rises (the gap between the optimal-policy and fixed-policy welfare lines widens at lower gamma).

Q6. What are the quantitative magnitudes of the dynamic stabilization, and why are they small?

In response to a one-SD negative bank risk shock, moving from baseline gamma = 0.34 (optimal phi_F = 0.1048) to high fragility gamma = 0.05 worsens GDP and bank default. Adjusting phi_F optimally to 0.1075 mitigates this. The quantitative effects are SMALL because uninsured deposits are nearly risk-free in the calibration (steady-state bank default only 2%, expected bail-in only 0.155%, high asset recovery), and because the economy is assumed to start at the optimal capital requirement. The authors note that if the economy instead started at the suboptimal Basel III minimum of 8% (CAR = 0.08), failing to adjust requirements would be considerably more consequential — the gap would be quantitatively bigger (shown in online appendix A1.5).

Q7. How do incomplete deposit insurance and risk-shock variance interact?

Holding requirements fixed, raising the variance of the entrepreneurial risk shock (sigma_e) modestly lowers mean output and raises its volatility; a lower gamma (higher bail-in risk) exaggerates all these effects, so the two uncertainty sources interact in a destabilizing way. Optimal macroprudential policy partly contains this. For corporate-bank risk-shock variance (sigma_F), the bank-default response is non-monotone: to the left of sigma_F = 0.0331 the default rate is higher under optimal policy (banks are sub-optimally OVER-capitalized there), and to the right it is lower (banks sub-optimally UNDER-capitalized). Optimal phi_F rises at an increasing rate with risk-shock variance, so countries with greater financial/aggregate volatility need higher capital requirements; combining high uncertainty with high fiscal frailty magnifies optimal requirements.

Q8. What does the model imply for banking union, and what is the scope condition?

If the banking union’s fiscal capacity is the weighted average of members’, fiscally strong countries face HIGHER optimal capital requirements on joining (worse off, due to the costly credit/output side of requirements) and fiscally weak countries face LOWER requirements (better off). This rationalizes southern EU countries favoring banking union and northern countries resisting (unwilling to share fiscal capacity for bailouts). The explicit scope condition: this is only ONE factor among many in the banking-union decision — a narrow fiscal perspective. Moreover, even removing the fiscal dimension (e.g., via an EU-wide deposit insurance scheme), differences in economic uncertainty across countries still make banking union problematic because optimal requirements differ.

Q9. What robustness exercises are run?

Six: (i) Extending government guarantees to all bank debt (gamma = 1) — full insurance mitigates the effect of bank risk shocks. (ii) Open-economy version with external public debt (Abad 2018 framework; debt burden 5% then 15% of GDP, gamma1 = -0.012, persistence rho_RB = 0.57): higher external-debt servicing costs reduce welfare, consumption, investment but RAISE output, deposit spreads, bank default, and optimal requirements — output rises because higher non-distortionary taxes create a negative wealth effect that makes households work more; higher external indebtedness mitigates the GDP/default impact of a bank risk shock. (iii) Lower repossession costs (30% to 10%) — higher welfare, lower optimal requirements, higher credit/output, lower default, better risk-shock insulation. (iv) Alternative welfare weights (baseline savers 0.5863, borrowers 0.4137) — no qualitative change; a higher weight on savers lowers welfare under optimal requirements (savers have lower marginal utility) and calls for higher optimal requirements to protect savings. (v) Dynamics around the suboptimal Basel III minimum CAR = 0.08 instead of the optimal level — yields bigger quantitative effects. (vi) A short-cut for the asset-side channel: combining a negative bank net-worth shock (-1% of steady-state output) with a negative public-debt-servicing-cost shock (-1%) — outcomes are worse except output, which falls by less due to the wealth-effect labor-supply response.

Q10. What are the main threats to the analysis / caveats the authors acknowledge?

The model deliberately omits the asset-side channel (banks holding long-term government bonds), which would require an extra state variable; they approximate it only via the combined-shock short cut in appendix A1.6. Fiscal capacity is not micro-founded — gamma is treated as exogenous, and because taxation is lump-sum the true optimal gamma is always 1, so there is no genuine fiscal trade-off generating an interior solution. Calibration of the deposit-insurance parameters (k and p separately) is speculative because no data exist; gamma0 = 0.34 is backed out from the deposit spread. DSGE methods are unsuitable for large crisis deviations, so calibration uses pre-crisis 2000-2010 data. The banking-union result is explicitly only one narrow fiscal consideration among many.

It builds directly on the Clerc et al. (2015) and Mendicino et al. (2018) three-layers-of-default DSGE models, adding incomplete deposit insurance tied to fiscal capacity. It contributes to the strand studying transmission of fiscal fragility to bank lending (Bocola 2016; Broner et al. 2013/2014) but via deposit insurance rather than bond exposure or selective default. Stavrakeva (2017) also finds a positive relationship between fiscal capacity and minimum capital requirements (in a model with moral hazard and pecuniary externalities) but does not pursue the macroeconomic implications. Farhi and Tirole (2017/2018) is the main exception that considers prudential policy and contagion, but their focus is on how banking union overcomes national regulators’ supervisory leniency (a doom loop from fundamentals), a different question.

Key Concepts

Fiscal robustness (gamma = p*k): The fraction of bank deposits that is EFFECTIVELY insured, equal to the nominally insured share k times the fraction p of the pledge the Deposit Insurance Agency actually honors. Robustness increases in gamma; 1 - gamma measures fiscal frailty. Baseline gamma0 = 0.34.

Incomplete deposit insurance / depositor bail-in: In this model the government, when fiscally fragile, honors only fraction p of insured deposits; the unhonored portion is added to the uninsured tranche as a junior claim on the failed bank’s repossessed assets. From a creditor’s view, one unit of dishonored insured debt equals one unit of uninsured debt.

Optimal capital requirement (phi_F): The corporate-loan capital requirement that maximizes the unconditional second-order approximation of the social welfare function. It rises with fiscal frailty (0.1048 at gamma = 0.34, 0.1075 at gamma = 0.05) and rises at an increasing rate with risk-shock variance. Its relation to welfare is hump-shaped, reflecting a trade-off between bank default and underinvestment.

Sovereign-financial credit-risk correlation reversal: The paper’s central result: the standard POSITIVE co-movement between sovereign and bank default risk becomes NEGATIVE once capital requirements are allowed to adjust optimally to fiscal frailty, because higher optimal requirements lower the bank default rate even as fiscal risk rises.

Direct vs indirect effects of fiscal frailty: Direct effects are output lost to default and savings on default costs from higher requirements; indirect effects work through the level of deposits and bank credit (financial intermediation). The indirect (credit) channel is found to be the larger driver of why optimal requirements support output.

Repossession cost (mu): The fraction of a defaulting unit’s asset value lost to creditors upon repossession, set to 0.3 (30%) in the baseline. Lowering it (e.g., to 10% via bankruptcy-law reform) raises welfare, supports LOWER optimal capital requirements, and improves insulation against bank risk shocks.

Global Factors in Noncore Bank Funding and Exchange Rate Flexibility

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

Layer 1: Overview

Research question and motivation: The paper asks how far global factors drive the foreign-borrowing component of advanced-economy banks’ non-core funding, and whether exchange rate flexibility (and macroprudential policy) can insulate national banking systems from those global factors. This speaks to the long-running “trilemma vs. dilemma” debate (Rey 2015 vs. Mundell 1963; Miranda-Agrippino and Rey 2020) over whether a flexible exchange rate buys monetary/financial autonomy under open capital accounts. Non-core funding (funding other than deposits — repos, debt securities, foreign borrowing) matters because, per Shin and Shin (2011), Hahm et al. (2013) and Jorda et al. (2017), it is an elastic, crisis-predictive funding source closely tied to credit booms and leverage.

Data and method: A balanced quarterly panel of 31 advanced (high-income) economies, 2004:Q1-2022:Q1, >2,000 country-quarter observations (most specifications drop Iceland as an outlier, leaving 30 countries, 72 periods, 2,160 obs). The non-core ratio is foreign liabilities (IFS line 26c) over deposits (lines 24+25); mean 78%, SD ~94%. The loan-to-deposit ratio (mean 122%, SD ~58%) is a robustness outcome; the two are correlated at ρ=0.92. Sample is ~53% fixed exchange rate (Ilzetzki et al. 2019 coarse classification, monetary union counts as fixed); average Chinn-Ito index 0.95, so capital accounts are essentially fully open. Identification combines the Pesaran (2006) Common Correlated Effects (CCE) estimator with the Mean Group (MG) estimator in a three-step procedure: (1) CCE-MG with observed global factors plus cross-section averages to absorb unobserved factors; (2) extract principal components (number set by Ahn-Horenstein 2013 criterion) from the composite residual; (3) re-estimate with PCs, allowing PC loadings to differ by exchange rate regime.

Main findings with magnitudes: (1) The non-core ratio is highly persistent (lagged dependent variable significant at 1% throughout; coefficient 0.659 in the baseline MG-PC specification) and overwhelmingly driven by global factors; the number of common factors in the non-core ratio is estimated at 3, and the three PCs explain ~80% of the explained variance (PC1 0.795, PC2 0.585, PC3 0.138 — note these sum to >1 and are reported as the lower panel of Table 3). (2) Standard two-way fixed effects leave strong residual cross-sectional dependence (CD test rejects), so are likely biased; the CCE step drives the residual CD statistic to a non-rejection 0.797 (p=0.425) with zero residual factors. (3) Central result: global factors raise non-core ratios more for fixers than floaters — the PC1 loading is 0.984 for fixers vs. 0.302 for floaters; PC2 is significant for fixers, PC3 for floaters; a test on the summed PC loadings (statistic 7.12) confirms larger loadings for fixers. So flexible exchange rates partially insulate. (4) Insulation is stronger away from crises: in the no-crisis 2010-2019 sample the fixer-floater gap in PC1 widens and PC3 (a crisis factor) turns insignificant. (5) Among domestic variables, only the lagged dependent variable, a more appreciated real exchange rate, and higher money/GDP significantly raise non-core ratios; country-specific factors play a minor role overall.

Mechanisms and implications: Relating PCs to observables, PC1 loads most on world macroprudential stringency (tighter regulation lowers non-core ratios), PC2 on the US shadow rate (positive in-sample, reflecting QE/QT dynamics), PC3 on financial-crisis dummies. VIX, oil prices and the US real exchange rate carry expected signs but smaller effects. Using BIS Locational Banking Statistics (23 of 30 countries), the global-factor effect works mainly through interbank borrowing (cross-border liabilities to banks), a flighty source; currency denomination matters little. Tighter macroprudential policy provides complementary insulation, especially for fixers against PC2 and PC3 (which together explain ~21% of non-core variation): for fixers the PC2/PC3 loadings of ~1.47/1.55 under loose regulation fall to essentially zero under tight regulation; for floaters macroprudential tightness adds no insulation. Policy upshot: the Mundellian trilemma is broadly supported for bank funding — flexible exchange rates and tighter macroprudential rules each dampen transmission of the global financial cycle to bank balance sheets, though not against crisis shocks.

In depth

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

The authors estimate a dynamic interactive-fixed-effects panel where the non-core ratio depends on its lag, country-specific variables, observed global factors, and unobserved common factors with country-specific (heterogeneous) loadings. Identification proceeds in three steps: (1) a CCE-MG regression (Pesaran 2006; Chudik-Pesaran) that includes observed global factors directly and approximates unobserved factors via cross-section averages of the dependent and independent variables, identifying the country-specific slopes off the variation in regressors orthogonal to common factors; (2) extraction of principal components from the composite residual u-hat that encapsulates the entire factor structure (number of PCs = 3, the estimated number of common factors in the non-core ratio); (3) re-estimation with the PCs, with loadings split by exchange rate regime. The main threat is that omitted/unobserved common factors correlated with the regressors cause strong cross-sectional dependence and biased, inconsistent estimates — exactly what they show afflicts two-way fixed effects (CD test rejects weak dependence; 2 residual factors remain). They verify the CCE step removes this: residual CD statistic 0.797 (p=0.425) and zero estimated residual factors, so the composite captures the full factor structure. They use one-quarter lags of all observables to limit endogeneity, and the rank condition is met with six cross-section averages exceeding the number of factors.

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

After establishing the PCs statistically, the authors give them economic content by regressing each standardized PC on observed global factors (Table 6). PC1 loads most strongly on world macroprudential stringency (coefficient -2.957 on the non-core ratio direction, i.e., tighter global regulation lowers non-core ratios), R2=0.971. PC2 is driven by the US shadow rate (coefficient 1.171, positive), R2=0.921. PC3 is driven by financial-crisis dummies — adding a US banking crisis dummy (2007:Q4-2011:Q4) raises the PC3 regression R2 and the crisis dummy (coefficient 2.050) dominates the macroprudential variable. The positive PC2-US-rate relation seems to contradict the GFC literature (lower US rates usually raise cross-border flows), but they explain it via QE: lower shadow rates from bond purchases flatten the yield curve and push banks to fund via long-term bond issuance rather than short-term interbank borrowing; since their non-core measure is dominated by interbank borrowing, lower shadow rates reduce it. They show the sign flips to the conventional negative when using the loan-to-deposit ratio (Appendix Table 11) or a pre-2007 (pre-QE) sample (correlation -15.7%).

Q3. What heterogeneity is documented?

Two main dimensions. (1) Exchange rate regime: PC loadings are larger for fixers than floaters — PC1 loading 0.984 (fixers) vs. 0.302 (floaters); PC2 significant for fixers, PC3 for floaters; the summed-loading difference test statistic is 7.12 (p in the test reported as 0.011 for PCF1>PCF0). (2) Macroprudential stance: countries that tightened macroprudential policy more than the median country are less affected by PC2 and PC3. The insulation from tight macroprudential policy is concentrated in fixers — for fixers the PC2 (PC3) loading of ~1.47 (1.55) under loose regulation falls to essentially zero under tight regulation; for floaters, macroprudential tightness gives no additional insulation. Beyond this, country-specific slopes are confirmed necessary by slope-heterogeneity tests (the delta tests reject homogeneity).

Q4. What robustness checks are run?

Five (Table 4): (1) dropping the United States (since observed global factors are US-dominated) — results hold, PC1+PC3 affect floaters, PC1+PC2 affect fixers. (2) Including Iceland — results similar but less precise and some residual cross-sectional dependence reappears. (3) Dropping COVID (sample ends 2019:Q4) — virtually unchanged, slightly lower significance. (4) A pure no-crisis sample 2010:Q1-2019:Q4 — PC1 and PC2 still larger for fixers, the fixer-floater PC1 gap widens (insulation stronger outside crises), and PC3 turns insignificant for both groups (consistent with PC3 being a crisis factor). (5) Loan-to-deposit ratio as alternative outcome — PC1 and PC2 significant for floaters, PC1 only for fixers; the apparent lack of flexible-rate insulation to PC1 here is driven by the crisis episodes, and disappears when GFC/COVID are dropped. The three-step CCE diagnostics (first-stage CD non-rejection, zero residual factors) hold across columns.

It extends the global-financial-cycle literature (Rey 2015; Miranda-Agrippino and Rey 2020; Bruno and Shin 2015; Obstfeld et al. 2019) and the non-core-funding literature (Shin and Shin 2011; Hahm et al. 2013) by focusing specifically on the non-core-to-core funding ratio of advanced-economy banking systems rather than capital flows or interest rates. Relative to Amiti et al. (2017) — who find global factors explain cross-border flows mainly in expansions — and Cerutti et al. (2019) — who find the global component explains less than a quarter of capital-flow variation — this paper finds global factors overwhelmingly dominate the non-core ratio. Methodologically it differs by combining Pesaran’s CCE estimator with PC extraction and MG estimation to identify and economically label the global factors, rather than relying on two-way fixed effects, which it shows are biased here by uneliminated cross-sectional dependence. It sides with the trilemma camp (exchange rate flexibility insulates, at least partially) against the strong ‘dilemma’ view.

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

Flexible exchange rates partially insulate bank non-core funding from the global financial cycle, and tighter macroprudential regulation provides complementary insulation — supporting the Mundellian trilemma for bank balance sheets. Scope conditions: (1) insulation works against regulatory/financial/real drivers (PC1, PC2) but NOT against financial-crisis shocks (PC3), which hit fixers and floaters similarly; (2) insulation is stronger away from global crises; (3) macroprudential insulation operates mainly for fixed-rate countries; (4) the global financial cycle cannot be summarized by a single observable (VIX or otherwise) — it is best captured by composite principal components, so policymakers should monitor a bundle of real, monetary and financial indicators. The authors explicitly caution the currency-denomination-doesn’t-matter result and the broader findings are advanced-economy-specific and may not extend to emerging markets with larger currency mismatches and more volatile exchange rates.

Q7. Through which liability channel does the global-factor effect operate?

Using BIS Locational Banking Statistics (23 of 30 countries) in fixed-effects regressions of cross-border liability components on the three PCs (Table 7), all three PCs are positively correlated with total cross-border liabilities. The effect materializes through both domestic- and foreign-currency liabilities (currency denomination matters little — sample correlations 80% foreign-currency, 82% domestic-currency) and, crucially, through cross-border liabilities vis-a-vis other banks (interbank borrowing, correlation 89% with the non-core ratio). Liabilities to nonbank financials (correlation 80%) and other sectors (correlation 18%) are hardly, or even negatively, related to the PCs. Interbank funding is emphasized as a particularly flighty source.

Q8. Why use the CCE/MG estimator instead of two-way fixed effects, and what is the cost?

Two-way fixed effects assume additive country and time effects and cannot absorb unobserved common factors that load heterogeneously across countries or are correlated with regressors; in this data they leave strong residual cross-sectional dependence (CD test rejects; two residual factors), implying biased and inconsistent slopes. The CCE estimator approximates unobserved factors by cross-section averages without needing to know the exact number of factors, and the MG estimator allows country-specific slopes (confirmed necessary by slope-heterogeneity tests). The pooled CCE estimator failed to remove residual cross-country correlation in every specification and was inferior to MG. A cost is that the PCs span observed and unobserved factors and lack a clean one-to-one economic meaning, which the authors address by separately regressing PCs on observables (Section 5.1).

Q9. What does the descriptive evidence show before the regressions?

The non-core ratio and loan-to-deposit ratio co-move strongly (ρ=0.92). The non-core ratio is generally higher for fixed-rate countries, shows long-term trend shifts and co-movement across regime groups, rose before the GFC to a global peak of 70% in 2008, then fell to about 30% by 2022, with short-term fixer-floater divergence only in 2015-2020. The benchmark non-core ratio correlates 88% with the overall BIS cross-border liability variable.

Key Concepts

Heterogeneity in Manufacturing Growth Risk

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

Layer 1: Overview

Research question and motivation. Since the Great Recession, quantifying downside risks to economic activity (rather than only expected outcomes) has become central for policymakers and investors. A large “growth-at-risk” literature documents that tightening financial conditions sharply raise downside risks to aggregate output while leaving upside potential roughly unchanged (Adrian, Boyarchenko and Giannone, 2019). This paper argues that the aggregate focus misses important structure: aggregate fluctuations can originate from industry-specific shocks, and recessions sharply raise cross-industry dispersion in growth (Bloom, 2014). The authors ask how downside output-growth risk from tight financial conditions differs across U.S. manufacturing industries, and which industry characteristics explain that heterogeneity.

Data and method. They use monthly industrial production (IP) growth for 74 U.S. manufacturing industries at the four-digit NAICS level over January 1973–July 2020 (Federal Reserve G.17; same industry selection as Chang and Hwang, 2015), and the Chicago Fed’s National Financial Conditions Index (NFCI) as the financial-conditions gauge. The method is a two-level (multi-level) quantile regression. Level 1 (following Adrian et al., 2019) regresses the τ-th quantile of average h-month-ahead IP growth on the current NFCI and current IP growth, industry by industry, focusing on h=3. Level 2 (inspired by Petersen and Strongin, 1996) regresses the estimated level-1 NFCI quantile coefficients cross-sectionally on standardized, time-invariant industry characteristics (capital, materials, energy, production-labor and overhead-labor intensities; a correlation-based labor-hoarding measure; four-firm concentration ratio; industry size measured by value-added share; and a durability dummy). Inference uses a stationary bootstrap (1,000 replications) that propagates level-1 estimation uncertainty into level 2. Industries split into 45 durables and 29 nondurables.

Main quantitative findings. Deteriorating financial conditions hit downside risk far harder than the center or upside of the growth distribution. On average across industries, a one-standard-deviation positive NFCI shock lowers three-month-ahead IP growth by 0.237% at the median and 0.773% at the 5% quantile, and raises the 95% quantile by 0.042%. The average 5% NFCI coefficient is -0.77 across all industries versus -0.31 (linear) and -0.24 (median); 47 of 74 industries (63.5%) have significant 5% coefficients, only 5 (6.8%) have significant 95% coefficients. Durables are about twice as sensitive in the left tail: average 5% coefficients are -0.96 (durables) versus -0.48 (nondurables), with 75.6% of durables versus 44.8% of nondurables significant at 5%. Some industries (computer, aerospace, food, dairy) are essentially unaffected across the whole distribution. The relationship is nonlinear for 46 of 74 industries (62.2%) at the 5% quantile (77.8% of durables, 37.9% of nondurables). Galvao et al. (2018) slope-homogeneity tests reject coefficient equality across industries for lower quantiles. Subsample analysis (1973-84 / 1985-2006 / 2007-2020) shows tail effects strongest in the most recent period (average 5% coefficient -1.38 vs -0.73 and -0.49), weakest during the Great Moderation.

Explaining heterogeneity / implications. In the all-manufacturing second level, large industries and durable-goods producers have significantly more vulnerable downside growth, while capital-intensive, overhead-labor-intensive, and labor-hoarding industries are less vulnerable. Within durables, size, materials intensity (more vulnerable) and overhead labor intensity (less vulnerable) matter; within nondurables, energy intensity (more vulnerable) and labor hoarding (less vulnerable) matter. Implication: industry-targeted stabilization policy may be more effective than nationwide policy given the heterogeneity, and investors can build industry-rotation strategies less exposed to financial-market shocks.

In depth

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

The strategy is descriptive-predictive rather than causal. Level 1 estimates industry-specific quantile regressions of average h-month-ahead IP growth on the current NFCI and current IP growth (Koenker-Bassett check-function minimization via the Frisch-Newton interior-point algorithm). Level 2 regresses the estimated NFCI quantile coefficients on standardized industry characteristics via OLS. The key inferential innovation is a stationary bootstrap (Politis-Romano 1994; block length via Politis-White 2004 with Patton et al. 2009 correction, expected block ~36.76 set by the NFCI series) that jointly resamples industry IP and NFCI and feeds level-1 estimation uncertainty into level-2 confidence bands. Main threats: (i) the relationship is associational, not identified as causal — the NFCI is endogenous to the macroeconomy; (ii) generated-regressor problem in level 2 (coefficients are estimates), addressed by the bootstrap; (iii) small cross-sections (45 durables, 29 nondurables, even fewer at the three-digit level) reduce power to detect characteristic effects; (iv) time-invariant characteristics are averaged over varying available windows, abstracting from time variation.

Q2. How is nonlinearity established, and against what benchmark?

Quantile coefficients are compared to OLS linear coefficients (constant across quantiles) using 95% bootstrap bands generated under a null that the data-generating process is a VAR(4) for the NFCI and IP growth (the Adrian et al. 2019 approach). Quantile estimates falling outside those bands are evidence of nonlinearity. 46 of 74 industries (62.2%) have a 5% coefficient significantly different from OLS; the total manufacturing sector is also nonlinear, mirroring Adrian et al. (2019) for aggregate GDP.

Q3. What heterogeneity is documented?

Three layers. (1) Durables vs nondurables: durables roughly twice as sensitive in the left tail (avg 5% coefficient -0.96 vs -0.48). (2) Within sectors: e.g. motor vehicles, motor bodies and motor parts have significant 5% coefficients below -2; resin and fiber below -1.5; while computer, aerospace and food are insignificant/unaffected. (3) Across the distribution: strong effects at low quantiles, near-zero at high quantiles (avg 95% coefficient 0.04). Industries with large negative 5% coefficients also tend to have larger positive 95% coefficients (higher conditional volatility under tight conditions), most clearly iron, motor vehicles, fiber and resin — though upside gains are generally smaller than the downside increase.

Q4. Which industry characteristics explain the heterogeneity, and in which direction?

All-manufacturing (74 industries): negative effects on lower-quantile NFCI coefficients (i.e. more downside vulnerability) from industry size and durability; positive effects (less vulnerability) from overhead labor intensity, labor hoarding, and capital intensity. Durables: significant negative effect of materials intensity, negative (small) effect of size, positive effect of overhead labor intensity; production labor intensity significant at some higher quantiles. Nondurables: significant negative effect of energy intensity, positive effect of labor hoarding. Energy intensity, production labor intensity and concentration ratio are NOT significant for total manufacturing or durables in the way Petersen-Strongin found for cyclicality.

Q5. What economic mechanisms are offered for each characteristic effect?

Size: mean reversion — an industry larger than average is more likely to see growth fall (Braun-Larrain 2005). Durability: durable production is inherently more cyclical (Petersen-Strongin 1996). Labor hoarding / overhead labor: firms retain trained (especially nonproduction) workers due to sunk hiring/training costs (Becker 1962; Oi 1962; Parsons 1986), lowering the incentive to cut production in downturns. Capital intensity: higher fixed-to-variable cost ratio reduces incentive to cut output, and tangible capital provides collateral easing financing (consistent with Braun-Larrain 2005). Materials intensity (durables): higher share of variable costs raises cyclicality; also links to the negative materials-intensity/TFP relation of Baptist-Hepburn (2013).

Q6. What robustness checks are run?

(i) Additional controls (Gilchrist-Zakrajsek variables: term spread, real federal funds rate, credit spread, excess bond premium, plus extra IP lags) — qualitatively similar, wider bands. (ii) Unobserved heterogeneity via Ando-Bai (2020) interactive-fixed-effects panel quantile model (one common factor optimal) — highly similar. (iii) Alternative NAICS disaggregation: three-digit (21 industries; capital intensity dropped for multicollinearity; only labor hoarding and durability significant) and six-digit (101 industries; more characteristics significant, including production labor intensity and concentration ratio). (iv) Longer horizons h=6 and h=12 — qualitatively similar but weaker/less significant as horizon lengthens. (v) Subsample analysis of both the growth-risk coefficients and the characteristic construction windows (1973-84, 1985-2006, 2007-2020; and start dates 1958/1973/1987) — effects relatively stable; size and labor-hoarding effects weaken in recent periods while overhead labor and durability stay significant.

Q7. How does this relate to and differ from Petersen and Strongin (1996) and Adrian et al. (2019)?

It extends Adrian et al. (2019) from aggregate to industry-level growth-at-risk, documenting substantial cross-industry variation that is invisible at the aggregate level — to the authors’ knowledge the first disaggregate growth-at-risk study. It extends Petersen-Strongin (1996), who used a linear cyclicality framework, by allowing a flexible/nonlinear quantile relationship specifically with financial conditions. Findings broadly echo Petersen-Strongin for downside risk (materials intensity most important in durables; labor hoarding for nondurables — their only significant nondurable effect), but deviate by NOT finding energy intensity, production labor intensity, or concentration ratio significant in durables, and by adding size and capital intensity (cf. Braun-Larrain 2005) as relevant for total manufacturing. The agreement is attributed to business and financial cycles being closely intertwined (Claessens et al. 2012).

Q8. What are the policy implications and their scope conditions?

Because vulnerability is highly heterogeneous, industry-level stabilization policy may be more effective than nationwide policy (OECD 2003), and policies can be targeted using the signalling characteristics (size, durability, materials/energy intensity vs capital/overhead-labor intensity and labor hoarding). Investors can build industry-rotation strategies less exposed to financial shocks. Scope conditions: evidence is U.S. manufacturing only, associational not causal, conditional on the NFCI as the financial-conditions measure, strongest at the three-month horizon and in the post-2007 subsample, and characteristic effects rest on relatively small cross-sections.

Q9. Are there caveats the authors themselves flag?

Yes: after splitting into durables/nondurables, fewer characteristic effects are significant, which the authors attribute to smaller cross-sections rather than absence of effects; the two-level model is estimated sequentially (two-step) not simultaneously; characteristics are treated as time-invariant averages (justified by stable cross-industry rankings, though production labor intensity shows a downward trend); and upside potential, while present, is generally smaller than the increased downside risk.

Key Concepts

Growth-at-risk / downside growth risk: The lower-quantile (e.g. 5%) of the conditional distribution of future output growth given current conditions; here the 5% quantile of average three-month-ahead industry IP growth conditional on the NFCI, capturing how bad growth could plausibly get under tight financial conditions.

Multi-level quantile regression: The authors’ two-step procedure: level 1 estimates industry-specific quantile regressions of future IP growth on the NFCI and current IP growth; level 2 regresses the estimated NFCI quantile coefficients cross-sectionally on industry characteristics, with a bootstrap carrying level-1 uncertainty into level-2 inference.

NFCI (National Financial Conditions Index): Chicago Fed weekly index of U.S. money, debt, equity, and (shadow) banking conditions built from a large dynamic factor model; positive values mean tighter-than-average financial conditions, negative values looser-than-average. Averaged to monthly here.

Labor hoarding: Retention of employees during downturns because of sunk search, hiring and training costs; measured here as the negative correlation between changes in materials usage and changes in production-worker hours (a value of -1 = no hoarding), so higher values indicate more hoarding and predict less cyclical, less vulnerable growth.

Overhead labor intensity: Cost of nonproduction (overhead) labor relative to value added. Because nonproduction workers embody more firm-specific investment, they are more subject to labor hoarding, so overhead-labor-intensive industries have less vulnerable downside growth.

Durable vs nondurable goods sector: Federal Reserve classification (45 durable, 29 nondurable industries here). Durable-goods production is more cyclical and, in this paper, about twice as sensitive in the left tail of the growth distribution to adverse financial conditions.

Slope homogeneity test: Galvao et al. (2018) Swamy-type and standardized Swamy-type tests for a quantile-regression fixed-effects panel, used to formally reject equality of NFCI quantile slopes across industries, especially at lower quantiles.

How Does Public Sector Employment Affect Household Saving Rates? Evidence from China

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

Layer 1: Overview

Research question and motivation: The paper asks whether and why the type of employment — specifically public-sector employment — affects household saving rates in China. This matters because Chinese household saving rates are extraordinarily high in international comparison (the paper reports an average gross household saving rate of roughly 35% in China versus only about 5% in OECD countries over the period considered), and the high rates remain a puzzle. Household saving feeds investment and long-run growth, its cyclicality can amplify or dampen crises, and via the “global saving glut” hypothesis Chinese saving has financed global imbalances and the US current account deficit. Prior literature on Chinese saving emphasizes economic transition, income growth/uncertainty, demographics (one-child policy), and culture, but neglects the role of employment type. Notably, the international finding (e.g., Bettoni and Santos, 2021, calibrated on Brazilian data) is that public employment REDUCES saving because of lower job/income uncertainty and higher compensation, so less precautionary saving. China appears to run the opposite way.

Data and strategy: Micro-level longitudinal data from the China Household Finance Survey (CHFS), a nationally representative survey covering 29 provinces (excludes Tibet, Xinjiang, Inner Mongolia). The authors use the 2013, 2015, and 2017 waves, restrict to urban households whose head is aged 16-60, and restrict the non-public control group to those with an above-one-year labor contract. The final sample is 5,539, 5,785, and 4,545 observations per wave (15,869 total; 25.18% public-employed). The saving rate is defined as (income minus consumption)/income, with the sample restricted to saving rates above -200% to remove extreme values. Crucially, SOE employees are classified as NON-public (following You and Zhang, 2016) because post-1990s SOE reform made them market players. Public employees = government workers (about 20% of public employees) plus Shiyedanwei (fiscally-financed public institutions: education, health, research). The empirical toolkit: (1) Correlated Random Effects (CRE) panel regressions with rich controls, plus IV-CRE using the head’s CPC membership as instrument; (2) Propensity Score Matching (one-to-one, k-nearest neighbor, radius, kernel) and a PSM-CRE panel model; (3) Heckman two-step treatment-effects model for self-selection; (4) a within-household differences estimator exploiting employment transitions; (5) life-cycle interaction analysis.

Main quantitative findings: Public-employed households save more, by roughly 3 to 8 percentage points depending on method and sample. Raw descriptive gap: mean/median saving rates are 23.16%/33.89% for public vs. about 5.6 and 4.8 pp lower for non-public. Baseline CRE: the public-employment dummy adds 3.589 pp (col 1); each additional public-employed member adds 2.028 pp (col 3). IV-CRE coefficients rise to 8.094 and 4.878 (significant only at 10%; first-stage F = 38.65 and 49.68). PSM cross-sectional ATEs are about 5-8 pp (mostly significant at 1%). PSM-CRE: 3.928 pp. Heckman: 3.557 pp, with an insignificant inverse Mills ratio (so self-selection is not driving the result). Employment-transition (within-household): households switching from non-public to public raise their saving rate by 14.245 pp relative to non-switchers (135 transitioning vs. 1,831 stable households). Life-cycle: the public-employment x age interaction is negative; the saving-rate gap is significant for heads roughly aged 24-38 (strongest for the young/middle-aged), with a U-shaped age-saving profile turning around age 35-40. Robustness on the definition of “public”: holding Bianzhi raises saving by 8.5 pp; broadening to include SOEs gives 4.5 pp.

Mechanisms and implications: The saving rate reflects both motive and capacity. On motives, public-employed households save more for children’s education (about 25% report saving for education/training vs. 19% non-public; 16.2% plan to send children to study abroad vs. 12.9%) and inheritance (about 16% vs. 11.4%); heterogeneity shows the effect is concentrated in one-SON households (Wei-Zhang competitive saving) and in households with high education-expense shares. On capacity, better social security coverage reduces public employees’ out-of-pocket expenditure needs (e.g., negative food-income interaction) and frees disposable income for saving; social-security interaction terms are negative, indicating public employment’s effect is dampened where social security is already held. Policy implication: changes to the public-employment share affect aggregate household saving, and reducing the benefit/guarantee disparity between public and non-public jobs could lower the high saving of public-employed households. Scope: results are Chinese institution- and culture-specific, possibly extendable to other East Asian Confucian societies, and may erode as ongoing public-sector reforms cut public employees’ benefits.

In depth

Q1. What is the core empirical claim and how large is the effect?

Households headed by a public employee have higher saving rates than non-public-employed households, by approximately 3 to 8 percentage points depending on method and sample. Point estimates: baseline CRE 3.589 pp (dummy) and 2.028 pp per additional public-employed member; PSM-CRE 3.928 pp; Heckman 3.557 pp; PSM cross-sectional ATEs about 5-8 pp; IV-CRE 8.094/4.878 pp (only 10% significant).

Q2. What is the identification strategy and what are the main threats?

Three threats are addressed: (1) confounders affecting both employment choice and saving (education, risk aversion, financial literacy, social security) — handled with rich CRE controls; (2) endogeneity/reverse causality (households with strong saving desire may sort into a sector) — handled with IV using the head’s CPC membership; (3) self-selection into public jobs — handled with PSM and a Heckman two-step treatment-effects model. The within-household employment-transition estimator further nets out fixed household characteristics. Main residual threat: the IV’s exclusion restriction cannot be formally tested (just-identified, instruments do not exceed endogenous variables); the authors argue CPC membership is plausibly excludable since many students join the CPC before graduation and many CPC members work in the private sector. The Heckman IMR is insignificant, indicating self-selection is not the driver.

Q3. Why is the instrument (CPC membership) argued to be valid?

Relevance: about 3 in 10 public employees are CPC members vs. 1 in 10 private employees; first-stage F-statistics are 38.65 and 49.68, well above weak-instrument thresholds. Exogeneity (argued, not tested): no direct channel from CPC membership to saving decisions because many college students join the CPC and many members work in private sectors. The orthogonality (third) condition cannot be tested due to just-identification.

Q4. What are the two main mechanisms, and how are they distinguished?

Saving motive and saving capacity. Motive: from the 2013 CHFS bank-deposit-purpose question and study-abroad plans, public-employed households more often save for children’s education (about 25% vs. 19%), inheritance (about 16% vs. 11.4%), health (10.25% vs. 8.49%), and housing (15% vs. 13.78%). Capacity: better social security reduces expenditure needs and frees disposable income — shown by consumption regressions (negative public-employment x income interaction for food, positive for education/travel/luxury) and by social-security interaction terms that are negative and by smaller public-employment coefficients in the with-social-security subsample. The two are distinguished by combining stated-motive data with consumption-category and social-security interaction analyses.

Q5. What heterogeneity is documented?

(1) Life-cycle: the saving gap is significant and strongest for heads aged about 24-38 (young/middle-aged) and narrows with age; the public-employment x age interaction is negative. (2) Child gender: the positive effect comes primarily from one-SON households (one-son public coefficient 6.067 significant; one-daughter insignificant; interaction with son gender 5.872), consistent with Wei-Zhang competitive/marriage-market saving. (3) Education-expense share: the effect is larger for households spending a higher share on children’s education (above-median 7.536 vs. below-median 4.471). (4) Definition of public sector: Bianzhi holders 8.5 pp; including SOEs 4.5 pp.

Q6. What robustness checks are run?

(1) IV-CRE to address endogeneity. (2) Alternative saving-rate measures: winsorizing at the bottom 1% instead of the -200% cutoff, and a log(income)-log(consumption) definition (saving relative to consumption); the positive effect holds (CRE 0.043, PSM-CRE 0.243). (3) Alternative thresholds (-100%, -300%) give similar results. (4) Different scopes of ‘public sector’ (Bianzhi-only narrow; SOE-inclusive broad). (5) Regressing each saving-motive dummy on public employment plus controls to avoid being misled by raw means. (6) Number-of-public-members measure as an alternative to the head dummy. (7) Multicollinearity checked via correlation matrix; regressions without singletons reportedly robust.

It contrasts directly with Bettoni and Santos (2021), who (using Brazilian micro data) find public employment LOWERS saving via reduced precautionary motive. This paper finds the opposite for China and argues the precautionary channel is only part of the story; Chinese-specific cultural factors (Confucian social status, competitive saving for sons, status investment in children) and capacity effects (better social security freeing disposable income) dominate. It complements He et al. (2018), who use SOE reform to document precautionary saving, and Lugauer et al. (2019) and Chen et al. (2019) on dependent children and social norms. Methodologically it extends the Chinese saving literature by foregrounding employment type, a political/occupational dimension prior work largely neglected.

Q8. What does the employment-transition (within-household) result show and what is its caveat?

Households whose head switches from non-public to public employment raise their saving rate by 14.245 pp relative to non-public households without a transition. This nets out time-invariant household characteristics, supporting causality. Caveat: the transition sample is small (135 transitioning households vs. 1,831 stable), and the coefficient is much larger than cross-sectional estimates, so it should be read as directional confirmation rather than a precise magnitude.

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

Changes in the public-employment share will affect aggregate household-sector saving; policymakers wishing to lower China’s high saving could reduce the benefit/guarantee disparity between public and non-public jobs. Scope conditions: results are specific to Chinese institutions and Confucian culture, may extend to other East Asian societies, and may weaken over time as ongoing public-sector reforms cut public employees’ benefits, shrinking the public/non-public gap.

Q10. What are the stated limitations?

(1) External validity is limited by Chinese-specific institutional and cultural settings, though possibly applicable to similar East Asian cultures. (2) Ongoing reduction of public employees’ benefits through public-administration reform may change saving behavior and reduce the documented gap over time. The dataset also covers only employed heads aged 16-60, so it does not capture post-retirement saving behavior.

Q11. What do the control variables show?

Higher household assets reduce the saving rate; higher income percentiles raise it (monotonically); male-headed households save more; a U-shaped age profile (low around middle age 35-40); high-school education lowers saving while university education is insignificant; larger household size, being married, and more dependent children all reduce saving; risk aversion raises saving while risk-loving and financial literacy are insignificant. In the Heckman first-stage probit, higher education, CPC membership, and risk aversion raise the probability of public employment, and the mother’s (not father’s) education and CPC membership significantly predict the head’s public employment.

Key Concepts

Public employee (paper’s definition): In this paper, employees who work directly for central/local government (about 20% of public employees) plus those in Shiyedanwei (fiscally-financed public institutions such as education, health, and research). SOE employees are deliberately EXCLUDED and classified as non-public, because post-1990s SOE reform made them resemble market players rather than public-sector actors.

Shiyedanwei: Public institutions and state organs mainly financed by fiscal spending (e.g., schools, hospitals, research institutes). Their staff are counted as public employees in this study, with relatively low unemployment risk and higher compensation.

Bianzhi: The authorized number of established posts/personnel in government and its affiliated institutions (per Brodsgaard, 2002). Employees holding Bianzhi are fully fiscally dependent — employment and wage guaranteed by the government — and thus the most secure subgroup of public employees; their saving-rate premium is the largest (8.5 pp).

Saving capacity vs. saving motive: The paper’s framing that a household’s saving rate is jointly determined by the desire to save (motive: education, inheritance, status) and the ability to save (capacity: how much disposable income is freed after needs, raised by better social security that lowers expenditure needs).

Iron rice bowl: The pre-reform notion of guaranteed lifetime job security in state employment; invoked to explain why public-sector jobs in China historically carried very low unemployment risk, a status partially eroded by SOE reform for SOE workers (but retained by core public employees).

Correlated Random Effects (CRE) model: A Mundlak (1978) random-effects specification that adds time-averages of time-varying regressors, allowing correlation between explanatory variables and the unobserved individual effect; chosen over fixed effects because employment type varies little within households across waves.

Competitive saving motive: The Wei-Zhang (2011) idea that households with a son save more to improve his marriage-market competitiveness amid China’s high male sex ratio. The paper finds this motive is concentrated among public-employed one-son households.

Inflationary Household Uncertainty Shocks

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

Layer 1: Overview

Research question and motivation: Macro-uncertainty is widely believed to depress activity, but existing measures are tied to financial markets, professional forecasters, or economic policy, while a key transmission channel runs through households’ propensity to consume, save, and work. Direct, macro-usable measures of household uncertainty are scarce. Ambrocio asks whether household uncertainty shocks behave like the negative demand shocks documented for the US (Leduc and Liu, 2016), and finds they do not in Europe.

Data and measurement: The paper builds a novel household uncertainty index (HUN) from the European Commission’s harmonized consumer survey, defined as the average fraction of “Don’t know” responses across the four forward-looking questions used to construct the pre-2019 Consumer Confidence Indicator (general economic situation, unemployment, household financial position, likelihood to save). The survey is monthly, covers all EU member states (and candidates), averaging over 40,000 households per month, conducted in the first two to three weeks of each month. HUN is constructed for January 2002 to December 2019. On average 3-6% of Euro area households respond “Don’t know” per round; at the national level the range runs from 2 to over 10 percent (e.g. Spain, France, Italy). HUN is standardized so 100 = mean and 10 points = one standard deviation. The Euro area HUN peaks around EU enlargement, the Global Financial Crisis, the European Sovereign Debt Crisis, and Brexit.

Empirical strategy: Following Leduc and Liu (2016), the author estimates monthly VARs with an uncertainty measure, unemployment, inflation, and the short rate, three lags, Bayesian estimation with Minnesota priors (ECB BEAR toolbox). Shocks are identified recursively with uncertainty ordered first, justified by the early-month survey timing and household inattention.

Main findings (with magnitudes/signs/scope): (1) For the Euro area, household uncertainty shocks are inflationary, with a delayed rise in unemployment only after about 20 months. By contrast, financial (Eurostoxx-50 implied volatility, IVOL) uncertainty shocks resemble negative demand shocks (raise unemployment, lower inflation), and policy (Baker-Bloom-Davis EPU) shocks have ambiguous inflation effects. (2) FEVDs: household or financial uncertainty shocks each account for about 20% of inflation forecast-error variance at roughly a 4-year horizon (policy uncertainty substantially less); household shocks account for about 10% of unemployment variation, financial and policy 20-30%. (3) Counterfactuals zeroing out the monetary-policy response to uncertainty: cumulated 48-month inflation IRF for HUN moves from 2.02 (baseline) to 1.66 (still inflationary); EPU from -0.79 to 0.68 (becomes inflationary); IVOL from -2.66 to -1.33 (less deflationary) - indicating monetary policy responds to financial/policy but not household uncertainty. (4) Cross-country (17 Euro-area countries excluding Ireland and Malta plus 8 non-Euro-area), cumulated 48-month inflation responses range from nearly 6% deflation (Lithuania) to over 12% inflation (Bulgaria); deflationary in Austria, Finland, Portugal, inflationary in Italy, Spain, Sweden. The cross-country inflation response correlates positively and significantly with average markups (De Loecker and Eeckhout, 2020; 13 countries, 2002-2016), regression slope ~1.86, robust to labor-market, institutional, and economic-structure controls.

Mechanism and implications: Results support a pricing-bias (precautionary pricing) channel: under nominal rigidities and monopolistic competition, firms raise prices when uncertainty rises because under-pricing is more costly than over-pricing. A calibrated New Keynesian model (Rotemberg pricing, third-order perturbation) matching country markups reproduces the deflationary-to-inflationary range for supply-side uncertainty; varying price rigidity and the monetary-policy response to uncertainty can jointly generate inflationary household and deflationary financial uncertainty shocks. Supply-side (productivity-volatility) uncertainty matches the data features better than demand-side uncertainty.

In depth

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

Recursive (Cholesky) identification in monthly VARs with the uncertainty measure ordered first, justified because the consumer survey is conducted in the first two weeks of the month (so contemporaneous monthly movements in other variables plausibly cannot affect HUN) and because households are inattentive and under-react to news. The main drawback is the assumption that the uncertainty measure is not contemporaneously affected by other shocks. The author argues monthly data mitigates this (Carriero et al., 2021, find limited contemporaneous feedback to uncertainty at this frequency) and shows results are robust to ordering uncertainty last and to the Carriero et al. (2021) time-varying-volatility identification (which allows uncertainty to respond contemporaneously). He also notes the recursive scheme can be read as a proxy-SVAR with the first variable as instrument, yielding more conservative (attenuated) impulse responses than a proxy SVAR.

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

The central mechanism is the pricing bias (precautionary pricing) channel under nominal rigidities and monopolistic competition: firms set higher prices when uncertain because ending up with too-low a price (selling more at thin margins) is costlier than too-high a price. This is distinguished from the standard precautionary-savings/negative-demand interpretation. Empirically: (i) household uncertainty is inflationary while financial uncertainty is deflationary; (ii) the cross-country inflation response correlates positively and significantly with average markups - the key comparative-static predicted by theory (elasticity of substitution governs markups); (iii) counterfactual VARs show monetary policy response, not the measure itself, drives part of the sign difference. The NK model then confirms only supply-side (not demand-side) uncertainty generates the observed positive markup-inflation relationship.

Q3. What heterogeneity is documented?

Large cross-country heterogeneity: cumulated 48-month inflation responses range from nearly 6% deflation (Lithuania) to over 12% inflation (Bulgaria); deflationary in Austria, Finland, Portugal and inflationary in Italy, Spain, Sweden. Splitting into core / periphery / non-Euro-area shows little difference in average response; geographically, Southern European responses are marginally higher than Northern. The cross-country variation is well explained by average markups: a regression of the cumulated inflation IRF on markups yields a positive slope (~1.86, significant) and country-group dummies are insignificant once markups are controlled for.

Q4. What robustness checks are run?

(1) Ordering uncertainty last - results virtually unchanged. (2) Carriero et al. (2021) time-varying-volatility identification - household uncertainty still inflationary. (3) Adding consumer sentiment (CSI) to the VAR - sentiment acts like a positive demand shock (lower unemployment, higher inflation), HUN remains inflationary, so results are not driven by first-moment sentiment. (4) A VAR with all three uncertainty measures (IVOL, EPU, HUN) - HUN still inflationary; policy uncertainty becomes inflationary in this setup. (5) Replacing the short rate with the Wu-Xia (2016) shadow rate to capture unconventional policy - results hold. (6) Adding linear trends and month-specific (seasonal) intercepts - results hold. (7) Alternative HUN built only from the two macro questions (HUN-Macro) and common-factor versions (HUN-F10, HUN-F16) - still inflationary. (8) Household belief dispersion (DIS) shocks instead of HUN are mildly deflationary, distinguishing uncertainty from disagreement. (9) Markup regressions remain significant controlling for labor-market, institutional-quality, and economic-structure variables.

It directly contrasts with Leduc and Liu (2016), who use the Michigan Consumer Survey and find US household uncertainty shocks resemble negative demand shocks (higher unemployment, lower inflation); here European household uncertainty shocks are inflationary. The inflationary result aligns with Mumtaz et al. (2018) (US state-level) and Mumtaz and Theodoridis (2015) (US shocks on the UK), while Carriero et al. (2018) find no significant price effect for the US. It builds on the pricing-bias literature (Born and Pfeifer, 2014, 2021; Fernandez-Villaverde et al., 2015; Bianchi et al., 2018) and on multi-source-uncertainty models. Relative to Bianchi et al. (2018), who find supply-side uncertainty deflationary and demand-side neutral under low price rigidity, this paper’s baseline (price duration over 3 quarters, calibrated shock volatilities) yields both demand- and supply-side uncertainty inflationary; their result is recoverable under low rigidity. The HUN measure newly exploits an under-explored source (households) with long time and broad country coverage.

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

The monetary-policy response to uncertainty matters for whether an uncertainty shock is inflationary or deflationary: counterfactuals show that when policy does not respond to household uncertainty it stays inflationary, while financial and policy uncertainty (to which policy does respond) shift toward inflation when that response is removed. In the model, very small monetary-response coefficients to uncertainty are sufficient to flip the sign (a_vb=0.0002 yields near-zero, 0.0004 yields about -1.1% deflation, against a 1.37% baseline). Scope conditions: results are specific to Europe / the Euro area’s common monetary policy; the counterfactual is subject to the Lucas critique (assumes the policy change is small enough not to alter agents’ behavior); and the paper explicitly does NOT evaluate whether monetary policy should respond - optimal policy is left for future research, noting that raising rates under uncertainty aggravates the output decline.

Q7. What does the New Keynesian model add and how is it calibrated?

A basic NK model with habit-forming risk-averse households, monopolistically competitive firms with Rotemberg price-adjustment costs, productivity (supply-side) and preference (demand-side) stochastic-volatility shocks, and a Taylor rule that can respond to uncertainty. The elasticity of substitution is calibrated to match average markups (baseline Euro area, eta=3.13; range Portugal-to-Italy 1.84-8.82 markups); baseline price stickiness matches a Calvo price duration of just over 3 quarters; shock-volatility variances are calibrated to match the VAR cumulated inflation IRF. Solved by third-order perturbation; IRFs are generalized impulse responses at the stochastic steady state (500-quarter burn-in). Findings: markup variation generates a wide deflationary-to-inflationary range for supply-side uncertainty (matching Italy high / Finland low) but not for demand-side; inflation responses are hump-shaped in price rigidity, with low rigidity giving deflationary supply / inflationary demand shocks and high rigidity reversing this; supply-side uncertainty better matches the markup-inflation correlation, suggesting HUN proxies uncertainty about productive capacity rather than relative consumption desires.

Q8. What are the notable caveats and limitations the author flags?

(i) The Rotemberg-vs-Calvo choice is not innocuous: Oh (2020) shows Rotemberg costs make uncertainty shocks more deflationary, so a Calvo model would likely be even more inflationary. (ii) The counterfactual monetary-policy exercise is subject to the Lucas critique. (iii) The empirical link between price rigidity and inflationary responses across countries is not tested - left for future research. (iv) The model has simple financial and labor markets; labor-market frictions known to matter for uncertainty transmission are abstracted from. (v) Some country HUN indices (Cyprus, Lithuania, Slovakia) may have unaddressed structural breaks. (vi) Cross-country markup regressions have only 13 observations, creating degrees-of-freedom limits in the slope-interaction specifications. (vii) HUN correlates positively (about 0.49) with the new European Commission uncertainty index and shows no detected structural break from the 2019/2021 survey-question change.

Key Concepts

Household uncertainty index (HUN): A survey-based measure equal to the average fraction of respondents answering ‘Don’t know’ across the four forward-looking questions (general economic situation, unemployment, household finances, likelihood to save) of the European Commission harmonized consumer survey; interpreted as households’ uncertainty about the economy, and argued to proxy supply-side (productive-capacity) uncertainty.

Pricing bias (precautionary pricing) mechanism: The transmission channel whereby firms in monopolistically competitive markets with nominal rigidities raise prices under higher uncertainty, because ending up with a too-low price (large volume, thin margins) is more costly than a too-high price; this makes uncertainty shocks inflationary, amplified by stronger nominal rigidities and higher markups.

Inflationary vs. deflationary uncertainty shock: In this paper, household uncertainty shocks raise inflation (inflationary) whereas financial (IVOL) uncertainty shocks lower it like negative demand shocks (deflationary); the sign depends on the relative strength of the pricing-bias channel versus precautionary savings and on whether monetary policy responds to that source of uncertainty.

Counterfactual monetary-policy IRF: Impulse responses computed by zeroing out the direct (contemporaneous and lagged) response of the policy-rate equation to uncertainty in an estimated recursive VAR (Bachmann-Sims, Kilian-Lewis), isolating how much of the inflation response is attributable to the systematic monetary-policy reaction to that uncertainty source.

Supply-side vs. demand-side uncertainty: In the NK model, demand-side uncertainty is a shock to the volatility of preference shocks and supply-side uncertainty a shock to the volatility of productivity shocks; only supply-side uncertainty reproduces the empirical positive markup-inflation correlation, leading the author to interpret HUN as closer to supply-side uncertainty.

Disagreement (DIS) vs. uncertainty: DIS is the average cross-household dispersion of survey views (a measure of disagreement/polarization), distinct from HUN (frequency of ‘Don’t know’); the two are negatively correlated, and DIS shocks are mildly deflationary, paralleling Born et al. (2020a)’s distinction between belief dispersion and forecast-error uncertainty.

Information Transparency of Firm Financing

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

Layer 1: Overview

Noël and Sun build an information-based theory of capital structure designed to explain the diversity of observed firm financing behavior and the coexistence of distinct optimal financial contracts. The motivating puzzle is that real-world financing methods (external equity, corporate bonds/bank loans, business credit lines/cards) differ systematically in how much firm-specific information investors require — equity and rated debt are “transparent” with firm-specific terms, while credit lines have general qualification standards and common interest rates. The paper asks three questions: what drives a firm’s optimal financing choice, why do equity, transparent debt, and opaque debt coexist as optimal contracts, and what is a firm’s optimal debt-to-equity ratio.

This is a pure theory paper (no data or sample period). The model has a continuum of ex-ante heterogeneous firms, each with internal funds n (support [0, ī]), productivity θ, and survival/success rate α, all i.i.d. With investment i, output is θ·min[i,ī] with probability α and 0 with probability 1−α. The model nests two information problems: (1) adverse selection over a firm’s quality (α, θ), which a costly verification technology can reveal at cost γ > 0; and (2) an ex-post agency problem, since a firm can hide output and auditing recovers only a fraction σ ∈ (0,1) of hidden output. Internal funds n are public. Firms choose among four options: opaque contract, separating contract, transparent contract, or self-funding. Investors are risk-neutral with outside storage return r > 0. Assumption 1 (αθ̲ > 1+r > σᾱθ̄) ensures all projects are worth investing and all firms prefer some external financing.

Main results (proved as a unique perfect Bayesian equilibrium):

Three contract types arise endogenously: equity (investors get a fraction of output / ownership, payout depends on θ), transparent debt (firm-specific interest rate (1+r)/α reflecting survival rate), and opaque debt (common interest rate (1+r)/αΩ). The transparent contract is implementable by either equity or transparent debt when n ≤ nT(αθ); only transparent debt when n > nT(αθ).
The separating (signaling without costly verification) contract does NOT survive for any firm except possibly the lowest type (α̲, θ̲); even that type is strictly better off pooling on opaque debt.
The unique equilibrium has θΩ = θ̲ and αΩ = E[α] (existence requires verification cost condition (26): γ/(σᾱθ̲ī) ≥ (1−σ)θ̲(ᾱ−E[α])/(1+r−σθ̲E[α])). It is either pooling on opaque debt or mixing (transparent + opaque), never pooling on transparent. There is a threshold cost γ̄ ∈ (0,∞) above which the transparent set is empty and the equilibrium becomes pooling.
Firm characteristics drive choice: all firms with αθ ≤ θ̲·E[α] use opaque debt regardless of internal funds; transparent contracts require sufficiently high quality satisfying condition (27) AND intermediate internal funds. Firms with n ∈ [n1(α,θ), nT(αθ)] are indifferent between equity and transparent debt; those with n ∈ (nT(αθ), n2(α,θ)] strictly prefer transparent debt; very low or very high n firms use opaque debt.
Partial capital structure irrelevance: only a strict subset of firms (those satisfying (27) with n ∈ [n1, nT(αθ)]) are indifferent between equity and transparent debt (a Modigliani-Miller equivalence within an asymmetric-information setting).
Debt weakly dominates equity: debt implements the optimal contract for all firms; equity does so only for the strict subset above. The optimal debt-to-equity ratio is not a smooth function of internal funds and need not be unique (a continuum is optimal for indifferent firms). The theory reconciles the conflicting empirical evidence of Myers (2001) (equity issues minor, mostly debt, across broad U.S. firms) versus Frank and Goyal (2003) (equity significant, often exceeding investment, for publicly-traded firms).

In depth

Q1. What is the model environment and the two layers of information frictions?

A continuum of ex-ante heterogeneous firms, each with public internal funds n ∈ [0, ī] and private quality (α, θ): productivity θ and survival/success rate α. Output is θ·min[i, ī] with probability α and 0 otherwise. Friction 1 is adverse selection over (α, θ), resolvable only via a costly verification technology (cost γ > 0) used before contracting. Friction 2 is an ex-post agency/moral-hazard problem: a firm can hide actual output, and auditing recovers at most a fraction σ ∈ (0,1) of hidden output — so the contract must induce truthful reporting. Investors are risk-neutral with storage return r > 0.

Q2. Why does the separating (signaling) contract collapse in equilibrium?

A separating contract must satisfy two incentive-compatibility constraints simultaneously: the financing firm’s own truthful-output-reporting constraint (identical to the transparent contract’s IC), AND a constraint that no other firm type wants to mimic it. Proposition 3 proves the first constraint makes the second impossible to uphold for all firms except possibly the lowest type (α̲, θ̲). Firms with lower expected quality but higher actual productivity (θ̃ ≥ θ) want to mimic at low funds; higher-risk firms (α̃ < α) want to mimic at high funds. Since any optimal separating contract is also an optimal transparent contract minus the cost γ, any firm that could separate would never use the costly transparent contract — but no firm can successfully separate. Even the lowest type prefers opaque debt (Proposition 7), so no separating contract is used in equilibrium.

Q3. Why is the opaque contract necessarily debt and never equity?

With opaque financing investors do not learn firm quality. A binding incentive-compatibility constraint reduces to zO = σθΩ·iO, and the participation constraint (which binds for all n < ī) gives payout zO = ((1+r)/αΩ)·(iO − n) — a fixed general interest rate (1+r)/αΩ on external funds. This is a debt contract. Equity is impossible because investors cannot be convinced to take ownership shares of output without firm quality being revealed to them. Opaque debt resembles a business line of credit: general qualification standards (Assumption 1) and a common interest rate reflecting E[α], independent of firm-specific information.

Q4. When are equity and transparent debt equivalent, and what distinguishes the information each reveals?

For firms with n ≤ nT(αθ), both the firm’s IC constraint (2) and investors’ participation constraint (3) bind. The optimal transparent contract is then implementable equivalently by equity (payout = a fraction of output, depends on θ) or transparent debt (firm-specific interest rate (1+r)/α, depends on α). This is a Modigliani-Miller-style equivalence obtained under asymmetric information. Conditional on survival, equity investors care about θ (commercial information — technology, product lines, outlook), while transparent-debt investors care about α (creditworthiness — financial condition), matching real-world distinctions between equity due diligence and credit-rating/bank scrutiny. The equivalence holds even if verifying α and θ costs differently, as long as both constraints bind.

Q5. What heterogeneity in financing behavior does the model generate (cross-section)?

Per Table 1 and Theorem 1: (a) Equity users have high quality (αθ), are lower-intermediate in internal funds (n ∈ [n1(α,θ), nT(αθ)]), reveal both α and θ, and have the highest financial leverage. (b) Transparent-debt users have high quality, intermediate funds, reveal α and θ, with firm-specific interest rate reflecting α. (c) Opaque-debt users span all quality types and all funds levels (often very low or very high funds), reveal only general information (E[α], θ̲), face a common interest rate, and have lower leverage. Better-quality but funds-constrained firms are most likely to use transparent financing; firms with αθ ≤ θ̲E[α] always use opaque debt regardless of funds, masking inferior quality by pooling.

Q6. What dynamic firm-financing patterns can the (static) model rationalize?

The authors interpret each capital-structure decision as a reaction to updated (n, α, θ). They reconcile: (1) startups using equity (high αθ, low n relative to capacity); (2) share buybacks (rising n moving a firm from the equity-indifference region into transparent-debt or opaque-debt regions); (3) small businesses starting with a credit line then adding equity/loans/bonds as n or quality rises into the transparent region; (4) firms issuing equity when prices are high (high price signals improved quality αθ, and funds raised via equity strictly increase in αθ); (5) firms using two or three financing types simultaneously, because the theory is per-project — different projects/purposes (e.g., main operations vs. routine liquidity) can optimally use transparent and opaque contracts at the same time.

Q7. How does the model reconcile the Myers (2001) vs. Frank-Goyal (2003) empirical discrepancy?

Myers (2001) reports that for broad U.S. nonfarm/nonfinancial corporations, external finance is a small share (mostly under 20%) of capital formation with equity issues minor and the bulk being debt. Frank and Goyal (2003) find that for publicly-traded U.S. firms (excluding financials, regulated utilities, major-merger firms), external finance is large (often exceeding investment) and net equity issues commonly exceed net debt issues. The theory explains both: equity finance is optimal only for high-quality, intermediate-funds firms, and amounts raised increase in quality, so publicly-traded (high-quality) samples show large, equity-heavy external finance, while broader samples include many debt-only and self-funded firms, yielding smaller, debt-dominated external finance. Verification cost γ varying over time, industry, and country also generates cross-dataset behavioral differences.

Q8. What is the structure of the optimal debt-to-equity ratio?

Proposition 10: it varies with firm characteristics and is not a smooth function of internal funds, and may not be unique. In a pooling equilibrium it equals σθ̲E[α]/(1+r−σθ̲E[α]) for n ≤ nO (constant across quality) and ī/n − 1 (strictly decreasing) for n > nO. In a mixing equilibrium, firms not satisfying (27) follow the same formula; firms satisfying (27) traverse: the constant ratio for n < n1; a continuum [0, σαθ/(1+r−σαθ)] over the equity/transparent-debt indifference region n ∈ [n1, nT(αθ)]; then the constant ratio; then ī/n − 1. The non-uniqueness over the indifference region is precisely the ‘partial capital structure irrelevance.’

Q9. How does the equilibrium switch between mixing and pooling?

Theorem 1(iv): all else equal, as the verification cost γ rises, the set of transparent-contract users shrinks and opaque-debt users expand. There is a threshold γ̄ ∈ (0,∞) above which no firm uses transparent financing, so the equilibrium is pooling on opaque debt; below it, the equilibrium is mixing. Existence of the unique PBE itself requires condition (26), ensuring γ relative to the tightest discipline σᾱθ̲ī is sufficiently high so that all firms with productivity θ̲ (any α) choose opaque debt, pinning down θΩ = θ̲ and αΩ = E[α].

Q10. How does this paper differ from prior optimal-contracting and capital-structure literature?

Prior costly-state-verification models (Diamond 1984; Gale-Hellwig 1985; Williamson 1986) yield debt as optimal with homogeneous entrepreneurs; adverse-selection models (Leland-Pyle 1977; Stiglitz-Weiss 1981; Myers-Majluf 1984 and others) and agency models (Jensen-Meckling 1976; DeMarzo-Sannikov 2006; DeMarzo-Fishman 2007) treat the frictions separately. This paper’s novelty is nesting BOTH adverse selection and the agency problem in a model of heterogeneous firms (along quality AND internal funds). That combination is what makes signaling/separating contracts fail and forces costly verification (transparency) for adverse-selection resolution, and it generates the coexistence of equity, transparent debt, and opaque debt, lends theoretical support to the pecking-order hypothesis (debt weakly dominates equity), and yields partial — not full — Modigliani-Miller irrelevance. It also contributes to the literature on optimal information control (Hirshleifer 1971, 1972; Diamond 1985; Dang-Gorton-Holmström-Ordoñez 2017; Monnet-Quintin 2017) by endogenizing the information-disclosure decision within contract design.

Q11. What are the key scope conditions and caveats?

Results hold under Assumption 1 (all projects worth investing; all firms prefer external financing — so ’lowest quality’ is not literally any inferior business). The model is static and per-project; ’low n’ means low funds relative to project capacity ī, not necessarily a small or young firm. The most severe misreporting penalty (recovering fraction σ) is imposed to make incentive compatibility least costly. ī can be made to vary across projects without changing main results. The verification cost γ is the central comparative-statics parameter governing whether the equilibrium is mixing or pooling. Equilibrium existence requires condition (26) on γ. There is no empirical estimation — quantitative claims are model-derived equilibrium objects, not data estimates.

Key Concepts

Information transparency: Defined in the paper as whether investors require business information considered confidential to the firm to aid their investment decisions. Equity and transparent debt are ’transparent’ because the firm pays cost γ to reveal its true (α, θ); opaque debt merely reflects general information about the pool of qualifying firms.

Opaque debt: A pooling debt contract carrying a common interest rate (1+r)/αΩ independent of firm-specific information, reflecting the lowest productivity θΩ and the expected survival rate αΩ = E[α] of all qualifying firms. Resembles a real-world business line of credit; the only contract implementable for firms needing small external funds.

Transparent debt: A debt contract whose firm-specific interest rate (1+r)/α reflects the firm’s verified survival rate α (creditworthiness). Resembles corporate bonds or bank loans with firm-specific rates set after credit-rating-style scrutiny.

Transparent (equity) contract: The optimal transparent contract implemented as equity: investors receive a fraction of actual output (ownership), with payout depending on productivity θ. Available only to high-quality firms with lower-intermediate internal funds (n ∈ [n1, nT(αθ)]); these firms are indifferent between equity and transparent debt.

Separating contract: A contract by which a firm signals its true quality (α, θ) WITHOUT paying the verification cost γ, designed so no other type mimics it. Proved not to survive in equilibrium for any firm except possibly the lowest type, which itself prefers opaque debt.

Partial capital structure irrelevance: A Modigliani-Miller-style equivalence holding only for a strict subset of firms — those satisfying condition (27) with n ∈ [n1(α,θ), nT(αθ)] — who are indifferent between equity and transparent debt. Outside this subset the financing choice is determinate, so irrelevance is ‘partial,’ not universal.

Verification cost γ: The cost of the technology (e.g., a rating agency, or the firm’s own effort to convince investors) that ascertains true firm quality (α, θ) before contracting. Its level governs whether the equilibrium is mixing (low γ) or pooling on opaque debt (γ above threshold γ̄), and existence of the unique PBE requires γ sufficiently high relative to σᾱθ̲ī (condition 26).

Interest Rate Pegs and the Reversal Puzzle: On the Role of Anticipation

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

Layer 1: Overview

This paper revisits the “reversal puzzle” — the counterintuitive result, first documented by Carlstrom, Fuerst and Paustian (CFP, 2015), that in standard New Keynesian models the effect of forward guidance (technically implemented as a perfectly anticipated interest rate peg) can switch from expansionary to contractionary as the duration of the peg increases. The authors’ central claim is that the appearance of the puzzle hinges on agents’ degree of anticipation of the peg, and they examine three polar/intermediate cases: perfect anticipation, no anticipation, and imperfect anticipation.

Model and setup: The laboratory is the medium-scale DSGE model of Carlstrom, Fuerst and Paustian (2017), which features funding constraints and market segmentation (only financial intermediaries can hold long-term public and private bonds, subject to a leverage constraint from a hold-up problem and net-worth adjustment costs; households face a loan-in-advance constraint on investment). These frictions break Wallace neutrality so that QE has real and inflationary effects. The model has standard New Keynesian features: habit consumption, monopolistic competition, Erceg-Henderson-Levin (2000) sticky prices and wages with Christiano-Eichenbaum-Evans (2005) indexation, investment adjustment costs, and a Taylor rule with interest-rate smoothing. It is estimated with Bayesian methods on eight euro-area observables over 1998Q1-2013Q4, with a subset of parameters calibrated to CFP (β=0.99, capital share α=0.33, depreciation δ=0.025, price/wage markup elasticities ε_p=ε_w=5, steady-state leverage 6). The initial impulse in all experiments is the launch of a QE programme, modeled as a single shock to an AR(2) process for the real market value of long-term bonds (purchases last 6 quarters). Without a peg, QE raises inflation (the orthodox result).

Main findings: (1) Perfect anticipation (perfect-foresight solution): reversals are a robust phenomenon. As peg duration P rises, the inflation response first grows and then explodes near a critical value; in the baseline this critical value is eight quarters. For P of 9-14 quarters inflation reverses sign (deflation instead of inflation); for 15-23 quarters the sign flips back to positive; for 24-50 quarters it turns negative again. Thus output and inflation responses oscillate with P. The authors give analytical intuition via the forward solution: complex unstable eigenvalues of matrix J, written in polar form, mean powers of J enter the solution as trigonometric functions of P (de Moivre’s formula), producing the oscillation. (2) No anticipation (extended-path method, agents expect E_t[ε_{t+n}]=0 each period and are “surprised”): the reversal puzzle is absent for all durations 0-50; the initial inflation response is always positive, because powers of J no longer enter the solution. (3) Imperfect anticipation (Markov-switching model solved with Maih’s 2015 RISE toolbox): two regimes — Taylor rule (regime 1) vs. peg (regime 2, where ρ=τ_Π=τ_y=0). Agents know transition probabilities, so the frequency F2 and average duration AD2 of the peg are known; frequency is interpreted as the degree of anticipation. Generalized impulse responses (50,000 draws) for average durations of 4, 11.5, 19, 37, 50 quarters and frequencies of 10%, 15%, 20%, 30%, 40%, 50% show: at the empirically relevant frequency of 10% (post-WWII US ZLB experience, ~7 years in 73) and at 15% and 20%, no reversals occur for any average duration. Reversals appear only at implausibly high frequencies: at 30% only for AD2=4 quarters; at 40% for AD2=4, 11.5, 19 quarters; at 50% for all average durations.

Implications: A Markov-switching treatment of pegs/ZLB delivers more plausible model outcomes than perfect foresight and is a promising tool for policy simulations to avoid the reversal pathology, since under realistic anticipation forward guidance is less powerful and reversals do not arise.

In depth

Q1. What exactly is the reversal puzzle and where did it originate?

It is the counterintuitive result that the macroeconomic effect of forward guidance — implemented technically as a perfectly anticipated interest rate peg — can switch from expansionary to contractionary depending on the peg’s duration, producing sizeable deflation instead of inflation. Carlstrom, Fuerst and Paustian (2015) first analyzed and named it. Similar sign reversals are noted in Lindé-Smets-Wouters (2016) and Binning-Maih (2017).

Q2. What is the identification/solution strategy for each anticipation case, and what distinguishes them?

Perfect anticipation: perfect-foresight (deterministic) solution where the peg is implemented via binary dummy shocks (ε^TR in {0,1}) set to one for P pre-announced quarters; agents know all future ε_{t+n}, so powers of the eigenvalue matrix J enter the forward solution. No anticipation: the extended-path method, running a deterministic simulation each period with the previous period as initial condition and steady state as terminal condition, imposing E_t(ε_{t+n})=0 — agents are surprised the peg continues, so powers of J drop out. Imperfect anticipation: a Markov-switching framework (Maih 2015) with non-zero transition probabilities between a Taylor-rule regime and a peg regime; the peg is a recurring stochastic event whose frequency and average duration are known to agents.

Q3. What is the formal mechanism for the oscillation under perfect foresight?

The forward-looking (explosive) variables solve as w2,t = -E_t{Σ J^{n-1} Ω22^{-1} Q2 Φ ε_{t+n}}. Some diagonal elements of J (the unstable generalized eigenvalues) are complex; in polar form z_jj = r(cos φ + i sin φ), and by de Moivre z_jj^k = r^k(cos kφ + i sin kφ) for k=0,…,P-1. Because nonzero anticipated future shocks bring in powers of J, the solution involves trigonometric functions of the peg length P, so simulations approach an asymptote, switch sign, approach another asymptote, switch again — hence oscillation as P grows.

Q4. Why are reversals absent under no anticipation, given the same complex eigenvalues?

Complex eigenvalues are only a necessary, not sufficient, condition. Under no anticipation E_t(ε_{t+n})=0, so the solution for w2,t no longer depends on powers of J; the simulations do not ‘move along’ the trigonometric functions, so the explosive complex eigenvalues cannot induce cyclical/explosive effects. A sufficient degree of anticipation is necessary for reversals to occur.

Q5. How are frequency and average duration of the peg pinned down in the Markov-switching model?

p12 is the transition probability from Taylor regime (1) to peg regime (2); p21 from 2 to 1. Average peg duration AD2 = 1/p21. Frequency F2 = AD2/(AD1+AD2) with AD1 = 1/p12. Table 2 maps the (AD2, F2) grid to the implied p12, p21. The authors check the mean-square-stability condition for each calibration before computing generalized impulse responses from 50,000 draws.

Q6. What is the empirically relevant peg frequency and how is it justified?

About 10%, based on the post-WWII US zero-lower-bound experience (7 years at the ZLB out of 73 years), the same value used by Dordal-i-Carreras, Coibion, Gorodnichenko and Wieland (2016). The paper stresses that even at double this value (20%) reversals are absent for all average durations considered.

Q7. How does the reversal pattern under imperfect anticipation differ from perfect anticipation?

The patterns differ. Under perfect foresight the lowest sub-range of durations (0-8 quarters) shows no reversal, whereas under imperfect anticipation at frequencies of 30% and 40% a reversal occurs for the lowest average duration (4 quarters). Reversals also appear ‘grouped’ across adjacent average durations. The regime-specific IRFs explain this: given the peg regime (regime 2), higher average durations lead to reversals at low frequencies; given the no-peg regime (regime 1), only frequencies of 30%+ permit reversals and there lower average durations reverse. The GIRF blends both regimes, so its resemblance to a regime’s IRF depends on how frequently that regime occurs.

Q8. What robustness checks are performed?

An extensive grid search (Appendix D) varies each structural parameter one at a time around benchmark values under perfect foresight. Reducing forward-lookingness (lower β) or raising habit, changing depreciation δ or investment adjustment cost ψi, varying the Calvo price/wage parameters (θp, θw) and indexation (ιp, ιw), and varying Taylor-rule coefficients (ρ, τπ, τy) all only change the peg duration required for the reversal to appear, not its existence. Notably, even shutting down price and wage indexation jointly (ιp=ιw=0) does not eliminate reversals in this medium-scale model, because other endogenous state variables (capital, wages, net worth) generate complex eigenvalues. More aggressive inflation stabilization (higher τπ) or longer Calvo durations (>0.9) require a longer peg before reversal appears.

It is complementary to CFP (2015), who showed reversals require complex eigenvalues from endogenous states and that switching from sticky-price to sticky-information removes the puzzle; this paper instead goes beyond perfect foresight to show the degree of anticipation is key. It differs from De Graeve-Ilbas-Wouters (2014), Maliar-Taylor (2019), and Bundick-Smith (2020), who rely on realistic calibration to weaken forward guidance; here the resolution comes from realistic modeling of expectations. Unlike de Groot and Mazelis (2020) — who modify the linearized solution so agents are fully aware of the peg — the Markov-switching approach treats the peg as a recurring stochastic event. Methodologically closest is Chen (2017), who compares perfect-foresight and Markov-switching implementations of the ZLB; consistent with her, the authors find Markov-switching delivers more plausible outcomes.

Q10. What are the policy implications and their scope conditions?

Because the ZLB and forward guidance must be accounted for in model simulations, and these are often modeled as interest-rate pegs, policy evaluations risk spurious reversals. The Markov-switching approach circumvents this pathology and yields qualitatively plausible outcomes. Scope conditions: the result holds for empirically relevant peg frequencies (up to ~20%, double the 10% benchmark) across average durations of 4-50 quarters; reversals can still arise but only under extreme, arguably implausible frequencies (30%+). The conclusions are derived within the CFP (2017) segmented-markets model estimated on euro-area data, with QE as the initiating impulse.

Q11. How is the QE programme modeled and what is its transmission?

QE is a single shock to a persistent AR(2) process for the real market value of long-term bonds held by the public, generating an inverse hump shape with purchases lasting 6 quarters before gradual return to steady state. Transmission: lower bond supply to FIs raises bond prices and lowers yield-to-maturity and the term premium; FI net worth and leverage fall but net-worth mobility is limited by adjustment costs, so FIs raise demand for (perfect-substitute) investment bonds, raising their price, relaxing households’ loan-in-advance constraint, boosting investment, output, and inflation; monetary policy then raises the policy rate under the Taylor rule.

Q12. Are there caveats about the no-anticipation case as a ‘solution’?

Yes. The authors state the no-anticipation case is obviously not a suitable solution to the puzzle — it is an unrealistic polar case (agents are surprised every period). Both polar cases (perfect and no anticipation) are unrealistic, which motivates the imperfect-anticipation Markov-switching analysis as the realistic middle ground.

Key Concepts

Reversal puzzle: The counterintuitive switching of forward guidance’s effect from expansionary to contractionary (deflation rather than inflation) as the duration of a perfectly anticipated interest rate peg increases; in this paper, the inflation response oscillates in sign across peg durations.

Degree of anticipation: The extent to which agents expect a future interest rate peg. The paper’s central organizing concept: in the stochastic case it is operationalized by the frequency of the peg regime, since a higher frequency makes agents consider a peg more likely.

Interest rate peg: A regime in which the central bank abandons the Taylor rule and holds the nominal short-term rate fixed for a period — the technical implementation of forward guidance and the ZLB in this analysis.

Imperfect anticipation (Markov-switching implementation): A scenario where agents attach non-zero transition probabilities to entering and exiting a recurring peg regime, so individual peg episodes are stochastic in occurrence and duration but their frequency and average duration are known.

Frequency of the peg (F2): The long-run share of time the economy spends in the peg regime, F2 = AD2/(AD1+AD2); interpreted as the degree of anticipation, with ~10% taken as the empirically relevant post-WWII US ZLB value.

Complex eigenvalues / forward solution: Unstable generalized eigenvalues of the solution matrix J that are complex-valued; their polar-form powers introduce trigonometric functions of peg length P into the forward solution — a necessary but not sufficient condition for reversals, which require sufficient anticipation to activate.

Wallace neutrality breakdown: The property, induced by FI funding constraints and bond-market segmentation in the CFP (2017) model, that asset purchases (QE) affect real activity and inflation rather than being neutral as in the standard New Keynesian model.

Liquidity Crises and the Market-Maker of Last Resort

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

Layer 1: Overview

This paper develops a theoretical model to explain why financial markets can suffer self-fulfilling liquidity crises and how a central bank acting as a “market-maker of last resort” (MMLR) can mitigate them. The motivation is policy-driven: during the 2008-09 crisis and the COVID-19 pandemic, the Fed, ECB, and other central banks purchased assets at above-market prices (e.g., Maiden Lane I/II/III and the TALF) to support markets, a function distinct from the traditional lender-of-last-resort (LLR) role. The authors note that formal theoretical analysis of MMLR remains sparse (citing Buiter et al. 2023) and aim to fill that gap.

Model setup: It is an overlapping-generations (OLG) model with two-period-lived agents and fully rational expectations. There are two assets: a risk-free storage technology with gross return 1-δ (0<δ<1, a negative net return capturing the cost of self-insurance) and a non-depreciating Lucas tree in unit measure paying a constant dividend r (0<r<1). Young agents receive a unit endowment and save (natural buyers); old agents sell their tree to finance consumption (natural sellers). The tree price p_t is set by decentralized Nash bargaining with β denoting the seller’s (old agent’s) bargaining power. Old agents face an i.i.d. idiosyncratic liquidity shock γ∈{0,1} with probability q; if hit (γ=1) they must pay one unit of the good or suffer a utility penalty ω times the shortfall, with ω>1 (focus on large ω). A key parameter restriction is 0<r<δ<1, which rules out a trivial case where liquidity crises could never occur.

Main results: Because trading is by bilateral bargaining (not Walrasian), the model has multiple Pareto-rankable stationary rational-expectations equilibria, each sustained by self-fulfilling beliefs about future prices; lower-price equilibria are Pareto-inferior, more pessimistic, and entail lower consumption. Three benchmark equilibria are derived: (1) an efficient stationary equilibrium with p_t=1 (zero storage), which exists for large ω if seller bargaining power β exceeds a threshold β̃=(1-δ)(1-r)/[δ+(1-δ)(1-r)]; (2) an inefficient stationary equilibrium at p_t=p*=1-r/δ, which exists for any β∈(0,1) and large ω; and (3) a nonstationary equilibrium where prices asymptotically approach p* via p_{t+i}=p*-(1-δ)^i(p*-p_t), requiring β below a threshold β*. The authors introduce a nonfundamental “sunspot” shock that occurs each period with small probability π, inducing pessimistic beliefs that lower the price below the continuation path (to C(p_{t-1})) and leave old agents illiquid (W<1) — a liquidity crisis with flight-to-quality (increased costly storage), run-like behavior, and fire-sale-like price collapse. Crucially, along non-crisis recovery paths all later generations remain liquid, and the increased output loss from storage is exactly offset by greater price appreciation (the wealth difference across adjacent non-crisis periods nets to zero).

Policy: An “aggressive” MMLR — government issuing bonds to young agents and buying trees via Nash bargaining with a positively sloped excess-utility function — can support the unique first-best (p=1) allocation, but the authors argue this is likely politically infeasible (looks like a Wall Street bailout) and fragile (requires persistent intervention if β<β̃). A “conservative” MMLR embedding a “no-bailout” constraint (buy low / sell high) can support p=p*, eliminating utility-cost (crisis) inefficiency but leaving storage-cost inefficiency. Finally, replacing bilateral bargaining with a centralized Walrasian auction yields a unique, efficient equilibrium (p_t=1) with no storage and no liquidity crises, motivating regulatory pushes toward centralized/transparent trading (e.g., Dodd-Frank swap execution facilities, Treasury central clearing proposals). The model abstracts from moral hazard and from distinguishing fundamental vs. nonfundamental price declines.

In depth

Q1. What is the core mechanism that generates multiple equilibria and liquidity crises?

The combination of (a) decentralized Nash bargaining as the trading mechanism and (b) the concavity of the indirect utility function when ω>1. With ω>1, the liquidity penalty makes storage relatively more valuable to a poorer young agent, so an equal fall in the tree price today and tomorrow reduces young agents’ wealth and shifts demand from the tree toward storage. This makes pessimistic beliefs self-fulfilling: a fall in p_t justified by expected low p_{t+1} is itself an equilibrium. With ω=1 (no liquidity penalty) Proposition 1 shows there is a single stationary equilibrium and no nonstationary equilibria.

Q2. How exactly is a liquidity crisis defined in the model?

An old agent is ’liquid’ if end-of-trading wealth W(p_t,p_{t-1})≥1, which is enough to fund a unit liquidity shock. A liquidity crisis is a state where W<1, so an old agent hit by γ=1 cannot fund the shock and incurs the utility penalty. The crisis is triggered by a nonfundamental sunspot that makes the young pessimistic, pushing the price to a crisis-deviation value C(p_{t-1}) satisfying p_underbar < C(p_{t-1}) < κ^o(p_{t-1}), which renders the date-of-crisis old agents illiquid.

Q3. What are the three benchmark equilibria and their existence conditions?

(1) Efficient stationary p_t=1 ∀t: exists for large ω if β>β̃=(1-δ)(1-r)/[δ+(1-δ)(1-r)]; under the tighter condition β>1-δ it exists for all ω>1; not an equilibrium if β<β̃ for large ω. (2) Inefficient stationary p_t=p*=1-r/δ: exists for any β∈(0,1) and large ω; here κ^o(p*)=κ^y(p*)=p* so all agents are liquid. (3) Nonstationary equilibrium p_{t+i}=p*-(1-δ)^i(p*-p_t) approaching p*: requires β<β*=(1-δ)p*/[δ+(1-δ)p*] and appropriate starting prices; along this path W=1 for all i≥1 so all agents are liquid.

Q4. Why does the recovery after a crisis leave subsequent generations liquid even though prices recover only gradually?

Although a crisis raises costly storage (flight to quality) and prices recover only asymptotically, the authors decompose wealth in adjacent non-crisis periods and show the reduction in output from increased storage is exactly offset by a greater rate of price appreciation: W_{t’+i}-W_{t’+i-1}=(p_{t’+i-2}-p_{t’+i-1})(1-δ) + (p_{t’+i-1}-p_{t’+i-2})(1-δ) = 0. So later generations remain liquid (W=1) until the next crisis hits.

Q5. What distinguishes the ‘aggressive’ from the ‘conservative’ MMLR policy?

Aggressive MMLR (Proposition 6): government traders act with an excess-utility function having strictly positive slope in p_t (prefer buying at higher prices), which can enforce p=1 and support the first-best. The authors deem it politically infeasible (appears to subsidize/bailout Wall Street) and fragile (if β<β̃, sustaining p=1 requires persistent intervention). Conservative MMLR (Proposition 7): government adopts a ’no-bailout’ excess-utility function strictly decreasing in p_t and increasing in expected future price (buy low, sell high), supporting p=p* and ruling out p=1 as an equilibrium. It eliminates utility-cost (crisis) inefficiency but not storage-cost inefficiency, and p* remains a natural equilibrium even if political support wavers (absent a current crisis).

Q6. What role does the Walrasian alternative play?

Proposition 8 shows that if trading occurs via a centralized Walrasian auction rather than bilateral bargaining, there is a unique equilibrium with p_t=1 ∀t, no storage, and no liquidity crises. The multiplicity arises in the bargaining model precisely because there is no market to sell storage and buy more trees, permitting interior solutions p_t∈(0,1). This yields the normative implication that regulators should favor centralized, transparent trading venues (cited examples: national bid/offer dissemination for stocks, Dodd-Frank swap execution facilities, proposals for Treasury central clearing).

Q7. How is bargaining power β interpreted, and what is its normative significance?

β∈[0,1] is the old agent’s (seller’s) bargaining power, taken as a primitive standing in for unmodeled market characteristics (e.g., the seller of an MBS may have superior information, or fire-sale conditions may disadvantage sellers). Bargaining power inheres in the role (seller vs. buyer), not the individual; the same agent has power β when old/selling and 1-β when young/buying. High β supports the efficient p=1 equilibrium; low β makes the economy prone to crises. The authors note the Hosios-type efficiency condition on β from labor-search models is not relevant here.

Q8. How does the paper relate to and differ from the closest prior work, Choi and Yorulmazer (2023, ‘CY’)?

Both study multiple equilibria in financial markets and the MMLR’s role in removing multiplicity. Differences: CY’s model is fundamentally static, whereas this is a dynamic stochastic equilibrium model used to generate periodic crises from exogenous bouts of pessimism. Price determination differs: CY uses the cash-in-the-market paradigm (Allen and Gale 1994), whereas this paper uses decentralized Nash bargaining, in which the Walrasian equilibrium is unique and efficient but many Pareto-inferior bargaining equilibria coexist, letting the authors ask whether MMLR can eliminate some or all inferior equilibria. The paper also relates to Holmström-Tirole (self-insurance via low-yield assets is suboptimal; government has a role), but there the friction is a pledgeability/principal-agent problem, whereas here suboptimality comes from a small-probability inferior equilibrium.

Q9. Is the Nash bargaining assumption robust to an alternative bargaining solution?

The authors check Kalai (1977) proportional bargaining. Holding the Kalai weight ν constant, there exist two values of ν supporting the efficient and inefficient equilibria of Propositions 2 and 3 (with parameters r=0.2, δ=0.25, ω=200, q=0.1, the young’s proportional weight is 0.243 in the efficient equilibrium and 0.555 in the inefficient one). For the nonstationary equilibrium of Proposition 4, the ratio of old-to-young excess utility changes over time, so no single constant ν supports it; the Nash solution, by contrast, holds over a range of weights. Inefficient equilibria are supported under both Nash and Kalai.

Q10. What are the main caveats and scope conditions on the policy conclusions?

The model is highly stylized: two-period OLG rules out LLR analysis (old agents do not live long enough to repay loans). In practice policymakers must distinguish price declines due to equilibrium shifts from those due to changing fundamentals (the authors say both were likely active in 2007-08), and must determine the ‘correct’ equilibrium price, which is nontrivial. The model abstracts entirely from moral hazard in public backstopping (citing Farhi-Tirole 2012, Gradstein 2022). The aggressive policy supporting p=1 is fragile and politically vulnerable; the conservative no-bailout policy only removes crisis (utility-cost) inefficiency, leaving storage-cost (flight-to-quality) inefficiency intact.

Q11. What real-world MMLR interventions does the paper map its model to?

Maiden Lane LLC (March 2008, Bear Stearns mortgage assets to facilitate the J.P. Morgan merger), Maiden Lane II and III (October 2008, addressing AIG’s exposure to RMBS and CDOs), and the TALF (supporting certain asset-backed securities). It also cites Buiter et al. (2023) documenting extensive MMLR use by the Fed, ECB, Sveriges Riksbank, Bank of Japan, and Bank of Canada during COVID-19 (repo participation, corporate bond and commercial paper purchases, restarting TALF).

Key Concepts

Loan Evergreening through Banks' Lenses: Evidence from Credit Product-Level Data

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

Layer 1: Overview

Research question and motivation. Banks reluctant to recognize losses on troubled borrowers engage in “loan evergreening”—rolling over or extending credit to delay loss recognition. This misdirected lending has been blamed for Japan’s Lost Decade and Europe’s post-crisis stagnation by steering credit to unproductive firms. Observing how banks do this, and their regulatory motives, is empirically hard. The paper studies a specific, previously hard-to-observe evergreening strategy that arises from banks’ incentive to avoid loan-loss provisions, which increase convexly as repayment delays lengthen.

Identification innovation. The authors depart from the firm-profitability-based zombie-lending literature and instead look at credit products. They identify evergreening as instances where a firm receives a new bullet loan (interest-only until maturity) of similar amount to its contemporaneous amortizing loan repayment to the same bank in the same month. They compute the ratio (new bullet loan / amortizing repayment) and observe an “excess mass” around 1; cases with a ratio between 0.5 and 1.5 are classified as evergreening. Bullet loans are common (~25% of firms with amortizing loans also have one); 70% of bullet loans have maturity ≤181 days. This strategy carries less capital consumption than restructuring, which forces higher provisioning.

Data and setting. Two monthly datasets from the Central Bank of Uruguay, 2006–2018: the exhaustive Credit Registry (loan-level: borrower, sector, amount, currency, maturity, delinquency) and bank balance-sheet/income data. Sample: 1,950,189 amortizing-loan observations, 14 banks, 39,698 firms. Public credit register means all banks can see borrowers’ delinquency elsewhere.

Validation of the measure. The share of evergreening is countercyclical (correlation with GDP growth = −0.55, highly significant), tripling from mid-2007 to early 2010. By end of sample, ~2% of amortizing-loan observations receive evergreening (0.5%–2% range overall—lower than the ~10% in zombie-lending literature, but measuring a different, narrower strategy). A placebo-style test: the dairy sector (hit by a large negative external shock around 2014 from China’s slowdown and Venezuela’s crisis) shows evergreening more than doubling, well above the whole economy and the comparable but unaffected livestock sector.

Main findings (linear probability models with rich fixed effects, including Firm×Month FE). (1) Determinants: Solvency (capital/RWA) is the only consistently relevant bank determinant; lower solvency → more evergreening. A one-SD lower solvency (SD = 0.083, or 8.3pp) raises evergreening probability by 0.546pp, an over-50% increase relative to the ~1% unconditional mean. Solvency matters more during booms, contradicting gambling-for-resurrection accounts. Loan-level: short-term loans (+0.7pp), higher USD share (0%→100% gives +0.8pp), being the firm’s top/main bank (+0.65pp), and longer relationships all raise evergreening likelihood. (2) Credit: Evergreening is associated with ~7pp (7.3pp) higher amortizing credit growth from the same bank over 12 months (excluding the bullet loan), and a 7.5pp higher probability of any credit increase (23.4% above the 32% baseline). (3) Relationship survival: No effect on probability of relationship ending. (4) Performance: Without Firm×Month FE, evergreening predicts +1.1pp higher future delinquency at 12 months, concentrated in low-solvency banks and ex-ante non-performing firms; the effect peaks ~16 months out (~2pp). With Firm×Month FE the sign reverses—a multi-bank firm is less likely to become delinquent with the bank that evergreened than the one that did not. (5) Access to new lenders: Single-relationship firms receiving evergreening are more likely to obtain a second bank after ~18 months. (6) Crowding-out: No aggregate displacement, but at the 5-digit-industry level, banks more engaged in evergreening are more likely to fully cut credit to non-evergreened firms in that industry.

Implications. The measure is an early-warning tool for supervisors; the strategy is regulatory arbitrage that avoids the provisioning penalty of formal restructuring.

In depth

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

The authors identify evergreening as a new bullet loan whose amount approximately matches a contemporaneous amortizing-loan repayment to the same bank-firm in the same month (ratio between 0.5 and 1.5). The bank-borrower-month granularity lets them saturate the determinants regression with bank and Firm×Month fixed effects, so firm-level credit demand and characteristics are absorbed, isolating bank/loan supply-side drivers. Main threats: (a) misclassification—the measure misses evergreening done via larger bullet loans or other instruments; the authors argue this biases results downward (attenuation). (b) The legality/intent of any single bullet loan is ambiguous (many legitimate reasons exist), but they rely on the statistical excess mass at ratio≈1 to argue the vast majority of selected cases are genuine evergreening. (c) Omitted bank-level confounders—addressed via Oster (2019) coefficient-stability: the bias-adjusted Solvency coefficient at R-squared=1 is −5.556, and unobservables would need to be ~11x (δ=10.9) more correlated with Solvency than observables to nullify the result.

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

Two motives. (1) Provision/capital management (regulatory arbitrage): provisions rise convexly with repayment delay, so banks issue bullet loans to keep firms current and avoid provisioning. Supported by the dominance of Solvency, the short-term-loan effect, and the Firm×Month-FE result that a firm receives evergreening from its non-delinquent bank (preventing the delay rather than reacting to it). (2) Relationship/reputation lending à la Hu and Varas (2021): banks evergreen to camouflage problems so the borrower can attract outside funding. Supported by the finding that single-relationship firms gain access to a second bank ~18 months after evergreening. The booms-matter-more result distinguishes this from gambling-for-resurrection (Bruche and Llobet 2014), which predicts weak banks pushing losses forward mainly in bad times.

Q3. What heterogeneity is documented?

Cyclical: Solvency’s importance is stronger in booms (at average ~4% GDP growth the coefficient is −5.267; a one-SD higher GDP growth of ~2.6pp shifts it to about −7.14). By bank: low-solvency banks evergreen riskier (ex-post worse) firms, so the evergreening→future-delinquency link is concentrated among low-solvency lenders and weakens/reverses for high-solvency banks (one SD above median: ~0.6pp lower delinquency, not significant). By relationship structure: single-bank firms drive the positive evergreening→delinquency result; multi-bank firms show the opposite (less likely delinquent with the evergreening bank). By ex-ante status: the delinquency effect is present for currently-performing firms and even stronger (triple interaction) for currently non-performing ones. The solvency effect on the probability of evergreening is concentrated in the top/main bank.

Q4. What robustness checks are run?

(1) Brodeur et al. (2020) specification-check: each of six bank controls is regressed against all 1,023 combinations of the other ten controls; only Solvency is consistently significant (always negative, t>1.65), while Size, Credit, Liquidity, Provisions never/almost never cross, and RoA’s significance is not robust. (2) Oster (2019) selection-on-observables bound (δ=10.9). (3) Progressive addition of fixed effects (Bank, Month, Firm, Firm×Month, Bank×Month)—Solvency coefficient stays stable (~−6) while R-squared rises from 0.7% to 45.5%. (4) Unreported Probit yields negative, significant Solvency. (5) Intensive-margin result re-run with a binary ‘credit went up’ outcome to guard against outliers, and dynamics traced from x=1 to 24 months. (6) Delinquency result decomposed (columns 7–8) to show the sign reversal is driven by Firm×Month FE, not just the changed sample. (7) Appendix numerical provisioning example and a stylized theoretical model of the restructure-vs-evergreen tradeoff.

It builds on Peek and Rosengren (2005) and Caballero et al. (2008) on Japanese zombie lending but shifts the lens from firm profitability to bank credit products. Among granular-data papers: Bonfim et al. (2020, Portugal) find low profitability and exclusive relationships drive refinancing of troubled borrowers, with supervisory inspections deterring some; Bergant and Kockerols (2020, Ireland) find capital-constrained banks forbear more to riskier borrowers, effective only short-run; Mourad et al. (2020, Brazil) and Tantri (2021, India) study restructuring/renewals. This paper’s distinctive contribution is identifying a regulatory-arbitrage strategy (bullet-to-repay-amortizing) that is more flexible and less provisioning-costly than restructuring, and tracing its determinants and consequences for credit supply, performance, access to new lenders, and other firms. It also speaks to theory: contra Bruche and Llobet (2014) gambling-for-resurrection (since the practice is used by well-capitalized banks and matters more in booms), and in favor of Hu and Varas (2021) relationship/reputation mechanism for single-relationship firms.

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

The measure serves as an early-warning indicator for supervisors, who can flag bullet-loans-matching-repayments as potential evergreening and (as has occurred) require restructuring. Scope: the strategy is narrow (0.5%–2% of observations) and not restricted to deeply distressed firms—7.8% of evergreening cases involve >60-day delays, almost identical to the 7.4% in the full sample—so it is partly preemptive provision management, not only zombie support. Crowding-out concerns are muted in aggregate but real at narrowly-defined (5-digit) industry level, where high-evergreening banks cut credit to other firms. The authors note relevance is heightened post-COVID with more firms in distress.

Q7. What is the provisioning/regulatory mechanism in detail?

Under Uruguayan regulation, borrowers are rated 1A/1C/2A/2B/3/4/5 by days past due; provisioning ranges from 0.5–1.5% (1C) up to 100% (rating 5, >180 days). The paper defines delinquent as ratings 3–4 (>60 days, <180 days) and excludes rating 5. In the stylized example (1,000-peso loan, zero collateral), total capital consumption (provisions + capital requirement) rises sharply with deterioration: ~84.6 at 1C to 236.4 at rating 3 and 540 at rating 4. Restructuring forces a worse rating than if the borrower had stayed current, so it carries even more capital consumption than the bullet-loan evergreening strategy—the core regulatory-arbitrage incentive.

Q8. What does the theoretical model show?

A stylized decision tree: facing a troubled borrower, the bank either restructures immediately (cost R) or extends an evergreen bullet loan. If it evergreens, with probability α the supervisor detects it and imposes restructuring plus penalty S; with probability 1−α it is not caught, and then the borrower repays with probability 1−β or defaults (forcing restructuring R) with probability β. The bank prefers evergreening when R > [(1−α)(1−β)/α]·S. Evergreening is less attractive when α→1 (supervisor catches often) or β→1 (loan almost surely needs restructuring). The model is not calibrated; it formalizes why low detection probability and modest penalties make evergreening attractive.

Q9. Are there caveats about the magnitude and comparison to zombie-lending estimates?

Yes. The 0.5%–2% prevalence is far below the ~10% typical of zombie-lending studies, but the authors stress the two are not comparable—they capture a specific regulatory-arbitrage strategy, not broad firm-level distress, and the strategy is also used for firms not (yet) delinquent. Misclassification (missing larger or differently-structured evergreening) biases estimates downward. The intensive-margin credit-growth effect loses significance after ~19 months as standard errors grow (fewer observations at long horizons), and the two-year credit effect, while similar in magnitude, is no longer statistically significant.

Key Concepts

Loan evergreening strategy (as defined here): A new bullet loan granted to a firm of an amount similar to its contemporaneous amortizing-loan repayment to the same bank in the same month (ratio between 0.5 and 1.5), used to extend the duration of exposure without increasing it and to delay loss/provision recognition. This is the paper’s specific, product-level operationalization, distinct from generic zombie lending.

Bullet loan: A loan whose principal is repaid in full at maturity with only interest paid before then. In this paper, bullet loans (70% with maturity ≤181 days) are the instrument banks use to repay existing amortizing loans and keep the firm current.

Amortizing loan: A loan whose principal is repaid gradually over its life. The benchmark credit product whose scheduled repayment is matched against new bullet loans to detect evergreening.

Solvency: Defined in the paper as regulatory capital over risk-weighted assets. It is the single consistently significant bank-level determinant of evergreening (lower solvency → more evergreening), and its importance rises in economic booms.

Regulatory arbitrage (provisioning avoidance): Using the bullet-to-repay-amortizing strategy to keep a borrower from being rated as delinquent, thereby avoiding the convex increase in loan-loss provisions and capital consumption that delinquency or formal restructuring would trigger. Restructuring is shown to consume even more capital than this strategy.

Delinquent: In this paper, a borrower delayed by more than 60 days in repayment (ratings 3–4 under Uruguayan regulation, i.e., 60–180 days past due); rating-5 loans (>180 days) are excluded from analysis.

Top bank: The bank providing the highest amount of amortizing credit to a firm; such main-relationship banks are substantially more likely to provide evergreening, and the solvency effect is concentrated among them.

Macroprudential Policy in the Euro Area

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

Layer 1: Overview

Research question and motivation. There is now broad consensus that monetary authorities should hold a financial-stability mandate and that macroprudential policy should be part of it, yet evidence on the macroeconomic effectiveness of these policies and their interaction with monetary policy remains thin and inconclusive. The paper addresses this gap for the euro area, a case of special interest because of its international structure and because, within the short life of the euro, member states experienced major episodes of financial instability (the great financial crisis, GFC, and the sovereign debt crisis). The contribution is twofold: (1) build a novel aggregate index of the euro-area macroprudential policy stance and document its stylized facts since 1999; (2) be the first to identify, within a structural econometric framework, both unanticipated (surprise) and anticipated (news) exogenous macroprudential policy shocks and trace their macroeconomic effects.

Data and method. The authors use MaPPED (Macro-Prudential Policies Evaluation Database), built by ECB staff and national central banks. For euro-area countries it records 1205 policy actions between 1995 and 2019 across 11 instrument types (capital buffers, lending standards, maturity mismatch tools, limits on credit growth, exposure limits, liquidity rules, loan loss provisions, minimum capital requirements and risk weights, leverage ratio, and ‘other measures’). Actions are signed (+ tightening, − loosening, 0 ambiguous) and weighted following Meuleman and Vander Vennet (2020): activation 1, change in level 0.25, change in scope 0.10, maintaining level/scope 0.05; deactivation resets the cumulative index to zero. This yields around 470 instrument-level indices, summed within each country and then aggregated across countries using GDP-share weights to form the EAMPP index. The empirical model is a seven-variable Bayesian SVAR at quarterly frequency over 1999:Q1–2019:Q2, estimated in levels with 4 lags and a Minnesota prior using the hyperparameters of Kurmann and Otrok (2013). Variables: the narrative EAMPP (which excludes countercyclical/financial-cycle-reactive policies so it is exogenous in the Romer-Romer sense), total credit to the private non-financial sector, real GDP, core CPI, inflation expectations (ZEW 6-month survey), VSTOXX, and a monetary policy rate (EONIA 1999–2009, Wu-Xia shadow rate thereafter). The surprise shock is identified by a Cholesky ordering with EAMPP first; the news shock is identified via the Barsky-Sims (2011) forecast-error-variance maximization (horizon k=0 to k=24), orthogonal to the surprise shock and not affecting EAMPP contemporaneously.

Main findings. Stylized facts: EAMPP shows a positive starting value (policies predating the euro), a small positive trend up to the GFC, a loosening on average at the start of the GFC in 2009, then a clear upward (tightening) trend over the following seven years driven by sovereign-debt-crisis concerns and Basel III/CRR-CRDIV; the level in 2016 is almost twice as tightening as pre-crisis. The largest quarterly EAMPP change occurred in 2013:Q3 (CRR/CRDIV announcements). Policy announcements averaged about 13 per quarter in 1999–2015 versus about 2 per quarter in 2016–2019. Macroprudential and monetary policy moved oppositely; their correlation is about −0.90, negative and significant. SVAR results: a tightening surprise shock persistently raises the policy index, lowers total credit (on impact, accentuating over the medium term), reduces output in a way negatively correlated with credit (lowering credit pro-cyclicality), and lowers VSTOXX over the medium term after an initial rise. The effect on core CPI is negligible and on inflation expectations insignificant, so no price-stability trade-off; the monetary policy rate declines (accommodative complement). The news shock produces a gradual, persistent tightening, reduces credit, lowers credit pro-cyclicality, has muted effect on VSTOXX, and an insignificant price effect; the policy rate first rises then turns negative over the medium term. FEV decomposition: the two shocks combine to explain about half of credit variability after 24 quarters; neither shock exceeds 12% of core-CPI forecast variance and combined they never exceed 15% of prices. News shocks explain about 20% of credit forecast variance within the first quarter. Granger-causality and serial-correlation tests support exogeneity of both shocks.

In depth

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

Two shocks driving non-systematic macroprudential variation are identified within a seven-variable Bayesian SVAR (1999:Q1–2019:Q2, 4 lags, Minnesota prior). The surprise (unanticipated) shock is identified by a Cholesky decomposition with EAMPP ordered first, so it can affect EAMPP contemporaneously. The news (anticipated) shock uses the Barsky-Sims (2011) forecast-error-variance maximization: it is the orthonormal column that maximizes the cumulated forecast error variance of EAMPP over horizons k=0 to k=24, subject to not affecting EAMPP contemporaneously and being orthogonal to the surprise shock. A key prior step is constructing a narrative EAMPP that drops all policies with a countercyclical design (those reacting to the financial cycle), making the remaining index exogenous in the Romer-Romer (2010) sense. The main threats are: foresight/anticipation contaminating shock identification (addressed by using announcement rather than enforcement dates and by identifying news shocks); reverse causality and contemporaneous effects that plague recursive/GMM panel approaches; and informational insufficiency (whether the series are genuine shocks), which the authors test via Granger causality against forward-looking credit-standard surveys and serial-correlation tests.

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

The mechanism is that a tightening macroprudential stance curbs total credit to the private non-financial sector, which is the most robust predictor of financial crises, thereby moderating systemic risk and the build-up of excess credit during booms. Crucially, output responds in a way negatively correlated with credit, so the policy lowers the pro-cyclicality of credit (the key financial-stability gain). Surprise and news shocks are distinguished by their dynamics and by the FEV decomposition: news shocks dominate at short horizons (agents react quickly to signals, ~20% of credit forecast variance in the first quarter), while surprise shocks build gradually to a comparable share at medium-to-long horizons. The monetary-policy interaction is read off the policy-rate response: it moves accommodatively (declines) after a surprise tightening, complementing macroprudential policy without a price trade-off.

Q3. What heterogeneity or differences across shock types are documented?

The two shock types differ. The surprise shock causes an immediate credit drop that accentuates over the medium term and an accommodative (declining) monetary policy rate; VSTOXX first rises then falls below baseline. The news shock causes a gradual, persistent policy tightening, a credit decline that moderates before dropping again over the medium term, a muted VSTOXX response, and a monetary policy rate that first increases (complementing the tightening and reflecting a small initial price rise) then turns negative over the medium term. Core prices show a small initial increase under the news shock before declining, whereas the surprise shock barely affects core CPI. Both shocks ultimately lower credit pro-cyclicality and have insignificant effects on price stability.

Q4. What robustness checks are run?

Several. (1) Alternative macroprudential target variables replacing total credit: a systemic-risk index (CISS) — results barely change; bank credit — results similar, with a more pronounced decline in bank credit; household credit — results similar but the household-credit decline is stronger, while under the surprise shock the credit decline becomes insignificant and output rises initially. (2) Replacing VSTOXX with VDAX (German analogue) — qualitatively the same. (3) Longer FEV truncation horizons k=30 and k=40 — quantitatively and qualitatively similar. (4) Including policies with missing announcement dates (182 of 1205 actions) in the empirical analysis — results barely change. (5) Granger-causality tests: the identified shocks are regressed on up to 3 principal components (explaining ~98.4% of variance) of seven forward-looking loan-officer credit-standard surveys; the null of no Granger causality cannot be rejected at any reasonable level (p-values range roughly 0.37–0.99). (6) Serial-correlation test regressing each shock on its own two lags: p-values 0.47 (surprise) and 0.77 (news), so no serial correlation.

It relates to (a) empirical work on macroprudential effectiveness and its monetary-policy interaction (Cerutti et al., Alam et al., Akinci and Olmstead-Rumsey, Kuttner and Shim, Budnik and Kleibl, etc.), most of which uses cross-country panels with GMM and cannot make clean causal claims; and (b) the SVAR/news-shock identification literature robust to foresight (Barsky and Sims 2011; Leeper et al. 2013; Kurmann and Otrok 2013; Ben Zeev et al. 2019). The two prior SVAR studies extracting exogenous macroprudential variation are Kim and Mehrotra (2017, four Asia-Pacific countries) and Klingelhofer and Sun (2019, China), both using recursive Cholesky orderings. Like Klingelhofer and Sun, the authors find macroprudential shocks explain a meaningful share of credit but little of prices. Unlike those studies, they find a strong macroprudential-monetary link (EAMPP-policy-rate correlation about −0.90, versus roughly +0.25 for Asia-Pacific in Bruno et al. 2017), and they are the first to identify both surprise and news macroprudential shocks. The narrative exclusion of cyclically-reactive policies follows Romer and Romer (2010), Richter et al. (2019), and Rojas et al. (2020).

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

Macroprudential policy in the euro area effectively safeguards financial stability over the medium term by reducing credit growth, credit pro-cyclicality, and systemic risk, without a significant trade-off against price stability (the ECB’s primary target). Because more than one objective cannot be met with one instrument, monetary policy complements macroprudential policy: it can move accommodatively to offset output/credit declines, yielding an effective overall policy mix. Scope conditions: the conclusions are specific to the euro area over 1999:Q1–2019:Q2, a sample dominated by the GFC and sovereign debt crisis and by deflationary pressures (which is why the strong, negative macroprudential-monetary correlation may not generalize, e.g., to Asia-Pacific where the correlation is positive); the narrative EAMPP only captures proactive, long-run-financial-stability-motivated policies; and price-stability effects, while insignificant overall, carry wide estimate uncertainty.

Q7. Why does the paper use announcement dates rather than enforcement dates?

Because foresight problems arise from inside and outside lags (Leeper et al. 2013): about 54% of euro-area policy tools in MaPPED experience a delay between announcement and implementation. Using the enforcement date would contaminate the identification of an ‘unanticipated’ shock, since agents would already know about the policy from its announcement, making the shock no longer exogenous. The authors assume agents react from the announcement moment.

Q8. Are there notable caveats about the index and impulse responses?

The first EAMPP value is not zero because 185 of 1205 policy actions were implemented before 1995, and MaPPED does not provide announcement dates for 182 of 1205 actions (assumed equal to enforcement dates only for the stylized-facts section; removed in the empirical analysis). GDP-share weights use the 2008–2015 average; time-varying weights have very limited impact since GDP shares are stable. Impulse responses report median with 16th and 84th posterior percentiles. The EONIA-shadow-rate splice is justified by a 0.98 correlation between the two over 2004:Q4–2008:Q4.

Key Concepts

Macroprudential, Monetary Policy Synergies and Credit Supply: Evidence from Matched Bank-Firm Loan-Level Data in Brazil

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

Layer 1: Overview

Research question and motivation: Reserve requirements (RRs) were largely abandoned as a monetary tool in advanced economies after inflation targeting, but emerging markets (EMs) — especially Brazil — kept using them countercyclically before, during and after the GFC and COVID-19 (53 EMs eased RRs during the pandemic). Despite their wide use, there was scarce loan-level evidence on whether RRs actually manage domestic credit cycles through credit supply, and on whether they have synergies with the short-term policy rate. The paper fills this gap.

Data and strategy: The authors use quarterly matched bank-firm loan-level data from Brazil’s credit registry (SCR), augmented with bank controls and firm employment data from RAIS, covering 2008Q1-2015Q2 (30 quarters). After cleaning and a 10% random firm sample, the working sample is 2,595,398 observations spanning 90,440 firms and 83 commercial banks. Identification rests on three moves: (1) firm-quarter fixed effects on multiple-bank-relationship firms (Khwaja-Mian/Jimenez approach) to absorb credit demand; (2) a bank-level counterfactual exposure variable, ΔResReq (the Camors et al. 2019 construction), measuring how much each bank is differentially “taxed” by RR rule changes given its ex-ante deposit mix, holding policy fixed at pre-September-2008 rules; ΔResReq averages -1.64 (sd 2.61) at bank level. (3) High-frequency monetary policy surprises (Kuttner 2001) from 30-day interest-rate swaps around Copom announcements, interacted with ΔResReq to identify policy synergies.

Main findings (signs, magnitudes, scope): A 1 pp tightening of RRs reduces a bank’s credit to a firm by 0.52-0.56 pp next quarter (no firm-quarter FE), and -0.67 pp with firm-quarter FE — coefficient stability across saturations suggests exposure is orthogonal to demand. Private domestic banks are roughly twice as responsive: -1.39 pp (Table IV) and -1.68 pp in the synergies specification (Table V). With a simultaneous one-standard-deviation surprise policy-rate tightening, the response rises to -1.90 pp — evidence of monetary-macroprudential synergy. A comparable interest-rate surprise alone contracts credit 0.63 pp; a 1 pp Selic increase, 0.71 pp. Bank capital matters: a private domestic bank one sd above mean capital/assets cuts credit only 0.85 pp (vs 1.68 pp), implying capital-liquidity substitution — but only during tightening, not loosening. After controlling for heterogeneity, there is no significant tightening-vs-loosening asymmetry for private domestic banks; the asymmetry found in cross-country work is driven by less-responsive government and foreign banks (foreign banks fully mitigate loosening). Economic policy uncertainty (EPU, Baker-Bloom-Davis) weakens transmission: a 1 pp loosening raises credit 1.50 pp, but only 1.22 pp when EPU is one sd (71 points) higher — about 19% mitigation. Using an aggregate macroprudential index instead of bank exposure yields qualitatively similar but weaker effects (a 1 sd index move gives -1.43 pp vs -2.02 pp for the intensity-sensitive aggregate counterfactual), so cross-country index studies underestimate RR effects and overestimate asymmetries. At the firm level, firms do not insulate themselves (no leakage). Real effects on employment are modest and not economically significant: no significant hiring effect; a 1 pp RR loosening reduces firings by ~1.6% (all banks) / ~2% (private domestic), requiring an 8.33 pp loosening to prevent one additional firing.

Implications: RRs are an effective state-contingent (Pigouvian) tax to manage domestic credit booms and busts via credit supply, can stimulate credit even with the policy rate unchanged (useful at the ELB or under “fear of floating”), and should be eased more aggressively when EPU is high.

In depth

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

Three layers. First, firm-quarter fixed effects on firms with multiple bank relationships absorb firm-level credit demand (Khwaja-Mian/Jimenez et al. 2014), so the within-firm-quarter comparison isolates supply. Second, a bank-level counterfactual exposure variable, ΔResReq, measures differential RR ’taxation’ from each bank’s ex-ante deposit mix relative to pre-September-2008 rules, holding policy fixed — this separates RR supply effects from the policy rate and from aggregate credit-cycle dynamics. Third, high-frequency monetary policy surprises (one-day swap changes after Copom) provide exogenous variation in the policy rate for the synergy interaction. Main threats: (a) banks could shift their liability mix toward less-affected deposits (evasion) — addressed in Appendix A.3 (no significant deposit reallocation); (b) more-exposed banks could be differentially exposed to other macro shocks — addressed via ‘horserace’ interactions with local and global variables (Tables VI-VII); (c) policy-rate endogeneity — addressed by using surprises; (d) excess/voluntary reserves as omitted variable — addressed in A.8-A.9 (insignificant). Coefficient stability when adding firm-quarter FE (Oster 2019) supports exogeneity of ΔResReq to demand.

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

The core mechanism is RRs acting as a countercyclical Pigouvian tax that withdraws liquid funds during tightening (constraining supply) and injects cash during loosening (stimulating supply). The synergy mechanism is that simultaneous policy-rate tightening amplifies the RR credit-supply contraction (-1.68 to -1.90 pp for private domestic banks). The EPU mechanism is that high policy uncertainty makes banks more cautious, reducing the amplification of stimulus policy (loosening becomes ~19% less effective). These are distinguished by interacting ΔResReq separately with policy-rate surprises, with EPU, and with bank characteristics, all within the saturated firm-quarter FE model, and by running separate loosening vs tightening subsamples (16 loosening quarters, 14 tightening quarters).

Q3. What heterogeneity is documented?

By bank ownership: government and foreign banks are less sensitive to RRs (government banks lend countercyclically; foreign banks respond to home-country policy and fully mitigate loosening effects), while private domestic banks are about twice as responsive as the average bank. By capital: higher-capital private domestic banks are insulated from RR tightening (one sd above mean capital cuts the response from -1.68 to -0.85 pp), consistent with capital-liquidity substitution (Acosta-Smith et al. 2019); this insulation appears only during tightening, not loosening. By state of EPU: transmission is weaker when economic policy uncertainty is high. NPL share is not associated with lower credit growth during tightening as it is during loosening.

Q4. What robustness checks are run?

(A.3) Bank-level panel regressing changes in savings/demand/time deposits on lagged exposure — no significant reallocation, so banks are not evading the policy. (A.4) Replicating Table V with the actual Selic change instead of surprises — a 1 pp RR tightening plus 1 sd (0.97) Selic tightening gives -2.02 pp (vs -1.9 pp with surprises). (A.5) Dropping influential policy quarters (2008Q4, 2009Q1, 2010Q1-Q2, 2010Q4, 2011Q1) — results unchanged. (A.6-A.7) Adding controls for ex-ante liability structure (shares of savings/time/demand deposits) — baseline qualitatively and quantitatively unchanged. (A.8-A.9) Controlling for / interacting with excess voluntary reserves (averaging 0.08% of liabilities) — insignificant and leaves estimates unchanged. Tables VI-VII horserace against local (inflation, GDP, current account, EPU) and global (Fed funds, US shadow rate, VIX, commodity prices, other macropru policies) variables — estimates stable.

It uses the same counterfactual exposure variable as Camors et al. (2019), who studied RRs as a tax on dollar deposits in Uruguay; and relates to Epure et al. (2018) on Romania and the global financial cycle. Unlike that literature, which focuses on FX/dollar-denominated deposits and global-cycle spillovers, Brazil’s low foreign-debt banking sector lets the authors isolate RRs targeting the DOMESTIC credit cycle. They claim to be the first loan-level paper to estimate RR effects on domestic credit cycles while disentangling and documenting monetary-policy synergies, the first to link higher EPU to lower macroprudential effectiveness, and the first to assess bank capital’s mitigating role for RR tightening. Against the cross-country macroprudential-index literature (Cerutti-Claessens-Laeven 2017, Akinci-Olmstead-Rumsey 2018, Alam et al. 2019), which finds borrower-targeted tools stronger than bank-targeted RRs and tightening more effective than loosening, this paper shows the index approach ignores policy intensity and bank exposure, thereby underestimating RR effects and overestimating asymmetries. On real effects, modest employment results echo Richter, Schularick, and Shim (2019).

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

RRs are effective for managing domestic credit booms and busts through credit supply, and can stimulate credit even when the policy rate is unchanged — relevant for EMs at the effective lower bound or constrained by ‘fear of floating’ from using the policy rate countercyclically. Synergies with the policy rate are relevant and significant mainly during tightening (statistically weaker, for firms, during loosening). Because high EPU mutes the stimulus, policymakers trying to unfreeze credit (e.g., COVID-19) must ease RRs more aggressively when policy uncertainty is high. Scope conditions: results are estimated on Brazil 2008-2015, on multiple-bank-relationship firms, for credit in local currency, with the strongest responses concentrated in lower-capital private domestic banks; real effects on employment are modest and not economically significant in either direction.

Q7. Are there leakage or general-equilibrium concerns at the firm level?

The authors test whether firms insulate themselves by substituting toward less-affected banks (Jimenez et al. 2017 found full insulation for Spanish dynamic provisions). Using firm-level regressions (equation 10), they find firms associated with more-exposed banks are NOT insulated from either loosening or tightening — strong effects survive at the firm level — so the transmission channel does not ’leak,’ confirming RRs are effective at dampening credit booms in aggregate.

Q8. What is the relationship between the policy variables and the credit cycle in the raw data?

Changes in RRs track aggregate bank credit countercyclically: the correlation between the system-wide counterfactual RR variable and aggregate credit is 0.50, far above the 0.14 correlation between credit growth and CPI inflation, supporting the financial-stability (not inflation) motivation. The correlation between RR changes and the Selic policy rate is 0.31, motivating the need to disentangle the two instruments.

Key Concepts

Monetary and Macroprudential Policies under Dollar-Denominated Foreign Debt

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

Layer 1: Overview

Research question and motivation: Emerging economies have rapidly accumulated foreign-currency (mostly dollar) debt — the dollar share of 14 emerging economies’ foreign debt rose from 75% in 2010 to 81% in 2018. Such debt is dangerous because sudden stops in capital inflows cause sharp currency depreciation that mechanically raises the domestic-currency value of the debt. The paper asks: when a country holds dollar-denominated foreign debt, does macroprudential policy mitigate depreciation and downturns during sudden stops, how should monetary policy be conducted, and how should the two policies cooperate? Existing sudden-stop models (with loan-to-value/debt-to-income collateral constraints and pecuniary externalities) do not model the channel by which depreciation inflates the value of dollar debt.

Model setup: The author builds a small open economy in the tradition of Bianchi and Mendoza (2018), with three innovations: (1) foreign debt is denominated in foreign currency; (2) home tradable exports face a downward-sloping foreign demand (price elasticity rho > 1); (3) New Keynesian (Rotemberg) price stickiness to give monetary policy a role. The borrowing constraint is occasionally binding and the borrowing limit is denominated in domestic currency, creating a currency mismatch between foreign borrowing and the limit. The author deliberately abstracts from the collateral-asset-price pecuniary externality (assets valued at book value) to isolate a new balance-of-payments (BOP) externality. The model is solved with a global numerical method; each period is a year. Calibration targets the average of the 14 countries: discount factor beta = 0.92 (to hit mean foreign-debt-to-GDP of 40%), R* = 1.04, labor share = 0.66, imported-input share targeting import-to-GDP of 22%, theta = 8, price-adjustment cost psi = 50, export price elasticity rho = 3, tight borrowing limit kappa = 0.2 set so the unconditional crisis probability is 7.2%; productivity and interest-rate processes are from Mendoza (2010, Mexican data).

Key mechanism: When the borrowing constraint binds, large debt repayment with limited new borrowing forces net capital outflows, which require larger net exports and thus real depreciation (because exports face downward-sloping demand). Depreciation raises the domestic-currency value of debt repayment, forcing further outflows and a second-round depreciation — an amplification loop. Because households take the exchange rate as given, they socially overborrow ex ante (“ex ante BOP externality”) and use too many imported inputs during crises (“ex post BOP externality”), both producing inefficiently large depreciation. Social costs are twofold: imported inputs become inefficiently expensive (lowering output, explaining the output drop without working-capital financing), and an inefficiently large share of output is exported (lowering consumption).

Main findings: The optimal discretionary monetary policy (without taxes) is contractionary both when the constraint is slack (to discourage overborrowing via real appreciation raising the effective interest rate) and when it binds (to discourage imported-input use). But anticipation of crisis-time intervention lowers the ex ante effective interest rate and induces larger borrowing, destabilizing the economy. In crisis dynamics, without taxes the real exchange rate depreciates 10% under inflation targeting vs 6% under discretion; output drops 6.2% under targeting vs 14.4% under discretion. With macroprudential taxes, depreciation is 6% (targeting) vs 2% (discretion), and output drops 3.8% (targeting) vs 9.2% (discretion). Under taxes, foreign debt at the stochastic steady state is 6-7% smaller. Welfare (permanent-consumption metric, benchmark = inflation targeting without taxes): discretion without taxes is worse by 0.02%; evaluated at the simulation-mean foreign bond (-0.45), discretion with taxes gives +0.07% and targeting with taxes gives +0.03%. If the simulation starts with a binding constraint, the welfare gain under discretion with taxes can reach about 0.2%. Implication: the optimal mix is an ex ante macroprudential tax on foreign borrowing to correct overborrowing plus ex post monetary intervention to mitigate depreciation; monetary intervention improves welfare only when paired with the macroprudential tax.

In depth

Q1. What is the core theoretical mechanism (the “amplification loop”) and why does it require a currency mismatch?

When the borrowing constraint binds, the country must repay outstanding foreign debt with only limited new borrowing, producing net capital outflows that must be matched by larger net exports via the balance-of-payments identity. Since exports face downward-sloping foreign demand, this requires real depreciation. Depreciation raises the domestic-currency value of the foreign-currency debt repayment (-e_t b*_{t-1}), but new borrowing is capped by the domestic-currency-denominated limit kappa*k, so the depreciation forces a cut in new borrowing, generating further outflows and a second-round depreciation. The loop continues. The currency mismatch — foreign-currency debt against a domestic-currency borrowing limit — is crucial: the author states explicitly that if the borrowing limit were denominated in foreign currency, the amplification loop would not occur.

Q2. What are the two externalities and how are they distinguished?

The “ex ante BOP externality” distorts borrowing in normal times: households do not internalize that reducing foreign debt today would reduce next-period net capital outflows and mitigate depreciation if the constraint binds, so they overborrow. The “ex post BOP externality” distorts imported-input use when the constraint is binding: households do not internalize that cutting imported inputs would improve the trade balance and mitigate depreciation, so they use socially excessive imported inputs. Both are formalized through the planner’s Lagrange multiplier gamma^SP_t (social value of real appreciation through BOP adjustment), which is strictly positive given rho>1 and negative net foreign assets. The ex ante term appears in the foreign-bond Euler equation; the ex post term appears in the imported-input first-order condition and is positive only when the constraint binds (mu^SP_t > 0).

Q3. Why is the optimal discretionary monetary policy contractionary in both states, and what does “contractionary” mean here?

The target inflation is zero (Rotemberg cost), so positive inflation is “expansionary” and negative inflation “contractionary.” When the constraint is slack but may bind, contractionary policy causes real appreciation, which raises the effective interest rate on foreign borrowing (via the exchange-rate term in the Euler equation), discouraging borrowing and partially correcting overborrowing. When the constraint binds, contractionary policy discourages production and imported-input use, improving the trade balance and partially correcting the ex post externality. Proposition 1 and Corollary 1 establish that strict inflation targeting is not optimal and that the optimal discretionary policy is contractionary in both states. Crucially, this period-by-period optimality does not imply discretion dominates inflation targeting in welfare, because it ignores how anticipation of future intervention shapes ex ante borrowing.

Q4. How does adding a macroprudential tax change the optimal monetary policy?

With an optimal time-consistent macroprudential tax on foreign borrowing available, Proposition 2 / Corollary 2 show the optimal discretionary monetary policy becomes pi_t = 0 when the constraint is not binding (the tax now corrects overborrowing, so the eta^EE term is zero and monetary policy focuses only on minimizing price-adjustment cost) but remains contractionary (pi_t < 0) when the constraint binds — because the ex ante tax cannot correct the ex post externality of excessive imported inputs during a crisis. The macroprudential tax is strictly positive whenever there is positive probability the constraint binds next period, and rises with outstanding debt; it is notably higher under discretion (by about 0.6% before a crisis) to offset the extra overborrowing induced by anticipated intervention.

Q5. What is the quantitative crisis-dynamics evidence across the four regimes?

Crisis is defined as the current account exceeding two standard deviations above its long-run mean; crisis events are picked under inflation targeting without taxes. Real exchange rate depreciation: 10% (targeting, no tax), 6% (discretion, no tax), 6% (targeting, with tax), 2% (discretion, with tax). Output drop: 6.2% (targeting, no tax), 14.4% (discretion, no tax), 3.8% (targeting, with tax), 9.2% (discretion, with tax). Macroprudential taxes reduce pre-crisis debt and capital-flow reversals; discretion raises pre-crisis debt through anticipation of intervention. Standard deviations (relative to targeting-no-tax = 100%): under discretion with tax, real exchange rate volatility falls to 37.9% and current-account/GDP to 82.0%, while output is 111.7% and consumption 88.3% — i.e., discretion lowers exchange-rate volatility but raises output/consumption volatility.

Q6. What are the welfare results and their scope conditions?

Welfare is measured as permanent-consumption gain/loss relative to inflation targeting without taxes. Without taxes, discretion is slightly worse (-0.02%). Evaluated at the simulation-mean foreign bond (-0.45) with no borrowing-limit shock at the initial period: discretion with tax gives +0.07%, inflation targeting with tax gives +0.03%. When a borrowing-limit shock hits at the initial period (constraint binding): discretion without taxes gives +0.03% and with taxes +0.09%, with larger gains for larger initial debt; the gain can be as high as about 0.2% when the simulation starts with the constraint binding. Scope condition: monetary intervention during a crisis improves welfare ONLY when combined with an ex ante macroprudential tax; absent the tax, anticipation of intervention induces overborrowing and reduces welfare.

Fornaro (2015) and Ottonello (2015) introduce nominal wage rigidities and emphasize the BENEFIT of depreciation (boosting exports, reducing unemployment); this paper emphasizes the NEGATIVE effect of depreciation through inflating the value of foreign-currency debt. Mendoza and Rojas (2019) model depreciation as REDUCING the debt-repayment burden (depreciation lowers the consumption-composite real interest rate); here depreciation increases the burden. Devereux et al. (2018) and Coulibaly (2018) are closest — both add NK price stickiness and study monetary-macroprudential combinations — but in those the collateral channel/asset price drives the externality; this paper’s contribution is to study optimal policy where depreciation raises the domestic-currency value of foreign debt and causes a severe crisis. The welfare result (inflation targeting dominates discretion without taxes, but discretion preferable with the optimal tax) mirrors Coulibaly (2018).

Q8. Why is the optimal policy time-consistent, and how is the planner’s problem set up?

The BOP externalities themselves do not generate time inconsistency (the macroprudential tax in this model is time consistent, unlike pecuniary externalities from collateral asset prices). However, NK price stickiness can create time inconsistency via firms’ forward-looking pricing, so the author assumes no commitment and solves for time-consistent policy in a Markov perfect equilibrium: each period’s planner optimizes taking future planners’ rules as given while internalizing how current policy affects them, and the optimal rules coincide with those expected by past planners. The Ramsey planner maximizes household utility subject to the decentralized equilibrium conditions as implementability constraints. The nominal interest rate R_t is backed out from the Euler equation after other variables are pinned down.

Q9. What real-side outcome does the model explain without standard assumptions, and what is the consumption-labor trade-off in welfare?

The model explains the output drop during sudden stops WITHOUT working-capital financing (commonly assumed in the literature): the inefficiently expensive imported inputs caused by real depreciation directly reduce output. On welfare, although contractionary monetary intervention causes output and labor (hence labor disutility) to drop more under discretion, consumption does not drop as much because mitigated depreciation means smaller exports and a larger share of output consumed domestically. Period utility (consumption minus labor disutility) can therefore be slightly higher under discretion when combined with taxes. An appendix (Section F) with fixed labor and no labor disutility shows monetary intervention under discretion actually raises crisis-period consumption above inflation targeting.

Q10. What robustness/extensions does the paper note?

Section E of the appendix studies the model WITH the asset-price pecuniary externality (as in Bianchi and Mendoza 2018), which the baseline shuts off via book-value asset valuation. Section A proves the constant tax tau_m = 1/(rho-1) corrects the terms-of-trade externality. Section F examines fixed labor supply with no labor disutility. The conclusion proposes three extensions: foreign-reserve accumulation and reserve interventions (as in Arce et al. 2019), endogenous choice of borrowing currency, and introducing financial intermediaries with currency mismatch (as in Aoki et al. 2018 and Mendoza and Rojas 2019).

Q11. What are the main caveats?

This is a theoretical/quantitative DSGE exercise, not an empirical-identification paper, so there is no causal identification strategy in the econometric sense; the model is calibrated (not estimated) to standard literature values and the average of 14 emerging economies. Results depend on parameter choices, notably the export price elasticity rho = 3 (within Simonovska-Waugh’s 2.79-4.46 range) and the domestic-currency denomination of the borrowing limit, which is essential to the amplification loop. The author also notes that introducing imported-input taxes only during crises may be difficult to implement in practice, motivating reliance on monetary policy for ex post intervention.

Key Concepts

Monetary Policy When Preferences Are Quasi-Hyperbolic

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

Layer 1: Overview

Research question and motivation: Experimental and survey evidence robustly documents “present bias” — people are more impatient over the short run than the long run, producing preference reversals inconsistent with standard exponential discounting. Dennis and Kirsanov ask how this behavioral feature, modeled as quasi-hyperbolic (quasi-geometric) discounting, changes the optimal conduct of monetary policy. Prior macro work on quasi-hyperbolic discounting concentrated on growth models, consumption/saving, and multiple equilibria; almost none examined monetary policy. The paper fills this gap.

Model setup: A nonlinear New Keynesian business-cycle model with monopolistically competitive firms that own capital, hire labor (Cobb-Douglas, alpha=0.33), and set prices subject to Rotemberg (1982) quadratic adjustment costs (omega=100, roughly a Calvo model with 1-year average price duration). Households consume a Dixit-Stiglitz bundle, supply labor, and save via one-period nominal bonds (zero net supply) and equities (fixed net supply of 1). Preferences are quasi-hyperbolic: the discount sequence is 1, betatheta, betatheta^2, … with theta in (0,1) the usual geometric factor and beta the present-bias factor (beta=1 restores geometric discounting; beta<1 is greater short-run impatience). Three shocks: technology, cost-push (elasticity/markup), and labor-supply. The central bank shares household momentary utility and sets the nominal bond return optimally under discretion (its discount factors gamma, xi may differ from household’s beta, theta); a Taylor-type rule is the comparison. The model is solved globally with Chebyshev polynomials and Gaussian cubature to obtain a unique interior solution to generalized Euler equations, avoiding log-linearization indeterminacy. A period is a quarter; theta=0.99, sigma=1 (log utility), Frisch elasticity nu=1, chi=1, depreciation delta=0.025, steady-state elasticity epsilon=11 (10% markup). The authors restrict attention to beta in [0.90, 1] because experimentally plausible values (beta around 0.60, per Meier-Sprenger 2015 and Wang-Rieger-Hens 2016, median ~0.60) generate implausible/extreme general-equilibrium outcomes.

Main quantitative findings (benchmark, central bank benevolent, beta=gamma): (1) Greater present bias lowers saving and capital accumulation. Lowering beta=gamma from 1.0 to 0.9 reduces output by about 10% (10.02%), with capital falling much more (24.55%), labor much less (1.84%), consumption 6.02%, and the real wage 7.77%; cutting beta to 0.7 cuts output ~30% (roughly linear). (2) Discretionary policy still produces positive average inflation (inflation bias), but the bias is SMALLER under present bias: average inflation falls from 2.553% (beta=1) to 2.362% (beta=0.9) under discretion, because firms, whose equity holders discount hyperbolically, spread costly price changes over time — present bias acts like greater price rigidity, so smaller inflation surprises suffice. (3) Asset returns balloon: a nonpecuniary return to capital (1-beta)/beta * KK(Z) appears, raising the total return on capital rcap and spilling into bonds. At beta=0.9 (discretion) the net real return on capital reaches 48.928% and the real interest rate 48.926% (annualized), versus ~4.0% at beta=1 — well above observed real rates, so experimentally-sized present bias is wildly counterfactual in general equilibrium. (4) The Taylor rule increasingly underperforms optimal discretion as households become more impatient (suboptimal-policy cost lambda_S rises with present bias). (5) Quasi-hyperbolic and geometric discounting are NOT equivalent because of the nonpecuniary (time-inconsistency) return to capital.

Policy implications: A benevolent central bank (sharing household preferences) keeps steady-state inflation under control across a wide range of discount factors. If instead the central bank does NOT adopt household time preferences and tries to discourage early consumption/delayed saving, it achieves only a marginal output gain at the cost of much higher average inflation. Conversely, delegating policy to a central banker who is MORE present-biased than households raises household welfare (akin to Rogoff’s conservative central banker), because it emphasizes the current-period cost of changing prices, lowering inflation volatility and average inflation toward zero.

In depth

Q1. What is the model’s solution strategy and why does it matter for the results?

The model is solved as a fully nonlinear global problem rather than log-linearized. The authors use Chebyshev polynomials (giving continuous decision rules and derivatives) and compute expectations via Gaussian cubature instead of finite-state Markov chains. They impose symmetry across households and firms in equilibrium (kt=Kt, ct=Ct, etc.; bonds in zero net supply Bt=0, stocks fixed St=1) and solve the interior solution to a system of generalized Euler equations, following Maliar and Maliar (2005). This matters because quasi-hyperbolic discounting creates strategic interaction between the household and its future self that can generate multiple equilibria (Krusell and Smith 2003); log-linearization can introduce indeterminacy (Maliar and Maliar 2006a). Allowing a large domain for wealth/capital is, per Cao and Werning (2018), key to ruling out local multiplicities. The result is a unique stable equilibrium.

Q2. What is the central economic mechanism through which present bias affects asset returns?

Equation (25): the total gross return on capital equals the pecuniary part (shadow rental rate rk + 1 - delta) PLUS a nonpecuniary part (1-beta)/beta * KK(Z), where KK(Z) is the derivative of next period’s capital decision rule with respect to current capital. This nonpecuniary term arises only under time inconsistency (it vanishes when beta=1): the firm/household uses capital accumulation to constrain its future self. Even small present bias makes this term large, raising rcap; because households arbitrage between stocks and bonds (bonds offer no nonpecuniary return), the real bond rate rises commensurately. This is why beta=0.9 pushes real rates to ~49% — counterfactual — and why the paper restricts to beta in [0.90,1].

Q3. Why does present bias REDUCE the discretionary inflation bias rather than raise it?

Quasi-hyperbolic discounting weights the cost of changing prices today more heavily than future price-change costs (since firms’ equity holders discount the future more). When shocks hit, firms make smaller price changes now and defer the rest, so present bias acts like an increase in price rigidity. The central bank then calculates that smaller inflation surprises are enough to boost output to the efficient level, so equilibrium average inflation falls (2.553% at beta=1 down to 2.362% at beta=0.9 under discretion). The structure of the policy trade-off (eq. 21) is unchanged by present bias; only the relative costs and benefits shift.

Q4. How do the three shocks differ in their interaction with present bias?

Technology shock (Fig 1): financial variables are affected most; relative to geometric baseline, consumption rises more and labor rises less, pushing real wages and real marginal costs up; the real and nominal interest rates rise by more due to increased demand for current consumption. Price-elasticity/cost-push shock (Fig 2): responses are generally more muted; labor rises less, consumption more, inflation falls by less (firms defer price changes); the real interest rate and nominal bond return are the most sensitive variables. Labor-supply shock (Fig 3): an adverse shock raises labor disutility, cutting labor, output, consumption, investment and capital while raising the real wage; inflation and real marginal costs are little affected, and policy eases (real and nominal rates fall); present bias mainly amplifies consumption/investment responses and raises impact responses, increasing unconditional volatility.

Q5. What welfare measures are used and how do they move with present bias?

Three consumption-equivalent costs: lambda_C (Lucas 1987 cost of business cycles), lambda_B (magnitude of the present bias), and lambda_S (cost of the suboptimal Taylor rule vs. optimal discretion). Greater present bias lowers the utility level U, raises lambda_C (e.g., 0.033 to 0.045 under discretion as beta=gamma goes 1.0 to 0.9), and raises lambda_B substantially (0 to 2.808). lambda_B rises much more than lambda_C, showing that discounting future consumption dominates cyclical-volatility effects. lambda_S also rises, meaning the Taylor rule becomes progressively more costly relative to discretion as households grow more impatient.

Q6. What does the comparison of quasi-hyperbolic vs. geometric discounting (Table 3) show?

Comparing quasi-hyperbolic (beta=gamma=0.99, theta=0.99) to a geometric model (beta=1, theta=0.992) calibrated to be comparable: the geometric model produces LOWER average capital, labor, output, consumption, investment, and real wage. Under quasi-hyperbolic discounting, household ownership of capital generates a nonpecuniary return that compensates for the lower rental rate and encourages higher saving, so the capital stock is larger even though the marginal product and rental rate of capital are lower. The two are genuinely non-equivalent because of the time-inconsistency-driven nonpecuniary return. Welfare cost of business cycles is higher under geometric than quasi-hyperbolic discounting and higher under the Taylor rule than optimal discretion; to be compensated for the Taylor rule’s suboptimality households would require a permanent consumption increase of 0.07% (geometric) or 0.10% (quasi-hyperbolic).

Q7. What is the policy-delegation result and its scope condition?

In Section 6 the central bank’s discount factor gamma is allowed to differ from the household’s beta. Allowing the central bank to be MORE present-biased than households (lower gamma) raises household welfare: welfare is higher in column (2) (gamma=0.9, beta=1) than column (1) (both =1), and higher in column (3) (both=0.9) than column (4) (beta=0.9, gamma=1). The mechanism is that a more present-biased central banker emphasizes the current-period cost of changing prices — like greater price rigidity or a conservative (Rogoff 1985) central banker — yielding less volatile and lower average inflation (e.g., inflation drops to 0.699% in column 2). Effects on real variables are small; effects on nominal variables are larger and quantitatively significant. This parallels Dennis (2014), where distorting the discretionary central bank’s objective (risk-sensitivity) improved welfare. Scope: this holds because policy is conducted under discretion, which is suboptimal; under commitment the delegation logic would differ.

Q8. Where does present bias enter, and not enter, the equilibrium conditions?

It does NOT enter the household’s intratemporal labor-leisure condition (eq. 7) or the firm’s static conditions defining the rental rate and real wage (eqs. 12-13). It enters the bond and stock Euler equations (eqs. 8-9) and the Phillips curve (eq. 11) only by changing how next period is discounted (via beta*theta). Most importantly, it enters the firm’s capital-accumulation Euler equation (eq. 10) in TWO ways: changing the discount rate AND adding the nonpecuniary term (1-beta)*KK(Z), which disappears when beta=1. The Phillips curve’s structure is otherwise unaffected because, in the symmetric equilibrium, all firms set the same price so the relative price equals one.

Q9. What robustness/extensions are considered?

Capital ownership: the main analysis has firms own capital, but Online Appendices 1-2 show households-own-capital (rented competitively) is equivalent even under quasi-hyperbolic discounting. Geometric-discounting benchmark is explored fully in Online Appendix 4. Numerical accuracy (consumption-Euler residuals) is reported in the appendix. The authors also vary the markup elasticity epsilon and note that values of 6 or 21 gave implausible steady-state inflation, so they use epsilon=11. They report results across beta=gamma of 1.00, 0.99, 0.95, 0.90 under both discretion and the Taylor rule.

Q10. How does this paper differ from the closest prior work?

Graham and Snower (2013) study a sticky-WAGE NK model where households prefer positive inflation because it erodes real wages over time, overturning the Friedman rule. This paper uses sticky PRICES (Rotemberg), firm-owned capital, and finds present bias LOWERS average inflation under optimal discretion. Maeda (2018) extends Krusell-Smith to a cash-in-advance monetary economy and recovers the Friedman rule via cash constraints. Most prior quasi-hyperbolic macro work (Krusell-Smith 2003, Maliar-Maliar, Krusell-Kuruscu-Smith 2002) focused on growth, consumption/saving, multiplicity, or income distribution — not monetary policy. This paper is distinctive in focusing on optimal discretionary monetary policy, quantifying the inflation bias, and identifying the asset-return implications and the welfare case for delegating to a present-biased central banker.

Key Concepts

Nonmonetary News in Fed Announcements: Evidence from the Corporate Bond Market

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

Layer 1: Overview

When the Federal Reserve unexpectedly tightens policy, do riskier assets fall relative to safer ones (the standard prediction), or do investors read tightening as a signal that fundamentals are stronger than they believed, leading riskier assets to outperform? Smolyansky and Suarez answer this through the cross-section of the roughly $9 trillion U.S. corporate bond market, arguing it offers cleaner identification than survey-based evidence because asset prices already reflect all macro news just before an FOMC release—largely sidestepping the omitted-variable critique of Bauer and Swanson (2023) and Karnaukh and Vokata (2022).

Data: transaction-level secondary-market trades from the regulatory version of TRACE (Aug 2002–May 2023), merged with Mergent FISD for bond characteristics. The sample covers 165 scheduled FOMC meetings and over 400,000 bond returns (Table 2 reports 474,771) across roughly 35,000 unique fixed-coupon, USD, U.S.-issuer bonds with 2–30 years to maturity. Monetary policy surprises are measured following Hanson and Stein (2015) as the change in the 2-year nominal Treasury yield over a t-1 to t+1 window, capturing both current-rate surprises and forward guidance. Credit risk is the average S&P/Moody’s/Fitch rating mapped to a 1–21 notch scale. The key regression interacts the 2-year yield change with the bond’s credit rating, with meeting-by-years-to-maturity, meeting-by-SIC2-industry, and meeting-by-callability fixed effects, so it compares same-maturity bonds differing only in credit risk. Standard errors are two-way clustered by meeting and firm.

Main finding: the interaction coefficient is positive (~0.2). For a hypothetical 100 bp rise in the 2-year yield, a one-notch worse rating (e.g., BBB to BBB-) is associated with a 0.2 percent higher return—riskier bonds outperform after surprise tightening. Expressed as spreads: for a 25 bp surprise rise, two bonds 10 notches apart (AA+ vs BB, average duration ~5) see the BB-AA+ spread narrow by about 10 bps. The authors call this magnitude “moderately sized,” noting it is the net effect after standard monetary and reaching-for-yield forces that push the other way.

The result is driven by the forward-guidance component, not current-rate surprises. Decomposing the 2-year change into a current fed-funds surprise and the 2-year-minus-fed-funds spread, only the spread (medium-term path) matters; the fed-funds coefficient is insignificant and oppositely signed. Riskier bonds also outperform when 1- and 2-year forward rates rise, when the 10-year-minus-2-year curve steepens, and following rises in both the 2-year real (TIPS) rate and breakeven inflation, suggesting non-monetary news reflects both outlook and risk-premia/risk-distribution news.

Sub-period: the effect is stronger pre-pandemic (~0.3, Aug 2002–Dec 2019) and statistically insignificant post-pandemic (Jan 2020–May 2023), plausibly because the aggressive 2022 anti-inflation tightening let standard monetary effects dominate. Results are stable excluding/isolating the 2008-09 crisis. Following Cieslak-Schrimpf and Jarocinski-Karadi, essentially all of the baseline effect comes from meetings where stock returns and Treasury yields move in the same direction (about one third of observations), the signature of non-monetary news. Policy implication: FOMC communications—especially forward guidance—transmit substantial non-monetary information, complicating the read of asset-price reactions to policy.

In depth

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

The strategy exploits the cross-section of corporate bond returns around FOMC announcements rather than time-series or survey responses. The regression interacts the 2-year Treasury yield change with a bond’s credit rating, saturated with meeting-by-years-to-maturity, meeting-by-industry (SIC2), and meeting-by-callability fixed effects, so identification comes from comparing same-maturity, same-industry, same-callability bonds that differ only in credit risk on a given meeting day. A positive interaction (riskier bonds outperform after tightening) is the opposite of what pure monetary/reaching-for-yield channels predict, so it isolates non-monetary news. The central threat the authors address is omitted-variable bias (Bauer-Swanson): they argue asset prices already embed incoming macro news just before the FOMC release, so a short event window around the announcement largely neutralizes this. A second threat is a ‘coupon/duration effect’—higher-coupon bonds have lower duration and price sensitivity—addressed in Table 3 columns 2-3. A third is illiquidity/stale prices, addressed by using actual TRACE trade prices and liquidity-based robustness tests.

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

Two opposing forces: (1) standard monetary news plus reaching-for-yield, under which tightening raises default/discount-rate risk and risk compensation, making riskier bonds underperform (predicting a negative coefficient); (2) non-monetary news, under which tightening signals a stronger outlook or a more favorable distribution of risks, making riskier bonds—more sensitive to economic strength and risk premia—outperform (positive coefficient). The estimated positive coefficient shows non-monetary news dominates on net. The authors further attribute non-monetary news to forward guidance: decomposing the 2-year yield into a current fed-funds surprise and the 2-year-minus-fed-funds spread shows only the spread drives results (fed-funds coefficient insignificant, wrong sign). They cannot fully separate ’expected outlook’ news from ‘risk premia/distribution-of-risks’ news (they note these are likely highly correlated), but provide suggestive evidence both operate: yield-curve steepening (10y-2y) and breakeven inflation also predict riskier-bond outperformance, and the curve/risk channel points to risk-premia effects.

Q3. What heterogeneity is documented across sub-periods?

The effect is stronger in the pre-pandemic sample (Aug 2002–Dec 2019), with a coefficient of about 0.3 versus 0.2 for the full sample. It is not statistically significant in the post-pandemic period (Jan 2020–May 2023), which the authors attribute to early-pandemic turbulence and the aggressive 2022 tightening cycle, where standard policy-tightening effects likely overwhelm any non-monetary component. Results are stable when excluding the 2008-09 financial crisis (Jul 2008–Jun 2009), when restricting to pre-July 2008, and when restricting to the post-crisis pre-pandemic window (Jul 2009–Dec 2019), indicating the non-monetary effect is present across different economic environments and FOMC communication regimes.

Q4. What robustness checks are run?

(1) Coupon/duration: controlling for coupon rate interacted with meeting-by-maturity fixed effects, and ‘duration-adjusting’ returns by subtracting a synthetic risk-free security’s return—results unchanged. (2) Liquidity: using only disseminated trades excluding agency/interdealer trades and trades under $100,000, and WLS weighted by each bond’s dollar volume—coefficients roughly unchanged and significant. (3) Alternative credit-risk measure: a market-based ’log discount’ (log price gap between a synthetic Treasury with the same cash flows and the corporate bond); a one-percentage-point larger discount is associated with ~0.1 percent higher return per 100 bp rise. (4) High-frequency window (15 min before to 45 min after): using 6- and 8-quarter Eurodollar futures and 2-year yields—same sign, somewhat smaller, with 2-year significant at 10%. (5) Online Appendix: bond fixed effects, excluding lowest-rated bonds, symmetry of rises vs cuts, extended return windows (up to 25 trading days), unscheduled meetings, and a CDS reconciliation.

It builds on the Fed-information-effect literature (Campbell et al. 2012; Nakamura-Steinsson 2018) and identification via stock-yield comovement (Cieslak-Schrimpf 2019; Jarocinski-Karadi 2020), but responds to the omitted-variable critique (Bauer-Swanson 2023; Karnaukh-Vokata 2022) by using asset prices on tight windows. Versus Guo, Kontonikas, and Maio (2020), who find lower-rated bond indices underperform after tightening: differences are the sample start (2002 vs 1989, since FOMC issued post-meeting statements only after mid-1999) and frequency (transaction-level daily event study vs monthly indices); the authors show extending the window 3+ weeks (when FOMC Minutes are released) can flip the sign toward Guo et al. Versus Palazzo and Yamarthy (2022), who find CDS spreads of riskier firms widen after tightening: reconciled by showing the CDS reaction is driven by the pure monetary component while the corporate bond reaction is driven by non-monetary news, with CDS-bond basis volatility (Bai and Collin-Dufresne 2019) explaining divergence. Versus Anderson and Cesa-Bianchi (2024), Gertler-Karadi (2015), and others using only current fed-funds shocks: this paper emphasizes forward guidance, and notes Gertler-Karadi’s results may reflect their earlier, more pre-1999-tilted sample. It complements Golez and Matthies (2023), who use S&P 500 dividend strips.

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

FOMC announcements—particularly the forward-guidance/expected-path component rather than current-rate decisions—convey substantial non-monetary information about the economic outlook and the distribution of risks. This matters for monetary policy transmission and communication design, and means asset-price reactions to FOMC news cannot be read as purely monetary. Scope conditions: results are concentrated in the pre-pandemic period and in meetings where stocks and yields comove (about one third of observations); they weaken or vanish when standard monetary effects dominate (e.g., the 2022 tightening). The authors stress this does not mean monetary news is unimportant, only that it is not always the dominant news type in all markets. They also note non-monetary effects are likely more detectable in recent samples given longer FOMC statements (late 1990s) and press conferences (2010s).

Q7. Does the outperformance reflect more than just risk premia?

The authors argue it is unlikely to be entirely risk-premia driven. In the Online Appendix (Table A11), following a surprise tightening the relative default rate of riskier versus less-risky bonds decreases the subsequent quarter, indicating that unexpected tightening provides a genuine positive signal about the expected credit outlook—an outlook channel, not only a risk-premia channel.

Q8. Why use a two-day (t-1 to t+1) window and the 2-year yield?

The 2-year nominal yield (Hanson-Stein 2015) captures both current fed-funds surprises and forward guidance over the next several quarters. The t-1 to t+1 window is used because the market may not incorporate the full information content instantaneously (Gurkaynak-Sack-Swanson 2005; press conferences from 2011 add post-statement information), because illiquid corporate bonds may not trade late on day t, and because it lets the same window measure both Treasury and corporate bond reactions. Robustness uses a high-frequency 15-min-before to 45-min-after window.

Key Concepts

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Nonresponse Bias in Household Inflation Expectations Surveys

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

Layer 1: Overview

Research question and motivation: Inflation expectations measured from household surveys are central inputs to monetary policy, but roughly half of respondents to the RBNZ Household Inflation Expectations survey decline to answer the quantitative inflation-expectations question. Because these item non-responses are not random across demographic groups, aggregate and subgroup measures derived only from those who answer can be systematically biased. The paper quantifies that non-response bias and proposes a simple, operational method to correct aggregate and subgroup inflation-expectation indices and disagreement measures.

Data and strategy: Micro-data from the RBNZ Household Inflation Expectations survey, quarterly, achieving about 1,000 household responses per wave, covering 1998Q2 to 2022Q4 with 89,834 individual responses treated as repeated cross-sections. The focal question asks the expected annual rate of inflation/deflation over the next 12 months. The survey switched from telephone to online mode starting 2018Q3. Outliers are removed using a 1.5xIQR rule (excluding 4,535 observations in the baseline). The empirical approach has three steps: (1) Probit models of the probability of responding on demographics (gender, age, region, ethnicity, income, employment) plus macro controls (lagged inflation and its square, a year trend, seasonal dummies, an online-mode dummy); (2) a Heckman sample selection model (selection equation = the baseline Probit extended with online-mode interactions; outcome equation = inflation-expectation bias regression) with four exclusion restrictions dropped from the outcome equation (region, employment, year trend, lagged inflation squared); (3) a regression-on-quarter-dummies index that adds the inverse Mills ratio to deliver bias-adjusted average and dispersion series. Estimates use survey weights, extending Heckman estimators to weighted form.

Main quantitative findings: Item non-responses average about 44% over the full sample, falling to about 24% after the move to online mode. Non-responses artificially raise average one-year-ahead inflation expectations by about 0.3 percentage points; the average selection adjustment is -0.288 over the full sample, ranging from -0.385 (2018Q1) to -0.138 (2022Q3). Females are about 20% less likely to respond than men; older, employed, higher-income individuals respond more; Maori and Pacific Islanders respond less. Online mode raises response probability by about 33%. Response rates rise non-linearly with lagged inflation: moving from 2% to 7% raises average response probability by about 12%, while it barely changes over the 0-4% range, with the slope turning steeply positive in the 5-7% range. There is a downward trend in response of about 1% more item non-response per year. The online switch narrowed the female-male response gap from 24.4% (telephone) to 5.5% (online) and rendered most ethnicity gaps insignificant. In the bias (outcome) regressions without selection (weighted), respondents over 25 show bias more than 0.23 pp above the under-25 base; Pacific Islanders 0.34 pp, Maori 0.15 pp, Asians 0.12 pp above the base ethnic group. After the Heckman correction, gender, ethnicity, and income differences become insignificant or shrink substantially, while age effects strengthen (older respondents over-predict; under the two-step estimator, bias for those over 35 is more than double the no-selection estimate). The online dummy in the outcome equation lowers predicted expectations by more than 2.27 pp (interpreted cautiously, as it also captures large 2020Q3-onward negative biases).

Implications: Survey weights correct unit non-response but not item non-response, so published aggregates overstate expectations by ~0.3 pp. The correction lowers all subgroup means, decreases cross-subgroup disagreement for gender/income/ethnicity (increases it across age), and generally decreases within-subgroup dispersion. Correcting also makes the household-vs-professional-forecaster intercept gap statistically insignificant. Policy: online survey modes and inclusive, layered communication (especially during high-inflation periods of greater public attention) can reduce measurement error.

In depth

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

Identification rests on a Heckman sample selection model. A Probit selection equation models the probability of answering the inflation-expectations question; its predicted probabilities yield the inverse Mills ratio, added to the outcome (bias) regression to correct for selection-as-omitted-variable bias. Identification is sharpened by exclusion restrictions: four variables (region, employment status, year trend, lagged inflation squared) enter the selection equation but are dropped from the outcome equation. The authors justify these because region and employment were found statistically insignificant in the outcome equation, and year trend and lagged inflation squared induced collinearity/variance inflation. The selection equation also includes online-mode interaction terms to better identify heterogeneity in response rates. Threats: the validity of the exclusion restrictions (the assumption that these variables affect participation but not the level of expectations bias) and the known sensitivity of the full-information ML Heckman estimator to collinearity; the authors address the latter by also reporting the two-step estimator.

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

Two mechanisms drive non-response. First, demographic propensity: young, female, low-income, and minority-ethnicity (Maori, Pacific Islander, Asian) respondents are less likely to answer, documented via Probit average partial effects. Second, state dependence on the inflation environment: response rates rise non-linearly when lagged inflation moves away from the target range (steeply positive slope at 5-7%), consistent with a ‘rational inattention’ interpretation where agents notice inflation only when it becomes salient, and with the finding that inflation uncertainty co-moves with the inflation level (Binder, 2017). The authors also test whether non-response reflects lack of understanding using a 2018Q3-2021Q4 sub-question: only 5% of respondents indicated not understanding inflation, so 81% of non-responses are not due to lack of understanding, pointing instead to factors like cultural norms/uncertainty rather than literacy.

Q3. What heterogeneity is documented?

Response heterogeneity: females respond ~20% less than males; response probability rises with age; Maori and Pacific Islanders respond markedly less; higher income and employment raise response; households with dependent children and non-freehold owners respond less; being the main grocery shopper slightly lowers response. Bias heterogeneity before correction: age, ethnicity (Pacific Islanders 0.34 pp, Maori 0.15 pp, Asian 0.12 pp), and income show differences. After Heckman correction, gender, ethnicity, and income differences become insignificant or shrink substantially, while age effects strengthen (older respondents over-predict inflation, with an upward-sloping age profile). Online mode reduces demographic gaps: the female-male response gap fell from 24.4% to 5.5%, and most ethnicity gaps became insignificant online.

Q4. What robustness checks are run?

(1) Four Probit specifications with progressively richer covariates (occupation, grocery shopping, dependent children, home ownership) across sub-periods, with baseline effects stable. (2) Two Heckman estimators, two-step and ML, mostly consistent (the main divergence is gender, insignificant under two-step). (3) Comparison against random imputation, which reproduces the distorted no-selection picture. (4) Six outlier-detection rules (fixed -2/15 interval, 1.5xIQR, 3xIQR, hybrid IQR, top/bottom 5% by quarter, top/bottom 5% overall): Probit estimates are insensitive to the outlier definition. (5) A separate Probit on outlier responses shows similar demographic patterns (low-income young minority females give more outlier responses) but with differing magnitudes and trend/inflation effects, indicating outlier responses and non-responses are related but distinct. (6) An Appendix-E forward-looking Phillips curve exercise where adjusted subgroup expectations are always preferred to unadjusted.

It builds on the heterogeneity-of-expectations literature (Bruine de Bruin et al. 2010; Pfajfar and Santoro 2010; Malmendier and Nagel 2016; D’Acunto et al. 2023) documenting demographic differences in expectations, and on studies finding non-response from young/female/low-income groups (Blanchflower and MacCoille 2009; Leung 2009). Its distinctive contribution is showing that part of the observed gender/ethnicity/income differences in expectations is an artifact of non-response (selection) rather than true belief differences, and proposing an operational correction. Unlike imputation methods (e.g., the US Michigan Survey’s distribution-based imputation), the Heckman approach accounts for the socio-demographic composition of responders. Unlike methods requiring randomized incentives or special survey-design features (McGovern et al. 2018; Comerford 2023), it works on long-running repeated cross-sections lacking such features. It differs from attrition-focused work (Burgi 2023) by addressing item non-response in repeated cross-sections rather than panel attrition.

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

First, because survey weights correct only unit non-response, published aggregates overstate expectations by ~0.3 pp; central banks should apply an item-non-response correction. Second, response engagement rises when inflation deviates from target, so central banks could leverage high-inflation periods of elevated public attention for broader communication beyond financial-market audiences, using layered messaging. Third, moving surveys online substantially reduces non-response bias and improves representativeness, but requires ensuring digital accessibility to avoid new selection bias. Scope conditions: the non-linear inflation-response relationship is based on few episodes of out-of-range inflation, possibly confounded by Covid/recessions, so it should be interpreted with caution; the large online-mode coefficient on expectations also captures the post-2020Q3 negative biases from sluggish expectation adjustment; and RBNZ owns the survey and could change methodology accordingly.

Q7. How is the adjusted index constructed operationally, and why is it attractive?

Average expectations are obtained by regressing micro inflation-expectations on quarter dummies (WLS); adding the inverse Mills ratio from the baseline Probit as an extra regressor yields the bias-adjusted average. Subgroup indices interact subgroup dummies with time dummies; an adjusted disagreement (dispersion) measure replaces the dependent variable with squared deviations from the quarterly mean. The approach is attractive operationally because updating each quarter only requires a new inverse Mills ratio from the pre-fitted, relatively stable Probit model, so the adjustment is unlikely to undergo severe revisions.

Q8. What does the comparison with professional forecasters show?

Regressing one-year-ahead Survey of Professional Forecasters expectations on household expectations, the unadjusted household series gives a negative, significant intercept (-0.294, confirming households’ upward divergence), but using the adjusted household average makes the intercept insignificant (-0.019), suggesting the household-professional gap is partly a non-response artifact. The slope remains below one (0.759 unadjusted, 0.740 adjusted), consistent with Carroll (2003), so household expectations still do not scale one-to-one with professional forecasters.

Key Concepts

Precautionary Saving against Correlation under Risk and Ambiguity

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

Layer 1: Overview

Research question and motivation: How much to save is a central household financial decision, and uncertainty drives the “precautionary saving motive.” The precautionary-saving literature has mostly studied one-dimensional (single-attribute) risk, yet households face multidimensional risk: both wealth and health conditions matter for saving. Because wealth and health are plausibly related, the authors argue the correlation between two risky attributes should be incorporated into precautionary-saving analysis. They further note that correlation between two attributes is harder to quantify than a single attribute’s risk (less experience, fewer observations), so they also introduce ambiguity about the correlation. The paper’s purpose is to characterize how the correlation between two risky attributes (wealth and health) affects optimal savings under multivariate preferences, both when correlation is known (risk) and when it is ambiguous.

Model setup: A purely theoretical two-date model (t=0, t=1). The individual has time-separable lifetime utility from a bivariate utility function u(x,y) over wealth x and health y, increasing and concave in both (u^(1,0)>=0, u^(0,1)>=0, u^(2,0)<=0, u^(0,2)<=0); the sign of the cross derivative u^(1,1) is left unrestricted. The risk-free interest rate is zero and there is no time discounting, so the analysis isolates the effect of risk on saving. At t=1 the individual faces “good” and “bad” income risks (epsilon_G, epsilon_B occurring with probabilities 1-p, p) and “good”/“bad” health risks (delta_G, delta_B with probabilities 1-q, q), all four mutually independent. Correlation between income and health risk is captured by a parameter k: the probability of simultaneous bad income and bad health is kpq. When k=1 the risks are independent (joint probability = pq); k>1 (k<1) indicates positive (negative) correlation; correlation increases in k. The individual chooses saving s to maximize lifetime utility (equation 1). “Good” vs “bad” risks are ranked by stochastic dominance (FSD, Nth-order NSD, and Ekern’s Nth-degree risk increase).

Main findings (theoretical propositions, no estimated magnitudes): (1) Proposition 1 — when income risk is ranked by Nth-order and health risk by Mth-order stochastic dominance, optimal savings increase (decrease) in correlation k if (-1)^(n+m) u^(n+1,m)(x,y) >= (<=) 0 for n=1..N, m=1..M. This condition defines “mixed correlation aversion (seeking).” In the special case N=M=1, optimal savings increase in k if u^(2,1)>=0, i.e., the individual is “cross prudent” (decrease if cross imprudent, u^(2,1)<=0). Intuition: cross-prudent individuals dislike the simultaneous occurrence of bad income and bad health, which becomes more likely as k rises, so they save more. (2) Proposition 2 (ambiguous correlation, smooth ambiguity model of Klibanoff et al. 2005, 2009) — if the second-order utility phi exhibits decreasing absolute ambiguity aversion (DAAA) and u exhibits mixed correlation aversion or seeking, then ambiguous correlation raises the optimal amount of savings relative to the risky benchmark with correlation k_O = sum q_theta k_theta. The result combines a “timing of uncertainty effect” (governed by beta(s_O)>=1 iff phi exhibits DAAA) and the sign of a covariance term. (3) Proposition 3 extends the same result to Nth-/Mth-degree risk increases: under DAAA and (-1)^(N+M) u^(N,M)>=(<=)0 and (-1)^(N+M) u^(N+1,M)>=(<=)0, ambiguous correlation raises savings.

Implications: Whether correlation raises or lowers precautionary saving depends entirely on the signs of higher-order cross derivatives of utility, and under ambiguity additionally on the absolute-ambiguity-aversion coefficient. The authors link results to experimental evidence (Attema et al. 2019 find both cross prudence and imprudence; correlation aversion in gains, seekingness in losses) and to empirical work on public health systems, which by changing the wealth-health correlation affect precautionary saving (e.g., Rosen and Wu 2004; Atella et al. 2012; Chou et al. 2003; Jappelli et al. 2007), broadly consistent with cross prudence.

In depth

Q1. What is the core mechanism linking correlation to saving, and how is it formalized?

Correlation between income and health risk is parameterized by a single scalar k that scales the joint probability of the simultaneous bad outcome to kpq (with k=1 = independence, k>1 = positive correlation, k<1 = negative correlation), following the representation of Doherty and Schlesinger (1990). The derivative of expected period-1 utility with respect to k reduces (Lemma 1) to pq times [E[f(eps_B,del_B)] - E[f(eps_G,del_B)] - E[f(eps_B,del_G)] + E[f(eps_G,del_G)]], so the sign of the response to correlation is governed by a cross-difference whose sign maps directly onto the signs of higher-order cross derivatives of u. As k rises, the simultaneous occurrence of two bad outcomes becomes more likely; agents who dislike that combination (mixed correlation averse / cross prudent) save more to protect against it.

Q2. What exactly is ‘mixed correlation aversion (seeking)’ and how does it relate to correlation aversion and cross prudence?

An individual is mixed correlation averse (seeking) if (-1)^(n+m+1) u^(n,m)(x,y) >= (<=) 0 for all n=1..N, m=1..M. It is a bivariate extension of Caballe and Pomansky’s (1996) univariate mixed risk aversion, and generalizes Epstein and Tanny’s (1980) correlation aversion (which corresponds to u^(1,1)<=0). Cross prudence (u^(2,1)>=0, per Eeckhoudt et al. 2007) is the third-order version of correlation aversion. The paper’s saving conditions use mixed correlation aversion (seekingness) excluding the second-order correlation-aversion term, expressed via the derivative pattern (-1)^(n+m) u^(n+1,m) >= (<=) 0.

Q3. How is the ‘good’ vs ‘bad’ ranking of risks made rigorous?

Through stochastic dominance. eps_G dominates eps_B in the sense of Nth-order stochastic dominance (NSD) iff E[u(w+eps_G,h)]>=E[u(w+eps_B,h)] for all u with (-1)^(n+1) u^(n,0)>=0, n=1..N (mixed risk aversion in wealth); analogously for health via Mth-order dominance (MSD). FSD corresponds to N=M=1. The paper also uses Ekern’s (1980) Nth-degree risk increase, where the first N-1 moments coincide (e.g., a 2nd-degree increase is a Rothschild-Stiglitz mean-preserving spread; a 3rd-degree increase is an increase in downside risk per Menezes et al. 1980).

Q4. How is ambiguity about correlation modeled, and what drives the ambiguity result?

The individual perceives a finite set of possible correlations {k_1<…<k_Theta} with subjective second-order probabilities q_theta, and evaluates them via the recursive smooth ambiguity model of Klibanoff et al. (2005, 2009) using an increasing, concave, thrice-differentiable second-order utility phi (concavity = ambiguity aversion). Evaluating the FOC at the benchmark s_O (the optimum under the mean correlation k_O = sum q_theta k_theta) decomposes the effect into a ’timing of uncertainty effect’ (Osaki and Schlesinger 2014), captured by beta(s_O) which is >=1 iff phi exhibits decreasing absolute ambiguity aversion (DAAA), plus a covariance term Cov(phi’(v), v_s). Under mixed correlation aversion/seeking, v(s,k) and v_s(s,k) move in opposite directions in k (Lemma 3), so because phi’ is decreasing the covariance is positive; combined with DAAA this yields higher savings (Proposition 2).

Q5. What is the role of decreasing absolute ambiguity aversion (DAAA)?

DAAA (lambda(z) = -phi’’(z)/phi’(z) decreasing in z) is the ambiguity analogue of decreasing absolute risk aversion. The Appendix proves (following Osaki and Schlesinger 2014) that beta(s)>=1 iff the ambiguity precautionary premium Psi_A >= the ambiguity premium pi_A, which is equivalent to DAAA. DAAA ensures the timing-of-uncertainty effect pushes toward more saving. The authors caution that empirical/experimental evidence on the sign of absolute ambiguity aversion is thin; Berger and Bosetti (2020) is cited as an exception finding evidence for DAAA, and the authors say more evidence is needed.

Q6. How do the theoretical predictions connect to experimental and empirical observations?

Experimentally, Attema et al. (2019) measure multivariate risk preferences (wealth and longevity as a health proxy) and observe both cross prudence and cross imprudence, and correlation aversion in the gain domain with correlation seekingness in the loss domain. So the model implies savings can rise or fall with correlation depending on the individual. Empirically, the wealth-health correlation is shaped by public health systems: a more protective system separates wealth and health risk (lowers correlation). Rosen and Wu (2004) find poor health leads to safer investment (consistent with cross prudence); Atella et al. (2012) find households invest more in risky assets when health risk is mitigated by a protective national health system; Chou et al. (2003, Taiwan) find public health insurance reduced precautionary saving (a correlation decrease); Jappelli et al. (2007, Italy) find higher precautionary saving where health care quality is lower (a correlation increase); Ayyagari and He (2017) and Christelis et al. (2020) find Medicare/Medicare Part D increased risky investment. These are described as consistent with cross prudence.

Q7. How does this paper differ from the closest prior work?

Versus Eeckhoudt and Schlesinger (2008), which studies how risky shifts in future income affect saving via higher-order stochastic dominance, this paper adds correlation between two attributes and multivariate preferences. Versus Courbage and Rey (2007), who compare a certain-health vs risky-health setting, this paper compares two settings where health is risky in both but the income-health correlation differs, using the simpler Doherty-Schlesinger (1990) correlation representation. Versus Osaki and Schlesinger (2014) and Gierlinger and Gollier (2017), who study ambiguity in future income, this paper introduces ambiguity into the correlation rather than into income itself. The mixed-correlation-aversion concept builds on Jokung (2011) and Eeckhoudt et al. (2007, 2009).

Q8. What are the policy implications and their scope conditions?

Because public health systems alter the correlation between wealth and health (e.g., medical-expense coverage separates the two risks, lowering correlation), they affect precautionary saving. The directional prediction is conditional: under cross prudence, lower correlation (more generous public health coverage) reduces precautionary saving and a positive wealth-health correlation raises saving above the independence benchmark; under cross imprudence the signs reverse. Under ambiguity the prediction additionally requires DAAA plus the relevant cross-derivative sign pattern. The authors stress that because experimental evidence shows both cross prudence and imprudence, no unconditional policy prediction follows – e.g., for cross-imprudent individuals ambiguous correlation might lower savings.

Q9. What are the main caveats and directions for future research?

The results are sufficiency conditions tied to signs of higher-order cross derivatives, which are hard to interpret and whose empirical signs are not firmly established (experimental evidence is insufficient). The model is a stylized two-date setup with zero interest rate, no time discounting, additive time-separable utility, interior unique optimum, and a single scalar correlation parameter. The authors note the framework extends straightforwardly to multi-period models and suggest studying settings where the value and uncertainty of correlation change over time.

Key Concepts

Real Effects of Exchange Rate Depreciation: The Roles of Bank Loan Supply and Interbank Markets

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

Layer 1: Overview

Research question and motivation. The paper asks how exchange rate movements affect the real economy and what role the banking system’s foreign-asset exposure plays in transmitting exchange rate shocks. The motivation is concrete: with the Federal Reserve’s “tapering” of quantitative easing, the euro lost slightly more than 20% against the US dollar between 2014:Q2 and 2015:Q1, a sharp, persistent and largely unanticipated move. Standard open-economy models predict depreciations raise output via the trade balance, but recent work questions this classical trade channel and emphasizes firm/bank balance-sheet channels. The paper complements this by examining how a depreciation reshapes the composition of bank credit and, ultimately, regional output—working through banks’ net foreign asset (NFA) exposure rather than trade.

Data and empirical strategy. The authors build two datasets. The first is a matched bank-firm panel from the German credit registry (quarterly; reporting threshold 1 million euro, 1.5 million before 2014; ~two-thirds of German bank loans), merged with Bundesbank bank balance-sheet data and Amadeus firm accounts, yielding more than 300,000 bank-firm observations (Table 1: 344,777 for the loan-growth variable). The second matches INKAR region-level data on 401 German administrative regions with local savings-bank balance sheets, exploiting that savings banks lend within a fixed administrative district. Identification uses a difference-in-differences design around 2014:Q2-2015:Q1. The dependent variable is the log change in bank b’s credit to firm f from the pre-depreciation average (2013:Q2-2014:Q1) to the post average (2015:Q2-2016:Q1). Identification rests on banks’ differential pre-shock USD NFA share; firm fixed effects (sample restricted to firms borrowing from at least two banks) absorb loan demand (Khwaja-Mian, 2008), and bank fixed effects are added in the interaction model. Regressions are weighted by credit exposure.

Main quantitative findings. (1) Only large banks with higher USD NFA expand lending after the depreciation. In the full sample the NFA coefficient is positive but just below 10% significance; for systemically important banks (SIBs) it is 5.651 (significant at 5%): a SIB with a 1-percentage-point higher NFA share than the median SIB has a 5.65 pp smaller credit contraction, and given the overall ~-7% credit decline, a SIB with a 1.24 pp higher NFA share than the median turns overall credit growth positive. (2) The effect is driven by interbank lending: dropping financial-sector borrowers makes the NFA coefficient negative and insignificant; for financial borrowers it is positive (significant at 10%), and for SIBs lending to financial borrowers the coefficient is 10.915 (1%). (3) Credit shifts toward export-intensive firms, not riskier firms: the NFA × export-intensity interaction is 0.092 (10%); a firm at the 75th vs 25th export-intensity percentile sees a credit-growth differential of about 2.4 pp per 1 pp higher NFA; Z-Score and leverage interactions are insignificant. (4) Large banks act as a central intermediary: NFA × borrowing-bank export-portfolio share is 0.268 (10%), implying a 6.9 pp credit-growth differential between borrowing banks at the 75th vs 25th portfolio-export-share percentile per 1 pp higher NFA, driven by small borrowing banks. (5) Small banks with high interbank dependence and high export-firm portfolio shares raise lending (coefficient 0.609, 5%). (6) Regional real effects: for high-interbank-dependence regions, the export-share coefficient is 0.030-0.031 (10%/5%), implying regions at the 75th vs 25th export-share percentile grow 1.2 pp more cumulatively over the two post-depreciation years relative to the two pre years; no effect (even negative) in low-dependence regions.

Mechanisms and implications. The depreciation raises NFA-rich banks’ net worth (Appendix B: NFA coefficient on equity growth is 4.571 for SIBs, 1%), expanding their lending capacity. They channel this mostly via interbank loans to small, geographically constrained banks holding many exporters, which pass liquidity to export firms whose demand rises post-depreciation. Investment (not employment) of more-affected firms rises (Appendix C). The policy implication: exchange-rate depreciations can have sizeable real effects via interbank liquidity even when local banks have no direct foreign exposure; estimates are likely downward-biased since cooperative and private banks are excluded.

In depth

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

A difference-in-differences design around the 2014:Q2-2015:Q1 euro depreciation. The dependent variable is the log change in bank-to-firm credit from a four-quarter pre-average (2013:Q2-2014:Q1) to a four-quarter post-average (2015:Q2-2016:Q1); this pre/post averaging mitigates serial correlation (Bertrand et al., 2004) and seasonality (Duchin et al., 2010). Cross-bank identification rests on differential pre-shock USD NFA shares. The Khwaja-Mian (2008) within-firm approach restricts to firms borrowing from at least two banks and includes firm fixed effects to absorb loan demand and isolate supply; bank fixed effects are added in the interaction model. The key threat is that the depreciation be endogenous to German bank lending—addressed by arguing the shock was driven largely by Fed tapering (exogenous to German lending) and ECB policy calibrated for the euro area as a whole, not Germany. A second threat is that NFA correlates with other exposures (e.g., interest-rate risk, since rates also fell); column (4) of Table 3 controls for interest-rate exposure and the NFA coefficient survives (if anything increases). A third threat is the parallel-trends assumption, addressed by placebo tests around 2002 and all quarters 2001-2014 where the NFA coefficient is never positive and significant at 5%+. Selection between firms and banks is argued away by low correlations between firm characteristics and bank NFA (-4% leverage, -0.5% export shares, 7% size).

Q2. What are the two competing hypotheses on credit allocation and how are they distinguished?

H1 (export channel): the depreciation disproportionately increases credit supply to firms with higher ex-ante export intensity, because exporters’ cash flows and creditworthiness improve. H2 (risk-taking channel): the depreciation disproportionately increases lending to riskier firms, because higher net worth loosens capital constraints (Martynova et al., 2020). They are distinguished by interacting bank NFA with (a) industry-median export intensity and proxies (size, TFP, labor productivity, capital intensity) for H1, and (b) Altman Z-Score and leverage for H2. The export interaction is positive and significant (0.092, 10% in Table 5 col 1), all four proxies are positive/significant, and in a horserace using residuals orthogonal to export intensity (col 6) only export intensity (and capital intensity) survives. The Z-Score and leverage interactions are insignificant. Conclusion: H1 confirmed, H2 rejected—no evidence of increased risk-taking.

Q3. How is the interbank intermediation mechanism established?

In three steps. First (Table 2), dropping financial borrowers kills the NFA effect while restricting to financial borrowers preserves it (col 7: 1.947, 10%; col 9 for SIBs: 10.915, 1%), showing the lending increase is interbank, not corporate. Second (Table 6), restricting to large lenders and financial borrowers, the NFA × borrowing-bank export-portfolio-share interaction is 0.268 (10%), a 6.9 pp differential per 1 pp NFA between borrowing banks at the 75th vs 25th portfolio export-share percentile—driven by small borrowing banks (col 2: 0.359 significant; col 3 large borrowers: 0.046 insignificant). Third (Table 7), small banks with high export-firm portfolio shares raise lending (full sample 0.452, 10%), and splitting by interbank dependence the effect is significant only for high-dependence small banks (0.609, 5%) and insignificant for low-dependence (0.141), confirming interbank liquidity—not pre-existing excess liquidity—drives the result. A double interaction (col 4: 0.025, 10%) shows small banks pass the liquidity especially to export-intensive firms.

Q4. What heterogeneity is documented?

Large vs small banks: only large/SIB banks with high NFA respond; small banks do not (Table 2 cols 3,5). Section 4.3 shows this is because only the largest banks have economically meaningful NFA (SIB average USD NFA/assets 4.6% vs 0.3% for others); dropping the 5 largest NFA banks among SIBs renders the coefficient insignificant (4.899) and dropping the 10 largest turns it negative and imprecise (-3.257). So it is NFA level, not size per se, that drives the response. Firm heterogeneity: export-intensive firms gain, riskier firms do not. Interbank-dependence heterogeneity: regional GDP and small-bank lending effects appear only for high-interbank-dependence banks/regions. Firm real outcomes (Appendix C): investment of exporters rises only when relationship banks have high interbank dependence (col 6: 0.146, 10%); employment effects are insignificant throughout.

Q5. What robustness checks are run?

Table 3: (1) broadening NFA to include CHF, JPY, GBP (5.850, 5%); (2) disaggregating into gross USD assets (3.829, 5%) and gross USD liabilities (4.369, 10%, counter-intuitive but attributed to 89% asset-liability correlation acting as a proxy); (4) adding interest-rate exposure as a control (NFA rises to 6.847, 5%); (5) eight-quarter pre/post windows (4.996, 5%); (6) a 2002 placebo where NFA is insignificant, plus all-quarters-2001-2014 placebos never positive-and-significant at 5%+, supporting parallel trends. Table 8 col 5 runs a regional placebo around 2002 with no disproportionate growth. Appendix D between-firm regressions (controlling for demand via Abowd et al. 1999 firm fixed effects) confirm more-exposed firms get higher overall credit (0.868, 5%), though the export interaction there is insignificant (all exposed firms benefit, no extra amplification for exporters in the between-firm dimension). Appendix B confirms the net-worth channel.

It is closest to Agarwal (2019), who exploits the 2015 Swiss franc appreciation and shows banks with high foreign-currency liabilities changed domestic credit and growth. This paper differs by: (i) studying a depreciation rather than appreciation; (ii) using disaggregated bank-firm credit-registry data covering non-listed firms (Agarwal uses listed firms); (iii) identifying interbank lending as the dominant channel explaining the credit increase; (iv) showing banks use interbank liquidity to lend especially to exporters; and (v) documenting higher regional GDP growth. It also contrasts with Bruno and Shin (2019), who find Mexican firms reliant on high-dollar-funding banks suffer credit and export declines after the taper tantrum; here the same taper tantrum has a positive credit effect because USD appreciation raises the value of USD assets where domestic banks hold significant foreign-currency exposure. It contributes to the interbank-markets-and-monetary-policy literature (Abbassi et al., 2014; Freixas et al., 2011; Allen et al., 2014) by showing monetary policy can affect interbank markets indirectly via the exchange rate.

Q7. What are the policy implications and their scope conditions?

Exchange-rate depreciations can have sizeable real effects through bank-balance-sheet and interbank channels, distinct from the trade channel, and these effects reach banks with no direct foreign exposure via interbank liquidity reallocation. Scope conditions: the result requires (a) a banking sector with significant, imperfectly hedged net foreign-currency (USD) assets concentrated in large banks; (b) an export-intensive economy where credit to exporters has aggregate bite (Germany has one of the world’s largest net-exports-to-GDP ratios); (c) a geographically segmented banking system (German savings banks) that lets regional output be linked to local-bank exposure; and (d) the depreciation being large, persistent, and largely exogenous/unanticipated (driven by Fed tapering). The 1.2 pp regional growth differential is between high- vs low-export-share regions among high-interbank-dependence regions only. The authors stress estimates are likely downward-biased because cooperative and private credit banks are omitted from the regional analysis.

Q8. What are the most important caveats and limitations?

(1) Export turnover is reported by only a minority of Amadeus firms, so export intensity is proxied by industry medians, introducing measurement error. (2) Regional GDP is nominal (no regional CPI), justified by low, stable German inflation. (3) Within-firm regressions capture only the intensive margin; new and terminated relationships are handled separately in Appendix D between-firm regressions. (4) Firm-level real-outcome regressions (Appendix C) have small samples covering a small subset of German firms and compare 2014 vs 2012 (firm data end 2014), so they are interpreted as merely indicative. (5) The gross-foreign-liability robustness result is counter-intuitive and attributed to high asset-liability correlation. (6) The paper studies a depreciation only; asymmetric responses to appreciation and the source of the exchange-rate move (domestic vs foreign monetary policy) are left for future research.

Key Concepts

Shock Propagation within Multisector Firms

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

Layer 1: Overview

This paper documents a novel channel through which trade shocks propagate across industries: the internal networks of U.S. multisector firms (the working paper circulated as “Import Competition and Firms’ Internal Networks”). The motivation is that prior China-shock research traced effects through input-output networks and agglomeration but overlooked multisector firms, which account for 71% of total U.S. manufacturing employment and 25% of overall U.S. employment. When a firm owns establishments in several industries with differing exposure to Chinese import competition, it is ex ante ambiguous whether an unexposed plant gains (worker reallocation toward it), loses (dampened firm-level production from complementarities or financial constraints), or is unaffected (independent plants).

Data: the Longitudinal Business Database (LBD), the Census administrative panel covering the universe of non-farm establishments with at least one paid employee. The sample is multisector firms operating at least one manufacturing establishment, including both manufacturing and non-manufacturing plants, restricted to establishments active in 1991; main period 1991-2007 (pre-trend window 1976-1991). The core sample has roughly 573,000 establishments and 62,000 firms. The average firm has 427 workers (median 22), operates in 3 SIC-4-digit sectors, and has 9 establishments (2 manufacturing, 7 non-manufacturing); over half of establishments exited during 1991-2007.

Strategy: direct China shock is industry-level growth in Chinese import penetration 1991-2007 (Acemoglu-Autor-Dorn-Hanson-Price measure). The key new variable, the “indirect shock,” is an employment-share-weighted average of direct China shocks hitting the firm’s OTHER industries (own industry excluded). Both shocks are instrumented using Chinese import penetration into eight other high-income countries (following Autor et al. 2014). Dependent variable is the Davis-Haltiwanger-Schuh arc-growth rate of establishment employment (bounded -2 to 2). Regressions are weighted by initial employment with county and SIC-2- or SIC-4-digit industry fixed effects; standard errors two-way clustered by state and firm.

Main findings: both direct and indirect shocks significantly reduce establishment employment growth at the 1% level. The indirect effect is an order of magnitude stronger - an interdecile increase in the indirect shock lowers the arc-growth rate by 0.126 (= -0.166 x 0.759), roughly 12 times the 0.011 reduction from an interdecile direct shock (OLS Table 2 col 2). IV estimates are larger: direct coefficient about -0.102 to -0.108, indirect about -0.131 to -0.208 (Table 3). The effect operates primarily through the extensive margin (establishment exit), not the intensive margin; the entry margin is statistically and economically insignificant. The shock spills over both across manufacturing industries within a firm (manufacturing-only indirect coefficient about -0.13 to -0.18) and from manufacturing to non-manufacturing establishments (non-manufacturing indirect coefficient between -0.25 and -0.135). The effect accumulated mainly during the 1990s and stabilized after 2001. Mechanisms: plants that use inputs from sister establishments respond more strongly (within-firm downstream linkages); firms with wider scope absorb the shock more easily; larger establishments respond more. No support for upstream-supply linkages, capital/skill intensity, firm size, or financial-constraint channels. At the sector level, the indirect shock significantly lowers manufacturing employment growth (indirect coefficient about -0.747, significant at 10%; exit margin significant at 1%), so spillovers survive aggregation.

In depth

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

Each establishment’s direct exposure is its SIC-4-digit industry’s growth in Chinese import penetration 1991-2007 (numerator = change in real U.S. imports from China; denominator = 1991 domestic absorption). The indirect shock is the 1991-employment-share-weighted average of direct shocks in the firm’s OTHER industries, excluding the establishment’s own industry. To purge U.S. demand-driven import growth, both shocks are instrumented by Chinese import penetration into eight other high-income countries (Australia, Denmark, Finland, Germany, Japan, New Zealand, Spain, Switzerland). Threats addressed: (1) selection/pre-existing trends - a pretrend test on 1976-1990 employment growth shows no relationship (coefficient -0.013, insignificant); (2) the indirect effect could reflect connectedness to sectors in general rather than the firm’s specific sectors - a placebo test randomizing sister-establishment sector affiliations over 500 draws yields an insignificant placebo indirect coefficient (-0.001); (3) a common clustered shock hitting all of a firm’s industries - direct and indirect shocks (and their IVs) show no significant correlation; (4) demand-shock correlation across countries - results hold when dropping computer, construction, and apparel industries.

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

Mechanisms are tested via heterogeneous treatment effects (Table 7), interacting the indirect shock with firm/establishment characteristics under SIC-4-digit FE. Within-firm trade: a ‘Use=1’ dummy (establishment’s industry uses inputs from sister establishments’ industries, from BEA I-O tables) significantly amplifies the indirect effect (interaction -0.090, significant at 5%), consistent with downstream plants losing relation-specific production; a ‘Supply=1’ dummy (upstream linkage) is insignificant. Economies of scope: interactions with number of SIC-4 sectors and with 1-minus-HHI are both significant at 5% and positive (wider scope cushions the shock). Establishment size: larger plants respond more strongly to the indirect shock (significant), rationalized via Holmes-Stevens - large plants make standardized goods facing fierce Chinese competition - but firm size is insignificant.

Q3. What heterogeneity is documented?

Spillovers occur both across manufacturing industries within a firm and from manufacturing to non-manufacturing establishments, with similar magnitudes (manufacturing indirect coefficient about -0.13 to -0.18; non-manufacturing about -0.135 to -0.25). Effects are stronger for establishments using inputs from sister plants, weaker for firms with broader scope, and stronger for larger establishments. Effects accumulated mainly in the 1990s and stabilized after 2001; subperiod analysis confirms the indirect shock was much stronger in 1991-1999 (indirect coefficient about -0.27 to -0.50) than 1999-2007.

Q4. What robustness checks are run?

Pretrend test (1976-1990, no trend); placebo random networks (500 draws, insignificant); no direct-indirect shock correlation; disaggregated industry FE up to SIC-8-digit using NETS data (indirect coefficient stays about -0.063 to -0.065, significant at 1%); controlling for other-sector within-firm characteristics (log wages, wage and employment-share growth 1976-1991); shift-share robust standard errors following Adao et al. 2019 (which are smaller than the two-way-clustered baseline); dropping outliers by firm size and by indirect-shock deciles; dropping affiliation and industry switchers; dropping demand-shock-prone industries (computer/construction/apparel); an alternative weight using only manufacturing employment in the denominator; unweighted regressions; and an entry-margin augmentation (entry remains insignificant, exit dominates).

It builds on the China-shock literature (Autor-Dorn-Hanson 2013; Acemoglu et al. 2016; Pierce-Schott 2016; Asquith et al. 2019) but introduces within-firm sectoral networks as a new propagation channel, arguing the China shock’s impact may be larger than previously estimated. It extends the firm-internal-network literature (Giroud-Mueller 2019; Hyun-Kim 2020 on regional shocks; Cravino-Levchenko 2017 and Boehm et al. 2019 on cross-country shocks) to sector-level shocks. Versus Ding (2020), who studies manufacturing multi-industry firms with at least one directly-exporting industry, this sample is over 12 times larger and includes non-manufacturing plants. The extensive-margin (exit) finding aligns with Asquith et al. (2019).

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

Because the indirect channel propagates the China shock to plants with no direct exposure - including non-manufacturing establishments - and operates through permanent establishment exit, the documented economic, social, and political consequences of import competition may be even larger than estimates ignoring within-firm networks suggest. The authors stop short of quantifying the channel against other channels (supply chains, financial networks, migration, local adjustment) and note that designing optimal trade/industry policy under within-firm linkages requires a full structural model, which they leave to future work. Scope: results pertain to U.S. multisector firms with at least one manufacturing plant over 1991-2007, which cover three-quarters of manufacturing but only about 20-25% of overall employment, so sector-level estimates are less precise once non-manufacturing is included.

Q7. Why does the entry margin matter and what is found?

Establishment exit is more permanent than intensive-margin cuts, so it signals persistent damage. The baseline decomposition lacks an entry margin; the authors augment the sample with post-1991 entrants (assigning arc-growth of 2, weighting by midpoint employment). The exit margin remains highly significant and accounts for the overall effect, while the entry margin is quantitatively small and statistically insignificant - multisector firms do not adjust to the China shock by opening new plants.

Q8. What is found at the sector level and why does it matter?

To rule out that laid-off workers are simply rehired by other plants in the same industry, the authors define sector employment as total employment of all plants (including single-sector firms) and build a sector-level indirect shock weighting each other sector by its within-firm importance averaged across firms. For manufacturing, the indirect sector shock is large and significant at the 10% level (coefficient about -0.747), with the exit margin significant at 1% (about -0.371). Results are strongest for manufacturing and less precise when non-manufacturing is included, because the sample covers about three-quarters of manufacturing but only about 20% of overall employment. Spillovers thus survive aggregation.

Key Concepts

Studying Generational Risk in a Large-Scale Life-Cycle Model

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

Layer 1: Overview

Hasanhodzic and Kotlikoff ask a question prior work assumed away: how large is generational risk, and can pay-go Social Security actually mitigate it? Earlier studies (Diamond, Bohn, Krueger-Kubler, etc.) presumed generational risk is large enough to merit policy and showed Social Security can in principle share it, but did not directly measure its size. This paper measures it directly, with and without Social Security, in a realistically large overlapping-generations (OLG) model.

Model setup: an 80-period annual OLG model with aggregate shocks. Agents work 45 periods (retire at R=45) and live 80, have isoelastic (CRRA) preferences with risk aversion gamma=2 (gamma=5 under the extra-large shocks calibration), annual discount factor beta=0.96 (quarterly 0.99). Production is Cobb-Douglas; log TFP is trend-stationary AR(1) (quarterly rho=0.95, sigma=0.01; annualized rho=0.814, sigma=0.019). Two calibrations add a normal capital-depreciation shock. Households invest in risky capital or one-period safe bonds (zero net supply); “soft” increasing borrowing costs (Chen-Mangasarian function, slope b) shut down private risk-sharing to expose generational risk in its purest form while still delivering a realistic risk and growth premium. Policy is pay-go Social Security with a fixed payroll tax tau=15% (also tested at 1%). The model is solved to high precision via a projection method (building on Marcet 1988; Judd, Maliar, Maliar 2011) over an 81-variable state space (79 cohort cash-on-hand values plus the TFP and depreciation shocks). Generational risk measures are evaluated 300 years into the transition; cohort utility uses generations born after year 300 of a 750-year run. The U.S. data targets cover the return to national wealth and one-month Treasuries, 1947-2015, and detrended NNP/consumption, 1929-2020.

Four calibrations: (1) baseline (TFP shock only, matched to output/consumption variability); (2) larger shocks (adds depreciation shock to match variability of the return to national wealth); (3) extra-large shocks (bigger depreciation shock to match U.S. equity-market return variability, a la Krueger-Kubler); (4) negative risk-free-rate baseline (steeper borrowing costs giving a roughly negative 2% safe rate, to test Blanchard 2019).

Main findings (compensating-consumption differentials needed to reach long-run average lifetime utility): generational risk is 1.396% under baseline, 2.128% under larger shocks, and 15.303% under extra-large shocks (without Social Security). The authors view baseline 1.396% as small (on the order of a good-sized distortion) and prefer the baseline calibration. Social Security slightly WORSENS baseline generational risk (rising to 1.462%), but reduces it by 8% in the larger-shocks and 19% in the extra-large-shocks calibrations. So Social Security’s risk-pooling value depends on calibration. Contemporaneous risk (absolute consumption adjustment for full risk sharing among living cohorts) is tiny: 0.206% baseline, 0.933% larger shocks, 0.437% extra-large; Social Security raises it to 0.310% in baseline but lowers it under the other two.

On welfare and Blanchard’s conjecture: pay-go Social Security at a 15% tax cuts long-run expected utility by 18% in baseline and larger-shocks, and by 56% in extra-large shocks, via crowding out (long-run capital falls 28% baseline, 56% extra-large). Under the negative-safe-rate calibration there is still an 18% long-run welfare loss; the average growth rate is zero in all simulations. The authors find no support for Blanchard’s (2019) claim that deficits can be Pareto-improving when safe rates run below growth: even under Blanchard-favorable conditions, crowding out swamps risk sharing (e.g., 17.83% utility loss at 15% tax, 1.17% at 1% tax). Macro shocks are second-order for policy: the capital transition under Social Security with shocks closely tracks the no-shock (deterministic) path, echoing Lucas (1987).

In depth

Q1. What exactly is the paper’s primary measure of generational risk?

It is the average absolute percentage adjustment to a cohort’s annual consumption needed to equate that cohort’s realized lifetime utility to the long-run cross-cohort average realized lifetime utility. Formally, for each generation born in period t they compute lambda_t = U-bar / U_t (U_t is realized lifetime utility, U-bar the average over generations born in years 301-750), then take the mean absolute deviation of lambda from 1. It captures both being born in a bad state and being hit by a bad sequence of lifetime shocks. A value near zero means birth date barely matters.

Q2. Why does annualizing to 80 periods matter relative to two-period models?

With one year per period, an agent experiences 45 annual wage shocks and 79 annual investment-return shocks that largely average out, and can self-insure by adjusting saving annually. In a two-period model a single negative TFP shock hits a worker’s entire lifetime earnings or a retiree’s whole old-age return. The authors note, however, that because TFP shocks are positively autocorrelated, amplifying multi-period shocks could in principle generate more risk, not less, so the result is not mechanical.

In three of four calibrations the authors impose ‘soft’ increasing borrowing costs (Chen-Mangasarian function, parameter b) calibrated so the marginal borrowing cost is 15-20 times the safe rate (b=28 baseline, 25 larger shocks, 45 for negative-safe-rate cases). This nearly closes the bond market, isolating generational risk with no private or public mitigation. The extra-large calibration omits borrowing costs because its large depreciation shock alone delivers a realistic risk premium (and to match Krueger-Kubler). Notably, adding borrowing constraints has little impact on key macro aggregates.

Five reasons given: (1) benefits depend on the prevailing wage, so autocorrelated TFP wage shocks now interact with capital-return shocks through retirement, extending nonlinear discounting past retirement; (2) crowding out lowers wages and raises risky returns, so the same percentage TFP shock is larger in absolute terms, making realized resources more variable; (3) Social Security is a random floor on old-age living standards, encouraging less risk-averse consumption and a higher propensity to consume; (4) positive TFP autocorrelation (high benefits today predict high benefits tomorrow) further raises the propensity to consume; (5) Social Security alters the stochastic distribution of the 79 cohort cash-on-hand state variables, producing complex consumption changes. This echoes Rios-Rull’s (1994) paradox that better micro insurance can amplify macro fluctuations.

Q5. How does the paper test Blanchard’s (2019) ‘deficits may be free’ conjecture and what does it find?

It uses Blanchard’s own ex-ante Pareto criterion but with 80 periods (vs his 2), realistic risk aversion, and dropping his assumption that half of wages are perfectly safe. Calibrations engineered with negative safe rates and large growth premiums (e.g. risky ~2%, safe ~negative 2%) still show Social Security reducing long-run expected utility: 17.83% loss at a 15% tax (1.17% at 1%) in the standard-premium case, falling to 12.51%/12.582% (15% tax) under even-larger growth premiums, but always negative. Crowding out dominates any risk-sharing gains. The authors find no support for the conjecture. They note Blanchard’s Pareto gains, when they arise, depend critically on his assumption that half of wages are certain, leaving workers ideally placed to insure the elderly.

Q6. What heterogeneity across cohorts is documented?

Baseline generational risk has mean 1.396%, s.d. 1.293%, max 4.949% (no Social Security). Decomposed: generations with worst luck need roughly +5.0% positive adjustment; those with best luck need roughly negative 5.1%. Extra-large shocks produce extreme spread: max positive adjustment 66.14%, max negative 44.10%. A separate exercise (Table 8) shows the cost of uncertainty depends on birth state due to mean reversion: those born with low capital actually prefer uncertainty (negative 1.482%) because capital and wages will rise, while those born with high capital would pay 2.374% to lock in their state.

Q7. What are the welfare-cost-of-uncertainty and precautionary-saving findings?

Under larger shocks, the compensating variation between the stochastic steady state and a no-shocks steady state is only 1.12% (newborns would need 1.12% more consumption each year to match a never-shocked long run), despite that calibration overstating macro variability. This is small because precautionary saving raises the stochastic economy’s average capital stock 18.4% above the no-shocks steady state: the uncertain long run is ‘riskier, but richer.’ A decomposition removing the 0.77% average age-specific consumption difference leaves a 0.34% residual (about one quarter of 1.12%) reflecting age-pattern and cohort-sequence heterogeneity.

Q8. How does this paper build on and differ from Krueger-Kubler (2006)?

Five differences: (1) many more periods (80 vs 9) permit better shock-averaging and more precise autocorrelation treatment plus more self-insurance opportunities; (2) two calibrations the authors view as more realistic than KK (who chose theirs partly to favor a Pareto improvement), using borrowing costs rather than excessively large depreciation shocks to get a realistic risk premium; (3) ex-ante rather than ex-interim expected utility; (4) explicit measurement of generational risk with and without Social Security; (5) testing whether a large growth premium can sustain an intergenerational Ponzi scheme at scale. Like KK, they find a negative net long-run welfare impact of pay-go Social Security.

Q9. What does the model deliberately omit, and why?

It is ‘intentionally bare bones to maximize the potential for generational risk’: no variable labor supply (which would help cohorts self-insure), no progressive income taxation (which redistributes from winning to losing generations), and no social insurance other than Social Security. It also omits capital-adjustment costs (which would raise asset-return volatility) because incomplete markets make firm investment policy ill-defined when differently-aged shareholders disagree; the depreciation shock is a crude proxy for adjustment-cost-driven asset-return shocks. The authors flag correlated idiosyncratic shocks (Harenberg-Ludwig) as important future work.

Q10. How well does each calibration match the data?

Baseline matches output (model 3.72% vs data 3.33%) and consumption (2.10% vs 1.75%) variability but understates the s.d. of the return to national wealth by an order of magnitude (0.14% vs 4.89%). Larger shocks reproduces the return-to-wealth s.d. (4.61-4.62% vs 4.89%) and a realistic wage/return correlation (negative 0.054) but overstates macro-aggregate variability. Extra-large shocks matches equity Sharpe ratio (model 0.333 vs target 0.286; risk premium 4.63%, return s.d. 13.92%) but overstates return-to-capital variability nearly three-fold and consumption variability sixteen-fold. The model’s overall risk premium ranges 3.55-6.03% vs 5.43% in data.

Q11. What is the role of the bond market across calibrations?

The one-period bond market only operates in the extra-large shocks calibration (borrowing costs close it in the others). There, the young short bonds and the old lend: because the young’s resources are mostly human capital (less risky than, and negatively correlated with, stock returns), the young use bonds to insure the old. Workers effectively borrow to hold equity, which the authors rationalize via student loans, credit cards, mortgages alongside 401(k) equity, or implicit long-term firm contracts.

Q12. What policy implications follow, and what are their scope conditions?

If macro shocks are calibrated to realistic macro-aggregate volatility (the authors’ preferred baseline), generational risk is small (about 1.4%) and pay-go Social Security slightly worsens it while imposing an 18% long-run welfare loss via crowding out; deterministic models (e.g. Auerbach-Kotlikoff 1987) then suffice to capture the long-run impact of intergenerational redistribution. Social Security’s risk-mitigation value emerges only under calibrations that overstate macro volatility (larger/extra-large shocks). The scope condition is decisive: the case for Social Security as generational insurance hinges on which calibration one finds realistic, and the authors’ preferred reading implies a weak case. They also caution the conclusions may not extend to models with correlated idiosyncratic risk.

Key Concepts

Uncertainty Shocks and the Cross-Border Funding of Banks: Unmasking Heterogeneity

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

Layer 1: Overview

Research question and motivation: How does country-specific uncertainty explain variation in the cross-border funding of banks? Studying this link is practically relevant given rising reliance on international borrowing under financial globalization and the role of international banking in transmitting the Global Financial Crisis (GFC). The few prior studies on uncertainty and cross-border bank funding (Cerutti et al. 2017; Choi and Furceri 2019) focus on a single uncertainty measure and aggregate flows. Bénétrix and Curran’s innovation is to decompose both the funding source (banks vs. non-banks) and the type of uncertainty measure, “unmasking” heterogeneity that aggregate panel studies hide.

Data and setup: International bank funding is measured as cross-border liabilities (loans plus debt securities) of banking systems reporting to the BIS Locational Banking Statistics (LBS), decomposed into liabilities vis-a-vis banks and non-banks (non-bank flows derived as the difference between all-sector and bank liabilities). The core sample is 24 reporter countries (excluding small states/financial centers driven by global shocks, e.g. Russia/China omitted for short coverage), quarterly 2003Q1–2018Q4. The crisis period is defined as 2008Q3–2012Q2 (start = TED spread record/Lehman; end = Draghi’s “whatever it takes”), with pre-crisis 2003Q1–2008Q2 and post-crisis 2012Q3–2018Q4 sub-samples. A newly compiled uncertainty dataset spans three classes: volatility-based (implied volatility at 1-month and 3-month maturities from Bloomberg OVM; realized volatility from national equity indices), news-based (EPU and the World Uncertainty Index WUI from policyuncertainty.com), and forecast-based (forecast dispersion = standard deviation of GDP-growth forecasts across forecasters, from Bloomberg ECFC). Coverage: 24/24 countries for realized vol, implied vol, and WUI; 16/24 for EPU; 15/24 for forecast dispersion.

Empirical strategy: Two parts. First, descriptive dynamics of banking and uncertainty series (moments, persistence via AR(1)). Second, dynamic panel regressions with country fixed effects and Pesaran-Smith mean-group (MG) estimators, plus country-by-country regressions, of log cross-border liabilities on log uncertainty and a lagged dependent variable (so beta is an elasticity); standard errors clustered by source country. Multivariate models add lagged conditioning factors (real GDP growth, stock-market growth, policy rates, credit growth, exchange-rate growth, inflation, external debt/GDP). A GFC dummy and uncertainty-GFC interaction capture the time dimension.

Main findings with magnitudes: Uncertainty is associated with less cross-border borrowing; effects are sizable but heterogeneous. A 1% rise in 3-month implied volatility can contract funding by up to 4.1%; across implied/realized volatility (same sample) elasticities run 1.5%–4.1% depending on measure, sector, and estimator. Volatility-based measures show the largest elasticities, then news-based. Contractions are largest for non-bank funding and smallest for aggregate (suggesting bank/non-bank substitution that mutes the aggregate). Economically, a one-standard-deviation uncertainty shock typically cuts aggregate funding by between $573 billion and $889 billion (the bounds correspond to 1-month vs. 3-month implied volatility; average aggregate funding is $820B, average non-bank funding $223B). Country regressions give similar but more often insignificant results. Over time: volatility-based uncertainty matters only during the GFC (interaction term strongly negative), while news-based uncertainty (EPU, WUI) is the only measure whose first two moments rose since the GFC and is the only one that dampens funding outside the crisis, particularly for European countries (EU15/euro area). Mechanisms discussed but not tested: deleveraging/precautionary saving, liquidity management, demand vs. supply channels (weaker supply channel for advanced “safe” countries).

In depth

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

The paper is explicitly descriptive/documentary, not structural (‘The goal of this paper is to document empirical evidence, not to model mechanisms’). Identification comes from dynamic panel fixed-effects and mean-group regressions of log cross-border liabilities on log uncertainty with a lagged dependent variable, plus country-by-country regressions. The main threat is reverse causality (uncertainty and bank flows co-determined). The authors mitigate this following Bruno and Shin (2015b) by re-estimating with uncertainty lagged one period (similar results, in the online appendix) and by lagging conditioning factors one quarter. They argue the lagged dependent variable absorbs much variation, leaving less for uncertainty and ameliorating omitted-variable bias, but they do not claim causal estimates. They do not use instruments; the multilateral (vs-the-rest-of-the-world) data is used to avoid purely idiosyncratic counterparty shocks.

Q2. What heterogeneity is documented?

Four dimensions. (1) Funding sector: non-bank funding grows faster and is more volatile than bank funding, which is more volatile than aggregate; non-bank funding grew faster than bank funding in 75% of countries over the full period (54% pre-crisis, 75% during, 75% post-crisis). Uncertainty contractions are largest for non-banks, smallest for aggregate. (2) Uncertainty measure: volatility-based show the largest elasticities, then news-based; forecast dispersion is weakest/often insignificant. (3) Country: riskier countries (emerging markets like Brazil/Turkey; peripheral euro members Italy/Portugal/Spain) show significance for bank flows, while safe havens (Germany, USA) show significance for non-bank flows; some countries (Singapore, Norway, Switzerland) are largely unaffected; Finland and Japan show positive (wrong-signed) responses. (4) Time: volatility-based uncertainty matters only during the GFC; news-based matters outside it, especially for Europe.

Q3. What are the candidate mechanisms and are they tested?

Mechanisms are discussed but explicitly left for future research. Deleveraging/precautionary saving: under higher uncertainty banks shrink balance sheets and borrow less abroad. Liquidity management: uncertainty creates liquidity concerns, so banks may borrow more or less depending on term horizons. Rebalancing: volatility-based uncertainty (tracking equity risk) may drive borrowing from a risk-management/rebalancing perspective, while news-based uncertainty may operate through liquidity. Demand vs supply: higher uncertainty can cut a country’s banks’ demand for funds or foreign supply of funds; advanced/safe-haven countries are argued to face a weaker supply channel because the rest of the world keeps trusting them, consistent with safe havens reducing non-bank funding demand while aggregate is little changed (a shift between bank and non-bank funding).

Q4. Why does volatility-based uncertainty produce the strongest results even though it is narrower than news-based?

A priori the broader news-based measures might be expected to matter more, but the authors find volatility-based the strongest. They reason that cross-border banking decisions place greater weight on financial-system conditions, which volatility-based uncertainty (tracking the stock market) captures directly; banks holding securities may need to rebalance, diversify, or recapitalize via international borrowing/lending in response to equity risk.

Q5. What robustness checks are run?

(1) Bivariate vs multivariate: adding conditioning factors (GDP, stock market, inflation, policy rate, exchange rate, credit, external debt) leaves the negative uncertainty relation; multivariate panel elasticities narrow to roughly -2.2% to +0.5% vs bivariate -4.1% to +0.3%, MG largely unchanged. (2) Balanced 13-country fixed sample (panels C/D of Table 1) to compare measures on identical samples; similar negative, heterogeneous results. (3) One-period lag of uncertainty to address reverse causality (similar). (4) Crisis dummy plus interaction and separate pre/post-crisis estimation. (5) Alternative forecast-based measures (forecast-error dispersion, mean absolute forecast error) gave similar results. (6) An earlier version purged realized/implied volatility of the VIX to get idiosyncratic volatility (similar). (7) Persistence robust to including a constant; AR(1)/half-life analysis.

Q6. How does this paper relate to and differ from Choi and Furceri (2019)?

It is closest in spirit to Choi and Furceri (2019), who find a negative relation between banking flows and uncertainty using realized volatility and EPU on bilateral, aggregate flows (assets and liabilities). Bénétrix and Curran instead decompose flows into bank vs non-bank sub-components and use a broad set of uncertainty measures (implied volatility at two maturities, realized volatility, EPU, WUI, forecast dispersion), arguing this avoids the limitations of relying only on backward-looking realized volatility or cross-country-incomparable EPU. The nuanced result that news-based uncertainty matters outside the GFC (because only it rose since the crisis) departs from existing panel studies like Choi and Furceri. From Cerutti et al. (2017) they take the relevant takeaway that cross-border flows decline when the US VIX rises.

Q7. What are the dynamic/descriptive findings on the data?

Cross-border funding grew over two decades, especially pre-GFC; non-bank funding dominates growth during/after the crisis and is the most volatile, aggregate the least (e.g., Singapore and Finland std devs of 4.1 and 21). Cross-country average growth of non-bank liabilities is 2.2% vs 1.3% for bank liabilities. 64% of countries show positive autocorrelation in aggregate liabilities for the full period, while ~60% show negative autocorrelation for the two sub-components; pre-crisis ~80% show negative aggregate autocorrelation. Means/medians of flows are u-shaped (positive-negative-positive across pre/during/post), std devs n-shaped. For uncertainty, volatility-based moments peak during the crisis; only news-based (EPU, WUI) rose during and since the crisis. Uncertainty shocks are short-lived (half-lives about one quarter); ordering from least to most persistent: forecast-based, WUI, EPU, 1-month implied vol, realized vol, 3-month implied vol.

Q8. What are notable country-specific results?

3-month implied volatility elasticities range -14.1% to 11.5% (non-negative ones all insignificant); 1-month range -11.4 to 10.3; realized volatility -18.7 to 14 (with some significant positive estimates: Japan +4.7 overall, Finland +13.6 and +13.9 for overall/bank). EPU ranges -11.2 to 20.9 (positive significant for Japan in aggregate/bank, Brazil non-banks); WUI tighter, -4 to 2.7 (max contraction 4% for Austria bank funding; India positive). Forecast dispersion -30.7 to 4.4 (or -8.2 to 4.4 excluding Brazil); significant negative for UK (all sectors) and Brazil/Italy/UK (non-banks). France, Portugal, Ireland show robust negative responses; Portugal is significantly negative for all measures and sectors.

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

Policymakers should note that uncertainty mattered most during the GFC and European Sovereign Debt Crisis, and that news-based uncertainty has a distinct, sizable dampening effect on cross-border flows since the Great Recession, particularly for European nations (EU15/euro area), because only news-based uncertainty rose post-crisis. A single uncertainty measure does not fit all, since banking systems differ in structure, ownership, cross-border activity, size, and local-economy exposure. Scope conditions: results are associations not causal effects; effects are concentrated in the crisis window for volatility measures; non-European and emerging markets show no significant news-based effect outside the crisis; the sample is 24 countries, 2003Q1–2018Q4, multilateral liabilities only.

Q10. What are the main caveats and limitations the authors acknowledge?

Data limitations prevent regression analysis on intragroup, financial, and non-financial flow sub-components (explored only preliminarily). Non-bank liabilities are derived as a residual (all sectors minus non-banks) because bank-counterparty data are partly missing, though the authors argue the impact is minimal. Uncertainty coverage is unbalanced across measures (EPU 16, forecast dispersion 15 of 24 countries). Implied volatility (OVM) and forecast (ECFC) series could not be automated and required manual snapshots. The AR(1) persistence choice may miss nonlinearities/structural breaks and gives an upper bound on persistence. Country-level coefficients are often statistically insignificant given the strong lagged dependent variable. Mechanisms/channels are not tested and left for future work.

Key Concepts

Asset Exemption in Bankruptcy, Access to and Cost of Credit

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

Layer 1: Overview

Research question and motivation: Under U.S. Chapter 7 bankruptcy, an individual entrepreneur has most unsecured debt discharged and only her non-exempt assets liquidated, producing an “insurance effect.” But this protection does not extend to assets voluntarily pledged as collateral, so a borrower can undo the insurance by posting sufficient collateral. The paper asks how asset exemption interacts with the decision to post collateral to shape access to and the cost of credit. The novel insight is that, because the opportunity cost of pledging collateral (forgoing the exempt assets one would otherwise keep in default) is lower for safe entrepreneurs than for risky ones, collateral becomes a more effective sorting device as exemption rises. Existing empirical work (Gropp et al. 1997; Berkowitz and White 2004; Berger et al. 2011) finds exemption reduces access and raises rates, but does not exploit the interaction between collateral and exemption.

Model setup: A competitive credit market with risk-neutral entrepreneurs heterogeneous in success probability (safe type-H with pH, risky type-L with pL, pH > pL) and in pledgeable wealth w over [w, w-bar]. Each needs one unit of credit; lenders face opportunity cost r and cannot observe type. Lending contracts are triples (cost of credit RB, collateral C, access probability pi). Exemption eta shields wealth up to eta from liquidation but not wealth posted as collateral; liquidated wealth is worth only lambda < 1 to lenders. Competition is modeled as a three-stage game (a la Hellwig 1997) so that a subgame-perfect equilibrium exists and delivers the contract most preferred by safe types. The setup extends Besanko and Thakor (1987) by allowing any exemption between zero and infinity, adding the third (acceptance) stage, and adding wealth heterogeneity.

Main theoretical results: With zero exemption, pooling is the only equilibrium and no rationing occurs. With positive exemption, the equilibrium involves separation (at least for intermediate wealth): safe entrepreneurs self-select into contracts with effective collateral and face a lower cost of credit, while risky ones post no collateral. As in Besanko and Thakor, separation entails rationing for safe entrepreneurs too wealth-constrained to meet collateral requirements. The key novelty: conditional on posting collateral, as exemption rises, access to credit rises and the cost of credit falls—collateral becomes a more powerful screening tool. The overall effect of higher exemption on aggregate rationing is ambiguous, because more safe entrepreneurs choose to separate (lowering their access probability) even as each separating safe type is rationed less; the net effect depends on the wealth distribution.

Data and empirical strategy: The 2003 wave of the Survey of Small Business Finances (SSBF), 4240 firms, restricted to 1761 creditworthy firms that were financed at least once (96% always financed). Cross-state exemption variation is collapsed to a high/low dummy across nine census divisions (West North Central and West South Central coded high). Firm type is identified by whether it posts collateral (posters = type-H). An endogenous switching / inverse Mills ratio approach (Maddala 1983) handles self-selection in the cost-of-credit equation; access to credit is estimated by probit with a collateral-by-exemption interaction.

Main quantitative findings: Descriptively, high-asset firms face loan rates 1.5 pp lower and rationing 3.8 pp lower. Collateral-posting firms pay 0.7 pp lower rates overall; this differential grows from 0.53% in low-exemption to 1.20% in high-exemption subsamples. The Mills-ratio coefficients are negative and significant, confirming collateral conveys private information. In the access regression, posting collateral is positively associated with rationing, but firms posting collateral are less likely to be rationed in high-exemption divisions (predicted access falls 0.6% on average from posting collateral, but rises 1.5% in high-exemption areas). Reduced-form OLS: collateral firms pay 0.30% less, with the discount rising 0.55% moving low-to-high exemption. The simultaneous structural system implies a 34-basis-point average reduction in cost of credit from guarantees, three times larger in high-exemption states (75 vs 17 bp). Heckman selection correction does not alter conclusions. All main model predictions cannot be rejected.

In depth

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

Identification rests on three pillars. (1) Firm type is identified by the collateral decision: the model implies only type-H (safe) firms post collateral, so posters are treated as type-H and non-posters as type-L. (2) Cross-sectional variation in asset exemption across census divisions (a high/low dummy, with West North Central and West South Central coded high) provides exogenous variation in the strength of collateral as a sorting device. (3) The cost-of-credit equation uses an endogenous switching model (Maddala 1983) identified by the non-linearity of the inverse Mills ratio, under the model-based assumption that observed loan rates are determined by the endogenous collateral decision. Threats: (a) Selection bias from restricting to creditworthy/financed firms—addressed with a Heckman selection model that leaves conclusions unchanged. (b) Coarse exemption measurement—location is only observed at the nine-census-division level rather than by state, and unlimited-exemption states must be aggregated, so the high/low dummy is a proxy; an alternative averaging procedure is reported to give the same results. (c) SSBF data are partly imputed; estimates use Rubin (1987) multiple-imputation combination rules (STATA mi estimate), which inflates variance and can reduce significance.

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

The central mechanism is the opportunity cost of posting collateral: in default a borrower who pledged assets loses them all, whereas without pledging she would keep the exempt part. This opportunity cost rises with exemption and is lower for safe borrowers (lower default probability), so collateral sorts types more sharply as exemption rises. Empirically this is distinguished through the collateral-by-exemption interaction: the cost-of-credit discount from posting collateral, and the access-to-credit advantage of posters, both should strengthen with exemption. The negative, significant inverse Mills ratio coefficients show the collateral choice reveals private information about type; the estimated lambda_1L,v being roughly double lambda_1H,v indicates safe firms choose contracts with lower cost-of-credit variance.

Q3. What heterogeneity is documented?

By wealth: high-asset firms face rates 1.5 pp and rationing 3.8 pp lower. The collateral cost discount is concentrated among low-asset firms (0.9 pp) versus high-asset firms (0.04%). The collateral-rationing association also depends on wealth: among low-asset firms, rationing is 4.4% higher for collateral posters, but for high-asset firms there is no difference. By exemption: the collateral cost differential grows from 0.53% (low) to 1.20% (high). Among collateral posters, the rationed fraction falls 1.1% moving low-to-high exemption, with a larger drop for low-asset firms (-1.9%) than high-asset firms (-0.5%). In the structural cost-of-credit table, wealth reduces the cost of credit for non-posters only in high-exemption areas and for posters only outside high-exemption areas—consistent with firms undoing exemption via collateral.

Q4. What robustness checks are run?

Three. (1) A reduced-form OLS loan-rate regression with collateral, exemption, and their interaction confirms posters pay less (about 0.30% on average) and the discount grows 0.55% moving to high exemption; signs match predictions (beta_3 < 0, beta_4 < 0, beta_2 > 0). (2) A simultaneous structural two-equation system jointly determining cost of credit and guarantees yields a 34-bp average reduction in cost from guarantees, three times larger in high-exemption states (75 vs 17 bp). (3) A Heckman-style selection model accounting for the application/creditworthiness/financing stages leaves all conclusions intact. The imputation-robust (mi estimate) procedure is also applied throughout.

It confirms Gropp et al. (1997), Berkowitz and White (2004), and Berger et al. (2011) that higher exemption raises both rationing and the cost of credit. Its contribution is to use the theoretical model as an identification tool for the joint, interactive effect of exemption and the collateral decision—a prediction absent in prior empirical work. The collateral-as-quality-signal interpretation aligns with Jimenez et al. (2006) for Spanish firms and with Berger et al. (2011) on ex ante asymmetric information. Theoretically, it complements Manove et al. (2001) (too little exemption induces lazy bank screening) by showing that lower creditor protection via exemption gives lenders incentive to screen with collateral. It differs from Krasa et al. (2008) and Tamayo (2015), where creditor protection is an exogenous fraction of retained assets; here that fraction is endogenous because collateral can undo exemption. The model setup extends Besanko and Thakor (1987) with arbitrary exemption levels, a third acceptance stage (Hellwig 1997), and wealth heterogeneity.

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

Asset exemption levels materially affect credit-market functioning. Positive exemption lowers access and raises the cost of credit on average. But raising exemption enhances collateral’s power as a sorting device, so safe entrepreneurs who signal by posting collateral gain better access and larger rate discounts as exemption rises. The net effect of higher exemption on aggregate credit rationing is ambiguous and depends on how collateralizable wealth is distributed across entrepreneurs: more safe types separate (each facing a lower access probability) even as each separating safe type is rationed less. Scope conditions: results apply to individual entrepreneurs under Chapter 7 where exemption does not protect pledged collateral; the insurance/opportunity-cost channel requires exemption to be non-zero (at zero exemption only pooling, no rationing, and collateral conveys no signal); and the empirical magnitudes are estimated for small U.S. firms financed at least once in 2001-2003.

Q7. What are notable caveats and data limitations?

The dataset does not record the amount of collateral posted, only whether collateral was posted, so type is inferred from a binary decision. Firm location is observed only at the nine-census-division level, forcing a coarse high/low exemption dummy rather than state-level variation. The sample is restricted to firms financed at least once, raising selection concerns (addressed via Heckman). Much SSBF data are imputed. The model abstracts from positive, non-negligible transaction costs of posting collateral (only a negligible cost is assumed to select the unique separating equilibrium with CL = 0); incorporating such costs is left as an extension.

Key Concepts

Insurance effect (of exemption and discharge): The protection an entrepreneur enjoys under Chapter 7 because most unsecured debt is discharged and only non-exempt assets are liquidated; in the paper this protection can be voluntarily undone by posting assets as collateral.

Opportunity cost of posting collateral: The exempt wealth a borrower forgoes by pledging assets: in default a collateral-poster loses everything pledged, whereas a non-poster keeps the exempt part. This cost rises with the exemption level and is lower for safe (low-default-probability) entrepreneurs, making collateral an informative sorting device.

Real guarantees (G): The effective amount of wealth a lender can actually recover in default, G = max(min(w_eta, RB/lambda), C): increasing in collateral C and decreasing in exemption eta. The model is stated in terms of guarantees rather than nominal collateral.

Separating vs. pooling equilibrium: Under positive exemption, safe entrepreneurs self-select into high-guarantee, lower-rate (possibly rationed) contracts while risky ones take no-collateral contracts (separation); under zero exemption all borrow under one contract with no rationing (pooling). The model selects the subgame-perfect outcome most preferred by safe types.

Type-H / type-L identification via collateral: The empirical convention, derived from the model, that firms posting collateral are safe (type-H) and those not posting are risky (type-L), since in equilibrium only safe firms post collateral.

Endogenous switching / inverse Mills ratio approach: The estimation method (Maddala 1983) that corrects for self-selection in the collateral decision; negative, significant Mills-ratio coefficients indicate collateral posting conveys private information lowering the cost of credit, identified by the Mills ratio’s non-linearity.

Does a Financial Crisis Impair Corporate Innovation?

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

Layer 1: Overview

Research question and motivation: Why do financial crises leave such deep and protracted economic wounds, with crisis-stricken economies failing to revert to pre-crisis growth trends even a decade later? Imai and Sawada test one specific channel: that crisis-induced disruptions in financial intermediation impair firms’ ability to fund innovation projects, stalling technological progress and thereby pushing the economy onto a permanently lower growth path. They study this in the context of Japan’s 1997-1998 financial crisis, which featured a sharp decline in bank credit, the collapse of three major banks (Hokkaido Takushoku Bank, Long-Term Credit Bank, Nippon Credit Bank), and a failure to recover the pre-crisis growth trend. Laeven and Valencia (2020) estimate the crisis’s fiscal cost to Japanese taxpayers at 8.5% of GDP and its economic cost (GDP deviation from trend, 1997-2001) at 45% of GDP.

Data and strategy: The authors link three firm-level longitudinal datasets. Innovation output is measured from the Institute of Intellectual Property (IIP) Patent Database (Japan Patent Office data): patent applications, granted patents (only ~30% of Japanese applications are granted, taking 7-8 years), and citation-weighted patents using forward citations accumulated in a 17-year window after application. The core sample period is 1994-2003 (a 10-year window around the crisis), with forward citations tracked up to 2018; this long post-crisis window is a deliberate design choice that lets truncation-prone citation data mature. Bank dependence is proxied by the ratio of total loans to total assets (drawn from Nikkei Financial Quest financial statements). Bank-failure exposure is identified from the Corporate Borrowings Database: firms borrowing more than 10% of total bank loans from a failed bank in the year before its failure are coded as client firms. Patent applicants are matched to financial data via NISTEP company-name identification codes, covering roughly 75% of patents by NISTEP-ID firms and 58% of all applications.

Two empirical designs: (1) A DiD interacting the loan-to-assets ratio with a Crisis dummy (=1 for 1997-2001), with firm, industry-year, and prefecture-year fixed effects, firm controls (log sales, log age, ROA, cash-to-assets, tangible-to-assets) lagged one year and also interacted with the crisis dummy. (2) A bank-failure DiD adding a Bank Failure dummy (=1 for HTB clients 1997-2001, LTCB/NCB clients 1998-2001).

Main findings with magnitudes: Bank-dependent firms cut both the quantity and quality of innovation more sharply and persistently after the crisis; the loan-ratio-x-crisis interaction is negative and significant for applications, grants, and citations, and robust to the fully saturated fixed-effects model. In the event-study, high bank-dependence (top quartile) firms gained roughly 50% fewer patents over 1997-2003 relative to low-dependence firms (marginally significant), with no pre-trend in 1994-1995. The effect is concentrated in small and medium firms (insignificant for large firms). Decomposing loan maturity, the short-term-loans-x-crisis interaction is negative and robustly significant while the long-term-loans interaction is not, pointing to rollover risk as the main mechanism. For bank failures, the average effect across all firms is small and insignificant, but for small firms it is negative and significant: bank failures are associated with declines of about 12% in granted patents and 17% in cited-weighted patents; the dynamic counterfactual implies small firms whose main bank failed would have been granted about 50% more patents absent the failure, with effects peaking ~2 years after failure and recovering to pre-failure levels within about 4 years.

Implications: Post-crisis innovation performance depends on the degree to which firms rely on monitored, difficult-to-replace relationship lending. The crisis-induced decline in innovation among opaque, bank-dependent firms is offered as a plausible explanation for Japan’s long-term post-1990s productivity and growth stagnation.

In depth

Q1. What are the two identification strategies, and what is the key identifying assumption?

First, a difference-in-differences design interacting a continuous bank-dependence proxy (loan-to-assets ratio) with a Crisis dummy (=1 for 1997-2001), identifying off differential responses of more- vs. less-bank-dependent firms. Second, a bank-failure DiD interacting a Bank Failure dummy (for clients borrowing >10% of bank loans from HTB/LTCB/NCB before failure) with the crisis period. The key identifying assumption is parallel trends: clients of failed banks and clients of surviving banks would have followed the same innovation path absent the failures. The authors support this with event-study coefficients showing no significant pre-trends (1994-1995 for bank dependence; 3-4 and 2 years before failure for bank failures).

Q2. What are the main threats to identification and how are they addressed?

(1) Bank-dependent firms might be concentrated in declining or cyclically sensitive industries or worse regions — addressed by adding industry-year and prefecture-year fixed effects, so estimates come from firms in the same industry and prefecture; results are insensitive. (2) The decline might reflect poor financial performance or other firm correlates — addressed by interacting the crisis dummy with firm-level controls (size, age, ROA, tangible-to-assets, cash-to-assets); results hold. (3) Exposure to the late-1990s East Asian crisis via exports — addressed by interacting an overseas-sales-to-total-sales ratio with the crisis dummy (losing over half the sample); results robust (Table A2). (4) ‘Cleansing’/zombie-lending selection (failed banks served unviable firms) — addressed by dropping non-innovative firms and restricting to manufacturing (least affected by zombie lending); effects persist. (5) Omitted-variable bias for bank failure — assessed via coefficient-stability arguments (Altonji et al. 2005, Oster 2019); estimates stable to inclusion/exclusion of controls.

Q3. What is the main mechanism and how is it distinguished empirically?

The bank lending channel: crises raise the cost of intermediated funds, disproportionately hurting firms reliant on bank finance. The authors further pin down rollover risk by decomposing loans into short-term (residual maturity <=1 year) and long-term relative to assets and interacting each with the crisis. The short-term-loan interaction is negative and robustly significant; the long-term-loan interaction is negative but not robustly significant and becomes insignificant when both are included. This indicates the impairment operates mainly through firms’ exposure to short-term rollover risk rather than long-term debt levels.

Q4. What heterogeneity is documented?

Effects are concentrated in small and medium-sized firms (terciles by 1996 sales). For large firms the bank-dependence-x-crisis interaction is insignificant. Bank-failure effects are insignificant on average but negative and significant for small firms (about -12% granted patents, -17% cited-weighted patents), and small/insignificant for medium and large firms. The interpretation is that smaller, opaque firms face more severe asymmetric-information problems and find it hardest to replace an informed relationship lender when their main bank fails.

Q5. What robustness checks are run?

Progressive fixed effects (firm+year; +industry-year; +prefecture-year); crisis-dummy interactions with firm controls; dropping non-innovative firms (never applied/granted patents); restricting to manufacturing (least zombie-affected); R&D-intensity-based industry exclusions; an alternative small-firm definition (first quartile vs first tercile — application results similar, citation results weaken since these firms’ patents are rarely cited); using R&D expenditure (Toyo Keizai self-reported) as an alternative outcome (bank-dependent firms cut R&D more, Table A1); interacting overseas-sales ratio with crisis (Table A2); separating loans from other debts (loans interaction more robust than other-debt interaction, Table A3); and an industry-linear-trend specification (qualitatively unchanged, unreported).

Q6. Did the financial health of the main bank matter, beyond the binary failure event?

No robustly. Using percentage change in main banks’ share prices from 1993-1998 (interacted with the crisis dummy) to proxy bank weakness, the authors find no robust evidence that clients of weaker-but-surviving banks innovated differently. They conclude differences in main-bank financial health are second-order relative to firm-level heterogeneity in bank dependence (Table A4).

It builds on Japanese bank-health-to-real-activity studies (Peek and Rosengren, Gibson, Amiti-Weinstein, etc.) but tracks much longer-horizon, persistent effects on innovation rather than short-term investment/employment. Relative to Nanda and Nicholas (2014, Great Depression patenting), it uses linked bank-firm data with industry-year and region-year fixed effects to control for demand shocks, and argues 1990s Japan (scarcer breakthrough opportunities) may be more relevant to contemporary settings than the technologically fertile 1930s US. Unlike Hardy and Sever (2021), which uses only US-office patents granted to foreign firms (selection concerns) at industry level, this paper uses all domestically granted Japanese patents at the firm level. It follows Duval, Hong, and Timmer (2020) on balance-sheet heterogeneity and Huber (2018) on bank failures, but adds invention-quality measurement via long forward-citation windows that the 2008-crisis literature cannot yet exploit. It complements Hombert and Matray (2017) on relationship lending and small-firm innovation.

Q8. What are the dynamics of the bank-failure effect on small firms?

In the event study, pre-failure coefficients (3-4 and 2 years before) are small and insignificant. Post-failure coefficients are largely negative, with the largest, significant declines about 2 years after failure (consistent with lags in producing innovation). Innovation performance recovers to pre-failure levels within about 4 years, but cumulative losses are large — implying small firms would have received roughly 50% more patents absent the failure. Effects are qualitatively similar excluding non-innovative firms or non-manufacturing firms.

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

The adverse real effects of a systemic banking crisis can linger because opaque, bank-dependent firms’ innovation declines persistently, plausibly contributing to Japan’s long-run post-crisis productivity and growth stagnation. Scope conditions: the effect is specific to small, opaque, bank-dependent firms reliant on relationship and especially short-term bank finance; it does not generalize to large firms; the mechanism is loss of monitored, difficult-to-replace relationship lending plus rollover risk, not generic financial weakness or main-bank fragility; and the setting (heavily bank-centered Japanese financial system, scarce breakthrough opportunities) shapes external validity.

Q10. What are notable caveats and data limitations?

Bank dependence is proxied by total loans (including loans from non-financial parents/affiliates) over assets rather than pure bank borrowings, because the cleaner Corporate Borrowings Database omits pre-1996 OTC firms; the authors verify total loans only slightly exceed bank borrowings and results hold on the cleaner sub-sample. Patent-financial matching covers ~58% of all applications. Cumulative bank-dependence effects (~50%) are only marginally significant. R&D-based outcomes are hampered by a 2000 Japanese accounting-standard change and inconsistent firm reporting. Citation data are truncated, motivating the long 17-year (and 15-year for 1994-2003) windows.

Key Concepts

News-Driven Household Macroeconomic Expectations: Regional vs. National Telecast Information

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

Layer 1: Overview

Research question and motivation: The paper asks whether and which television news topics shape French households’ one-year-ahead macroeconomic expectations (inflation, unemployment, economic situation), over and above information already in national statistics, and whether REGIONAL (not just national) news matters. This is important because media are the primary information intermediary between households and the economy, household expectations feed into consumption/spending decisions and thus monetary-policy transmission, and the literature had largely ignored that households’ information sets may depend on local/regional economic conditions.

Data and sample: Monthly data, January 2004 to December 2019. Household expectations come from INSEE’s monthly consumer-confidence survey (~2,000 households interviewed by phone each month, each interviewed three consecutive months). The author uses three qualitative questions (future prices, unemployment, economic situation) to build national and regional “balances of opinions,” plus a quantitative inflation-expectation question (answered on average by only 56% of monthly respondents, which prevents building regional quantitative series). News data come from the French National Audiovisual Institute archives of TF1 and France 2 (national, 8pm newscasts watched daily by roughly 20% of households) and France 3 (7pm regional newscasts). National and regional newscasts discuss roughly 24 and 11 stories per day, respectively. Human archivists assign standardized expert keywords/topics. The author constructs coverage indicators for 73 topics (12 aggregate + 61 socio-economic), selected if discussed in more than 75% of months. Two coverage measures are built: count-based (frequency of stories) and a novel time-based “viewer time exposure” (seconds spent on a topic). Metropolitan France is split into 13 administrative regions (Corsica/overseas excluded).

Empirical strategy: Penalized predictive regressions (LASSO, Tibshirani 1996), following Larsen et al. (2021), with the rigorous data-driven plug-in penalty of Belloni et al. (2012, 2014) and post-LASSO OLS with Newey-West HAC standard errors. News variables are lagged one month (to avoid simultaneity/look-ahead); statistical controls lagged two months (except EPU index and diesel price, lagged one). National statistical controls include 10-year bond yield, CPI, exchange rate, unemployment rate, industrial production, EPU index, diesel price; milk and bread prices added for inflation regressions. Regional regressions are run separately per region adding national plus regional news and three regional controls (job seekers, dwelling permits, business failures). Household-level regressions use OLS (quantitative) and probit (binary) with demographic, year, and region effects.

Main findings (with magnitudes): From 73 candidate topics, 14 are selected, with on average about four topics per regression in addition to statistical series, confirming news carries information not in national statistics. Average inflation expectations are significantly driven by news on energy and taxes; decomposing energy shows OIL news is consistently selected (gas to a lesser extent, not robust to statistics). Future-economic-situation expectations load on purchasing power, living cost, and economic plan; unemployment expectations load negatively on economic crisis and oppositely on economic life. Regional results: both regional AND national labor-market news predict the unemployment balance of opinions; regional lay-off and unemployment topics are consistently selected, and more regional unemployment coverage makes households more pessimistic about NATIONAL unemployment. At the household level, one additional energy story raises the probability of expecting price increases by 0.19% and one additional fiscal-policy story by 0.10%; one additional regional-unemployment story raises the probability of expecting more unemployment by 0.36% (0.33% in panel specification; energy 0.17% and fiscal policy 0.08% in panel). The unemployment balance-of-opinions dispersion across regions averages 24 percentage points. Independent/self-employed workers are most sensitive to regional unemployment news; the effect is weaker for young and below-first-quartile-income households. Implications: news topic fluctuations carry expectation-relevant information complementary to official statistics, regional news reveals a geographical dimension to household attention consistent with endogenous information acquisition / rational inattention, and this matters for using inflation expectations as a monetary-policy tool.

In depth

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

The strategy is predictive: LASSO (with the Belloni et al. rigorous plug-in penalty) selects, from 73 candidate news topics plus statistical controls, those with predictive power for one-year-ahead expectations, followed by post-LASSO OLS with Newey-West HAC standard errors. The paper is explicit that it estimates a predictive relationship, not a structural causal effect. Threats addressed: simultaneity/look-ahead bias is handled by lagging news one month and statistics two months (one for diesel/EPU/milk/bread, which households observe in real time); overfitting and spurious selection are reduced by the data-driven penalty (more parsimonious than cross-validation, robust to heteroscedasticity). A residual threat is that news coverage and expectations could both respond to an unobserved underlying economic state; the author partially addresses this by showing news survives inclusion of official national and regional statistics and that ‘partial adjusted R2’ attributable to news is non-zero.

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

The core mechanism is endogenous/limited-capacity information acquisition: households cannot absorb all information and incorporate a subset heard from media intermediaries. Expectation-specificity is the key empirical discriminator: energy/oil and tax/fiscal-policy news affect ONLY inflation expectations; labor-market topics (lay-off, unemployment) affect MAINLY unemployment expectations; broad topics (economic crisis, living cost, economy) affect economic-situation and unemployment expectations. The regional dimension is distinguished by separating France 3 regional newscasts from TF1/France 2 national newscasts and running region-specific LASSO, showing regional labor-market news is selected even after controlling for national news and official regional indicators.

Q3. What heterogeneity is documented?

Regional heterogeneity: balances of opinions and news topic coverage vary substantially across the 13 regions (e.g., unemployment balance-of-opinions min-max gap averages 24 pp; lay-off/unemployment air-time differs markedly by region). Sentiment heterogeneity: economic crisis carries negative sentiment, economic life positive, yielding opposite-signed coefficients. Household heterogeneity: by employment sector, independent/self-employed workers are MOST sensitive to regional unemployment news (vs public and private sector employees); the regional-unemployment-news effect is less significant for young households and not significant for those below the first income quartile.

Q4. What robustness checks are run?

(1) Count-based vs time-based (‘viewer time exposure’) coverage measures give nearly identical selections and R2; time-based is somewhat more parsimonious and more significant for energy on inflation. (2) Outlier-robust inflation-expectation measures (5%, 10%, 15% trimmed means and the median) preserve the energy/tax/fiscal-policy results. (3) Including perceived inflation as a regressor: it is selected but insignificant and does not change energy/tax results; a separate analysis shows news matter for inflation EXPECTATIONS directly, not via perceptions (the selected topic sets are nearly mutually exclusive). (4) Household-level panel exploiting the up-to-three-month repeated interviews (household fixed-effects / random-effects probit) confirms results (energy 0.17%, fiscal policy 0.08% for prices; regional unemployment 0.33% for unemployment). (5) Energy decomposition by source confirms oil (and lesser gas) drives the energy effect. (6) Bootstrapped confidence intervals and demographic-stability checks address the concern that regional series differences are noise or demographic composition.

It builds directly on Larsen et al. (2021), adopting their topic-based LASSO approach, and on Carroll (2003), Doms and Morin (2004), Pfajfar and Santoro (2013), Lamla and Lein (2014), Draeger and Lamla (2017), Ehrmann et al. (2015) on media and expectations. Four novelties distinguish it: (1) it uses TELEVISION content rather than newspaper corpora (television being the main source of household economic information per Blinder-Krueger, Curtin); (2) it separates REGIONAL from national newscasts to identify regional drivers of expectation heterogeneity; (3) it uses HUMAN-EXPERT-assigned topics rather than algorithmic topic models (more accurate for short TV stories, allows distinguishing sub-topics like deficit, lay-off, tax); (4) it adds a time-based ‘viewer time exposure’ coverage measure capturing duration, not just frequency. The regional finding extends Kuchler-Zafar (2019) and Malmendier-Nagel (2016) extrapolation results: households extrapolate not just personal experience but their region’s labor-market experience to national expectations.

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

Understanding which news households incorporate is key for using inflation expectations as a monetary-policy tool; energy/oil and tax/fiscal news drive inflation expectations, so central-bank communication and expectation management must account for media salience of these topics. The regional finding implies a geographical dimension to household attention relevant for modeling information frictions (rational inattention, sparsity, sticky information with endogenous updating). Scope conditions: results are predictive (not causal), specific to France 2004-2019, rest on expert-assigned TV topics, and the regional analysis applies to qualitative balances of opinions only (the quantitative inflation question’s 56% response rate prevents regional quantitative series). Whether households OVERWEIGHT local labor markets is explicitly stated to be beyond the paper’s scope.

Q7. What other significant findings, extensions, or caveats appear?

Correlations between national and regional news indicators are limited, confirming regional news carries information absent from national news (only country-wide topics like tourism, tax, economic crisis, demonstration, and prices are highly correlated). Regional peaks reflect identifiable local events (the 2013 ‘Red Beanies’ movement and 2016 agricultural crisis in Brittany). Past inflation and official statistics are heavily selected for inflation/price expectations (consistent with Larsen et al.); milk and bread price changes matter for quantitative inflation expectations but not the qualitative price balance, suggesting households extrapolate frequently-bought items for quantitative answers. Electricity is absent from selection despite a larger basket weight than gas, plausibly due to France’s regulated electricity prices. The author notes media exhibit a documented negative-news asymmetry (Soroka 2006), so sentiment-neutral topics tend to carry predominantly negative news.

Key Concepts

Balance of opinions: A monthly index computed as the difference between the share of households expecting one macroeconomic direction and the share expecting the opposite (e.g., for unemployment, share expecting an increase minus share expecting a decrease; for prices, share expecting an increase minus share expecting prices to stay the same, since households rarely expect deflation). Used as the qualitative expectation measure at national and regional levels.

Viewer time exposure: The paper’s novel time-based coverage measure: the monthly number of seconds viewers are exposed to a given news topic, as opposed to the count-based measure (number of stories). It captures both frequency and duration, reflecting the importance given to a story and its effect on viewer recall.

Expert-assigned topics: News topics assigned by trained archivists of the French National Audiovisual Institute using a standardized grid (relying on title, image, and sound), rather than algorithmic topic models. The author argues these are more accurate for short TV stories and allow distinguishing specialized sub-topics (deficit, lay-off, unemployment) that algorithms would pool.

Endogenous information acquisition: Used in the paper’s own sense as the theoretical frame in which households with limited capacity to acquire/process information choose what to attend to based on expected benefits — invoked to explain why households incorporate regional labor-market news (believing they are more affected by local conditions). Linked to rational inattention, sparsity, and sticky-information models.

Rigorous (plug-in) LASSO penalty: The data-driven penalty of Belloni et al. (2012, 2014) for choosing the LASSO regularization parameter, preferred over cross-validation because it yields a more parsimonious variable selection, lowers overfitting, and is robust to heteroscedasticity; followed by post-LASSO OLS with Newey-West HAC standard errors.

Geographical dimension of attention: The paper’s term for its central regional finding: households’ information collection and attention have a spatial structure, whereby they incorporate regional news (especially on local lay-offs and unemployment) into their NATIONAL expectations, producing geographical heterogeneity in aggregate beliefs.

The Macroeconomic Effects of a European Deposit (Re-)Insurance Scheme

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

Layer 1: Overview

Research question and motivation: The first two pillars of the European Banking Union (single supervision and single resolution) are in place, but the third pillar — a European deposit insurance scheme (EDIS) — is still missing. Recent policy proposals favor a reinsurance design, where European deposit insurance steps in only after national deposit insurance (DI) funds are depleted. The paper asks how well such a deposit reinsurance scheme absorbs macroeconomic and financial shocks relative to alternatives, and quantifies its stabilization, welfare, and moral-hazard implications.

Model and method: The authors build a two-country regime-switching open-economy DSGE model with bank default, calibrated to Germany (home) and the euro area excluding Germany (foreign). Banks face idiosyncratic log-normal asset-return shocks and limited liability, so they can default and leave depositors (facing state-verification/monitoring costs) with losses. National DI funds collect risk-weighted contributions from banks and compensate insured depositors; when a fund is exhausted (DI_t <= 0), the share of insured deposits drops to zero and the economy enters a “constrained” regime. Four regimes capture whether home and/or foreign national DI is unconstrained or constrained, with Markov-switching transition probabilities (sigmoid functions). Two bank-government linkages are modeled: banks finance sovereign debt, and the fiscal authority provides tax/debt-financed guarantees on bank insolvencies. Three reinsurance arrangements are compared once national DI is exhausted: (A) no backstop, (B) national fiscal backstop, (C) EDIS. Most series are calibrated for 1999:Q1-2019:Q4 using ECB/Eurostat/OECD, Bundesbank, IMF, and micro data (Bloomberg, Eikon, Datastream). Key preset parameters: capital share 0.3, household habit 0.8, trade elasticity 1.5, home bias in traded goods 0.6, Basel III steady-state bank capital requirement 10.5 percent, LTV ratio 0.35, bank monitoring costs 0.3, DI and EDIS contribution sensitivity 0.45. Twelve remaining parameters are set by first-moment matching (total distance 2.836). The EDIS fund target is 0.8 percent of insured deposits; the simulated bank risk shock doubles the standard deviation of idiosyncratic bank asset returns to deplete national DI.

Main quantitative findings: In response to an adverse home bank risk shock that depletes national DI (regime switch in period three), EDIS stabilizes the affected economy better than the fiscal or no backstop. Peak-to-trough GDP declines 0.3-0.4 percent across scenarios (deepest under no-backstop). Home output decline is about 10-20 percent smaller with EDIS; home consumption falls about 0.4 percent peak-to-trough with EDIS; investment declines are 30-40 percent smaller and bank loans 30-50 percent smaller with EDIS versus the other scenarios. The abstract/intro summarize the investment/consumption/loan gains as roughly 20-35 percent lower in the trough. The debt-to-GDP ratio rises markedly under the fiscal backstop but stays broadly stable under EDIS, since costs are covered by bank contributions rather than public debt. Costs of EDIS: banks contribute to both national DI and EDIS, raising the total burden and making national-fund recovery slowest under EDIS; foreign banks must contribute more, reducing margins and foreign lending. In a robustness analysis taking IRF differences one year after the shock, the baseline EDIS effect on home GDP is +0.1 ppt (range 0.05 to above 0.3 ppt across parameters) and on foreign GDP +0.06 ppt (range 0.02-0.2 ppt). Welfare (consumption equivalents, 100 x lambda_w, vs fiscal backstop baseline): differences are small but EDIS benefits savers in constrained economies, with the largest union-wide gains when both economies are constrained (regime 4). Risk-weighting contributions by country-specific default costs (baseline home share ~32 percent, foreign ~68 percent) renders EDIS risk-neutral in the long run so it does not foster additional moral hazard; only non-risk-weighted contributions induce structurally higher risk-taking that macroprudential policy can correct. The link between steady-state capital requirements and activity is hump-shaped with an optimum at 12 percent; the best stabilization comes when both EDIS and macroprudential policy are active and capital requirements are at 10.5 percent. A novel bank-run extension (state-dependent monitoring costs of 0.3 vs 0.6, plus a sunspot shock) shows runs deepen the output trough by about 40 percent relative to the no-run case, and that EDIS can prevent a self-fulfilling run by stopping the economy from entering the “in-between” region.

Implications: A European deposit reinsurance scheme can deliver union-wide welfare gains and macro-financial stabilization, but regulators must design contribution and deductibility rules to avoid overburdening banks and constraining credit, ensure EDIS can pay out instantaneously once introduced, and recognize that costs and benefits are unequally distributed across countries, savers, and borrowers.

In depth

Q1. What is the modeling/identification strategy and what are its main limitations?

The strategy is a calibrated two-country regime-switching DSGE model (solved with the RISE toolbox), not an empirical causal-identification design. Identification of mechanisms comes from comparing counterfactual policy scenarios (no backstop, national fiscal backstop, EDIS) under the same bank risk shock. The authors themselves flag that the analysis is counterfactual: the euro area has not actually experienced explicitly exhausted national DI funds (the closest episode being October 2008 government deposit pledges). The main limitations are parameter uncertainty (the model is calibrated, not fully estimated) and the fact that the home/foreign calibration to Germany and the rest of the euro area does not imply general validity for other member states, motivating the robustness analysis.

Q2. What are the four regimes and how does regime switching work?

Regimes are defined by whether each country’s national DI is unconstrained (fund positive, insured share = kappa-bar) or constrained (fund <= 0, insured share = 0): Regime 1 both unconstrained; Regime 2 home constrained; Regime 3 foreign constrained; Regime 4 both constrained. Transition probabilities follow sigmoid (Markov-switching) functions: the probability of entering the constrained regime is one when the fund level hits zero (scaling alpha2 = 200), and the probability of switching back becomes one when bank default rates drop below a financial-stress threshold (scaling alpha1 = 300).

Q3. What are the main mechanisms distinguishing EDIS from the fiscal backstop?

Under the fiscal backstop, depositor losses enter the national government budget constraint, raising the debt-to-GDP ratio and affecting taxes/expenditure. Under EDIS, losses are covered by internationally shared, risk-weighted bank contributions, so public debt stays broadly stable. The trade-off: EDIS imposes a higher total burden on banks (they fund both national DI and EDIS), slows national-fund recovery the most (because EDIS contributions are deductible from national payments, stretching the refilling of two funds), and transmits the contribution burden to foreign banks, reducing their margins and lending. For the foreign economy, EDIS has an expansionary trade/financial channel that dominates in the first ~5-6 quarters and a contractionary higher-contribution channel that dominates in the medium-to-long run.

Q4. What heterogeneity is documented across the two countries?

Germany (home) has a higher home bias in bank equity (~80 percent) attributed to Landesbanken, savings and cooperative banks, and lower bank default risk (lower sigma of idiosyncratic asset-return shocks). The rest of the euro area (foreign) is the riskier banking sector with a higher default-shock standard deviation, so under risk-weighted contributions it bears the larger EDIS share (~68 percent vs ~32 percent home). Welfare effects differ: EDIS raises entrepreneurial welfare in the riskier foreign country but lowers it in the safer home country; savers in constrained economies gain.

Q5. What robustness checks are run and what do they show?

The authors re-simulate the same home bank risk shock over minimum/maximum plausible ranges for calibrated and matched parameters, taking IRF differences one year out. The positive EDIS effect on home GDP is robust across all ranges where national DI depletes (0.05 to above 0.3 ppt; baseline 0.1 ppt); the foreign GDP effect ranges 0.02-0.2 ppt (baseline 0.06 ppt). Influential parameters include the goods home-bias/openness (more open economies gain less from EDIS), the LTV ratio, bank monitoring costs, and the idiosyncratic asset-return shock standard deviation (larger sigma means a more severe crisis and larger EDIS benefit). Higher fund target rates or insured-deposit shares can prevent depletion, in which case EDIS does not intervene and its effect is zero. Higher household-to-banker transfers and banker survival rates raise net worth, lower default risk, and shrink the EDIS effect. A sensitivity analysis on monitoring costs affects only quantitative, not qualitative, conclusions.

Q6. How is welfare measured, and what does the contribution-weight analysis find?

Welfare is computed in the stochastic steady state (Coeurdacier et al., 2011) using a second-order approximation, expressed in consumption equivalents (lambda_w), aggregating borrowers and savers with Pareto weights (welfare weight zeta = 1). Conditional welfare is reported by regime relative to a fiscal-backstop baseline; EDIS gains are largest in regime 4 (both constrained), and deductibility (EDIS 1) is welfare-improving especially in the affected country versus no deductibility (EDIS 2). Varying the contribution split via alpha_RW shows low alpha_RW (contributions falling on the riskier foreign banks) is welfare-optimal union-wide (’excessive risk-sharing’), but deviations toward a more moderate split impose negligible welfare cost. Higher contributions in a country raise intermediation costs, cut loans and deposits, and lower borrower welfare there.

Q7. What does the paper conclude about EDIS and moral hazard?

Because individual bank contributions are weighted by aggregate observable default risk, the steady-state default threshold is unaffected by deposit-insurance coverage, so under risk-weighted contributions EDIS does not induce additional moral hazard in the long run (defaults, firm loans, and corporate borrowing rates are unchanged by higher insurance shares in steady state). Moral hazard arises only if contributions are not risk-weighted or if long-run insurance payments do not match contributions, in which case low capital regulation fosters extra risk-taking and long-run macroprudential policy can correct it. Cyclically, EDIS can still temporarily foster risk-taking because insurance payouts are large during a crisis while contributions accrue with a lag, enlarging the complementary role for macroprudential policy.

Q8. How does the bank-run extension work and what is the key result?

The RS-FF (regime-switching financial friction) model makes monitoring costs state-dependent (0.3 in low distress, 0.6 in high distress, with the high-distress threshold set at a 2.5 percent quarterly default rate, following Linde et al. 2016). A sunspot shock can trigger a partial run in an ‘in-between’ state where depositors wrongly believe they are in high distress; non-fundamental beliefs raise the default threshold above its fundamental level (omega* > omega), some sound banks face liquidity problems and default, making beliefs self-fulfilling. A run amplifies the recession: in the no-backstop run scenario the output trough is about 40 percent lower than the no-run case (default costs roughly double, deposits about one ppt lower), a relative magnitude (ratio ~2.7) close to Gertler et al. (2020). Crucially, EDIS, by compensating depositor losses, keeps the economy out of the ‘in-between’ region and can prevent the self-fulfilling run.

It extends Mendicino et al. (2018) — a closed-economy model with bank default, deposit insurance, and optimal capital regulation — to an open two-country setting with a detailed government sector and a bank-financed deposit fund (rather than direct household transfers). Unlike Dedola et al. (2013), where financial-friction degrees are equal across countries, it allows heterogeneous bank riskiness. Unlike representative-global-bank models (Mendoza-Quadrini 2010; Kollmann et al. 2011; Kollmann 2013), it allows heterogeneous national banking sectors. Unlike Dubois (2021), which has a linear two-country bank-run model, its regime-switching nonlinearity permits an explicit reinsurance/backstop comparison. Relative to Amador and Bianchi (2022) (partial runs, U.S., no deposit insurance), it adds deposit insurance and EDIS risk-sharing and models runs as a combination of financial-regime switches and sunspot shocks.

Q10. What are the short-term implementation costs of EDIS and how can they be mitigated?

Filling the EDIS fund requires up-front bank contributions over about 3.5 years in the baseline. With deductibility, payments into national DI fall, temporarily lowering national coverage; households then demand higher deposit risk premia, reducing intermediation and activity. Removing deductibility keeps national coverage on target but the double burden lowers bank margins, lending, and raises defaults, though stress is shorter-lived. Extending the implementation horizon (e.g., to 7.5 years) lowers per-period contributions and mitigates peak default rates, but leaves coverage lower for longer, protracting the downturn. Policy options include ensuring EDIS pays out instantaneously once introduced and temporarily suspending contributions during acute distress.

Key Concepts

EDIS reinsurance scheme: In this paper, a European deposit insurance arrangement that acts as a second line of defense, paying out only once a country’s national deposit insurance fund is exhausted (the constrained regime), financed by risk-weighted bank contributions deductible from national DI payments.

Constrained vs unconstrained regime: States distinguished by whether a national DI fund is positive (unconstrained, insured deposit share = kappa-bar) or depleted (constrained, insured share = 0); the model has four such regimes across home and foreign and switches between them via Markov sigmoid transition probabilities.

Risk-weighted contributions (‘polluter-pays’): EDIS contributions allocated across countries in proportion to country-specific expected bank-default costs, so the riskier banking sector pays more; this design renders EDIS risk-neutral in the long run and prevents additional steady-state moral hazard.

Deductibility of contributions: The assumption that banks can subtract their EDIS payments from contributions to national DI funds, keeping total bank contributions from exceeding the no-EDIS level but slowing the refilling of both funds.

Bank default threshold (omega): The realization of a bank’s idiosyncratic asset-return shock below which the bank defaults on depositors; its steady-state value is shown to be independent of deposit-insurance coverage, which is the analytical basis for the no-long-run-moral-hazard result.

In-between state / sunspot-driven partial bank run: A region where a bank risk shock is large enough to bring the economy near the high-distress (high monitoring cost) state but not into it; a sunspot shock then makes depositors wrongly believe in high distress, raising the non-fundamental default threshold (omega* > omega) and triggering a self-fulfilling partial run that EDIS can prevent.

Hump-shaped capital-requirement effect: The relationship between steady-state bank capital requirements and long-run output/intermediation/welfare, peaking at an optimum of 12 percent: below it, higher default costs dominate; above it, the equity-crowding-out of lending dominates.

A Heterogeneous Agent Model of Energy Consumption and Energy Conservation

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

Layer 1: Overview

Audzei and Sutóris ask whether inflation-targeting monetary policy affects households’ incentives to invest in energy conservation, and whether the standard central bank response to energy price shocks is welfare-optimal when agents are heterogeneous. They embed energy in both the consumption bundle and the production function of a tractable heterogeneous-agent New Keynesian (HANK) model that features Challe–Ravn–Sterk search-and-matching frictions in the labor market, nominal bond holdings, and — the paper’s central innovation — household-level energy conservation (abatement) capital that converts raw energy into energy services. The model is calibrated to the Czech Republic, with an energy share in household consumption of 10%, an energy share in production of 5%, a steady-state job-finding rate of 0.15 (targeting a poor hand-to-mouth share of 9%), and a capitalist share of 12%. The main quantitative findings are that a tighter monetary policy shock reduces abatement capital investment, increases the energy intensity of consumption, and depresses the job-finding rate, all of which fall disproportionately on lower-wealth households; conversely, a weaker policy response to a persistent energy price shock — one with a lower inflation coefficient (φ_π = 1.1 rather than the baseline φ_π = 2) — generates welfare gains for all agent groups (capitalists, employed workers, newly unemployed, long-term unemployed) despite higher measured inflation, because it preserves employment and stimulates abatement investment, reducing households’ long-run exposure to energy price shocks. The paper also shows that a “looking-through” policy (reacting to core rather than CPI inflation) does not deliver welfare benefits because it is too accommodative when energy prices rise but too restrictive once they start to fall; Ramsey-optimal policy instead features a sharp front-loaded rate spike followed by a rapid decline, minimizing aggregate consumption volatility through higher abatement capital.

In depth

Q1. What is energy conservation capital, how is it modeled, and why does it matter for the monetary policy transmission channel?

Energy conservation capital (abatement capital) is a durable investment good held by households that reduces raw energy required to produce a unit of energy service; because unemployed workers cannot afford it and its return competes with nominal savings, it creates a novel interaction between labor market outcomes and monetary policy. Households derive utility from a CES composite of non-energy consumption and energy services, where energy services are produced from raw energy multiplied by an efficiency factor that is increasing and concave in abatement capital: $E^s = f(K^e_{t-1}) E^r$, with $f(K^e) = \varphi_{1,e} (K^e)^{\varphi_{2,e}}$ and $\varphi_{2,e} = 2$. The elasticity of substitution between energy and non-energy goods is set to $\lambda_e = 0.3$, reflecting limited short-run substitutability. Abatement capital depreciates at 1% per quarter (equivalent to 4% annually, matching housing and heating systems lifetimes of ~25 years). Crucially, workers lose their abatement capital when they become unemployed (they move to a communal stock at the steady-state unemployed level $\bar{K}^e_u$), so abatement capital is not a precautionary savings vehicle and unemployed workers have no incentive to invest in it. Employed workers who optimally invest must account for the probability of becoming unemployed and therefore losing their capital. This structure means that monetary policy tightening — by raising unemployment and raising the return on nominal bonds — simultaneously pushes more workers into the non-investing unemployed pool and reduces the relative attractiveness of abatement investment for employed workers, raising the energy intensity of consumption.

Q2. What are the four agent types, and how do their asset positions differ?

The model compresses the household distribution into four types — employed workers, first-period unemployed, long-term unemployed, and capitalists — each with sharply different asset positions that determine how they are affected by monetary policy. Employed workers hold positive nominal bonds ($B’{e,t-1} > 0$) and invest in abatement capital ($K^e{e,t-1}$); they are the only group making active portfolio and investment decisions. First-period unemployed workers consume all their precautionary savings in a single period (their IMRS × R < 1) and receive 75% of unemployment benefits; they hold $B_{e,t-1} > 0$ (inherited from their last employed period) but make no new saving or abatement decisions. Long-term unemployed workers hold zero assets, receive full unemployment benefits indexed to the real wage, and maintain abatement capital at the fixed communal level $\bar{K}^e_u$. Capitalists ($\xi = 12%$ of population) own all firms, invest in productive capital and abatement capital, and are net borrowers in the steady state (rich hand-to-mouth in the Kaplan–Moll–Violante sense); they are subject to an endogenous discount factor that stabilizes the capital stock. Risk-sharing among employed workers — all employed household members pool their nominal bonds — enables tractability while preserving precautionary saving motives.

Q3. How does a monetary policy shock propagate through energy conservation decisions?

A 0.25 percentage-point positive monetary policy shock reduces abatement capital and raises energy intensity, operating through two reinforcing channels: the labor market channel (more unemployment, fewer households able to invest) and the intertemporal substitution channel (higher returns on nominal bonds reduce the relative attractiveness of abatement investment). Following the shock, the policy rate rise suppresses output and raises unemployment (Figure 3 of the paper). The increase in the job-destruction-net-of-finding probability $\omega(1-\eta_t)$ shifts more workers into the first-period unemployed pool, which carries no abatement investment. Among employed workers, the higher nominal bond return means that saving in bonds is relatively more attractive than investing in illiquid abatement capital, so their abatement holdings fall. The result is a rise in raw energy per unit of consumption, meaning the economy becomes more energy-intensive precisely when energy prices may also be elevated — a double vulnerability.

Q4. What are the welfare effects of different policy rules in response to a persistent energy price shock, and what are the magnitudes?

After a persistent hump-shaped energy price shock, welfare losses (measured as discounted infinite-horizon utility) are smaller for all agent groups under the weak-reaction policy (φ_π = 1.1, φ_y = 0) than under the baseline (φ_π = 2, φ_y = 0), even though inflation is higher under the weaker rule; the welfare gap is largest for employed workers and capitalists, and broadly preserved under alternative calibrations. Policies that react more weakly to inflation result in a smaller output recession and lower unemployment (Figures 7–9 of the paper). In the welfare simulation (Figure 9), all four agent types — capitalists, employed workers, newly unemployed, and long-term unemployed — show smaller welfare declines under the weak-reaction rule compared with baseline. Capitalists benefit because lower interest rates reduce their debt service and higher output raises firm profits. Employed and unemployed workers benefit primarily because of the higher job-finding rate, which lowers the probability of falling into the HtM state. Additionally, accommodative policy supports more investment in abatement capital, which reduces all agents’ long-run exposure to energy price fluctuations, further boosting welfare. The welfare ranking is robust to: (i) benefits fixed in nominal terms (narrower but preserved gap), (ii) more flexible wages (narrower gap; welfare ranking of capitalists reverses under flexible wages), and (iii) larger steady-state household savings (wider gap).

Q5. Why does the “looking-through” policy fail, and how does it differ from the weak-reaction policy?

The looking-through policy (φ_π = 2 on core inflation, ignoring energy-price CPI inflation) does not deliver welfare gains because it creates an asymmetric response profile: it is too accommodative during the energy price surge and too restrictive once energy prices start to fall, generating a welfare trajectory that is inferior to a consistently weaker policy. When energy prices are rising, CPI inflation exceeds core inflation; reacting only to core means the central bank does not raise rates as much as under the baseline, so the policy is more stimulative in the short term and supports output and abatement investment in the near term. However, once energy prices start declining, CPI inflation reverts to the steady state faster than core inflation (which is still elevated due to nominal rigidities), meaning the looking-through policy becomes more restrictive relative to the baseline at precisely the time when agents need support. The result is that long-run welfare, which discounts the entire future path, does not improve under looking-through relative to either the baseline or the weak-reaction rule. This finding provides an important caution against the standard “look through supply shocks” recommendation in a HANK environment with abatement capital.

Q6. What does Ramsey-optimal policy look like, and why does it differ from Taylor-type rules?

Ramsey-optimal policy — which minimizes the volatility of population-share-weighted aggregate utility — features a sharper and faster initial rate spike than the baseline Taylor rule, followed by a more rapid decline; it results in the highest abatement capital investment and lowest energy intensity of all policies considered. The Ramsey planner’s first-order conditions (solved with Dynare’s Ramsey tool, taking private-sector FOCs as constraints) imply that the policy rate peaks before the energy price shock itself peaks, reflecting the planner’s desire to front-load inflation stabilization while ensuring that rates fall quickly enough to not suppress abatement investment in the medium term. The Ramsey rate path is lower than the baseline Taylor rule after the shock peak. Compared with all Taylor-type rules, Ramsey policy results in the largest negative deviation in consumption energy intensity and the largest positive deviation in abatement capital (Figure 8). Ramsey policy also delivers the highest welfare for all agent groups (Figure 9), validating the intuition that protecting abatement investment is an important channel for central bank welfare optimization in this setting.

Q7. What is the role of heterogeneity in shaping these results, and what would be missed by a representative-agent model?

The distributional effects are essential to the paper’s core conclusions: a representative-agent model would miss the asymmetric impact of unemployment risk on energy conservation investment and would fail to generate the welfare reversal whereby a weaker inflation response dominates. Figure 6 of the paper shows the distributional responses to an energy price shock: capitalists reduce energy intensity the most because they can invest in abatement capital and their consumption is less constrained; employed workers also reduce energy intensity but less so; poor HtM households (unemployed workers) cannot adjust abatement capital and their energy intensity rises because the raw energy share in their limited consumption basket increases. The welfare comparison across agent types in Figure 9 shows that even newly unemployed workers — who lose their abatement investment and consume their precautionary savings — are better off under accommodative policy because the higher job-finding rate reduces the expected duration of unemployment. The key heterogeneity-driven mechanism absent from representative-agent models is the labor market channel: changes in unemployment risk affect who can and cannot invest in energy conservation, generating an indirect channel from monetary policy to aggregate energy intensity.

Q8. What are the model’s main limitations and scope conditions?

The paper abstracts from variable policy rule coefficients, wage-price spirals, unanchoring of inflation expectations, and open-economy dimensions beyond energy-price pass-through; the welfare ranking is conditional on the persistent energy price shock used for calibration and should not be extrapolated to short-lived or demand-driven inflation episodes. The authors explicitly note that the model operates under full-information rational expectations, which rules out the possibility that accommodation generates self-fulfilling inflation or credibility loss. Wage rigidity plays an important role: with more flexible wages, the welfare benefit of accommodative policy narrows and the capitalist welfare ranking reverses (baseline strict inflation targeting is preferred by capitalists). The “looking-through” and weak-reaction findings are specific to the persistent, hump-shaped energy price shock analyzed; for short-lived shocks the standard result (no reaction) would reassert itself. The model is also calibrated to the Czech Republic as a small open economy with above-average energy intensity; the qualitative conclusions extend to other European small open economies with similar energy share profiles, but quantitative magnitudes may differ.

Key Concepts

energy conservation capital (abatement capital) : a durable household investment good that converts raw energy into energy services more efficiently; modeled as $E^s = f(K^e_{t-1}) E^r$ with a quadratic abatement function; the level determines the energy intensity of consumption and is chosen optimally only by employed workers and capitalists.

energy intensity of consumption : the ratio of raw energy used to final consumption $E^r / C$; the paper’s key outcome variable for tracking how efficiently households use energy; a rise signals less efficient usage, a fall signals improved conservation.

looking-through policy : a monetary policy rule that reacts to core inflation (excluding energy) rather than CPI inflation, intended to avoid responding to transient supply shocks; the paper finds this does not improve welfare in a HANK setting because it creates an asymmetric response profile that is too accommodative when energy prices rise and too restrictive when they fall.

Ramsey-optimal policy : the interest-rate path that minimizes the volatility of population-share-weighted aggregate utility subject to the full set of private-sector equilibrium conditions; in this model it features a sharper front-loaded rate spike than Taylor-type rules followed by a rapid decline, and delivers the highest welfare for all agent groups by protecting abatement investment.

hand-to-mouth (HtM) households : households that are highly sensitive to income shocks but do not respond to interest rate changes as predicted by the Euler equation; in this model, poor HtM are both types of unemployed workers (zero savings, zero abatement investment), and rich HtM are capitalists (large debt, no labor income); their presence is central to the distributional welfare results.

search-and-matching frictions : the Challe–Ravn–Sterk labor market structure in which the job-finding rate $\eta_t$ is determined endogenously by the vacancy-unemployment ratio (Cobb-Douglas matching function) and job destruction is exogenous at rate $\omega$; this structure makes unemployment risk stochastic and endogenous to monetary policy, creating the key link between policy rates and energy conservation decisions.

A Housing Portfolio Channel of QE Transmission

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

Layer 1 — Overview

Research Question

This paper identifies and quantifies a housing portfolio channel of quantitative easing (QE) transmission that operates through household portfolio rebalancing toward second homes (as opposed to the well-studied bank credit channel). The central question is whether, and how much, the ECB’s formal adoption of QE in January 2015 induced households with larger pre-existing bond holdings to shift wealth into residential real estate—specifically second homes held for investment—and what the downstream effects on regional housing market outcomes were.

Setting and Motivation

Germany is used as the empirical laboratory because it experienced a sustained housing boom from 2009 onward that was not accompanied by a household credit boom—a “housing boom without a credit boom.” The national house price-to-rent ratio rose markedly from 2009, especially accelerating after QE adoption in 2015, while the stock of mortgage credit to households as a share of GDP was flat or declining. This decoupling makes Germany well-suited for isolating a non-credit portfolio rebalancing mechanism.

Data

Household-level data come from the Deutsche Bundesbank’s Panel on Household Finances (PHF), a triennial survey fielded in 2011, 2014, and 2017, from which the authors construct a panel of 1,651 households. The key exposure variable is each household’s pre-QE (2014) share of total wealth invested in bonds, both directly and indirectly via mutual funds and insurance. Regional housing outcomes (prices, rents, rental yields) are from Bulwiengesa AG for all 401 German administrative regions (Kreise) at annual frequency, and listing data come from Immoscout 24, Germany’s largest online real estate platform.

Methodology

The household-level analysis uses a difference-in-differences (DiD) specification comparing changes in housing portfolio shares between the pre-QE wave (2014) and the post-QE wave (2017), against the pre-period change (2011 to 2014), with the degree of exposure measured by the 2014 bond share. The specification includes household and time fixed effects. A parallel-trends check using all three survey waves (Figure 2) shows that more- and less-exposed households tracked identically before QE adoption, diverging sharply thereafter. Two indirect placebo tests—using households’ share in non-financial, non-housing assets as a spurious treatment, and using the change in non-financial assets as a spurious outcome—both return null results, supporting the identification assumption. For regional housing outcomes, the authors use a panel regression interacting lagged ECB debt-securities-to-GDP (the QE intensity measure) with a regional exposure variable—the 2008 pre-QE share of refugees housed in independent accommodations—across 401 regions from 2010 to 2017.

Main Findings with Quantitative Magnitudes

Benchmark portfolio rebalancing: A household with an ex-ante bond share that is 10 percentage points higher (roughly the interquartile range of the bond share distribution) increases its portfolio share of second homes by 1.72 to 1.87 percentage points more than a less-exposed household after QE adoption, conditional on household and time fixed effects. This result is statistically significant at the 1% level across multiple specifications and is robust to alternative bond share definitions, alternative portfolio denominators, and controlling for negative interest rate policy exposure (via initial deposit shares).
Equity rebalancing: Controlling for risk aversion does not attenuate the second-home result. Strikingly, households with larger ex-ante bond shares reduce, rather than increase, their equity shares after QE (coefficient: −0.042, significant at 5%), ruling out the interpretation that the housing result merely picks up broad rebalancing toward all risky assets. This implies that cash purchases of second homes are funded by liquidating bonds, drawing down deposits, and also selling equities.
Heterogeneity—household characteristics: Rebalancing is stronger for (a) bank-advised households (triple-interaction significant at 5%), (b) financially more literate households (significant at 1%), and (c) households aged 40–60 (significant at 5%), consistent with a lifetime-income-peak, tax-optimization motive rather than a bequest motive. The result for age 61+ is positive but statistically insignificant.
Tax-motive heterogeneity: In Germany, rented-out second homes (or those declared for future letting) benefit from substantial tax deductions not available for owner-occupied primary residences, with the advantage rising in marginal tax rates. Rebalancing is stronger for higher-income households (triple interaction with income per capita positive and significant, especially after controlling for deposit shares) and for church-affiliated households, who face an additional 8–9% church tax surcharge on their regular tax bill, amplifying the tax gain from rental property deductions. For church members, the income-interaction triple coefficient is statistically significant; for non-church members it is not, directly linking the rebalancing gradient to the church tax burden.
Buy-to-let motive: The benchmark result is driven entirely by households that already owned a second home in the pre-QE period and were generating rental income from it (coefficient 0.821, significant at 1%); households without a pre-owned second home show a near-zero, statistically insignificant coefficient (0.000). This establishes that the rebalancing is driven by experienced buy-to-let investors, not vacation-home buyers or commuters.
Credit channel control: The portfolio rebalancing result is not driven by credit access or credit growth. The triple interactions of the bond-share × Post term with both (a) pre-QE leverage (mortgage credit to housing wealth) and (b) post-QE mortgage credit growth are statistically insignificant. Restricting the sample to households with no mortgage credit growth leaves the main coefficient essentially unchanged (0.175, significant at 1%). Nonetheless, an independent credit-channel effect is also present: mortgage credit growth has its own positive and significant effect on second-home share increases, confirming the two channels operate in parallel but independently.
Regional housing market outcomes—prices and yields: In regions more exposed to rental market tightness (higher refugee-in-independent-accommodation share), QE is associated with larger declines in rental yields. A one-standard-deviation increase in QE (approximately 4.3 pp higher ratio of ECB debt securities to GDP) reduces the rental yield in the 75th-percentile-exposure region relative to the 25th-percentile region by 2 to 12 basis points per year (depending on whether the refugee share or the renter share is used as the exposure measure). As ECB holdings rose from 7% of GDP in 2014 to 24% in 2017, the cumulative implied rental yield decline at the regional interquartile range is 8 to 48 basis points, sizable relative to the average regional rental yield decline of 140 basis points (from 7.4% to 6.0%) over the same period. House prices increase more than rents in more exposed regions.
Regional housing market outcomes—listings: Using Immoscout 24 data, both sale and rental listings decline in more exposed regions as QE expands, but the ratio of sale to rental listings falls significantly: sale listings decrease significantly more than rental listings in more exposed regions. This relative shift in supply toward the rental market is interpreted as evidence consistent with the buy-to-let motive documented at the household level and as potentially having benign implications for housing affordability through increased rental supply.

Scope Conditions

All household-level findings are conditional on the German institutional setting: Germany’s combination of a low-homeownership norm, substantial tax incentives favoring rental properties, triennial household survey data spanning one pre- and one post-QE wave, and a housing boom that was decoupled from household credit prior to 2015. The regional results apply to 401 German administrative regions (Kreise) over 2010–2017, using exposure instruments that are argued to capture rental-market tightness or depth rather than direct household bond holdings.

In depth

Q1. What is the housing portfolio channel of QE transmission, and how does it differ mechanically from the credit channel?

A: In the housing portfolio channel, the ECB’s bond purchases reduce the net supply of bonds available to private investors, raising bond prices and reducing expected bond returns. Under the assumption that bonds and houses are substitutes in household portfolios, households with larger initial bond positions rebalance toward housing to restore their target allocation, bidding up house prices. This mechanism operates through changes in risk premia rather than through future short-term rates or bank reserves and loan supply. The credit channel, by contrast, operates through increased bank reserves enabling expanded mortgage lending. The authors show empirically that the two channels operate in parallel and independently, but that greater prior credit access and post-QE mortgage credit growth do not amplify the portfolio rebalancing effect.

Q2. What is the key exposure variable and why is it a valid identification strategy?

A: The exposure variable is each household’s 2014 (pre-QE) share of total wealth invested in bonds, including both direct holdings and indirect holdings via mutual funds and insurance companies. The logic, drawn from the bank-portfolio-rebalancing literature (Rodnyansky and Darmouni, 2017; Luck and Zimmermann, 2020) and from the authors’ own portfolio model, is that the larger a household’s bond share, the stronger its incentive to rebalance when the central bank reduces bond supply. Identification rests on the parallel-trends assumption: Figure 2 shows that before 2015, more- and less-exposed households (defined by a median split on the 2014 bond share) followed identical trends in second-home shares; the trends diverge sharply post-QE. Two indirect placebo tests corroborate this: using a spurious treatment variable (non-financial, non-housing asset share) and using a spurious outcome (change in non-financial, non-housing asset share) both yield null results.

Q3. What is the benchmark magnitude of the portfolio rebalancing effect and how robust is it?

A: A 10-percentage-point higher 2014 bond share (the approximate interquartile range) is associated with a 1.72–1.87 percentage point larger increase in the second-home portfolio share post-QE relative to the pre-QE period (Table 3, columns 1–2, significant at 1%). This result is robust to: scaling second-home shares by a model-consistent denominator (bonds + housing + deposits, column 3); using total housing wealth instead of second-home wealth alone (column 4); using the count of second homes rather than their value share to rule out valuation-effect confounds (column 5); using direct bond holdings without imputation, or indirect holdings only, as alternative exposure measures (columns 7–8, where the coefficients are if anything larger at 0.403 and 0.420); controlling for a broad set of time-varying household characteristics including net worth, age, household size, financial literacy, and risk aversion (Table 4, range 0.19–0.23); and explicitly controlling for the deposit-share post-interaction to rule out the negative interest rate policy as a driver (column 6, main bond coefficient unchanged at 0.122).

Q4. Do households with higher bond exposure also rebalance toward equities after QE?

A: No. Column (7) of Table 4 shows that households with larger ex-ante bond shares reduce their equity shares after QE adoption (coefficient: −0.042, significant at 5%). This rules out the interpretation that the second-home finding merely captures broad rebalancing toward all risky assets due to general risk-appetite changes. Combined with the evidence that deposit shares also decline (though not precisely estimated), the result implies that households fund second-home purchases by selling bonds, drawing down deposits, and reducing equity positions.

Q5. Which household characteristics amplify the rebalancing, and what do they reveal about the mechanism?

A: Five characteristics are shown to amplify rebalancing (Table 5 and Table 7): (1) being actively advised by a bank on asset allocation (triple interaction significant at 5%), consistent with banks that own real estate agencies steering clients toward property; (2) higher financial literacy (significant at 1%), consistent with more informed investors acting more quickly on QE-induced return differentials; (3) middle age (40–60), significant at 5%, but not older age (61+), ruling out bequest motives and pointing to households near their lifetime income peak optimizing their tax burden; (4) higher income per capita (positive and significant, especially among church members), reflecting the progressive German tax schedule that makes property-related deductions more valuable; and (5) church affiliation (the income-triple interaction is significant only for church members, who face an 8–9% church tax surcharge, amplifying the tax advantage of rental property ownership). Tenure status (renter vs. owner of main residence) shows that both groups rebalance, but the triple interaction is significant only at 10%, suggesting the effect is not confined to existing homeowners.

Q6. How is the buy-to-let motive established directly in the data, as opposed to vacation-home or commuter motives?

A: The authors use variation in whether households owned a second home and generated rental income from it before QE adoption (Table 8). Households that owned a second home and reported rental income in the pre-QE wave rebalance very strongly (coefficient 0.821 on Bonds × Post, significant at 1%). Households that owned a second home but did not generate rental income show a positive but imprecisely estimated coefficient (0.641, significant at 10% in a very small sub-sample of 138 households). Critically, households that did not own any second home prior to QE show a coefficient of essentially zero (0.000). This pattern establishes that rebalancing is driven by experienced buy-to-let investors rather than by households acquiring second homes for personal use, and is consistent with the income-seeking motive documented in the Australian context by Gargano and Giacoletti (2022).

Q7. How does the paper demonstrate that the effect is independent of the credit channel, while also acknowledging the credit channel operates?

A: The paper employs three complementary tests (Table 6). First, triple interactions of the Bonds × Post coefficient with pre-QE leverage (mortgage-to-housing-wealth ratio) and with post-QE mortgage credit growth are both statistically insignificant (columns 5–6 of Table 5), meaning that greater credit access does not amplify the bond-share rebalancing effect. Second, restricting the sample to households with zero mortgage credit growth between 2014 and 2017 leaves the main coefficient unchanged at 0.175 (column 1 of Table 6). Third, including the two credit variables as additional controls only marginally reduces the bond-share coefficient without affecting its significance (columns 2–3 of Table 6). At the same time, column 3 of Table 6 shows that mortgage credit growth does have its own statistically significant positive effect on second-home shares (coefficient 0.009, significant at 1%), confirming a separate, independently operating credit channel.

Q8. How is regional exposure to the channel proxied, given that household survey data cannot be aggregated to the regional level?

A: Because the 1,651-household panel provides only 3–4 observations per region on average across 401 German Kreise, the authors cannot construct representative regional averages of household bond shares. Instead, they use the pre-QE (2008) share of refugees housed in independent accommodation in each region as developed by Bednarek et al. (2021), arguing that a larger refugee share creates tighter rental housing market conditions and therefore makes buy-to-let investment more attractive. For robustness, they also use the 2011 census share of renters in each region as an alternative measure of rental market depth. Both regional exposure variables take higher values in urban areas (refugee share: 21% urban vs. 10% rural; renter share: 70% urban vs. 46% rural), consistent with household-level rebalancing being stronger in urban regions.

Q9. What are the quantitative effects on regional rental yields, house prices, and rents?

A: Table 9 shows that a one-standard-deviation increase in QE (approximately 4.3 percentage points higher ECB debt securities-to-GDP ratio) reduces the rental yield in a region at the 75th percentile of the refugee-share exposure distribution relative to the 25th percentile by 2 basis points per year (using the refugee share) to 12 basis points per year (using the renter share). Comparing the 5th vs. 95th percentile of exposure, the yield differential is 5–24 basis points per year. Over the full 2014–2017 QE expansion (from 7% to 24% of GDP), the cumulative implied rental yield decline at the interquartile range of exposure is 8 to 48 basis points—sizable relative to the average regional decline of 140 basis points. House prices increase more than rents in more exposed regions. Using the Campbell-Shiller decomposition, about 70% of return variation is attributable to future price-to-rent increases, 36% to lower future rent growth (consistent with more rental supply), and only 5% to discount rate differentials.

Q10. What do the listing data reveal about the supply implications of the channel?

A: Table 10 shows that QE reduces both sale and rental listings in more exposed regions (both significant at 1%), consistent with the aggregate national decline visible from 2015 onward. Critically, the ratio of sale listings to rental listings declines significantly in more exposed regions: sale listings fall more than rental listings (columns 3 and 6, significant at 1% with both exposure measures). This relative shift implies that the share of properties available for rent increases relative to properties available for sale in regions more exposed to the portfolio rebalancing channel, providing evidence of an expanded rental supply. This finding is interpreted as a potentially beneficial side effect of QE-induced buy-to-let investment for housing affordability, to the extent that a larger rental supply mitigates rent increases even as house prices rise.

Q11. What is the theoretical model underlying the empirical analysis?

A: The model (Appendix C) features a representative local household with mean-variance preferences managing a portfolio of bonds, housing, and cash (equities are omitted for tractability). Preferred habitat investors segment both the national bond market and the local housing market. QE reduces the fixed net supply of bonds, raising bond prices and reducing expected bond returns. Under the substitutability of bonds and houses, households rebalance toward housing to restore optimal allocation, bidding up house prices; the larger the initial bond share, the larger the required rebalancing. Housing supply constraints determine how much rebalancing depresses expected housing returns (rental yields). The model does not unambiguously predict the response of the cash (deposit) share, motivating the empirical investigation reported in column (6) of Table 3.

Q12. What are the aggregate household balance sheet patterns consistent with the individual-level results?

A: Table 1 shows that Germany’s aggregate household real estate share rose from 55% of total assets in 2014 to 56–57% in 2017–2018, while the bond share declined by roughly 0.5 percentage points. The homeownership rate declined by about 2 percentage points over the sample period (from 52.5% in 2014 to 51.4–51.5% in 2017–2018), consistent with an increasing share of landlords and renters—which is compatible with the buy-to-let mechanism since more than 60% of German renters lease from other households. Household leverage also declined (loans-to-assets from 13% in 2014 to 12% in 2017), consistent with portfolio rebalancing rather than credit-driven housing acquisition. The deposit share remained constant over the period, weighing against the negative-interest-rate policy as a driver of portfolio rebalancing.

Key Concepts

Housing portfolio channel of QE transmission: The paper’s central concept—a mechanism by which central bank bond purchases (QE) induce households holding bonds to rebalance their portfolios toward second homes held for investment (buy-to-let), operating through changes in risk premia (bond prices and expected returns) rather than through bank lending channels or future short-term interest rates.

Ex-ante bond share (QE exposure measure): Each household’s share of total wealth invested in bonds (direct holdings plus indirect holdings via mutual funds and insurance) measured in the 2014 pre-QE survey wave. Used as a continuous household-level treatment intensity: the larger this share, the stronger the portfolio pressure to rebalance when the ECB reduces bond supply to the private sector. Corresponds roughly to 10 percentage points per interquartile range.

Buy-to-let motive: In the paper’s usage, the investment purpose of purchasing second homes specifically to rent them out—or to declare them for future letting—in order to exploit Germany’s substantial tax advantages for rented properties (depreciation allowances, deductibility of mortgage interest, management costs, and property taxes against rental income), which are unavailable for owner-occupied primary residences. Distinguished from vacation-home or commuter motives by the presence of pre-QE rental income.

Segmented housing markets / preferred habitat investors: Assumptions embedded in the paper’s theoretical model (following Flavin and Yamashita, 2002; Gete and Reher, 2018; Greenwald and Guren, 2021) that local real estate markets are insulated from national or international housing markets, and that some investors have a binding preference to hold bonds or local housing, so that QE-induced price changes in the bond market are not fully arbitraged away by shifting into liquid alternatives.

Parallel trends (DiD validity): The identifying assumption that, absent QE, households with larger and smaller initial bond shares would have followed the same trajectory in their second-home portfolio shares. The paper documents this graphically using all three survey waves (Figure 2) and supports it with two indirect placebo tests involving unrelated treatment and outcome variables.

Regional rental yield: The rent-to-price ratio at the regional (Kreise) level, derived from Bulwiengesa data. Used as the primary regional outcome variable because it jointly captures discount rate, rent-growth, and price-to-rent dynamics. A Campbell-Shiller decomposition decomposes its predictive content into three components: discount rates (5%), future rent growth (36%), and future price-to-rent ratio changes (70%) in the German regional panel.

Sale-to-rental listing ratio: The ratio of sale listings to rental listings for apartments on Immoscout 24, used as a quantity-side outcome variable. A decline in this ratio in more-exposed regions is interpreted as evidence of a relative increase in rental supply, consistent with the buy-to-let motive and with potentially beneficial implications for housing affordability.

Church tax (Kirchensteuer): A German institutional feature—formally affiliated church members pay an additional 8–9% surcharge on their regular income tax bill (varying by state). Because the tax advantage of owning rental property is proportional to the marginal tax rate, church members face a higher effective marginal tax rate and thus derive larger tax benefits from buy-to-let investment, producing stronger QE-induced portfolio rebalancing for this sub-group.

A Tale of Two Bailouts and Their Impact on Subprime Consumer Debt

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

This paper examines the effects of the Troubled Asset Relief Program (TARP) and the Paycheck Protection Program (PPP)—two government bailout programs during the Global Financial Crisis and the COVID-19 crisis, respectively—on subprime consumer debt, using over 11 million credit bureau observations of individual consumer debt combined with banking, bailout, and local market data. TARP and PPP are found to have opposite effects: subprime consumers in markets with more TARP institutions experienced significantly increased debt burdens following the bailouts, while PPP was associated with reduced subprime consumer debt. Both programs are treated as quasi-natural experiments due to their rapid, largely unanticipated assembly. The findings yield policy implications regarding bailout structures and the conditions attached to bailout funds.

In depth

Q1. What are the two bailout programs studied and why are they treated as natural experiments?

TARP (2008) and PPP (2020) are treated as quasi-natural experiments because they were assembled quickly during crisis conditions and were largely unanticipated, providing relatively exogenous financial shocks to markets based on the presence of eligible institutions, rather than on prior local demand for credit. Both programs had distinct structures and intended targets—TARP aimed at stabilizing financial institutions directly, while PPP aimed at supporting small business payrolls to prevent employment losses—making their differential effects on subprime consumer debt informative about the channels through which bailout design matters.

Q2. How did TARP affect subprime consumer debt and why?

Subprime consumers in markets with more TARP institutions had significantly increased debt burdens following TARP, consistent with a channel in which bank stabilization via TARP relaxed credit supply conditions (especially for lower-quality borrowers) or with a moral hazard channel in which TARP-recipient banks extended credit more aggressively knowing they had government backing. Subprime mortgages played a central role in the buildup to the GFC, growing from 2.5% to 8.4% of mortgage balances outstanding between 2001 and 2007; the finding that TARP increased rather than reduced subprime debt burdens raises concerns about whether bank stabilization programs sufficiently constrain the subsequent lending behavior of recipient institutions.

Q3. How did PPP affect subprime consumer debt and why?

PPP was associated with reduced subprime consumer debt, consistent with a channel in which the payroll support prevented the expected wave of unemployment-driven debt distress and credit score deterioration that would otherwise have converted prime consumers into subprime borrowers during the COVID-19 crisis. Prior to PPP, the COVID-19 recession—with unemployment peaking at 14.7% in April 2020—was expected to cause a ballooning of subprime consumer debt; the failure of this ballooning to materialize and the actual decline in subprime debt is attributed in part to PPP’s employment and income support function.

Q4. What are the policy implications for bailout design?

The opposite effects of TARP (which increased subprime debt) and PPP (which reduced it) yield policy implications for bailout structures and the conditions attached to bailout funds: bailouts directed at banks without explicit restrictions on subsequent lending behavior may inadvertently stimulate the accumulation of high-risk household debt, while bailouts directed at supporting household incomes and employment may reduce systemic credit risk. These findings suggest that the distribution channel of bailout funds (through banks vs. directly to households and employers) has first-order effects on the resulting debt accumulation and credit risk in the household sector.

Key concepts

TARP (Troubled Asset Relief Program) : the 2008 U.S. government program that provided capital injections to financial institutions during the Global Financial Crisis; found in this paper to be associated with increased subprime consumer debt burdens in affected markets. PPP (Paycheck Protection Program) : the 2020 U.S. government program that provided small business loans/grants to support payrolls during the COVID-19 crisis; found in this paper to be associated with reduced subprime consumer debt, opposite to TARP’s effect. subprime consumer debt : obligations of consumers with low credit scores; the paper’s key outcome measure; elevated levels associated with systemic credit risk (as seen in the buildup to the GFC) and used as a barometer of financial vulnerability in the household sector.

Bank Opacity and Safe Asset Moneyness

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

This paper studies when a bank is more effective as a supplier of privately produced money-like safe assets (repo, commercial paper), finding that a bank produces safer, more liquid assets when (1) its return on equity (ROE) is relatively lower, and (2) it is relatively more opaque about its balance sheet. A three-period model is presented in which safe asset investors focus on the left tail of the bank asset value distribution that ultimately determines the debt’s moneyness: a higher ROE signals riskier investment activities with higher return volatility, exposing investors to greater left-tail risk and lowering the moneyness of the bank’s debt. Bank opacity mitigates the strength of the ROE-moneyness relationship because opacity limits investors’ ability to infer asset risk, making it optimal for the banking system to maintain a certain level of opacity. Empirical tests on dealer banks and money market mutual funds’ (MMFs) funding relationships confirm that higher ROE leads to MMF withdrawal due to lower moneyness of safe assets.

In depth

Q1. Why does higher ROE lower the moneyness of a bank’s safe assets?

Higher ROE signals that a bank is more likely to be engaging in riskier investment activities with higher return volatility, which exposes safe asset investors—who care almost entirely about the left tail of the bank asset value distribution—to a higher likelihood of complete insolvency, lowering the moneyness of the bank’s debt. The intuition is asymmetric: for a debt holder, the upside is limited to the contracted interest rate, while the downside involves potential total loss if the bank becomes insolvent. A higher ROE thus signals higher left-tail risk rather than higher credit quality from the safe asset investor’s perspective, contradicting the positive signal that higher ROE sends to equity investors.

Q2. How does the model formalize the moneyness concept?

In the three-period model, the bank issues a money-like safe asset (deposit) to finance itself, and the household holds it both to transfer wealth intertemporally and to use it as a medium of exchange; moneyness captures both the safety and the liquidity of the asset as experienced by the holder. The model embeds the Gorton-Pennacchi (1990) and Dang-Gorton-Holmström (2012) notion that money-like assets are purposefully designed to be information-insensitive, so that investors have little incentive to acquire private information about them. The model shows how ROE—a piece of public information—nonetheless predicts moneyness and triggers withdrawal.

Q3. Why is bank opacity an equilibrium feature that improves moneyness?

Bank opacity mitigates the predictive power of ROE for the moneyness of safe assets because if investors cannot observe detailed information about the bank’s asset side, they cannot fully infer the riskiness of the investments backing the bank’s debt from the ROE signal, making it optimal for the banking system to maintain a certain level of opacity to preserve the information-insensitive character of its safe assets. This result is consistent with Dang et al. (2017)’s argument that banks are intentionally opaque: opacity is not merely a byproduct of complexity but a deliberate design feature that preserves the moneyness of privately produced safe assets.

Q4. What is the empirical evidence using MMF and dealer bank data?

Empirical tests using data on MMF funding of dealer banks confirm that higher bank ROE leads to MMF withdrawal from the bank, consistent with the model’s prediction that higher ROE reduces the moneyness of the bank’s safe assets for institutional investors; the relationship is attenuated for more opaque banks, consistent with the model’s opacity mechanism. The wholesale banking sector (dealer banks and institutional investors like MMFs) is the natural testing ground because its participants are more informed than retail depositors and therefore more sensitive to signals about the riskiness of the assets backing the bank’s debt.

Key concepts

moneyness of safe assets : the degree to which a financial asset is safe and liquid—traded at par with no questions asked; determined in this paper by how well a bank’s debt protects investors against the left tail of the bank asset value distribution. return on equity (ROE) as a risk signal : the paper’s key insight that, for safe asset investors (debt holders), higher bank ROE signals riskier investments with higher return volatility rather than lower credit risk; this contrasts with the positive signal ROE sends to equity investors. information-insensitive safe asset : a financial asset purposefully designed to be immune to private information acquisition by investors (Gorton-Pennacchi 1990; Dang et al. 2012); bank opacity preserves this property by limiting investors’ ability to infer asset-side risk from public signals.

Banking with Inside Money: An Efficiency Analysis

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

Layer 1: Overview

This paper demonstrates that the canonical efficiency result of Diamond and Dybvig (1983) — that banks using maturity transformation can decentralize the first-best risk-sharing allocation — breaks down when banking is conducted with inside money rather than real contracts. The paper constructs a minimal modification of the Diamond-Dybvig (DD) model in which output requires combining labor (supplied by workers) and technology (owned by entrepreneurs), so that bank deposits arise as inside money created ex nihilo when loans are extended, and shows three results: (1) non-contingent nominal demand deposits cannot reproduce the first-best allocation, because the constraint that nominal deposits earn the same real return as the productive technology prevents banks from providing state-contingent real payoffs; (2) state-contingent deposit rate contracts, which are proposed as an efficiency fix in the DD tradition, also fail to reach the first best — Proposition 2 establishes that contingent deposit rates produce a consumption allocation inconsistent with efficiency (specifically, aggregate consumption at each date cannot satisfy the efficiency ratio required by equation 8), and the allocation under contingent contracts is no better in welfare terms than the non-contingent baseline; (3) allowing entrepreneurs to liquidate loans before maturity (Proposition 3) likewise leaves the equilibrium inefficient, because competition equalizes deposit and lending rates in a way that prevents supply of goods from matching the efficient schedule across periods. The paper then characterizes when central bank intervention can improve welfare and shows that outside money is not demanded in the baseline economy, limiting the central bank’s leverage, and that the lender-of-last-resort function can prevent bank runs even when efficiency is unachievable.

In depth

Q1. What is the core model and how does inside money arise?

The paper adds a single departure from the original DD real model: output requires labor from workers and technology from entrepreneurs, which introduces a motive for money to be valued — entrepreneurs borrow units of account (inside money/deposits) from banks at date 0 to pay workers’ wages, and these deposits then circulate as a means of payment for consumption goods at dates 1 and 2. Unlike the outside-money models in Allen and Gale (1998), Skeie (2008), and Allen et al. (2014), inside money is created ex nihilo on the bank’s balance sheet when loans are extended — deposits do not represent a transfer of pre-existing funds but are liabilities created through lending. Banks in this model are price-takers and cannot take direct decisions on real investments or liquidations, which are the responsibility of entrepreneurs. This is the key distinction from the DD and subsequent literature: it is the production of deposits in the provision of loans that generates inside money, and it is the impossibility of making these nominal claims produce state-contingent real payoffs that prevents efficiency.

Q2. Why can’t non-contingent nominal deposits achieve the first best?

In any competitive equilibrium with valued deposits, the no-arbitrage condition requires that the real return on deposits equals the real return on the productive technology R in each period, so the ratio of patient-to-impatient consumption (c₂/c₁) for workers must equal R — but the first-best allocation requires c₁ and c₂ to satisfy the planner’s Euler equation u′(c₁) = Ru′(c₂), which for coefficient of relative risk aversion greater than 1 implies 1 < c₁*/c₂* < R, not c₂/c₁ = R.** This is formalized by comparing the equilibrium allocation (Proposition 1 and the Corollary) — where workers’ consumption satisfies cᵢW(1) = 1/p₁ and cᵢW(2) = R/p₁ with p₁ ∈ (0.5, ∞) — against the efficiency condition (equation 8). Because the real value of deposits is pinned by the price level in the goods market, and competitive banks have no power to engineer the price adjustments needed to create state-contingency, the nominal deposit contract is generically inefficient. This contrasts with Allen and Gale (1998) and Skeie (2008), where central bank control over either prices or real investment liquidation allows efficient outcomes.

Q3. What is the formal result on state-contingent deposit contracts?

Proposition 2 establishes that introducing contingent deposit rates (paying a higher rate to impatient depositors, id₂(1) > id₂(2)) yields an aggregate allocation in which total consumption at date 1 is at most 2 (the liquidation value) and total consumption at date 2 is at least 2R — the same aggregate feasibility constraints as the non-contingent case — and this allocation is incompatible with efficiency and no better in welfare terms than the baseline. The reason is structural: for goods to be supplied at both dates 1 and 2, the rate id₂(2) must satisfy id₂(2)·(P₁/P₂) < R ≤ id₂(1)·(P₁/P₂), but this means only impatient entrepreneurs supply goods at date 1, leaving the aggregate supply schedule identical to the non-contingent case. Even if banks had perfect information about depositor types and could implement contingent contracts without incentive compatibility concerns, the first-best allocation would remain outside the consumption possibility set of the competitive equilibrium.

Q4. What is the result on early loan liquidation?

Proposition 3 shows that allowing entrepreneurs to choose how much of their loan to repay early (at date 1 versus date 2) produces a unique equilibrium in which entrepreneurs are indifferent about when to liquidate, equilibrium deposit and loan rates satisfy id₁ = ib₁ = 0 and (1 + ib₂)(P₁/P₂) = (1 + id₂)(P₁/P₂) = R, and the resulting allocation remains inefficient. The key constraint is unchanged: competition across banks drives both deposit and lending rates to equalize in real terms, so the supply of goods at each date is still not controlled by the bank and cannot reproduce the first-best schedule. Allowing borrowers to prepay their loans does not alter the fundamental tension between fixed nominal contracts and state-contingent real outcomes.

Q5. When can banks be welfare-dominated by bilateral trade?

In the symmetric equilibrium (P₁ = D₁), the banking allocation gives E(uB) = λu(1) + (1−λ)u(R), which is welfare-dominated by the bilateral labor market allocation E(uLM) whenever the coefficient of relative risk aversion and/or the technology return R exceed a threshold — specifically, when agents are risk averse enough that the midpoint consumption available under bilateral bargaining (2R/(R+1)) is preferred to the lottery {1 with probability λ, R with probability 1−λ} — contradicting the presumption that bank intermediation is necessarily superior to direct contracting. This result, formalized by condition (41), implies that the social value of banking as an institution depends on the degree of risk aversion and the illiquidity premium R: the banking allocation is preferred when agents are relatively risk tolerant and/or R is large (so the lottery’s spread is attractive), but bilateral trade may dominate when agents are risk-averse and R is modest.

Q6. What role can central banks play and what is the lender-of-last-resort result?

The paper shows that in the baseline nominal economy, outside money is not demanded by any agent — deposits dominate cash in rate of return and the interbank payment flows net to zero — so the central bank has no leverage to affect real allocations through open-market operations; efficiency is out of reach even for a central bank. However, the paper identifies a limited but important role for central bank intervention: the lender-of-last-resort function can prevent bank runs that would otherwise be self-fulfilling equilibria in the model, even though the central bank cannot restore the first-best allocation. This is because the existence of an emergency liquidity backstop eliminates the coordination failure that makes runs self-fulfilling, without requiring the central bank to replicate the state-contingent real payoffs needed for efficiency. A central bank could potentially be incorporated into an extended model with an uneven distribution of payment flows across banks (creating a demand for reserves), but the paper argues that even then, competition across banks would still prevent contingent deposit rates from achieving efficiency.

Key Concepts

inside money : bank-created deposits that arise ex nihilo when loans are extended to borrowers and circulate as means of payment between agents; the paper’s key departure from the prior banking literature, which modeled deposits as outside money (central-bank-issued fiat money) intermediated by banks rather than money created through lending.

consumption possibility set : the set of feasible allocations achievable by the competitive equilibrium with inside-money banking; the paper’s central result is that the efficient first-best allocation — satisfying u′(c₁*) = Ru′(c₂*) — lies outside this set, so the inefficiency is not correctable by improving incentive design within the existing contract space.

nominal deposit contract : a demandable deposit that specifies a fixed nominal interest rate independent of the realization of individual liquidity preference shocks; the paper’s analysis shows that such contracts cannot produce the state-contingent real payoffs required for efficient risk-sharing in an inside-money economy, even when supplemented with contingent rates or early loan liquidation.

lender of last resort : the central bank’s capacity to provide emergency liquidity to banks facing runs by coordinating expectations away from the bank-run equilibrium; the paper’s limited positive result for central bank policy — it can prevent runs even when it cannot achieve efficiency.

Capital Income Taxation and Self-Fulfilling Aggregate Instability

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

Layer 1: Overview

This paper overturns the longstanding consensus established by Schmitt-Grohé and Uribe (1997) that relying on capital income tax adjustments to balance the government budget immunizes the economy against self-fulfilling aggregate instability. The key departure from the prior literature is endogenous capital utilization: when the capital income tax rate adjusts to close budget imbalances and capital utilization is an optimal decision by households, a “fiscal increasing returns” mechanism emerges in which higher economic activity lowers the tax rate, raises the after-tax return to capital, and induces further expansion — rendering the economy prone to sunspots-driven fluctuations. Calibrated to the United States, United Kingdom, and Japan using effective tax rates and public debt-to-GDP ratios, the paper finds that all three economies lie within the indeterminacy region under their current capital income tax rates and capital depreciation allowances of approximately 0.2; stabilization would require raising the depreciation allowance rate from 0.2 to 0.76 or reducing income tax rates by 39–52 percent. Capital depreciation allowances serve as a stabilization device: full allowances (allowance rate = 1) make indeterminacy entirely impossible regardless of the tax rate, because they extinguish the fiscal increasing returns mechanism, and the paper also shows analytically that public debt can be destabilizing rather than stabilizing when capital taxes are used for fiscal adjustment.

In depth

Q1. What is the fiscal increasing returns mechanism that overturns the Schmitt-Grohé-Uribe result?

When the government adjusts the capital income tax rate to balance the budget, higher labor input raises output and the capital tax base, allowing a lower tax rate; under endogenous capital utilization, this triggers an additional channel in which a lower after-tax depreciation cost induces firms to utilize capital more intensively, further raising the effective capital stock and output — generating fiscal increasing returns to scale and a factor share redistribution from capital to labor that together make indeterminacy possible. In log-linearized terms, the effective output-labor elasticity in the equilibrium aggregate production function exceeds unity for tax rates in the interval (τ̄, τ̂) where τ̄ = ρ/(ρ+δ) and τ̂ is the Laffer-curve peak, and this greater-than-unity elasticity is the formal condition for indeterminacy (Corollary 1). With a constant utilization rate as assumed in prior work, both the factor share redistribution and fiscal increasing returns effects vanish, the effective output-labor elasticity falls below unity, and indeterminacy becomes impossible — confirming that endogenous capital utilization is the essential ingredient.

Q2. What are the formal conditions for indeterminacy under the baseline capital tax rule?

Proposition 1 establishes that the fiscal policy with capital income taxation induces indeterminacy of equilibrium if and only if the long-run capital income tax rate τk lies strictly in the open interval (τ̄, τ̂), where τ̄ = ρ/(ρ+δ) and τ̂ is the unique Laffer-curve peak. Under the standard calibration (ρ = 0.04, δ = 0.1, α = 0.3), this interval is (0.286, 0.717) — a wide range covering the effective capital income tax rates of the U.S., UK, and Japan. The determinant of the Jacobian of the linearized dynamic system is positive and the trace is negative over this interval, implying that both eigenvalues are negative, which is the condition for indeterminacy with one predetermined variable (capital) and one jump variable (marginal utility of income).

Q3. How do capital depreciation allowances serve as a stabilization device?

When the taxable capital income base is reduced by a fraction γ ∈ [0, 1] of depreciation expenses, the effective degree of fiscal increasing returns to scale decreases strictly with γ, and the lower bound of the indeterminacy interval τ̄D strictly rises with γ; with full depreciation allowances (γ = 1), the quadratic equation characterizing the lower bound has a repeated unit root, the indeterminacy interval becomes empty, and multiplicity of equilibria is entirely impossible regardless of the capital income tax rate. Corollary 2 formalizes this result analytically. The intuition is that depreciation allowances reduce the procyclicality of the effective tax burden on capital, so the after-tax return to capital responds less strongly to activity, weakening the self-fulfilling loop. Partial allowances — even well below γ = 1 — can sufficiently shrink the indeterminacy region to require implausibly high tax rates for instability.

Q4. What is the role of public debt and what new result does the model deliver?

Contrary to the established view that public debt can serve as an automatic stabilizer that exempts balanced-budget fiscal policy from beliefs-driven instability (Schmitt-Grohé and Uribe 1997, Huang et al. 2018), this paper shows that public debt can be destabilizing when capital income taxes adjust to balance the budget: a higher public debt-to-GDP ratio expands the indeterminacy region, and this destabilizing effect is amplified when capital depreciation allowances are low. Figure 5 in the paper illustrates numerically that raising the public debt-to-GDP ratio from an average of 0.975 (US/UK average) to 1.429 (Japan) dramatically widens the indeterminacy region, particularly at low depreciation allowance rates. This novel result — that public debt destabilizes rather than stabilizes under capital income tax adjustment — constitutes a third main contribution of the paper alongside the indeterminacy result and the stabilization role of depreciation allowances.

Q5. What are the quantitative results for the US, UK, and Japan?

Under the calibrated depreciation allowance rate of approximately 0.2 (the GDP-weighted European average from D’Erasmo et al. 2017, also consistent with the US), all three large economies lie within the indeterminacy region at their current effective income tax rates; stabilization requires either raising the depreciation allowance rate to 0.76 for all three, or reducing income tax rates by 47% for the US, 52% for the UK, and 39% for Japan from their calibrated levels while holding depreciation allowances at 0.2. Less dramatic combination policies also work: for the US, a 10% income tax cut combined with raising the depreciation allowance to 0.67 would suffice, as would a 5% tax cut combined with raising the allowance to 0.70. These calculations are calibrated to effective factor income tax rates from Mendoza et al. (1994) updated to 1996 and public debt-to-GDP ratios from OECD Economic Outlook (2014).

Q6. How does the paper relate to and contribute to the broader indeterminacy literature?

The paper’s mechanism — fiscal increasing returns arising from the interaction of optimal capital utilization and capital income taxation — is novel relative to both strands of the indeterminacy literature: unlike Benhabib-Farmer-style models that require the aggregate production function to have increasing returns as a primitive assumption, and unlike the Schmitt-Grohé-Uribe labor-tax indeterminacy that also does not require increasing returns but found capital taxation immune, this paper shows that increasing returns can emerge endogenously from a constant-returns-to-scale production technology via fiscal policy, requiring no externalities or other non-standard features. The mechanism provides a policy-based micro-foundation for aggregate increasing returns that resolves the empirical criticism of the prior indeterminacy literature; it also distinguishes the result from Huang et al. (2018), who showed that endogenous capital utilization under labor income tax adjustment raises indeterminacy likelihood but leaves the production function at constant returns to scale.

Key Concepts

fiscal increasing returns : the mechanism in this paper whereby higher economic activity lowers the capital income tax rate (via a higher tax base), raises the after-tax return to capital, and induces greater capital utilization and further output expansion; operationally defined by the effective output-labor elasticity exceeding unity in the equilibrium aggregate production function.

equilibrium indeterminacy : the existence of multiple rational-expectations equilibria converging to the same steady state, arising from the fiscal increasing returns mechanism and permitting self-fulfilling sunspots fluctuations unrelated to economic fundamentals; characterized by both eigenvalues of the Jacobian being negative (both predetermined structure of the dynamic system).

capital depreciation allowance : the fraction γ ∈ [0, 1] of capital depreciation costs deductible from the taxable capital income base; the stabilization device the paper identifies, which works by attenuating the procyclical component of the effective capital tax burden and thereby reducing the fiscal increasing returns to scale.

factor share redistribution : in this paper, the shift of the effective factor income share from capital to labor that results from endogenous capital utilization interacting with the capital tax rule; contributes to indeterminacy by raising the effective output-labor elasticity above the share of capital in the production function.

Central Bank Digital Currency with Collateral-Constrained Banks

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

The paper analyzes the implications of introducing a retail central bank digital currency (CBDC) that competes with commercial bank deposits for household liquidity, in a model where banks must post government bonds as collateral to access central bank lending. The authors revisit Niepelt’s (2022) “equivalence of payment systems” result and find that equivalence survives even under a collateral constraint: the central bank can still offer loans to banks that replicate the no-CBDC equilibrium allocation, but at a lending rate lower than Niepelt’s unconstrained rate, because tighter terms are needed to incentivize sufficient loan uptake when banks must redirect portfolio holdings toward government bonds to qualify. A structural cost remains: banks must hold government bonds as collateral at the expense of extending credit to firms, so equivalence in allocation does not imply full neutrality — banks’ business models and the government’s intermediation role change even when aggregate output and prices are unchanged. In the dynamic extension where the central bank does not sterilize the CBDC introduction, banks respond by narrowing deposit spreads to attract inflows, with the result that a CBDC ramp-up to 5 percent of steady-state output expands rather than contracts bank credit to firms.

In depth

Q1. What is the equivalence of payment systems result and how does the collateral constraint change it?

Brunnermeier and Niepelt (2019) and Niepelt (2022) established that the central bank can neutralize the real effects of CBDC introduction by lending to banks at an appropriate rate to replace lost deposit funding, a result the present paper revisits by adding a collateral requirement on central bank lending — specifically, that banks must hold eligible government bonds up to a fraction θb of their central bank loan value. Under this constraint, Proposition 1 shows that equivalence survives: there exists a central bank lending rate that replicates the no-CBDC equilibrium allocation and price system. However, this lending rate is lower than Niepelt’s unconstrained rate by a factor increasing in the restrictiveness of the constraint (lower θb requires a lower lending rate), because when banks are collateral-constrained, cheaper terms are needed to induce them to borrow enough from the central bank to offset deposit outflows.

Q2. What is Corollary 1 and why does “full neutrality” fail?

Corollary 1 states that even when the central bank achieves allocation equivalence by setting the appropriate lending rate, banks must redirect portfolio holdings from firm loans to government bonds to meet the collateral requirement — crowding out bank credit to firms by an amount equal to the bond uptake, with the crowding-out diminishing as the collateral constraint becomes less restrictive (higher θb). This is the sense in which “full neutrality” fails under the collateral constraint: aggregate output and prices are unchanged, but the composition of credit changes — banks extend less to firms and hold more government bonds — and the government or household sector must absorb the gap in firm financing. In the limiting case where CBDC and deposits are equally valuable to households (λ = 1), the government alone compensates for the reduction in bank loans, effectively expanding its own intermediation role.

Q3. What does the dynamic extension show about bank disintermediation?

Simulating a gradual and near-permanent increase in CBDC to 5 percent of steady-state output without central bank sterilization, the paper finds that banks respond by narrowing their deposit interest spread to attract deposit inflows, such that total deposits do not fall and bank loans to firms expand rather than contract — the opposite of the disintermediation hypothesis. The mechanism relies on the assumption that banks have market power in their regional deposit markets (each bank is a monopsonist): in response to CBDC competition, the bank voluntarily reduces the rent it extracts on deposits (the spread between the risk-free rate and the deposit rate), attracting more deposit inflows. This deposit inflow, combined with central bank loan uptake, expands the bank’s balance sheet and increases credit extension to firms. The result stands in contrast to models with competitive deposit markets, where banks cannot respond to CBDC competition through deposit pricing.

Q4. What changes even if credit is not reduced?

Even when the dynamic model shows credit expansion rather than contraction, the paper establishes that CBDC introduction alters banks’ balance sheet composition and business model: banks shift toward holding more government bonds and away from firm loans, the government assumes a larger credit intermediation role, and the aggregate distribution of capital ownership changes — constituting the form of non-neutrality that survives even when total credit is unchanged. This is what Corollary 1 calls the failure of “full neutrality”: the real allocation equivalence holds at the aggregate level, but the sectoral distribution of who provides credit to firms shifts from the banking sector toward the public sector. The paper interprets this as a structural consequence of the collateral requirement on central bank lending that is absent in the frictionless equivalence benchmark.

Key concepts

equivalence of payment systems : the theoretical result (from Brunnermeier-Niepelt 2019 and Niepelt 2022) that the central bank can ensure the same equilibrium allocation whether or not CBDC exists, by adjusting its lending terms to banks; this paper revisits and extends the result to environments with a collateral constraint.

collateral constraint (θb) : the requirement in this model that banks hold eligible government bonds as a fraction of the central bank loans they take on; adding this friction to Niepelt’s framework preserves equivalence in allocation but requires a lower central bank lending rate and crowds out bank loans to firms.

disintermediation : the concern that CBDC adoption would cause households to shift en masse from bank deposits to CBDC, reducing bank funding and contracting bank credit; the paper finds this does not occur in either the equivalence analysis or the dynamic extension.

monopsony in deposits : the market structure assumption that each regional bank is the sole deposit provider in its region, giving it pricing power over deposit rates; this is what enables banks in the dynamic model to narrow the deposit spread in response to CBDC competition, generating deposit inflows rather than outflows.

full neutrality : a stronger invariance result requiring that not only the equilibrium allocation but also banks’ balance sheet composition and business model are unchanged by CBDC introduction; the paper shows this fails under the collateral constraint even when allocation equivalence holds.

Central Bank Independence at Low Interest Rates

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

This paper constructs a new measure of political pressure on the Federal Reserve from textual analysis of Fed Chairs’ testimonies at Humphrey-Hawkins congressional hearings, and documents that the use of non-traditional monetary policy instruments at the effective lower bound (ELB) led to increased political criticism that predicts legislative actions threatening central bank independence. A model is developed in which the probability of the monetary authority’s future loss of independence is increasing in the use of non-traditional instruments, leading to attenuated monetary responses and higher inflation volatility. The attenuation can be mitigated under an institutional framework with clearly defined targets where the central bank is evaluated by how efficiently it achieves its goals.

In depth

Q1. What is the new measure of political pressure and what does it capture?

The paper constructs a measure of political pressure on the Federal Reserve by analyzing the evolution of critical questions and statements directed at Fed Chairs during semi-annual Humphrey-Hawkins Act testimonies to Congress, and finds that the number of critical statements specifically referencing non-traditional instruments increased significantly following the 2008 financial crisis. The measure tracks not only the volume of criticism but also its content—distinguishing criticism that specifically references the ELB tools from general discontent associated with low interest rate environments—allowing the paper to isolate the effect of unconventional policy use from other factors associated with the ELB subsample.

Q2. What is the empirical link between political criticism and legislative threats?

Following Hess and Shelton (2016), the paper analyzes bills introduced to Congress that threaten the powers of the Federal Reserve, and finds that the new measure of congressional criticism correlates highly with the introduction of such threatening legislation; moreover, the number of threatening bills specifically mentioning unconventional monetary policy is predicted by the amount of criticism referencing new policy tools. This provides an empirical chain from the use of non-traditional tools to political blowback to concrete legislative risk to Fed independence, motivating the theoretical model.

Q3. How does the threat to independence affect monetary policy in the model?

In the model, when the probability of future loss of independence is increasing in the use of non-traditional instruments, the optimal monetary authority chooses attenuated responses—using non-traditional tools less aggressively than the unconstrained inflation-minimizing policy would prescribe—thereby generating higher inflation volatility as a consequence of the political risk. The model captures the democratic reality that a central bank’s independence is inherently revocable by the legislature; a central bank that interprets congressional criticism as a credible signal of independence risk will internalize this constraint in its policy decisions.

Q4. How can institutional design mitigate the attenuation?

An institutional framework with clearly defined targets where the central bank is evaluated by how efficiently it achieves its goals—rather than by discretionary judgments about the appropriateness of its tools—mitigates the attenuation of monetary responses by narrowing the scope for politically motivated criticism of non-traditional instruments. If critics must evaluate the central bank against transparent targets, they face a higher evidentiary bar for threatening its independence when non-traditional tools are being used to meet those targets; this reduces the political risk of using such tools and restores the unconstrained optimal policy.

Key concepts

Humphrey-Hawkins testimony measure : the paper’s text-based measure of political pressure on the Fed, constructed from the volume and content of critical questions and statements directed at Fed Chairs during semi-annual congressional testimonies; found to predict threatening legislative actions. attenuation of monetary responses : the reduction in the aggressiveness of non-traditional monetary policy use relative to the unconstrained optimal policy, arising from the central bank’s internalization of the political risk of independence loss associated with using non-traditional instruments. clearly defined institutional targets : an institutional framework in which the central bank’s mandate is operationalized as specific measurable targets and the bank is evaluated by its efficiency in achieving them; shown here to mitigate the political risk of non-traditional instruments and restore optimal monetary responses.

Climate Policies, Macroprudential Regulation, and the Welfare Cost of Business Cycles

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

This paper embeds a carbon pricing sector into an extended DSGE model with a financial accelerator (E-DSGE) featuring heterogeneous firms, bank monitoring, and a borrowing-constraint amplification mechanism, then compares the welfare cost of business cycles under a cap-and-trade (CAT) scheme versus a carbon tax. The central result is that, in the presence of financial frictions, CAT generates lower welfare costs than a carbon tax: under TFP and risk shocks calibrated to US quarterly data, the baseline welfare cost of business cycles is 0.6178 percent of consumption under CAT versus 1.5231 percent under a carbon tax — roughly 2.5 times larger under a tax. The mechanism is that permit prices under CAT are procyclical (they fall in downturns, reducing firms’ carbon compliance burden precisely when balance sheets are most stressed), acting as an automatic stabilizer for financial amplification, while the carbon tax holds a fixed price and provides no such buffer. A countercyclical optimal carbon tax rule that reacts vigorously to output (optimal sensitivity parameter τ = 52.2245) can mimic CAT’s stabilizing behavior, but even optimized environmental rules leave a significant welfare gap between regimes. Reserve requirement macroprudential regulation narrows this gap substantially: a static 2 percent reserve requirement brings CAT welfare costs to 0.1957 and carbon tax costs to 0.3863; an optimal dynamic rule keyed to credit growth or asset price growth brings both regimes below 0.20, effectively aligning them. A deposit interest rate subsidy can also narrow the gap when combined with a dynamic subsidy rule, but a static subsidy actually worsens welfare costs because it raises leverage and amplifies shocks around a more fragile steady state.

In depth

Q1. What is the model structure and how does the environmental policy sector integrate with financial frictions?

The model is an E-DSGE built on the Christiano, Motto, and Rostagno (2014) financial accelerator framework, extended to include a carbon price instrument and heterogeneous firms that face both standard borrowing constraints and carbon compliance costs. There is a representative household and three firm sectors: a continuum of capital-producing entrepreneurs, retailers, and a goods sector. Banks extend loans to entrepreneurs at a spread over the risk-free rate; the external finance premium is endogenous because bank monitoring is costly and borrowers face costly state verification (as in Bernanke, Gertler, and Gilchrist, 1999). Environmental policy is introduced through a carbon permit or tax that enters firms’ marginal cost, so the carbon price affects both production decisions and the entrepreneur’s net worth, which in turn feeds back into the spread through the financial accelerator. Calibration uses US quarterly data (Table 1 in the paper), and the model is solved by log-linearizing around a deterministic steady state.

Q2. Why do financial frictions create a welfare advantage for cap-and-trade over carbon taxes?

Under a carbon tax, the tax rate is fixed by the regulator regardless of macroeconomic conditions; when a TFP or risk shock contracts output and reduces firm net worth, the fixed carbon cost amplifies the contraction by reducing the entrepreneur’s retained earnings, worsening the external finance premium, and deepening the financial accelerator loop. Under a CAT scheme, the equilibrium permit price is endogenous: it falls when aggregate activity and emissions decline, automatically lowering the compliance cost burden for firms at exactly the moment when balance sheets are most constrained. This procyclicality of permit prices functions as an automatic stabilizer, partially offsetting the financial accelerator’s amplification. The paper shows this via impulse response functions (Figures 1 and 2 in the paper) to TFP and risk shocks: under CAT, the responses of investment, bankruptcy, spread, and output are systematically more muted than under a carbon tax. Quantitatively, the baseline welfare cost of business cycles is 0.6178 percent of consumption under CAT versus 1.5231 percent under a carbon tax — a gap of nearly 0.91 percentage points of consumption.

Q3. How do optimal environmental policy rules affect welfare costs, and do they close the gap between regimes?

An optimal flexible CAT rule that allows permit prices to respond countercyclically to a macroeconomic indicator (net output) reduces welfare costs from 0.6178 to 0.4528 percent; an optimal flexible carbon tax rule reduces costs from 1.5231 to 1.1811 percent. In both cases, the optimal rule specifies vigorous countercyclical response: the optimal sensitivity parameter for the carbon tax rule is τ = 52.2245, meaning the tax rate must decrease sharply in recessions to mimic the automatic procyclicality of permit prices under CAT. Despite these improvements, the welfare gap between the two regimes persists even under optimal environmental rules: the optimized CAT still generates roughly 0.73 percentage points lower welfare costs than the optimized carbon tax. The paper concludes that countercyclical environmental policy can reduce but not eliminate the inherent stabilization advantage of CAT in the presence of financial frictions — because the fundamental mechanism (endogenous permit prices vs. fixed tax rate) cannot be fully replicated by a tax rule with a single output-gap indicator.

Q4. How do reserve requirement macroprudential regulations interact with the carbon pricing choice?

Introducing a static 2 percent reserve requirement (banks can loan out only 98 percent of deposits) already strongly reduces welfare costs and partially aligns the two regimes: CAT welfare costs fall from 0.6178 to 0.1957, and carbon tax costs fall from 1.5231 to 0.3863 (Table 5 in the paper). The mechanism is that reserve requirements limit bank credit expansion, lowering equilibrium leverage and reducing the severity of the financial accelerator — when firms’ balance sheets are less leveraged, adverse shocks cause smaller spirals in net worth and spreads. Dynamic reserve requirement rules — keyed to credit growth (optimal ψ_B ≈ 1.047) or asset price growth (optimal ψ_Q ≈ 0.722) — reduce welfare costs further, to 0.1207 under CAT and 0.2300 under a carbon tax with a credit-growth rule, effectively narrowing the gap to around 0.10 percentage points. The optimal policy mix (jointly optimizing both the macroprudential and environmental rules) achieves minimal additional improvement beyond the macroprudential optimum alone, suggesting the dominant stabilizing role is played by financial regulation rather than the choice of carbon pricing instrument when both are available and optimally calibrated.

Q5. How does macroprudential regulation affect the volatility of emissions and permit prices under each regime?

Table 6 in the paper reports coefficients of variation (CVE for emissions volatility, CVP_E for permit price volatility) across policy combinations. Under baseline CAT with no macroprudential regulation, CVE = 0 (the cap fixes aggregate emissions by construction) and CVP_E = 8.3578 — permit prices are very volatile. Adding a static reserve requirement reduces CVP_E to 2.5125; an optimal credit-growth rule reduces it to 1.0935, a reduction of nearly 87 percent from baseline. Under baseline carbon tax, CVP_E = 0 (the tax price is fixed by regulation) but CVE = 0.0574 — emissions are volatile. Adding a static reserve requirement reduces CVE to 0.0273; an optimal credit-growth rule reduces it to 0.0153. The paper interprets this as macroprudential regulation fostering convergence between the two instruments in their business cycle properties: it substantially stabilizes permit prices under CAT and substantially stabilizes emissions under a carbon tax, reducing the distinguishing uncertainty of each pricing approach. The optimal policy mix under a carbon tax with a dynamic subsidy achieves CVE = 0.0090 and CVP_E = 0.4956, showing that well-designed financial regulation can make a carbon tax nearly as emissions-stable as a CAT while also reducing permit price volatility.

Q6. What happens under an interest rate subsidy to depositors as an alternative macroprudential tool?

A static deposit interest rate subsidy of the welfare-maximizing level (1 percent) worsens welfare costs of business cycles — from 0.6178 to 1.1028 under CAT and from 1.5231 to 3.5597 under a carbon tax — because the subsidy moves the economy to a higher-leverage steady state, around which financial amplification is more severe (Table 7 in the paper). The intuition is that the subsidy encourages saving by raising the return on deposits, which raises equilibrium loan supply, which raises leverage; a more leveraged economy is more sensitive to adverse shocks. A dynamic subsidy rule that responds countercyclically to credit growth (optimal κ ≈ 1.319) mitigates this problem: it discourages saving when credit is expanding and encourages it when credit is contracting, partially stabilizing leverage dynamics. The dynamic subsidy reduces welfare costs substantially — to 0.2506 under CAT and 0.4706 under a carbon tax — and a joint optimization of the subsidy and the carbon pricing rule achieves 0.1926 under CAT and 0.4366 under a carbon tax with a dynamic subsidy. The authors note that the static subsidy result illustrates a general principle: macroprudential policies that move the steady state toward higher leverage can amplify cycle costs even while achieving efficiency gains around the steady state, and that distinguishing between steady-state and fluctuation welfare effects is essential when comparing such policies.

Q7. What are the main welfare and policy conclusions?

The paper establishes three conclusions. First, climate policy instrument choice has macroeconomic stabilization consequences in financially frictionous economies: CAT dominates a carbon tax for welfare when financial frictions are operative and macroprudential policy is absent or limited. Second, macroprudential regulation — particularly dynamic reserve requirement rules — is the more powerful tool for reducing the welfare cost of business cycles under both carbon pricing regimes, and can largely align the two regimes, making the instrument choice less consequential when macroprudential policy is well-calibrated. Third, the interaction between financial regulation and carbon pricing is non-trivial: the optimal sensitivity parameters for macroprudential rules differ depending on whether the economy uses CAT or a carbon tax, because the endogenous procyclicality of permit prices changes how financial shocks propagate through the economy.

Key concepts

financial accelerator: the mechanism by which adverse shocks to entrepreneurial net worth raise the external finance premium (the spread between the loan rate and the risk-free rate), reduce investment and output, further depress net worth, and generate amplified cycles; the core friction in the E-DSGE model and the channel through which carbon pricing affects welfare costs.

procyclical permit prices: the endogenous tendency of permit prices under a CAT scheme to fall when aggregate economic activity and emissions decline; the paper’s central mechanism through which CAT acts as an automatic stabilizer for the financial accelerator — permit prices fall precisely when firms’ balance sheets are most stressed, reducing compliance costs and partially offsetting amplification.

welfare cost of business cycles (Lucas measure): the percentage of consumption that a representative household would be willing to give up to move from a world with business cycle fluctuations to one without, evaluated relative to the deterministic steady state; in the paper’s baseline calibration, this is 0.6178 percent under CAT and 1.5231 percent under a carbon tax.

reserve requirement macroprudential regulation: a regulatory constraint requiring banks to hold a fraction of deposits in reserves, limiting loan supply; implemented in the model as Φ_t ∈ (0,1] where lower Φ_t requires banks to hold more reserves; a static 2 percent reserve requirement already substantially narrows the welfare gap between carbon pricing regimes, and an optimal dynamic rule nearly closes it.

E-DSGE (Environmental DSGE): the paper’s model class — a DSGE with financial frictions (Christiano-Motto-Rostagno financial accelerator) and a carbon pricing sector; used to analyze the interaction between environmental policy instruments and macroprudential regulation in an economy with both climate and financial externalities.

coefficient of variation of emissions (CVE) / permit prices (CVP_E): volatility measures used to assess how macroprudential regulation affects the business-cycle properties of each carbon pricing instrument; macroprudential regulation substantially reduces CVP_E under CAT and CVE under a carbon tax, making each instrument’s uncertainty properties more symmetric.

Credit Easing versus Quantitative Easing: Evidence from Corporate and Government Bond Purchase Programs

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

Using security-level data on individual corporate bond prices and the Bank of England’s published purchase quantities across its gilt purchase programs (QE1: £200bn, QE2: £125bn, QE3: £50bn, QE4: £60bn) and Corporate Bond Purchase Scheme (CBPS: £10bn of investment-grade sterling corporate bonds), this paper estimates supply effects of QE and CE on UK corporate bond prices, credit spreads, and new issuance separately, exploiting cross-sectional variation in quantities purchased as identifying variation via an instrumental variables approach. In the case of QE alone, supply effects on corporate bond prices are significant at announcement and larger over the full stock-effect horizon, but pass-through to credit spreads is found to be limited to the default-free component of corporate yields under normal market conditions — an exception is QE1 during the financial crisis, when QE’s cross-asset supply effects also significantly lowered credit spreads in the longer run. CE via the CBPS is found to be more effective than QE in reducing credit spreads for higher-rated investment-grade bonds even under normal conditions, and is the only program that generates a statistically significant increase in sterling corporate bond issuance. The results are consistent with QE and CE working through partially distinct channels — QE primarily affecting the default-free component of corporate yields, CE additionally compressing the credit-spread component — and complementing each other for higher-rated bonds.

In depth

Q1. What is the empirical strategy and why use a security-level approach?

The paper uses a two-stage instrumental variables (IV) approach at the individual corporate bond level, with pre-program bond characteristics — maturity, yield-curve fitting errors, the BoE’s prior ownership share in the gilt bucket — serving as instruments for the expected distribution of purchases across bonds, allowing isolation of the supply channel from signaling and duration channels. The security-level approach offers three advantages over aggregate or event-study methods: it enables construction of “substitute buckets” (bonds whose maturity is close to the purchased bonds’) to estimate cross-asset supply effects; it permits direct comparison of the price elasticity with respect to gilt purchases (cross-asset effect) versus corporate bond purchases (within-asset effect); and it allows estimation of both the announcement-day effect and the stock effect — the cumulative price and spread change over the life of each program — which captures the longer-run portfolio-rebalancing contribution separately from the initial market reaction.

Q2. What are QE’s effects on corporate bond prices and credit spreads?

For QE alone (QE1–3), the instrumented gilt substitute purchases have positive and statistically significant effects on corporate bond prices at announcement across all three programs — in the case of QE1, the average 30 basis-point decline in corporate yields on the announcement day is attributed in full to QE supply effects in the paper’s regression. The stock effect — estimated over the full life of each program — is significantly larger than the announcement-day effect, consistent with gradual portfolio rebalancing as predicted by Greenwood, Hanson, and Liao (2018). However, except for QE1, the supply effects do not carry through to credit spreads in either the short run or the longer run, which the paper interprets as consistent with QE working primarily through the default-free component of the corporate yield: corporate yields fell in line with gilt yields, but spreads over gilts were unchanged.

Q3. When does QE affect credit spreads?

QE1’s cross-asset supply effects significantly lowered credit spreads in the longer run, even though QE2 and QE3 do not generate significant credit spread compression in either the short or long run, suggesting that the supply channel interacts with the liquidity channel specifically under conditions of financial market distress. The paper interprets the QE1 exception as reflecting the severe disruption during the 2008–09 financial crisis: when capital mobility across markets is constrained and liquidity premia are elevated, central bank purchases of safe assets may also improve trading conditions in indirectly targeted, less liquid markets such as the corporate bond market, reducing the liquidity component of corporate spreads. This interaction does not appear to be operative in the more normal market conditions of QE2 and QE3.

Q4. How does CE compare to QE in reducing credit spreads and stimulating issuance?

CE via the CBPS is found to be more effective than QE in reducing credit spreads for higher-rated investment-grade bonds even under normal financial market conditions, and a corporate bond’s price sensitivity to its own CBPS purchases is substantially higher than its price sensitivity to gilt substitute purchases; CE is also the only program with a statistically significant positive effect on new sterling corporate bond issuance. Across QE1–3, there is no statistically significant impact of gilt purchases on sterling corporate issuance, while CBPS purchases have positive and statistically significant effects on new sterling corporate bond issuance. The paper characterizes CE and QE as complementary for higher-rated bonds: CE’s credit-spread reduction layers on top of QE’s default-free component effect, making the total stock effect larger than either program alone.

Q5. What happens for lower-rated investment-grade bonds?

For lower-rated investment-grade bonds, the evidence for both cross-asset QE supply effects and within-asset CE supply effects is weaker, and the paper suggests that CE’s stimulation of new bond issuance may have counterbalanced its positive price effects for these bonds through the dilutive effect of new supply. The mechanism is that CE’s reduction in the cost of corporate bond issuance for lower-rated firms induced enough new bond issuance to partially offset the price increase from CBPS purchases, consistent with the issuance channel being most active for the market segment where CBPS created the largest pricing improvement. This dilution effect implies that the net price benefit of CE for lower-rated bonds is smaller than the gross supply-effect estimate.

Key concepts

stock effect : the cumulative effect of the total quantity of bonds purchased under a program on bond prices and spreads, estimated over the full life of the program; in this paper the stock effect is significantly larger than the announcement-day effect, consistent with gradual portfolio rebalancing.

cross-asset supply effect : the pass-through of government bond (gilt) purchase supply shocks to the prices of corporate bonds — an asset class not directly targeted by QE; the paper provides the first estimates of this cross-market supply channel at the security level.

credit spread : the difference between the yield on a corporate bond and the yield on a risk-free government bond of the same maturity; the paper finds QE pass-through is generally limited to the default-free component of corporate yields rather than the credit spread.

default-free component : the part of a corporate bond’s yield attributable to the risk-free interest rate rather than credit risk; the paper finds that QE supply shocks affect this component but generally leave the credit spread unchanged in normal market conditions.

within-asset substitution effect : the price effect of CE purchases on the bonds directly purchased and their corporate bond substitutes, as distinct from cross-asset effects; the paper finds this effect is substantially larger in magnitude than the cross-asset QE effect on corporate bonds.

issuance channel : the mechanism by which lower corporate borrowing costs induced by CE stimulate new corporate bond issuance; the paper finds this channel operates under CE (CBPS) but not under QE (gilt purchases).

Cyberattacks on Small Banks and the Impact on Local Banking Markets

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

This paper studies what happens to local banking markets when a small bank suffers a successful cyberattack, using a stacked difference-in-differences design on 16 cyber incidents at small U.S. banks drawn from the Privacy Rights Clearinghouse database over 2005–2017. Attacked small banks experience a deposit growth rate roughly 22 percentage points lower than matched control banks in the two years following a breach, reflecting depositors’ loss of confidence in the targeted institution’s cybersecurity capacity. The deposit attrition is sharply stronger in counties with lower digital literacy, consistent with less-informed depositors placing disproportionate weight on a visible security failure. Deposit losses do not flow evenly to all competitors: positive spillovers accrue only to the dominant or largest banks in the local market, not to other small banks, concentrating market share toward large incumbents. Affected small banks subsequently attract riskier mortgage borrowers — proxied by higher loan-to-value ratios and lower FICO scores — suggesting that the deposit-cost pressure from a cyberattack induces yield-seeking behavior. The aggregate effect is a reduction in credit access for informationally opaque small borrowers that slows local small-establishment growth.

In depth

Q1. What is the identification strategy and what variation does it exploit?

The paper uses a stacked difference-in-differences design that stacks sub-experiments around each of the 16 cyberattack events, comparing the attacked small bank against a matched set of control banks in the same local market that did not experience a breach, with the event window centered on the quarter of the reported breach. The primary data source for cyber incidents is the Privacy Rights Clearinghouse (PRC) database, which records data breaches across industries; the paper restricts attention to incidents at U.S. commercial banks with total assets below a size threshold that classifies them as small. The stacking design allows each attack event to contribute its own two-by-two (pre/post, treated/control) comparison while controlling for time fixed effects across all events, which is important because cyberattacks cluster in certain periods. Identification relies on the parallel-trends assumption: absent the cyberattack, the deposit growth trajectory of the attacked bank would have evolved like that of matched local competitors. The paper validates this assumption with pre-trend tests and provides a battery of robustness checks including alternative matching procedures and excluding events that coincide with other bank-specific news.

Q2. How large is the deposit effect at attacked small banks and what is the direction of deposit flows?

Attacked small banks see deposit growth rates approximately 22 percentage points lower than control banks over the two years following a breach, a decline that is economically large relative to the unconditional mean deposit growth rate in the sample. The market-share impact is of the order of 1 percentage point lower for the attacked bank. Crucially, the deposit outflows do not disperse evenly to all rivals: the paper finds positive and statistically significant deposit spillovers only at the dominant large bank (or banks) in the local market, with no measurable increase at competing small banks. This asymmetric spillover is consistent with depositors fleeing to scale — perceiving large banks as having the technological resources and regulatory scrutiny to maintain cybersecurity — rather than simply seeking any alternative.

Q3. What role does digital literacy play in moderating the deposit response?

The deposit effect is significantly stronger in counties with below-median digital literacy, measured using population-weighted indices of internet connectivity and self-reported computer use from the American Community Survey, suggesting that less-digitally-literate depositors rely more heavily on observable security signals — such as a publicized breach — when assessing bank safety. In high-digital-literacy counties, the average customer may already have some prior belief about cyber risk across institutions and may discount a single breach as less informative, dampening the flight-to-quality response. In low-digital-literacy counties, the breach is a more salient and credibility-destroying event. The heterogeneity is quantitatively meaningful and survives controlling for MSA-level income, education, and urbanization.

Q4. How does the competitive position of large banks in the local market moderate the spillover?

When a large bank holds a dominant market position prior to the attack — measured by having a market share above the 75th percentile of the local deposit distribution — the positive deposit spillover to that large bank is more than 30 percentage points larger than in markets where large banks hold a weaker position, pointing to a flight-to-incumbency effect that operates on top of the flight-to-scale effect. This finding implies that cyberattacks on small banks are particularly concentrating in markets where large banks are already dominant: the attack accelerates an existing market-share gradient rather than creating a new one. The result has policy relevance for local banking market competition: communities that already have concentrated banking sectors are more exposed to structural concentration following cyber events.

Q5. Do deposit rates at attacked small banks rise or fall, and does this signal a funding-cost channel?

Deposit rate evidence in the working paper suggests that attacked small banks do not uniformly raise deposit rates to retain customers, which is consistent with the deposit outflows being driven by non-price concerns about security rather than competitive pricing, and which rules out a simple funding-cost-through-repricing mechanism. The absence of a strong deposit-rate increase at the attacked bank indicates that depositors are responding to a qualitative signal about the bank’s cybersecurity capacity rather than being price-insensitive. This matters for the economic interpretation: the mechanism is loss of depositor confidence rather than increased funding costs passed through from the attack’s direct remediation expenses.

Q6. What happens to the loan portfolio and borrower risk profile of attacked small banks after a breach?

In the post-attack period, affected small banks shift their mortgage originations toward riskier borrowers, with originations showing higher average loan-to-value ratios and lower average FICO scores relative to the pre-attack period and relative to control banks, consistent with yield-seeking behavior driven by the deposit-funding squeeze. This borrower-quality deterioration implies a second-order financial stability concern beyond the immediate deposit loss: attacked banks may take on more risk in the loan book at precisely the moment when their funding base is weakening. The evidence is thus consistent with a mechanism in which the cyberattack triggers a cascade — deposit loss → funding pressure → reach-for-yield → loan-quality deterioration.

Q7. What are the real-economy consequences at the local market level?

Counties that experience a cyberattack on a local small bank show lower subsequent small-establishment growth relative to control counties, measured using County Business Patterns data on establishments with fewer than 20 employees, consistent with reduced small-business credit availability as small banks contract lending. Large banks that absorb deposit inflows from the attacked institution do not offset this credit reduction: the deposit inflows do not translate into proportionate increases in small-business or small-mortgage lending, reflecting the well-documented diseconomy of scale in relationship lending by large institutions. The real-economy effect is concentrated in counties where small banks had a larger pre-attack share of local deposits and credit, consistent with the mechanism that the effect operates through credit-supply disruption rather than demand shocks.

Q8. How does this paper relate to the literature on bank runs and financial contagion?

Unlike classic bank-run models in which depositor withdrawals are self-fulfilling or triggered by sunspot-like coordination failures, this paper’s results suggest that cyberattacks constitute an information event that rationally updates depositors’ beliefs about the attacked bank’s technological competence, generating a fundamentals-based run on the specific institution rather than systemic panic. The results complement the emerging literature on cyber risk in financial institutions (e.g., Kashyap and Wetherilt 2019, Eisenbach et al. 2022) by documenting market-level spillovers and real effects beyond the attacked institution. The finding that large banks absorb deposits following attacks on small banks also connects to the “too-big-to-fail” literature by showing that size confers a competitive advantage in moments of localized financial stress.

Key Concepts

stacked difference-in-differences : an event-study design in which multiple treatment events are each assigned their own pre/post comparison window, the sub-experiments are then stacked into a single dataset, and pooled regressions with event-by-period fixed effects estimate the average treatment effect; used in this paper to exploit variation across 16 separate cyberattack events at small banks.

Privacy Rights Clearinghouse (PRC) database : a publicly available database of data-breach incidents across industries in the United States, which the paper uses as the primary source for identifying confirmed cyberattacks on commercial banks; the paper restricts to incidents classified as hacking or skimming rather than physical theft or accidental exposure.

deposit spillover : the increase in deposit inflows to competitor banks in the same local market following a cyberattack on a rival institution; in this paper, measured as the change in deposit growth at non-attacked banks relative to their own pre-attack trends.

flight-to-scale : the pattern in which depositors shift funds from smaller to larger banks following a cyber incident, driven by the belief that larger banks have superior cybersecurity resources; the paper documents that this flight benefits only the largest local bank rather than all large banks.

digital literacy : a county-level index measuring residents’ familiarity with digital technologies, internet access, and computer use; used in the paper to test whether depositor reactions to cyberattacks are stronger where depositors have less prior information about cyber risk.

reach-for-yield : the tendency of a bank with a weakened funding base to shift its loan portfolio toward higher-yielding, riskier borrowers to maintain net interest margins; documented in this paper as a behavioral response of attacked small banks in the post-breach period.

Debasements and Small Coins: An Untold Story of Commodity Money

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

This paper applies a multiple-denomination commodity money model — building on Lee, Wallace, and Zhu (2005) — to coinage episodes in late medieval England, and derives two main findings. Shortages of small coins are severely inconvenient because halfpennies and farthings serve not merely as small change but as consumption-smoothing instruments: parameterized to 15th-century England (per-capita silver approximately 35 grams, penny approximately 1 gram), the model shows that adding a halfpenny is highly welfare-improving for poor agents even at infrequent expenditure, and welfare-improving for all agents when monetary transactions occur at least twice weekly. Debasing the penny by 50 percent has approximately the same welfare effect as introducing a halfpenny and replicates the three stylized facts of the debasement puzzle — large minting volumes, cocirculation of old and new coins, and no additional mint inducement — as equilibrium outcomes rather than paradoxes. However, full-bodiedness creates a commitment device against over-issuance that cannot be replicated by sufficiently small coins, since precious metals have a practical lower bound on coin content, so debasement relieves but does not solve the structural small-coin problem, pointing to the historical necessity of a transition to fiat money.

In depth

Q1. What is the debasement puzzle and how does the paper resolve it?

The debasement puzzle, documented by Rolnick, Velde, and Weber, consists of three facts: following a debasement, minting volumes rose sharply, old and new coins cocirculated sometimes by weight, and yet people still paid minting fees rather than receiving inducements — all of which are puzzling because the absence of an inducement suggests no straightforward arbitrage. The paper resolves the puzzle by modeling a debasement as equivalent to introducing a new denomination: it draws agents to the mint because it supplies the welfare-improving small denomination that agents wanted, not because of a price arbitrage. Cocirculation by weight emerges naturally along the equilibrium path because agents hold both old and new coins in optimal portfolios, and the counterfactual welfare calculation shows the welfare gain from eliminating the shortage is large, explaining why agents willingly pay minting fees to obtain the new coins.

Q2. How does the paper measure the inconvenience of a coin shortage?

The paper measures inconvenience as the welfare difference between the shortage equilibrium and a hypothetical scenario in which the mint suddenly eliminates the shortage — an unanticipated shock that adds the missing denomination to the coinage structure. This counterfactual is tractably computable in the model and directly mirrors the intuition of a historical agent who compares their constrained experience to the imagined experience of having access to the missing coins. Applied to the penny, the model shows that adding a halfpenny (debasing the penny by 50 percent) yields a welfare gain equivalent to the full shortage inconvenience; the result is large for poor agents even at once-monthly expenditure and extends to all agents when transactions are at least twice weekly.

Q3. Why can debasement not permanently solve the small-coin problem?

Full-bodied coinage — coins whose face value equals their precious-metal content — constrains the minimum viable coin size: very small coins are practically too easy to counterfeit and too difficult to handle, so debasement merely pushes the lower denomination boundary down without eliminating it. The model uses this practical indivisibility of precious metals as the structural constraint that prevents an infinite regress of smaller and smaller coins. This constraint points to why fiat money — which severs the link between value and metallic content — ultimately emerged as the only way to provide arbitrarily small denominations at negligible production cost. The paper frames this as the resolution to the historical “big problem of small change.”

Key concepts

debasement puzzle : the simultaneous occurrence of unusually large minting volumes and cocirculation of old and new coins following a debasement, without any additional mint inducement; resolved in this paper as the equilibrium response to supplying a welfare-improving small denomination.

full-bodiedness : the property of commodity coins whose face value equals their precious-metal content; acts as a commitment device against over-issuance in the model but creates a practical indivisibility constraint on the minimum coin size.

multiple-denomination model : the Lee-Wallace-Zhu framework extended in this paper; explains the social demand for multiple coin denominations via wide transaction-value heterogeneity and the burden of carrying many coins.

Does Deposit Insurance Promote Deposit Stability? Evidence from the Postal Savings System during the 1920s

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

Overview

Research question. Does deposit insurance promote financial depth by arresting the outflow of deposits from the banking system during periods of bank distress? The paper tests and quantifies the deposit-stabilizing effect of state-level deposit insurance schemes operating in the United States during the 1920s.

Setting and identification. Between 1908 and 1929, eight primarily Midwestern states adopted some form of deposit insurance. The paper exploits the discontinuity in deposit insurance coverage at state borders to identify the causal effect of insurance on depositor behavior. The identification strategy compares outcomes in contiguous city pairs straddling deposit-insurance (DI) and non-deposit-insurance (NDI) state borders — a quasi-experimental design that controls for observed and unobserved confounders by using narrow geographic areas where the only relevant policy difference is the presence or absence of deposit insurance.

Proxy for “mattress money.” The paper uses postal savings deposits as a proxy for money withdrawn from the banking system. The U.S. Postal Savings System (established 1911) was backed by the full faith and credit of the federal government, with a maximum individual account limit of $2,500, and was widely viewed as a far safer alternative to commercial bank deposits. The authors validate this proxy by demonstrating, via Johansen cointegration tests, that the nationwide ratio of postal savings balances to total bank deposits is cointegrated (rank 1) with the currency-deposit ratio — a well-established indicator of banking distress.

Data. The empirical analysis covers 1921–1929. The main postal savings dataset is drawn from Annual Reports of the Postmaster General. Bank suspension data are drawn from FDIC manuscript lists compiled in the 1930s by FDIC economist Clark Warburton, providing location, charter type, and suspension/reopening dates. The sample includes 74 city pairs across 14 states (7 DI: North Dakota, South Dakota, Nebraska, Kansas, Oklahoma, Texas, Mississippi; 7 NDI: Minnesota, Iowa, Missouri, Arkansas, Louisiana, Tennessee, Alabama), with an average distance between paired cities of approximately 18 miles.

Main findings — postal savings regressions (Table 4). Using OLS with city-pair and year fixed effects and standard errors clustered at the NDI city level, the paper finds that following a bank suspension within a 10-mile radius, postal savings deposits in NDI cities grew 16 percent more than deposits in the corresponding DI city. The effect is positive and statistically significant at the 20-mile radius but smaller — approximately 9 percent — and is statistically indistinguishable from zero at the 30-mile radius. The localized decay with distance is consistent with a geographically contained flight-to-safety response. Critically, when the same specification is estimated for periods after deposit insurance was discontinued, the effect at all radii is statistically nil, providing a falsification test ruling out omitted unobserved factors as the driver.

Persistence of effects (Table 5). Arellano-Bond GMM dynamic panel regressions confirm that the disintermediation effects are persistent. The lagged dependent variable enters with a negative and statistically significant coefficient (approximately −0.20 for the 10-mile regression), indicating mean reversion, but the bank suspension coefficients remain robust. Implied long-run effects for the 10-mile and 20-mile equations are approximately 0.151 and 0.100, respectively, suggesting sustained rather than transitory deposit diversion away from the banking system in the absence of deposit insurance.

Banking capacity (Table 6). Because the postal savings deposit limit constrained the intake of funds — particularly severely during distress episodes, as documented through narrative evidence from the 1915 Congressional Record — the postal savings regressions underestimate the true effect of deposit insurance. The paper therefore estimates an alternative specification at the county level, comparing deposits at state-chartered banks in paired DI and NDI border counties. The results indicate that deposit insurance is associated with approximately a 56 percent increase in county-level deposits at state-chartered banks (coefficient 0.574, significant at 5 percent, robust to inclusion or exclusion of year fixed effects). By contrast, the analogous coefficient for national banks — which were prohibited by the OCC from participating in state deposit insurance schemes — is positive but statistically insignificant, providing a placebo test consistent with the interpretation that deposit insurance, not unobserved county characteristics, drove the banking capacity difference.

Scope conditions. All effects are estimated for state-chartered bank deposits in predominantly agricultural, Midwestern border counties during 1921–1929, a period characterized by an average annual bank suspension rate of 2.22 percent (versus 0.3 percent during 1911–1920). The paper acknowledges that state deposit insurance schemes of this era generated moral hazard (as established by prior literature), and frames the contribution as quantifying the stability-enhancing component rather than the net welfare effect.

Policy implication. The 56 percent banking capacity differential implies that deposit runoffs in the absence of insurance are substantially higher than the 3–10 percent runoff rates assumed in the Basel III Liquidity Coverage Ratio (LCR) framework, and more consistent with the 25–50 percent runoffs observed in non-systemic institutions in Denmark following an exogenous reduction in deposit insurance limits (Iyer et al., 2016).

In depth

Q1. Why is the Postal Savings System a valid proxy for “mattress money,” and what evidence supports this?

The postal savings system was backed by the full faith and credit of the United States, making it categorically safer than commercial bank deposits, and was explicitly designed to attract savings hidden in mattresses. The authors validate the proxy empirically by showing that the nationwide ratio of postal savings balances to total bank deposits is cointegrated (Johansen test, rank 1) with the currency-deposit ratio — a series that rises during banking distress as depositors convert bank funds to currency. Contemporary narrative accounts from the 1915 Congressional Record further confirm that postal savings offices experienced sharp deposit inflows during local banking distress, with deposit intake frequently constrained by the $2,500 individual account cap.

Q2. What is the identification strategy, and why does it address endogeneity concerns?

The strategy exploits the discontinuity in deposit insurance at state borders by comparing relative postal savings deposit growth in contiguous city pairs — one city in a DI state, one in an adjacent NDI state — conditioning on bank suspensions within 10, 20, or 30 miles. The authors argue that deposit insurance legislation was a statewide political decision driven largely by partisan composition (Democrats favored it, Republicans opposed it), making it implausible that interests concentrated at border cities systematically determined which states adopted it. Six of the seven NDI control states introduced deposit insurance legislation but failed to pass it, underscoring that the policy variation was not determined by border-specific characteristics. A falsification test using the same city pairs after deposit insurance was discontinued shows zero effects, ruling out time-invariant unobserved heterogeneity as the driver.

Q3. What are the main quantitative results from the city-pair postal savings regressions?

Following a bank suspension within 10 miles, postal savings deposits in NDI cities grew 16 percent more than in DI cities (coefficient 0.162, significant at 5 percent). At the 20-mile radius the differential is approximately 9 percent (coefficient 0.0933, significant at 5 percent). At the 30-mile radius the coefficient is 0.0997 and statistically indistinguishable from zero. These results are estimated with OLS using city-pair and year fixed effects and standard errors clustered at the NDI city level, based on 524 observations for the 10- and 20-mile specifications and 66 observations for the post-discontinuation falsification regressions.

Q4. How does the paper establish that distance matters for the flight-to-safety effect?

The monotonic decline in the estimated coefficient from 0.162 (10 miles) to 0.093 (20 miles) to a statistically insignificant 0.100 (30 miles) indicates that the diversion of deposits into postal savings was geographically localized. This pattern is consistent with depositors responding primarily to nearby bank failures rather than to distant ones, and it supports the interpretation that the effect is driven by local banking distress rather than by state-level or regional macroeconomic shocks that would affect all pairs symmetrically.

Q5. Are the disintermediation effects of bank suspensions temporary or persistent?

The Arellano-Bond GMM dynamic panel regressions (Table 5) show that the effects are persistent. The lagged dependent variable coefficient is approximately −0.205 (10-mile) and −0.188 to −0.201 (20-mile), indicating partial mean reversion but not full reversal. Year-1, Year-2, and implied long-run dynamic effects are all statistically significant and of similar magnitude (approximately 0.145–0.152 for the 10-mile equation and 0.096–0.100 for the 20-mile equation), indicating that once depositors shift funds to postal savings in response to bank suspensions, a substantial portion of the effect persists in subsequent years. This is consistent with prior literature showing that deposits leave the banking system quickly but return slowly.

Q6. Why are the postal savings coefficient estimates considered a lower bound on the true effect of deposit insurance?

Two institutional features constrained the postal savings system from fully capturing flight-to-safety deposits. First, individual accounts were capped at $2,500, and narrative evidence shows that this limit was severely binding during distress — depositors attempted to place far more than the ceiling allowed. Second, the re-depositing rate of postal savings funds back into local banks was not 100 percent: during 1921–1923 only 32–47 percent of postal savings deposits were re-deposited in banks, compared to 72–82 percent in calmer years. Because the postal savings system could not absorb unlimited deposits and did not fully recycle absorbed funds into local banking, its level understates the true flight of deposits from the banking system in NDI states.

Q7. How does the county-level banking capacity test address the censoring problem?

The paper estimates log-ratio regressions comparing county-level deposits at state-chartered banks in DI versus NDI border counties, using a “DI Active” indicator that switches on when deposit insurance is in effect in a given state-year and switches off when schemes are discontinued. Because different states discontinued their insurance at different times, there is sufficient within-county variation to identify the DI coefficient even with year fixed effects. The estimated coefficient of 0.574 (without year FE) and 0.557 (with year FE) translates to approximately a 56 percent higher deposit level in state-chartered bank counties with deposit insurance, with virtually identical estimates across specifications.

Q8. What is the placebo test for national banks, and what does it show?

National banks were prohibited by the Office of the Comptroller of the Currency from participating in state deposit insurance schemes. If deposit insurance — rather than unobserved county characteristics — is responsible for the 56 percent banking capacity premium, then county deposits at national banks in DI states should show no corresponding premium. The Table 6 results confirm this: the DI Active coefficient for national bank deposits is positive (0.165 to 0.267) but statistically insignificant, providing a falsification result consistent with the causal interpretation for state-chartered banks.

Q9. How does the paper situate deposit insurance’s stabilizing benefits relative to its moral hazard costs?

The paper explicitly frames its contribution as quantifying the stability-enhancing component of deposit insurance separately from the moral hazard component. It cites extensive prior literature (Calomiris 1992, 1993; Wheelock 1992, 1993; Wheelock and Wilson 1994) establishing that the 1910s–1920s state schemes generated moral hazard: insured banks reduced capital-to-asset ratios, relaxed lending standards, and increased risk exposure. The paper does not contest those findings but argues that the two effects are analytically separable and that the stabilization benefit had significant quantitative magnitude — a benefit that should be accounted for when assessing the net welfare effects of deposit insurance design.

Q10. What are the implications for the Basel III Liquidity Coverage Ratio framework?

The Basel III LCR formula assumes that during distress 3 percent of “stable deposits” and 10 percent of “less stable deposits” run off. The paper’s finding that deposit insurance is associated with a 56 percent increase in banking capacity implies that in the absence of insurance, deposit runoffs are far higher than these Basel assumptions — substantially larger than 10 percent and more consistent with the 25–50 percent runoffs observed for non-systemic banks in Denmark following an insurance limit reduction (Iyer et al. 2016). The authors argue their results suggest that empirical grounding for the LCR runoff assumptions remains insufficient, consistent with critiques by Allen (2014) and Diamond and Kashyap (2016).

Key Concepts

Postal Savings System (as “mattress money” proxy). The U.S. Postal Savings System (1911–) accepted deposits up to $2,500 per individual, backed by the full faith and credit of the United States. In this paper, postal savings deposits are used as a quantitative proxy for money withdrawn from the banking system during distress — “money under the mattress” — validated by cointegration with the currency-deposit ratio.

Policy discontinuity / border-pair design. The identification strategy exploits the fact that deposit insurance was adopted at the state level, creating a sharp policy discontinuity at state borders. Contiguous city pairs straddling DI and NDI state borders are treated as quasi-experimental units, with the within-pair difference in postal savings deposit growth serving as the outcome, controlling for time-invariant city-level heterogeneity and common time effects.

Relative Postal Savings Deposit Growth (RPS). The dependent variable defined as the log-ratio of postal savings deposits in the NDI city to postal savings deposits in the DI city within a pair, and then first-differenced over time. This construction controls for city-pair-level time-invariant characteristics and isolates the differential response to bank suspensions.

Bank suspension. In this paper’s context, a bank suspension is any closure of a bank (state-chartered or national) at a specific geographic location, as recorded in FDIC manuscript lists compiled by Clark Warburton during the 1930s. The variable used in regressions is the change in the number of suspensions within R miles (R = 10, 20, 30) of the paired postal savings offices.

Financial depth / local banking capacity. The paper uses county-level deposits at state-chartered banks as a measure of local banking market size. Deposit insurance is hypothesized to increase financial depth by preventing the diversion of funds out of the banking system during distress, and the 56 percent estimated premium is the paper’s primary measure of the insurance’s capacity-enhancing effect.

DI Active indicator. A time-varying binary variable equal to 1 when deposit insurance was legally in effect in a given state at a given time, and 0 otherwise (including after repeal). Because different states repealed their schemes at different times (Oklahoma 1923, Texas 1927, South Dakota 1927, North Dakota 1929, Kansas 1929, Nebraska 1930, Mississippi 1930), this variable provides within-county variation that identifies the banking capacity coefficient after controlling for county and year fixed effects.

Moral hazard vs. stability-enhancing components. The paper distinguishes analytically between the moral hazard effect of deposit insurance (insured banks undertake riskier projects, reduce capital buffers, relax lending standards) and the stability-enhancing effect (depositors retain funds in the banking system, preventing runs). The paper’s contribution is to quantify the latter component in isolation, using a setting where the two effects can be separated by focusing on depositor — rather than banker — behavior.

EU ETS Market Expectations and Rational Bubbles

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

This paper tests whether the sharp rise in EU Emissions Trading System (EU ETS) allowance prices from 2018 onward was driven by a rational bubble. The methodological contribution is to modify the Fama (1984) Predictive Regression (FPR) approach to remain valid for rational bubble testing when the risk premium is time-varying — potentially stationary, integrated of order one, or even explosive — and when the fundamental price process exhibits a unit root or mildly explosive behavior. Standard bubble tests (including the KPSS applied to the price-expectations differential, and the Phillips-Shi-Yu SADF/GSADF tests applied to price levels) lose size control when the risk premium follows a nonstationary process; the paper’s FPR approach combined with the IVX estimator of Kostakis, Magdalinos, and Stamatogiannis (2015) retains correct size under all risk premium specifications. Using weekly EU ETS spot and futures data from 2013 to 2023 (T = 563), the paper finds: (1) explosive behavior in both spot and futures price levels during the third and fourth trading phases (2018–2023), confirming a necessary condition for a bubble; (2) no evidence of a rational bubble in the FPR test — the IVX-AR Wald statistic fails to reject the null of no bubble (β₂,ₙ = 0) in full-sample and sub-sample analyses across delivery horizons of 4, 8, 12, and 16 weeks; (3) no evidence of explosiveness in the differential between future spot rates and futures rates; (4) no evidence of co-explosiveness between spot and futures prices within either the third or fourth trading period separately. The paper concludes that the EU ETS price surge reflects a shift in market expectations about future allowance scarcity — driven by policy tightening of the cap trajectory and reform of the Market Stability Reserve — rather than speculative excess.

In depth

Q1. What is the Fama Predictive Regression approach to testing rational bubbles, and what is its key limitation with a dynamic risk premium?

The Fama (1984) decomposition splits the futures price F_{n,t} into expected future spot price E_t[P_{t+n}] and a risk premium RP_{n,t}; from this, two predictive regressions (FPR 1 and FPR 2) have slope coefficients β₁,ₙ and β₂,ₙ that equal 1 and 0, respectively, in the absence of a rational bubble, and deviate from these values (β₁,ₙ < 1, β₂,ₙ > 0) when a bubble is present. The paper shows analytically (equations 27–33) that when a rational bubble is present, β₁,ₙ decreases monotonically as Var(B_t) increases and β₂,ₙ increases monotonically, with the direction of the bias confirmed under both zero and nonzero covariance between the bubble and the risk premium. The key limitation of standard OLS inference in this regression is that when the regressor (F_{n,t} − P_t) is highly persistent or mildly explosive, the OLS t-statistic has a non-standard distribution, and Stambaugh (1999) bias can lead to over-rejection of the no-bubble null. The paper addresses this by applying the IVX estimator, which replaces the persistent regressor with an instrument of controllable lower persistence, yielding a Wald statistic that converges to a standard chi-squared distribution regardless of the persistence or trending behavior of the risk premium.

Q2. Why does the KPSS test applied to the price-expectations differential fail in the presence of a nonstationary risk premium?

The KPSS test applied to P_{t+n} − F_{n,t} tests whether this differential is stationary; under the no-bubble null (equation 16 in the paper), the differential equals the negative risk premium RP_{n,t}, so the KPSS test has correct size when RP is stationary but incorrectly rejects the no-bubble null when RP is integrated of order one or explosive — because non-stationarity in the risk premium is incorrectly attributed to a bubble. The paper’s Monte Carlo simulations (Table 1) confirm that the KPSS test maintains nominal size of 5 percent only when the risk premium is stationary (λ ∈ {0, 0.5} under RP 1); when λ = 1 or λ = 1.01, the KPSS test rejects far more often than 5 percent under the null. The FPR approach with IVX inference, by contrast, maintains size close to 5 percent across all risk premium specifications including explosive ones. This is the central methodological motivation: prior EU ETS bubble tests that relied on KPSS may have detected non-stationarity in the risk premium rather than a genuine bubble component.

Q3. What does the SADF/GSADF test find for EU ETS spot and futures prices, and what is its role in the paper’s empirical strategy?

The paper applies SADF and GSADF tests (Phillips, Shi, and Yu, 2015a,b) to weekly EU ETS spot and futures price levels from 2013 to 2023 and finds evidence of explosive behavior at the 5 percent significance level in both series, with consistent timing of explosive phases across spot and all four futures contracts. The explosive episodes are date-stamped using the BSADF sequence with wild-bootstrapped critical values (999 repetitions): explosive periods are identified during the end of the third trading period (2018–2022) and at the commencement of the fourth trading period (2021–2023). These results confirm that the necessary condition for a rational bubble — an explosive price component — is satisfied. However, the paper emphasizes that explosiveness in levels is not sufficient for a rational bubble: a mildly explosive fundamental or an explosive risk premium would produce the same SADF/GSADF result without any bubble component. The FPR-IVX test is designed to distinguish between these cases and constitutes the primary bubble test.

Q4. What do the FPR-IVX tests find for the presence of a rational bubble?

Across the full sample (January 2018 to October 2023, T = 302), the IVX-AR Wald statistic (denoted W̃_β, adjusting for serial correlation in FPR 2’s error term using the Yang, Long, Peng, and Cai (2020) procedure) fails to reject the null β₂,ₙ = 0 against β₂,ₙ ≠ 0 for all four delivery horizons n ∈ {4, 8, 12, 16} weeks. The Bayesian Information Criterion selects models with lagged error terms for both the full sample and sub-samples, confirming the need for the IVX-AR procedure over the standard IVX Wald statistic. The sub-sample analysis separates the third trading period (January 2018 to December 2020, T = 156) and the fourth trading period (January 2021 to October 2023, T = 146); in both sub-samples the null is not rejected for all delivery horizons. The conventional OLS t-statistic (|t_β|) sometimes provides marginal evidence against the null, but the paper interprets this as reflecting the Stambaugh bias problem and defers to the IVX-AR inference. These results contradict both the collapsing bubble hypothesis (which would require β₂,ₙ < 0) and the ongoing bubble hypothesis (which would require β₂,ₙ > 0).

Q5. What do the tests on the differential between future spot rates and futures rates find?

Applying the SADF/GSADF test to the differential P_{t+n} − F_{n,t} for n ∈ {4, 8, 12, 16} weeks reveals no evidence of explosiveness in this differential across all horizons (Table 9 in the paper). This is consistent with the absence of a rational bubble: under the FPR framework, a rational bubble would generate an explosive component in the futures basis (F_{n,t} − P_t), which would in turn produce explosiveness in the differential between actual future spot prices and futures prices. The absence of explosiveness in this differential therefore provides an additional check corroborating the FPR-IVX finding.

Q6. What does the co-explosiveness test find, and why does a structural break affect the full-sample result?

The co-explosiveness test of Evripidou, Harvey, Leybourne, and Sollis (2022) tests whether spot and futures prices share a common explosive trend (null: co-explosive, no bubble) versus the alternative that they diverge by an explosive component (rational bubble or explosive risk premium). In the full sample from January 2018 to October 2023, the test rejects the null for all n ∈ {4, 8, 12, 16}, apparently indicating a non-stationary component separating spot and futures prices. However, sub-sample analysis dividing the sample at December 2021 reveals that neither the third trading period (January 2018 to December 2021) nor the fourth trading period (January 2022 to October 2023) sub-samples show rejection of the null — the co-explosive null cannot be rejected in either period alone. The paper interprets the full-sample rejection as reflecting a structural break in the risk premium at the boundary between the two trading periods (a mean shift in the risk premium) rather than a bubble, consistent with the KPSS size problem and with the lack of any significant positive serial correlation between the phases. The sub-sample co-explosiveness results align with the FPR-IVX findings.

Q7. What explains the EU ETS price surge if not a rational bubble, and what are the policy implications?

The paper interprets the consistent co-movement of spot and futures prices in an explosive common trend — without any divergence between them — as evidence that the fundamental value of allowances itself became explosive, driven by a regime shift in market expectations about future allowance scarcity. The scarcity shift is traced to two policy changes: (a) the progressive tightening of the EU ETS cap trajectory under the European Green Deal and the Fit-for-55 legislation, which reduced the total number of allowances available over time; and (b) reform of the Market Stability Reserve, which removed surplus allowances from circulation, making the cap effectively more binding than its nominal level. When market participants updated their expectations about how scarce allowances would become, the fundamental value — the present discounted value of allowance scarcity rents — rose along an explosive path without any bubble component. For policy, this distinction matters: if the price surge reflected a rational bubble, regulatory intervention to deflate it could be efficiency-improving (bubbles misallocate resources and their bursting creates financial instability); if the surge reflects genuine scarcity expectations, intervention would undermine the price signal that guides firms’ decarbonization investment decisions. The paper concludes there is no basis from historical data to justify bubble-prevention intervention in the EU ETS architecture.

Key concepts

rational bubble (in the EU ETS context): a component of the allowance price that exceeds the present discounted value of future allowance scarcity rents and grows at the discount rate; theoretically possible because allowances are storable and have positive returns from banking across periods; the paper finds no evidence of this component in EU ETS prices during 2018–2023.

Fama Predictive Regression (FPR): a regression of the basis (F_{n,t} − P_t) on itself or on subsequent spot-futures differentials, used here to test rational bubbles; FPR 2 (the regression of P_{t+n} − P_t on F_{n,t} − P_t) has slope β₂,ₙ = 0 under no bubble and β₂,ₙ > 0 under an ongoing bubble, with the direction of β₂,ₙ identifying both the presence and type (ongoing vs. collapsing) of the bubble.

IVX estimator: the instrumental-variable estimator of Kostakis, Magdalinos, and Stamatogiannis (2015) that instruments a mildly explosive or highly persistent regressor with an instrument of controllable lower persistence; produces a Wald statistic with a standard chi-squared limiting distribution regardless of the persistence or trending behavior of the risk premium, enabling valid inference on bubble hypotheses in the FPR when the risk premium is nonstationary.

IVX-AR procedure: the extension of the IVX estimator by Yang, Long, Peng, and Cai (2020) that additionally accounts for serial correlation in the error term of the predictive regression; the paper applies this as its primary inference procedure because BIC selects models with lagged errors in both full-sample and sub-sample analyses.

allowance scarcity expectations: market participants’ beliefs about the future tightness of the EU ETS cap relative to aggregate emissions; the paper finds that the price surge since 2018 is consistent with a shift in these expectations driven by cap trajectory tightening and Market Stability Reserve reform, rather than with a speculative bubble.

mildly explosive process: a time series with autoregressive root θ = 1 + c·T^{−α} for c > 0, α ∈ (0,1), converging to unity as T → ∞; used in the paper’s Monte Carlo and theoretical analysis to model the fundamental price process and the risk premium under the alternative hypothesis of ongoing rational bubble behavior, following Phillips and Magdalinos (2007).

From Interaction to Business Fluctuations: How Credit Network Explains Cycles

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

Layer 1: Overview

This paper investigates how the endogenous structure of credit, deposit, and interbank networks shapes business cycle fluctuations and large financial crises in the U.S. economy. Ciola and Tedeschi build and estimate a microfounded heterogeneous-agents macroeconomic model in which households, firms, and banks interact through decentralized matching in three markets — deposits, credit, and interbank lending — with agents choosing partners based on both posted interest rates and the size of the counterpart, generating a preferential-attachment mechanism that endogenously concentrates the financial sector. The structural parameters governing network formation are estimated on U.S. quarterly interest rate and GDP growth data from 1947 to 2019 via an Extended Method of Simulated Moments (EMSM) procedure combined with a Bayesian Adaptive Random Walk Metropolis–Hastings sampler; the calibrated model reproduces the empirical autocorrelation structure of these series. The model’s key finding is that preferential attachment endogenously concentrates roughly three-quarters of deposits, credit, and interbank transactions into a single hub bank, whose dominance raises markups, suppresses deposit rates, and depresses aggregate capital accumulation relative to the initial symmetric state. Bank runs against this hub — rare but endogenously generated when households reallocate deposits simultaneously — collapse the interbank market completely and produce deep recessions that last multiple quarters, with recovery requiring approximately five years.

In depth

Q1. What is the model’s core structure and how do agents interact?

The model consists of a fixed number of households (N_H = 1,000), banks (N_I = 10), and firms (N_F = 1,000) who interact in deposit, credit, and interbank markets through a decentralized preferential-attachment matching mechanism in which agents assess both current interest rates and the size of potential counterparts. Households deposit savings in a single bank chosen based on a fitness index combining the bank’s promised deposit rate and its size (used as a proxy for long-run quality), and they search for a new partner each period with probability ζ_H. Firms borrow from one bank at a time, also choosing based on a fitness that weighs the promised profit share against bank size, and switch with probability ζ_F. Banks set interest rates in all three markets to maximize expected profits, exploiting their monopolistic power (higher when they are larger), subject to a balance sheet constraint that links deposits, credit extended to firms, and interbank borrowing. The interbank market exists specifically to cover unexpected deposit withdrawals: when a bank’s deposits fall below its outstanding credit, it borrows in the interbank market or closes credit lines.

Q2. How does the estimation methodology work and what parameters does it identify?

The paper employs the Extended Method of Simulated Moments (EMSM) of Smith (1993) and Gourieroux et al. (1993), which minimizes the weighted distance between the coefficients of a VAR auxiliary model estimated on observed U.S. data and on H simulated time series generated from a given structural parameter vector, with the optimal weighting matrix set to the inverse of the Newey–West covariance of the auxiliary parameter estimates. Because gradients of the criterion function are not analytically available for this nonlinear agent-based model, the authors use a two-step approach: first, a Particle Swarm Optimization (PSO) algorithm explores the parameter space to locate a neighborhood of the global minimum; second, a Bayesian Adaptive Random Walk Metropolis–Hastings (ARWMH) algorithm generates posterior draws from the structural parameter distribution using the chi-square distributional properties of the EMSM criterion function. The estimated structural parameters include the nine network formation parameters {ω_X, ζ_X, ψ_X} for each of the three markets — governing competition intensity, switching probability, and the weight agents assign to counterpart size — while the production coefficient (α = 0.37) and household discount factor (β = 0.997) are calibrated directly to U.S. labor share and real interest rate data. Estimation uses 1947:Q1–2019:Q4 U.S. real GDP growth and real interest rate data; with three VAR lags and d = 9 structural parameters, the overidentification chi-square test can be assessed.

Q3. What are the long-run dynamics and how does the financial network concentrate?

Starting from an equal distribution of agents across banks, the model converges to a pseudo-steady-state in which a single hub bank intermediates approximately three-quarters of deposits, credit lines, and interbank transactions, because the preferential-attachment mechanism is self-reinforcing: larger banks attract more depositors (providing more stable funding), more firms (generating more profit), and more interbank counterparts, which further enlarges their size and attractiveness. This concentration has clear aggregate consequences: as the hub’s monopolistic power grows, it widens the markup over the perfect competition interest rate in the credit market and the markdown below it in the deposit market, reducing the deposit rate paid to households and thereby depressing household capital accumulation. Simulations across 1,000 independent replicas show that the aggregate production level in the pseudo-steady-state is below the initial competitive equilibrium, credit and interbank interest rates rise, and approximately 10% of total capital circulates through the interbank market as periphery banks rely on the hub for liquidity provision.

Q4. How do cyclical fluctuations and crises emerge endogenously?

Business cycles arise from the continuous reallocation of household deposits across banks, which generates endogenous liquidity shocks that do not require an exogenous crisis trigger: when a critical mass of households simultaneously reallocates away from the hub — a rare but endogenous event driven by the stochastic matching process — the hub faces a severe liquidity shortage, must close credit lines and interbank lending, and produces a systemic economic contraction. In a representative 100-year simulation, aggregate production fluctuates around a stable trend with mild recessions most of the time, but the model occasionally generates a catastrophic bank run against the hub. When this occurs, the hub’s weighted degree in all three markets collapses to near zero within one or two quarters, the interbank market freezes completely, and firm production stops because firms cannot immediately reallocate their credit demand to alternative banks. The impulse response to a sudden reduction in hub deposit centralization shows that aggregate production falls sharply in the short run (as credit contracts) and only surpasses its pre-run level after approximately five years (20 quarters).

Q5. What does the VAR impulse response analysis reveal about recovery dynamics?

An estimated VAR on all simulations — with aggregate production and the volume, centralization, and interest rates of each of the three markets as endogenous variables — shows that a negative shock to deposit market centralization (i.e., a bank run against the hub) triggers an immediate spike in deposit interest rates (as competing banks compete for the displaced funds), a contraction in credit and interbank supply (as periphery banks lack sufficient liquidity to expand), and a rise in credit interest rates (as the pool of surviving credit lines is concentrated in the most profitable projects). In the medium run, higher deposit rates promote household capital accumulation, which ultimately expands the aggregate supply of productive capital; at the same time, the dissolution of the old hub reduces the sector’s average monopolistic markup, permanently lowering credit market interest rates. This self-correcting mechanism underlies the five-year recovery window and also illustrates why prompt policy intervention during hub-collapse crises is particularly effective — early stabilization prevents the reinforcing deposit-withdrawal spiral that deepens the contraction.

Q6. What is the paper’s contribution relative to existing macroeconomic network literature?

The paper makes three distinct contributions over prior agent-based macroeconomic network models: first, it treats households as active depositors whose reallocation choices generate endogenous liquidity shocks rather than simply passive shock absorbers; second, it models banks as profit-maximizing agents that optimally set interest rates exploiting market power rather than assuming perfect competition or regulatory constraints; and third, it produces a Bayesian estimator of all structural parameters rather than relying on calibration to observed moments. Prior work in this tradition (Delli Gatti et al. 2010; Riccetti et al. 2013; Lenzu and Tedeschi 2012) typically either omits households from the deposit market or assumes exogenous mechanisms of crisis formation. By endogenizing all three sources of network dynamics — deposit, credit, and interbank — and estimating the model on U.S. data, the paper provides a framework in which large financial crises emerge as intrinsic system properties rather than imposed scenarios, and quantifies the structural parameters driving them.

Key Concepts

preferential attachment : a matching mechanism in which agents preferentially form links with larger counterparts; in this model it causes households and firms to favor large banks, endogenously concentrating the financial sector into a hub-and-spoke structure with a dominant hub bank.

hub bank : the single largest financial intermediary that endogenously emerges in the model’s long-run equilibrium, intermediating approximately three-quarters of deposits, credit lines, and interbank transactions; its size confers monopolistic power but makes it the systemic node whose failure triggers economy-wide crises.

Extended Method of Simulated Moments (EMSM) : the estimation strategy used to identify the nine network formation structural parameters; it minimizes the weighted distance between VAR coefficients estimated on observed U.S. data and on model-simulated data, with a Bayesian ARWMH sampler used to generate the posterior distribution given the chi-square-distributed criterion function.

endogenous bank run : the crisis mechanism in this model — a simultaneous reallocation of household deposits away from the hub, triggered by the stochastic matching process rather than an external shock, that freezes the interbank market and produces a deep recession lasting approximately five years (20 quarters) in impulse response analysis.

FX Interventions and Capital‐Constrained Banks: Evidence from USD/ILS Spot, Forward, and Option Markets

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

This paper uses confidential daily data on the Bank of Israel’s (BOI) foreign exchange purchase program in the USD/Israeli new shekel (ILS) spot market from 2013 to 2019 to study how FX interventions affect the spot exchange rate, the forward rate (through covered interest parity deviations), and the risk-neutral probability distribution of future exchange rates reflected in the options market. Interventions of USD 1 billion are found to be associated on average with a depreciation of the ILS by 0.82%–0.85%—at the upper bound of estimates in the existing literature—while the indirect effect on the forward rate is smaller because the BOI’s USD purchases widen the negative deviation from covered interest parity (CIP). The higher moments of the risk-neutral distribution—including crash risk—are found to be unaffected; USD purchases shift the entire distribution toward higher USD/ILS values without altering its shape. An additional finding is that the USD/ILS options market appears to anticipate intervention episodes and prices them in before they occur. This paper is the first academic study to empirically quantify the effect of FX interventions on CIP deviations. Note: this summary is based on Bundesbank DP 20/2022 “Foreign exchange interventions and their impact on expectations: Evidence from the USD/ILS options market,” an earlier version; the published JMCB paper title indicates expanded scope including capital-constrained banks and spot/forward/option markets.

In depth

Q1. What is the data and research design?

The paper uses confidential daily data on the BOI’s intervention program in the USD/ILS spot market from 2013 to 2019, together with USD/ILS option price data, to identify the effect of sterilized FX purchases on the spot rate, forward rate, and option-implied expectations. The authors note that results from older studies may not be representative because FX markets have changed substantially over the past decade and the sustained low-interest-rate environment of this period is historically exceptional, making updated empirical evidence important.

Q2. What is the estimated effect on the spot exchange rate?

Interventions of USD 1 billion are associated on average with a depreciation of the ILS by 0.82%–0.85%, which is at the upper bound of the estimated impact found in other studies. The direction is consistent with portfolio balance and signaling channels: BOI purchases of USD increase demand for dollars and supply of shekels, driving the spot USD/ILS rate higher.

Q3. How do interventions affect the forward rate and covered interest parity?

The indirect effect of BOI USD purchases on the forward rate is smaller than the spot effect because the purchases widen the negative deviation from covered interest parity—this paper is the first to empirically quantify the effect of FX interventions on CIP deviations. The CIP deviation widens because the spot rate moves more than the forward rate, creating a cross-currency basis that is not fully closed by the intervention.

Q4. How are the higher moments of the exchange rate distribution affected?

The higher moments of the risk-neutral probability distribution of future exchange rates—including crash risk—are found to be unaffected by BOI USD purchases; the purchases simply shift the entire distribution toward higher USD/ILS values without compressing its variance or altering its shape. This finding indicates that FX interventions move the level of expected future exchange rates but do not reduce tail risk or change the perceived skewness of the distribution from the market’s perspective.

Q5. Do options markets anticipate interventions?

The USD/ILS options market is found to anticipate intervention episodes and price them in before they occur. This anticipation is consistent with market participants forming rational expectations about the BOI’s reaction function based on observable exchange rate dynamics, and adjusting option prices accordingly ahead of actual intervention.

Key concepts

risk-neutral probability distribution (RND) : the probability distribution over future exchange rates recovered from observed option prices; reflects market forward-looking beliefs including higher moments such as crash risk and skewness, under risk-neutral pricing conventions.

covered interest parity (CIP) deviation (cross-currency basis) : the departure from the no-arbitrage relationship linking spot rates, forward rates, and interest rate differentials; a negative CIP deviation for the ILS means the forward USD premium exceeds the USD-ILS interest rate differential, implying the dollar is cheap in the forward market relative to the spot-and-roll strategy.

sterilized FX intervention : central bank foreign currency purchases or sales offset by domestic open market operations to prevent the domestic money supply from changing, isolating the exchange rate channel from monetary policy effects.

Heterogeneity and the Macro-Economic Effects of Changes in Loan-to-Value Limits

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

Layer 1 — Overview

Research Question

De Veirman and de Jong develop a new approach to estimating the macroeconomic effects of changes in regulatory loan-to-value (LTV) limits on mortgage loans. The central questions are: (1) how do changes in an LTV cap translate into changes in the average LTV and, through that channel, into house prices and real output; and (2) how do heterogeneity in the cross-sectional LTV distribution, non-linearity, and asymmetry shape those effects?

Motivation and Gap

Prior empirical literature on macroprudential LTV policy typically pools across countries using coded indicator variables, which imposes the restriction that all LTV policy actions have the same effect regardless of the size of the change or the position of the limit relative to the distribution. Standard TANK models with homogeneous borrowers imply either full symmetry or threshold asymmetry precisely at the point where the constraint ceases to bind. The authors are the first to relate borrower heterogeneity to non-linearity and asymmetry in LTV policy effects.

Data and Setting

The empirical application focuses on the Netherlands, which introduced an LTV cap of 106 percent on August 1, 2011, subsequently reduced in annual one-percentage-point steps to 100 percent by January 2018. Cross-sectional LTV distributions are constructed from the De Nederlandsche Bank Loan Level Data (LLD), covering 77-81 percent of outstanding Dutch mortgage debt in 2012Q4-2014Q4, restricted to borrowers aged 35 or younger as a proxy for first-time buyers. A survey-based average LTV series spanning 1979-2015 was fielded in January 2016 across the CentERpanel and LISS panel (7,943 respondents combined; 2,238 usable observations after cleaning), measuring LTV at the time of first home purchase. This survey-based annual LTV series, together with the log relative house price, log real GDP, and the real mortgage rate, forms a four-variable Vector Error Correction Model (VECM) estimated over 1981-2015, with a single cointegrating vector identified by Johansen maximum likelihood.

Methodology

The authors’ core innovation is to translate changes in the LTV cap into changes in the cross-sectional average LTV by applying each successive cap level to the underlying distribution: observations above the cap are moved to the cap value (with adjustments for exceptions in the ex post variant). These implied annual changes in the average LTV serve as a succession of impulses fed into the VECM. Two variants are implemented: an ex ante approach using only the pre-cap 2010M8-2011M7 distribution, and an ex post approach that uses the most recent empirical distribution prior to each cap change. The Cholesky identification ordering is [LTV, house prices, GDP, mortgage rate].

Main Findings with Quantitative Magnitudes

Non-trivial macroeconomic effects of Dutch LTV policy: Under the ex post approach (the preferred estimate), the imposition of the cap at 106 percent in 2011 and its gradual reduction to 100 percent by 2018 imply, twenty years after the first shock, that relative house prices are 4.84 percent lower and real GDP is 1.15 percent lower than they would have been in the absence of the cap sequence. The bulk of these responses materializes within ten years, at 4.18 percent and 1.05 percent respectively.
Non-linearity: For a given underlying distribution, changes in the cap have progressively larger effects as the cap tightens. In the ex ante approach, the fraction of households constrained by the cap rises from approximately 20 percent at a limit of 105 percent to approximately 40 percent at a limit of 100 percent. A 10 percentage point tightening from 110 to 100 percent implies a long-run relative house price response of 6.12 percent, while a tightening from 100 to 90 percent implies a response of 14.27 percent — a pronounced non-linearity traceable to the substantial mass of observations in the 90-110 range of the Dutch distribution.
Heterogeneity matters substantially: In mean-preserving comparisons using Pearson-family approximations to the pre-cap Dutch distribution, the macroeconomic effects of the actual Dutch LTV policy sequence are 2.58 times larger in the high standard deviation case (standard deviation 25 percent above the Dutch baseline of 17.09) than in the low standard deviation case (standard deviation 25 percent below). Specifically, twenty-year house price responses are 12.34 percent (high SD) versus 4.79 percent (low SD), and GDP responses are 2.93 percent versus 1.14 percent.
Asymmetry is conditional on the position of the cap relative to the distribution: For the Dutch distribution, symmetry is a good approximation for LTV limits at around 80 percent or lower, where the cap is binding for the bulk of households. Asymmetry is pronounced for higher levels. At an initial cap of 100 percent, the absolute effect of a ten-percentage-point tightening is 2.33 times that of a ten-percentage-point loosening. At 80 percent, the asymmetry ratio is only 1.17. Tightenings have smaller effects when they start from a point where few households are constrained; conversely, loosenings can have larger effects when starting from a point where many are constrained.
Homogeneity assumption understates effects above the mean LTV: Under the homogeneous-borrower benchmark (all borrowers at the Dutch mean of 93.72 percent), asymmetry is infinite at cap levels of 100 and 95 percent but zero at other levels — a feature that causes effects to be entirely absent for caps above the mean. In the heterogeneous Dutch setting, an increase in the LTV limit from 95 to 105 percent raises house prices by 10.72 percent in the long run; the homogeneous case implies no effect at all.

Scope Conditions and Caveats

The paper does not address welfare or financial stability effects. The VECM impulse responses do not establish economic causality. Anticipation effects — if households front-loaded high-LTV purchases before the cap — would cause the procedure to overstate the effect. The LTI robustness check (which smooths the loan-to-income ratio due to noisy survey responses) yields twenty-year responses of 3.32 percent (house prices) and 0.74 percent (GDP), somewhat lower than the baseline, indicating that not controlling for LTI tends to overstate the LTV-macroeconomy connection. The approach requires a usable pre-cap or recent-prior LTV distribution; it is not directly portable to settings where a loosening is studied and no recent pre-cap distribution is available.

In depth

Q1. What is the fundamental identification challenge this paper faces, and how does the proposed approach address it?

A: The standard challenge is that LTV caps are changed infrequently and have no long time series suitable for regression, so panel studies typically pool countries and use coded dummy variables that impose size-independence of effects. The authors bypass this by using the cross-sectional LTV distribution itself: they measure how each cap level would truncate the underlying distribution and track the implied change in the cross-sectional mean LTV, which is then fed as a shock into a time-series VECM. This approach does not require the cap to have been in place previously, imposes no cross-country coefficient restrictions, and explicitly accounts for the size of the policy change.

Q2. What are the ex ante and ex post approaches to translating cap changes into average LTV changes, and how do their cumulative estimates differ?

A: The ex ante approach applies all successive cap levels to the single pre-cap distribution of 2010M8-2011M7 (after correcting for the June 2011 sales-tax reduction from 6 to 2 percent), without allowing for exceptions. The ex post approach uses the most recent empirical distribution prior to each cap change and accounts for the observed share of borrowers above the cap as exceptions. The ex ante approach yields a cumulative decline in the average LTV of 3.08 percentage points over 2011-2018; the ex post approach yields 1.96 percentage points, roughly one percentage point less. The difference is largely concentrated in 2011-2012 and stems from the ex ante approach not accounting for exceptions to the cap.

Q3. How does the paper correct for the coincident 2011 sales-tax reduction, and why does this matter?

A: In June 2011, the Dutch sales tax on housing purchases fell from 6 to 2 percent, approximately coinciding with the August 2011 imposition of the LTV cap. Without correction, the observed drop in high LTVs in the 106-cap period would conflate the two policy changes. The authors apply a tiered correction: LTVs at or below 100 percent are left unchanged (the data show no notable change in that range); LTVs between 100 and 110 percent are reduced proportionally to the share of total closing costs attributable to the tax; LTVs at or above 110 percent are reduced by the full magnitude of the tax decline. This yields the “tax-adjusted pre-cap distribution” with a mean of 93.72 percent, down from 94.46 percent in the unadjusted data.

Q4. Why does the fraction of constrained households matter so much, and how does it drive non-linearity?

A: The key mechanism is that the average LTV changes when and only when the cap binds for a given borrower. The larger the share of borrowers whose LTV (in the counterfactual uncapped distribution) would exceed the cap, the larger the share of individual LTVs that move in lockstep with any change in the cap, and therefore the larger the aggregate average LTV response and, through the VECM, the house price and GDP response. As the Dutch cap tightened from 105 to 100 percent, the constrained fraction rose from roughly 20 percent to roughly 40 percent, and the annual implied decline in the average LTV grew from 22 basis points to 42 basis points — illustrating monotonically increasing non-linearity within the ex ante approach.

Q5. How does the survey design address the risk of selection bias relative to alternative data sources such as the American Housing Survey?

A: The survey, fielded in January 2016 across both the CentERpanel and LISS panel, asks retrospectively about respondents’ first home purchase, irrespective of whether they still reside there. This avoids the selection bias in the American Housing Survey, where the first-time-buyer flag captures only those still living in the first home — disproportionately selecting homes that are traded less frequently. A single-wave design also avoids the methodological discontinuities that arise from combining multiple survey waves. The resulting series covers 2,238 observations over 1979-2015 (average 60.49 per year).

Q6. What does the VECM cointegration evidence suggest about the long-run relationship between LTV, house prices, GDP, and the real mortgage rate?

A: Augmented Dickey-Fuller tests do not reject a unit root in any of the four series in levels, while all four are stationary in first differences (with the borderline case of log relative house price inflation when an intercept is included). Both the Johansen L-Max and Trace tests reject no cointegration at the 1 percent level, and neither test indicates more than one cointegrating vector. The authors therefore estimate a single-cointegrating-vector VECM with one lag (selected by the Schwarz Information Criterion) over 1981-2015. The long-run relation is normalized so that the coefficient on the log relative house price is one.

Q7. What do the impulse responses in the baseline VECM specification imply for the long-run macro effects of Dutch LTV policy?

A: Under the preferred ex post approach, twenty years after the first shock in 2011 the VECM implies that relative house prices are 4.84 percent lower and real GDP is 1.15 percent lower than the no-cap counterfactual. The bulk of the response materializes within ten years, with house prices 4.18 percent lower and GDP 1.05 percent lower at the ten-year horizon. The twenty-year real mortgage rate response is positive but negligibly small. When the ex ante approach is used instead, responses are larger owing to the larger cumulative LTV impulse.

Q8. How does the paper conduct the mean-preserving heterogeneity exercise, and what are the key quantitative results?

A: The authors generate Pearson-family distributions that match the first four moments of the Dutch pre-cap distribution (mean 93.72, standard deviation 17.09, skewness -1.16, kurtosis 5.97 under the convention that a normal has kurtosis 3), truncated to support (0, 200]. Two alternative distributions are constructed with standard deviations 25 percent below (12.97) and 25 percent above (21.61) the Pearson proxy, holding mean, skewness, and kurtosis constant. The same VECM and Cholesky ordering are applied. Twenty-year house price responses are 12.34 percent (high SD), 8.46 percent (Pearson proxy), and 4.79 percent (low SD). Twenty-year GDP responses are 2.93, 2.01, and 1.14 percent respectively. The ratio of high-to-low-SD responses is 2.58 for both variables.

Q9. How does asymmetry vary across different initial levels of the LTV cap for the Dutch distribution, and what is the intuition?

A: At a starting cap of 100 percent, a ten-percentage-point tightening produces a long-run house price response 2.33 times larger (in absolute value) than a ten-percentage-point easing from the same starting point. At 80 percent the asymmetry ratio falls to 1.17, meaning the effects of tightening and easing are nearly symmetric. The intuition is that at 80 percent the cap is binding for the bulk of the distribution, so both tightenings and easings move a similarly large fraction of borrowers and have large, roughly comparable effects. At 100 percent, far fewer borrowers are currently constrained, so an easing from 100 to 110 moves almost no one whereas a tightening from 100 to 90 moves substantially more.

Q10. What does the comparison of the heterogeneous-borrower and homogeneous-borrower cases reveal about the implications for TANK and HANK models?

A: Under the homogeneous benchmark — all borrowers at the mean Dutch LTV of 93.72 percent — changes in the cap produce infinite asymmetry at cap levels of 100 and 95 percent (tightening has a full effect, easing has zero effect) but zero asymmetry and zero effect for any cap level above 95 percent. For example, an increase in the cap from 95 to 105 percent has no effect in the homogeneous case but raises house prices by 10.72 percent in the heterogeneous case. In sum, homogeneous-borrower models — including TANK frameworks and linearized models with always-binding constraints such as Iacoviello (2005) — overstate asymmetry in a narrow range around the mean LTV and simultaneously understate the effects of cap changes above the mean LTV. The results are more consistent with heterogeneous-agent frameworks, though the authors note they are not aware of any existing HANK paper that investigates asymmetry and non-linearity specifically in response to changes in the borrowing limit.

Q11. What do the robustness checks show about sensitivity of results to LTV measurement choices?

A: The results are robust to all alternative Cholesky orderings, to using the real mortgage rate computed as the nominal rate minus current (rather than two-year moving average) inflation, to using the computed LTV without cross-checking, and to using the directly reported LTV after cross-checking. The most notable alternative is the directly reported LTV without cross-checking, which yields a twenty-year house price response of 3.81 percent and a GDP response of 0.72 percent (ex post approach), somewhat lower than the baseline of 4.84 and 1.15 percent but in the same direction. A further robustness check using an LTV series that extrapolates 2011-2015 values from the Loan Level Data yields larger estimates (cumulative twenty-year house price response of 6.65 percent and GDP response of 1.40 percent), reflecting the LLD series’ more moderate drop in 2014.

Q12. What is the policy implication regarding the importance of distributional information for gauging LTV policy effects?

A: The results imply that knowing the mean of the LTV distribution is not sufficient for estimating the effects of cap changes: the variance — and specifically the fraction of borrowers constrained by the cap — is critical. This is analogous in spirit to the finding of Krueger, Mitman, and Perri (2016) that matching the tails of the wealth distribution, and not just the mean, is essential for determining the aggregate consumption effects of shocks. Existing empirical literature that focuses on the first moment of the LTV distribution will therefore systematically mismeasure the macro effects of LTV limits, and the direction of the bias depends on where the cap stands relative to the distribution.

Key Concepts

Loan-to-value (LTV) cap / limit: The regulatory maximum on the ratio of total mortgage loan amount to the purchase price of the property (excluding buyer-incurred closing costs such as sales taxes and notary fees). In the Netherlands, this was set at 106 percent from August 2011 and reduced annually by one percentage point to 100 percent by January 2018. The paper explicitly distinguishes the cap (the regulatory threshold) from the average LTV (the cross-sectional mean of the distribution, which the cap may or may not bind for all borrowers).

Underlying (or pre-cap) LTV distribution: The cross-sectional distribution of LTV ratios that would prevail in the absence of any LTV cap — approximated in the paper by the empirical distribution in the twelve months before the cap was introduced (2010M8-2011M7, adjusted for the June 2011 sales-tax cut). The shape, mean, and variance of this distribution determine the fraction of borrowers who are constrained by any given cap level and therefore govern the magnitude and symmetry of policy effects.

Mean-preserving change in heterogeneity: A change in the standard deviation of the LTV distribution that holds the mean (and, in the paper’s stylized scenarios, also the skewness and kurtosis) constant. The paper uses this construct to isolate the effect of dispersion per se on the macroeconomic consequences of cap changes, showing that a 25 percent increase in the standard deviation relative to the Dutch baseline more than doubles the macro effects relative to a 25 percent decrease.

Ex ante approach: The method of translating cap changes into average LTV changes that uses only the pre-cap distribution, applying successive cap levels to that single distribution. It does not require an LTV cap to have been in place and is therefore applicable for prospective analysis. It does not account for exceptions to the cap.

Ex post approach: The method that uses the most recent empirical LTV distribution preceding each cap change as the proxy for the counterfactual uncapped distribution, and that explicitly accounts for the observed share of borrowers above the cap (treated as exceptions). Preferred by the authors when feasible because it incorporates information about how the underlying distribution has evolved for reasons unrelated to the current cap change.

Asymmetry ratio: The ratio of the absolute value of the long-run house price (or GDP) response to a ten-percentage-point tightening in the cap to the absolute value of the response to a ten-percentage-point easing from the same initial cap level. A ratio exceeding one indicates that tightenings have larger effects than easings of equal magnitude from the same starting point. In the paper, this ratio is shown to depend critically on where the initial cap sits relative to the underlying distribution.

Non-linearity in LTV effects: The property that changes in the cap from a lower starting point have larger macroeconomic effects than changes from a higher starting point, for a given underlying distribution. This arises because the fraction of constrained borrowers increases as the cap is tightened, so a further tightening moves a larger share of individual LTVs. In the paper, this is documented through the increasing year-on-year effects in Table 1 and the large difference between the house price response to a tightening from 110 to 100 percent (6.12 percent) versus from 100 to 90 percent (14.27 percent).

Pearson system (as used in this paper): A parametric family of distributions in which every combination of the first four moments (mean, variance, skewness, kurtosis) corresponds to a unique distribution. The authors use it to construct smooth approximations to the empirical Dutch distribution with the same mean, skewness, and kurtosis but varying standard deviations, enabling a controlled comparison of heterogeneity scenarios.

How Bad Are Weather Disasters for Banks?

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

Using FEMA disaster declarations matched to SHELDUS property-damage estimates and Call Report data for 1995–2018, this paper finds that weather disasters — even at their most severe — have had modest effects on U.S. bank safety over the last quarter century. For single-county banks exposed to 95th-percentile disasters, Z-scores decline by roughly 9 percent at a five-year horizon under the panel estimates; reaching failure thresholds from sample mean Z-score levels would require a disaster approximately 6.7 standard deviations more destructive than a 95th-percentile event. Federal disaster aid does not appear to be the primary driver of this resilience, since banks exposed to weather events without FEMA declarations exhibit similar stability. Instead, the paper points to a loan demand channel — multi-county bank lending increases roughly 0.25 percentage points per standard deviation of damage at five years without an accompanying interest-rate increase — and to local banks’ apparent avoidance of mortgage lending in flood-prone areas beyond what official flood maps predict, consistent with local information about true flood risk limiting exposure before disasters strike.

In depth

Q1. How severe are weather disaster effects on bank safety?

The paper finds that weather disasters at any severity level produce small and often statistically insignificant effects on the key bank safety measures — charge-offs, capital ratios, return-on-assets volatility, and Z-scores — at single-county banks, with the largest measured effect being roughly a 9 percent decline in Z-scores at the 95th percentile of disaster damage at a five-year horizon. The regression framework uses bank and state-year fixed effects, with SHELDUS damage as the continuous severity measure and FEMA disaster declarations as a binary indicator. For multi-county banks, charge-offs increase by roughly 10 percent at five years, but net income also rises, suggesting disaster-area loan demand partially offsets credit losses. The paper’s calculation is that pushing a typical bank from its mean Z-score of 135.9 to the failure threshold would require a Z-score decline of 127.9 — far exceeding the estimated −9 percent impact of a 95th-percentile disaster, which would need to be approximately 6.7 standard deviations more destructive to close that gap.

Q2. Is bank resilience an artifact of federal disaster aid?

The paper presents evidence that federal disaster aid is not the primary source of bank resilience, since banks exposed to weather events that did not receive FEMA disaster declarations exhibit similarly modest effects on bank safety measures. The test is designed to separate the insurance mechanism (FEMA aid replacing household income and debt service capacity) from intrinsic bank resilience. The fact that non-FEMA disasters produce comparable stability redirects attention to the demand-side and local-knowledge channels as the more fundamental explanations for the resilience finding.

Q3. What is the loan demand channel and how large is it?

Multi-county banks experience an increase in lending of roughly 0.25 percentage points per standard deviation of SHELDUS damage at a five-year horizon, and the authors find no accompanying increase in loan interest rates, which is consistent with a demand-side shift rather than a tightening of lending standards. The demand interpretation is that disasters create a wave of borrowing demand as households and firms repair or replace damaged assets, and the increased loan volume helps offset the increase in charge-offs. The pattern is found at multi-county banks — which can serve affected and unaffected areas simultaneously — but not at single-county banks, consistent with lending capacity mattering for capturing the demand increase.

Q4. What does “local knowledge” mean in this context?

Local banks originate approximately 6.4 percent fewer log mortgage dollars per application in FEMA flood zones than would be predicted by the official flood map classifications alone, with the gap widening to 7–8 percent in areas that have experienced more than five FEMA flood declarations compared to areas with fewer than three, which is consistent with local lenders holding information about true flood risk not captured in official maps. The finding is consistent with local banks having access to community-level information — observed flooding history, property-level characteristics, local drainage and elevation — that is not incorporated into official FEMA flood zone classifications. This pre-disaster selectivity limits mortgage accumulation in the highest-risk areas before disasters occur.

Q5. What are the implications for climate risk assessment?

The paper explicitly frames the historical resilience documented for 1995–2018 as informing rather than settling assessments of physical risk to banks from future climate change, since more frequent or more severe disasters could overwhelm the demand-offset and local-knowledge mechanisms that the paper identifies as sustaining bank performance. The key qualification is temporal scope: the demand-side recovery effect requires that affected areas have the income and economic capacity to service new loans, and the local-knowledge effect requires that banks have experienced enough repeated flooding to develop accurate private flood risk assessments. Both conditions could become less reliable as climate change alters the frequency, geography, and severity of weather events relative to the historical distribution.

Key concepts

Z-score : a bank-level distance-to-insolvency measure equal to (return on assets + capital ratio) divided by return-on-assets volatility; higher values indicate greater distance from failure; used here as the primary measure of disaster impact on bank safety.

SHELDUS : the Spatial Hazard Events and Losses Database for the United States, providing county-level property damage estimates for weather events; used in this paper as the continuous measure of disaster severity in panel regressions.

single-county bank : a bank whose entire depositor base is drawn from one county, making it fully exposed to local disaster effects with no geographic diversification across other counties.

loan demand channel : the mechanism by which disasters increase demand for credit from households and firms repairing or replacing damaged assets, generating new loan volume that partially offsets credit losses at banks serving affected areas.

local knowledge : the paper’s label for the informational advantage that local banks appear to have about true flood risk beyond what official FEMA flood zone classifications capture, inferred from lower mortgage originations in areas with a history of repeated flooding.

How Banks Create Gridlock in Payment Systems to Save Liquidity: The Case of Canada

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

This paper uses detailed transaction-level data from Canada’s new high-value payment system (HVPS) to show how participants save liquidity by strategically exploiting the gridlock resolution arrangement built into the system. Observed behaviors are found to be consistent with the equilibrium of a “gridlock game” that captures the key incentives participants face: by withholding outgoing payments to induce gridlock events, participants trigger the system’s bilateral netting algorithm, which settles stuck payment queues at lower liquidity cost than bilateral sequential settlement would require. The findings have implications for the design of high-value payment systems and shed light on financial institutions’ liquidity preference in payment system environments.

In depth

Q1. What is the gridlock resolution arrangement and why do banks exploit it?

Modern high-value payment systems (HVPSs) include a gridlock resolution mechanism that activates when a set of payments are mutually stuck in queues—each waiting for an incoming payment before it can be sent—and resolves them simultaneously via bilateral netting, which requires less settlement liquidity than sequential settlement; banks strategically withhold outgoing payments to trigger these events and thereby save liquidity. The HVPS studied is Canada’s new large-value transfer system, which replaced the older LVTS. The gridlock game captures the incentive structure: if a bank expects counterparties to send payments that would be netted against its own obligations in a gridlock, it is optimal to withhold and wait rather than settle bilaterally at higher liquidity cost.

Q2. How is the gridlock game formalized?

The “gridlock game” is a formal game-theoretic model that captures the key incentives participants face in the HVPS: players choose whether and when to send payments, and the equilibrium characterizes the strategic withholding behavior as a rational response to the liquidity-saving opportunities created by the gridlock resolution mechanism. The equilibrium of this game is shown to be consistent with the actual patterns observed in the HVPS data: the timing, magnitude, and counterparty structure of strategic withholding are aligned with the game’s equilibrium predictions.

Q3. What are the implications for HVPS design?

The finding that participants strategically exploit the gridlock resolution mechanism has implications for HVPS design: while gridlock resolution was intended as an exception-handling mechanism for unintended payment queue build-ups, participants have adapted to use it as a routine liquidity management tool, changing the system’s effective operation in ways the designers may not have anticipated. System designers must account for the strategic response of sophisticated participants when evaluating the performance of gridlock resolution mechanisms, since the equilibrium behavior changes the frequency, timing, and magnitude of gridlock events relative to the non-strategic benchmark.

Q4. What does the evidence reveal about banks’ liquidity preferences?

The strategic gridlock behavior reveals that financial institutions place significant value on conserving payment system liquidity—enough to coordinate timing of payment submissions in ways that exploit system-level netting opportunities—consistent with liquidity being a scarce and valuable resource in modern payment systems. This preference for liquidity conservation is amplified in environments where central bank reserves are costly and where payment system participants face collateral or reserve constraints.

Key concepts

gridlock in high-value payment systems : a situation in which a set of payments are mutually stuck in queues—each waiting for incoming funds before outgoing payment can be made—requiring the system’s bilateral netting algorithm to simultaneously settle them; exploited strategically by banks to save settlement liquidity. gridlock game : the paper’s game-theoretic model of strategic payment submission timing in an HVPS; captures the incentive to withhold outgoing payments to trigger gridlock resolution events that settle payment queues at lower net liquidity cost. bilateral netting in HVPS : the gridlock resolution mechanism that settles multiple mutually stuck payments by computing net obligations among participants and settling only the differences; requires less total settlement liquidity than sequential bilateral settlement and is the mechanism banks exploit in the gridlock game.

How Do Rising U.S. Interest Rates Affect Emerging and Developing Economies? It Depends

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

Layer 1 — Overview

Research Question

This paper examines how the effects of rising U.S. interest rates on emerging market and developing economies (EMDEs) depend on the underlying source of the interest rate increase. Specifically, it asks: what mix of inflation, reaction, and real shocks has driven changes in U.S. interest rates in recent years; how do these different shock types affect EMDE financial markets, capital flows, borrowing costs, and fiscal outcomes; and how do they affect the likelihood of EMDE financial crises?

Motivation and Context

Written in late 2022 against the backdrop of the Federal Reserve’s most aggressive tightening cycle since the 1990s, the paper argues that the standard practice of treating all interest rate increases as equivalent is misleading. Whether rising U.S. rates reflect strengthening growth, rising inflation expectations, or a perceived hawkish shift in the Fed’s reaction function carries very different implications for EMDEs already burdened by post-COVID debt at record highs and scarring from the pandemic.

Methodology

Three distinct empirical approaches are used, chosen to match the data frequency and parsimony requirements of each research question.

A sign-restricted Bayesian VAR model with stochastic volatility is estimated on monthly U.S. data (January 1982 - September 2022) using four variables: 2-year Treasury yield, 10-year Treasury yield, S&P 500 index, and 5-year breakeven inflation expectations. Sign restrictions identify three shocks: (i) real shocks raise both yields, equity prices, and inflation expectations; (ii) inflation shocks raise yields and inflation expectations but lower equity prices; (iii) reaction shocks raise yields but lower both equity prices and inflation expectations.
Panel local projection models (Jorda 2005) are estimated at quarterly frequency for 17-38 EMDEs over 1997Q2-2019Q4, excluding the 2008Q4-2009Q4 global financial crisis and the COVID-19 pandemic. The models link the VAR-identified quarterly shock series (normalized to represent a 25-basis-point move in the 2-year yield) to EMDE financial, real, and fiscal variables, including local-currency bond yields, EMBI+ sovereign spreads, capital flows, real GDP components, CPI inflation, the real effective exchange rate, primary fiscal balance, government revenues, expenditures, gross debt, and debt composition.
A panel logit model with random effects is estimated on annual data for 139 EMDEs over 1985-2018, linking the three shock types to the probability of banking, currency, and sovereign debt crises (as defined by Laeven and Valencia 2020).

Key Findings

Shock decomposition: Real shocks account for the largest share of variance in 2-year U.S. yields over the full sample (39 percent at a 10-month horizon); inflation shocks explain 14 percent and reaction shocks 13 percent. However, since the start of 2022, reaction and inflation shocks together account for approximately three-quarters of the cumulative increase in yields, with real shocks playing a negligible role.

Financial market and macroeconomic spillovers: Conditional on a 25-basis-point shock, reaction shocks produce significantly adverse EMDE outcomes: widening sovereign spreads (EMBI+), declining capital flows, real exchange rate depreciation, and unlike inflation shocks, statistically significant declines in private consumption and fixed investment. Inflation shocks raise domestic EMDE CPI significantly. By contrast, real shocks are associated with declining sovereign spreads, rising capital flows, real exchange rate appreciation, and higher real exports, with other real GDP components unaffected.

Fiscal outcomes: In response to inflation and especially reaction shocks, EMDE governments improve their primary balances almost exclusively through expenditure cuts, consistent with tighter credit availability constraining fiscal space. Real shocks also improve primary balances, but through both revenue gains and expenditure reductions. Government debt declines in response to all three shock types, though the decline is statistically significant only for real shocks.

Debt composition: Reaction shocks shift debt composition toward shorter maturities and foreign-currency instruments (the latter reflecting exchange rate depreciation mechanically raising the local-currency value of foreign-currency debt). Real shocks shift composition toward longer maturities and higher external creditor participation, consistent with improved market access.

Heterogeneity by credit rating: Investment-grade and noninvestment-grade EMDEs show broadly similar responses to reaction shocks, with the exception of statistically larger yield responses for noninvestment-grade economies. The paper notes this finding contrasts with several prior studies that find stronger fundamentals buffer spillovers.

Crisis probabilities: A 25-basis-point increase in 2-year U.S. yields driven by a reaction shock almost doubles the baseline probability of financial crisis in the average EMDE, from 3.5 percent to 6.6 percent. Extrapolating the nonlinear logit relationship to the 114-basis-point reaction-shock-driven increase in 2-year yields that occurred from January through September 2022 implies the probability of financial crisis in the average EMDE rising approximately 36 percentage points, to nearly 40 percent. The paper cautions that no comparable yield episode occurred in the 1985-2018 estimation sample, so this extrapolation carries substantial uncertainty. Inflation shocks are associated with only small, statistically insignificant changes in crisis probability; real shocks reduce the probability of sovereign debt crisis while raising currency crisis probability by less than reaction shocks do.

Historical episode analysis: The 2013 taper tantrum was dominated by reaction shocks, causing 10-year yields to rise by approximately 100 basis points; sovereign spreads widened by 60 basis points in the May-June 2013 window and capital flows dropped sharply. The 2022 tightening episode was driven by reaction and inflation shocks (reaction shocks adding 114 basis points to 2-year yields through September 2022), with five-year breakeven inflation expectations breaching 3 percent for the first time in the two-decade history of the series. The 2004-2006 build-up to the global financial crisis involved a mix of all three shock types with real shocks prominent, and EMDE financial conditions remained broadly benign.

In depth

Q1. How are the three shock types identified, and what makes this identification strategy credible?

The identification uses sign restrictions imposed on a Bayesian VAR with stochastic volatility. A real shock is identified as one that simultaneously raises 2-year yields, 10-year yields, S&P 500 equity prices, and inflation expectations. An inflation shock raises all yields and inflation expectations but lowers equity prices the equity decline signals that higher rates are not accompanied by stronger growth prospects. A reaction shock raises all yields but lowers both equity prices and inflation expectations the fall in inflation expectations distinguishes it from an inflation shock and signals that markets perceive the Fed is tightening beyond what current inflation warrants. Covering both short- and long-maturity yields in the sign restrictions ensures the identified shocks capture both conventional and unconventional (e.g., quantitative easing tapering) policy moves.

At a 10-month horizon, real shocks explain 39 percent of the forecast error variance in 2-year U.S. Treasury yields, making them the dominant driver over the full sample (January 1982 - September 2022). Inflation shocks account for 14 percent and reaction shocks for 13 percent. Together the three identified shocks explain roughly two-thirds of total yield variation; the remaining one-third reflects residual or unclassified movements.

Q3. How did the composition of shocks driving 2-year yields change from 2021 into 2022?

Starting in September 2021, as inflation mounted and the Fed pivoted toward aggressive tightening, reaction and inflation shocks became the dominant drivers of 2-year yield increases. By September 2022, reaction and inflation shocks together accounted for approximately three-quarters of the cumulative increase in yields from the beginning of 2022, with reaction shocks alone contributing 114 basis points to the 2-year yield.

Q4. What are the financial market effects of a 25-basis-point reaction shock on EMDEs?

Reaction shocks produce significant adverse effects on EMDE financial markets within one quarter: 10-year local-currency government bond yields rise significantly, EMBI+ sovereign spreads widen significantly, capital flows decline significantly, and the real effective exchange rate depreciates significantly. Short-term (3-month) yields and equity prices also deteriorate, but these movements are not statistically significant at conventional levels.

Q5. How do financial market effects of inflation shocks compare to reaction shocks?

Inflation shocks generate adverse directional effects similar to reaction shocks rising 10-year yields, declining capital flows, real exchange rate depreciation, and falling equity prices but with the notable difference that, except for equity prices, these effects are generally not statistically significant. The paper thus finds that reaction shocks are more potent drivers of EMDE financial market tightening than inflation shocks.

Q6. How do real shocks affect EMDE financial conditions?

Real shocks produce outcomes broadly opposite to those from inflation and reaction shocks. They are associated with significant declines in EMBI+ sovereign spreads, significant increases in capital flows, significant real effective exchange rate appreciation, and significant increases in equity prices. Ten-year government bond yields do rise consistent with global bond market integration but this occurs alongside improving risk sentiment, not financial stress.

Q7. What are the macroeconomic (real activity) effects of the three shock types?

Reaction shocks produce a statistically significant decline in real GDP components, particularly in private consumption expenditure and gross fixed capital formation (fixed investment), within one quarter. Real shocks lead to higher real exports consistent with beneficial demand spillovers from stronger U.S. activity while leaving other GDP components unchanged. Inflation shocks induce a large and statistically significant increase in domestic EMDE CPI inflation, while real shocks reduce it; neither produces significant real GDP effects beyond the export channel.

Q8. How do EMDE fiscal balances respond differently to the three shock types?

Both inflation and especially reaction shocks are followed by an improvement in the EMDE primary balance (smaller deficit or larger surplus), achieved almost exclusively through declines in government expenditure. The paper attributes this to tighter credit availability and higher borrowing costs constraining fiscal space. Real shocks also improve primary balances, but the mechanism differs: both revenue increases and expenditure decreases contribute to the improvement. Declines in gross government debt occur in response to all three shocks but are statistically significant only for real shocks.

Q9. How does the composition of government debt shift in response to the different shocks?

Following inflation and reaction shocks, debt held by external creditors declines significantly as a share of total government debt, consistent with reduced access to global credit markets. Short-term debt eventually rises following both shock types. Foreign-currency debt rises considerably following reaction shocks likely reflecting the mechanical effect of currency depreciation boosting the local-currency value of pre-existing foreign-currency obligations. Conversely, following real shocks, external creditor participation rises significantly (improved market access), foreign-currency debt shares remain broadly stable, and short-term debt declines significantly (consistent with maturity extension by fiscal authorities seeking to minimize rollover risk under favourable conditions).

Q10. Do investment-grade and noninvestment-grade EMDEs respond differently to reaction shocks?

The paper finds little evidence of important differences between investment-grade and noninvestment-grade EMDEs in their responses to reaction shocks across most variables. Noninvestment-grade economies do show statistically larger increases in 10-year bond yields, and larger increases in EMBI+ spreads and 3-month yields than investment-grade economies though the latter two differences are not statistically distinguishable. For fiscal, GDP, and capital flow outcomes, the two groups respond similarly. The paper notes this finding is inconsistent with several prior studies but consistent with others, concluding the role of fundamentals remains unresolved.

Q11. How does the probability of financial crisis in EMDEs respond to the three shock types?

In the baseline (explanatory variables at sample means), the average EMDE faces a 3.5 percent probability of experiencing any type of financial crisis in a given year, with currency and banking crises the most common and sovereign debt crisis the least. Reaction shocks drive by far the largest increase: a 25-basis-point increase in 2-year yields from a reaction shock almost doubles the crisis probability to 6.6 percent. Inflation shocks produce small and statistically insignificant effects. Real shocks reduce the probability of sovereign debt crisis (consistent with their benign effects on financial markets) while raising currency crisis probability by less than reaction shocks.

Q12. What does the nonlinear logit relationship imply for the 2022 tightening cycle specifically?

Because the logit function is nonlinear, a doubling of the shock size leads to a more-than-proportional increase in crisis probability. Applying the estimated model to the 114-basis-point reaction-shock contribution to 2-year yields from January to September 2022, the model implies that the probability of financial crisis in the average EMDE increased by approximately 36 percentage points, to nearly 40 percent. The paper emphasizes this estimate carries wide uncertainty because no comparable yield increase occurred during the 1985-2018 estimation period, placing this extrapolation well outside the sample’s support.

Q13. What crisis dynamics were already materializing in 2022 consistent with the model predictions?

By the time of writing (late 2022), seven EMDEs had experienced currency depreciations of at least 30 percent against the U.S. dollar meeting the Laeven and Valencia (2020) threshold for a currency crisis and 21 EMDEs had reached agreements with the IMF for additional financing. The paper notes these developments had occurred despite standard macroeconomic factors (interest rate differentials and flight-to-safety flows) not fully explaining the magnitude of depreciations.

Q14. What robustness tests were conducted, and did they alter the main conclusions?

The VAR decomposition was re-estimated using weekly rather than monthly data. The three-shock model was simplified to two shocks (real versus monetary, combining inflation and reaction). The VAR was extended to include real GDP and PCE inflation with contemporaneous exclusion restrictions to insulate shock identification from current macroeconomic conditions. Inflation expectations were replaced with the Haubrich, Pennacchi, and Ritchken (2012) model-based measure throughout, rather than only pre-2003. For the crisis probability models, panel probit with random effects and panel logit with fixed effects were estimated alongside the baseline panel logit with random effects. In all cases, the results were not materially different: inflation and reaction shocks remained more adverse than real shocks for EMDE financial and fiscal variables, and only reaction shocks produced statistically significant increases in overall crisis probability. One noteworthy robustness finding: when combining inflation and reaction into a single monetary shock, the relative importance of the inflation component appears somewhat larger than when the two are separated.

Q15. What are this paper’s main contributions relative to existing literature?

The paper makes three stated contributions. First, it is the first to decompose the evolution of U.S. interest rates over the COVID-19 pandemic recession, subsequent recovery, and 2021-22 inflation surge into the separate contributions of real, inflation, and reaction shocks. Second, it extends prior work on EMDE spillovers (e.g., Arteta et al. 2015; Hoek, Kamin, and Yoldas 2021, 2022) by showing how different shock types affect government budget balances, revenues, expenditures, and debt composition, and by expanding the EMDE country sample. Third, it is the first to examine how real, inflation, and reaction shocks differentially affect the probability of banking, currency, and sovereign debt crises in EMDEs.

Key Concepts

Reaction shock: In this paper’s framework, a change in U.S. interest rates caused by a perceived shift in the Federal Reserve’s reaction function toward a more hawkish policy stance. Identified as a shock that raises both 2-year and 10-year Treasury yields while simultaneously lowering equity prices and lowering inflation expectations. The fall in inflation expectations distinguishes this shock from an inflation shock and signals that markets believe the Fed is tightening beyond what current inflation alone would warrant.

Inflation shock: A change in U.S. interest rates caused by rising expectations of U.S. inflation. Identified as a shock that raises both yields and inflation expectations but lowers equity prices. The equity decline signals that higher rates reflect inflationary pressure rather than improved growth prospects.

Real shock: A change in U.S. interest rates driven by improved prospects for U.S. real economic activity. Identified as a shock that simultaneously raises both yields, equity prices, and inflation expectations. The equity increase distinguishes this shock from the other two and signals that higher rates are accompanied by strengthening U.S. growth.

Sign-restricted Bayesian VAR with stochastic volatility: The paper’s primary model for decomposing U.S. yield movements. Sign restrictions on four variables (2-year yield, 10-year yield, S&P 500, 5-year inflation expectations) identify the three shock types without requiring timing restrictions. Stochastic volatility is incorporated to handle the heteroskedastic financial data and the COVID-19 period’s unusual size and nature; the model covers February 1982 to September 2022 at monthly frequency.

Panel local projection (Jorda 2005): The empirical framework linking the VAR-identified shock series to EMDE outcomes at quarterly frequency. Direct estimation of impulse responses at each horizon h avoids the misspecification accumulated in iterated VAR forecasts and permits straightforward incorporation of state-dependent (investment-grade vs. noninvestment-grade) heterogeneity via a dummy-variable interaction specification.

Capital flows (as used in this paper): Defined specifically as increases in net portfolio and other investment liabilities of EMDEs, excluding foreign direct investment liabilities. This definition isolates the more volatile, financially driven flows rather than the longer-horizon FDI component.

Financial crisis typology (Laeven and Valencia 2020): The crisis classification underlying the logit analysis. Sovereign debt crises are defined as a government default or restructuring of debt owed to private creditors. Banking crises require significant distress in the banking system combined with significant policy intervention measures. Currency crises are defined as a sharp nominal depreciation of at least 30 percent against the U.S. dollar. The paper uses these definitions from Laeven and Valencia (2020), extended through 2018 in Kose et al. (2021).

Primary budget balance improvement via expenditure compression: In the paper’s framework, the fiscal adjustment mechanism triggered specifically by inflation and reaction shocks: EMDE governments improve their primary balance (reduce deficits or increase surpluses) almost exclusively by cutting expenditures, rather than raising revenues, as a response to the credit tightening and higher borrowing costs associated with adverse U.S. interest rate shocks.

Joined at the Hip: Monetary and Fiscal Policy in a Liquidity-Dependent World

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

Layer 1 — What this paper finds and why it matters

Calvo and Velasco study an economy where both money and government bonds provide liquidity services, and they show that this shared role implies bond-financed fiscal expansions can be neutral or contractionary — not merely less effective than hoped. The mechanism turns on a fundamental asymmetry: the price of money in terms of goods is pinned down by sticky prices, whereas the price of long-term bonds is free to jump immediately in response to expected changes in bond supply. When the government announces a future bond-financed transfer to households, bond prices fall right away, compressing total liquidity before a single new bond is actually issued; the liquidity-in-advance constraint then forces aggregate demand and output down, producing a recession that precedes and is qualitatively separable from any subsequent boom. The paper maps four distinct timing cases — unanticipated permanent, anticipated permanent, unanticipated transitory flow, and unanticipated temporary stock — and shows each has a different (and sometimes opposite) short-run sign for output. To prevent these contractionary liquidity effects, the central bank must cut the interest rate on money and expand the money supply in ways that are precisely coordinated with the timing of the bond helicopter drop; in this sense fiscal and monetary authorities are, the authors conclude, joined at the hip. The paper also distinguishes this result from standard fiscal-dominance stories: the monetary authority is not compelled to finance the deficit but to stabilize bond prices in order to protect aggregate demand.

In depth

Q1. What is the central question and how does the paper differ from the standard New Keynesian framework?

The central question is whether bond-financed government transfers raise, lower, or leave unchanged aggregate demand and output when bonds provide liquidity services. Standard Keynesian and New Keynesian treatments focus on whether expansionary fiscal policy crowds out private investment through higher interest rates, or amplifies demand when the zero lower bound binds. Calvo and Velasco instead focus on the liquidity channel: because long-term bond prices are free to jump on news about future bond supply, increases in expected bond issuance can immediately reduce the market value of outstanding bonds, compressing total liquidity in private portfolios and thereby reducing consumption and output even before any new bond is issued. They call this a “non-standard” result and note that, by contrast, the price of money is insulated from such anticipatory jumps by sticky goods prices.

Q2. What is the model structure?

The paper uses a bare-bones, continuous-time, closed-economy model with a single infinitely lived household, one consumption good, and two assets in positive net supply: money (equated with central-bank reserves) and a long-term government bond (a perpetuity paying a coupon). The key friction is a liquidity-in-advance constraint — households must hold sufficient liquidity (a weighted combination of real money balances and the real market value of bonds) to consume. The supply side is a standard Calvo (1983) Phillips curve. Policy instruments are the nominal interest rate on money, the nominal money supply, the nominal bond supply, and the bond coupon; the price of long-term bonds is endogenous. Commercial banks are abstracted away: money is effectively a CBDC. The paper notes that all main results also go through under a money-in-the-utility-function specification, provided the elasticity of substitution between consumption and liquidity is sufficiently low.

Q3. What does “liquidity” mean in the paper’s own sense, and why does the bond price matter for it?

Liquidity is defined as a CES-weighted sum of real money holdings and the real market value of bond holdings, where the market value of bonds equals the bond price times the real quantity outstanding. Because the bond price is free to jump, the market value of bonds (and therefore total liquidity) can change instantaneously in response to news, even when neither the nominal money stock nor the nominal bond stock has yet changed. Money does not share this vulnerability: its “price” in terms of goods is fixed in the short run by nominal price stickiness. This asymmetry — sticky price of money, flexible price of bonds — is the paper’s central mechanism. The authors attribute the stickiness insight to Keynes’s General Theory (the “price theory of money” as labelled by Calvo 2012).

Q4. What happens when the bond supply rises unexpectedly and permanently?

An unanticipated and permanent step increase in the nominal (and, on impact, real) supply of long-term bonds is neutral: consumption and output are unchanged. Bond prices fall immediately so that the total market value of bonds outstanding — and therefore total liquidity — is the same as before. The analogy drawn is to an unanticipated permanent increase in the money supply under fully flexible prices, which also has no real effects. The coupon must rise proportionally so that the return on bonds remains at its steady-state level. The paper notes that neutrality may not hold if bond holdings are distributed non-uniformly (e.g., concentrated in financial intermediaries that use bonds as repo collateral), because the drop in bond prices could trigger runs on those institutions.

Q5. What happens when a permanent bond-supply increase is anticipated in advance?

An anticipated and permanent future step increase in nominal bond supply causes a recession during the announcement-to-implementation interval, before any new bond has been issued. Because arbitrage prevents an anticipated capital loss on bonds, the bond price cannot jump down at the implementation date T. Instead it must fall gradually starting at announcement date 0, reaching its new (lower) steady-state level exactly at T. This declining bond price reduces the market value of bonds and thereby compresses total liquidity throughout the interval [0, T), generating deflation and a negative output gap over that entire period. A naïve observer who notes an output boom just as the government begins to issue bonds at T would incorrectly conclude the policy is expansionary, when in fact the boom is the recovery from the pre-implementation recession.

Q6. What happens when the fiscal authority issues bonds at a constant rate for a finite period (transitory flow)?

An unanticipated, transitory, constant-rate bond issuance over an interval [0, T) also has a recessionary impact on impact and during the issuance period. Bond prices fall faster than the nominal bond stock accumulates, so the total market value of bonds declines and liquidity is compressed. The Calvo-Phillips equation evaluated with negative and rising inflation implies a negative output gap throughout the early part of the episode. A boom follows after bond issuance ends — not because “confidence is restored” or fiscal sustainability has improved, but because the boom is mechanically part of the same liquidity-adjustment cycle as the earlier recession.

Q7. What happens under an unanticipated but temporary step increase in the bond stock?

An unanticipated but temporary step increase in bond supply — one that will be reversed at a known future date T — is expansionary on impact. Because the price of bonds cannot be anticipated to jump at T, the bond price must rise from its impact level back to the initial steady state by T. On impact, the bond price falls but by less than the increase in nominal bond supply, so the market value of bonds rises and total liquidity increases, pushing aggregate demand and output above their natural rates. The initial boom is thus followed by a recession around the time bond supply is cut back, which the authors note could generate political pressure to extend the “expansionary” fiscal policy.

Q8. What is the common mechanism linking the contractionary cases?

In both contractionary cases (anticipated permanent and unanticipated transitory flow), the bond price falls more rapidly than the bond stock rises, so the total market value of bonds declines, compressing liquidity. From the model’s liquidity identity (equation 18 in the paper), total liquidity depends on real money balances (fixed on impact) plus a weight on the relative position of bonds to money. When that relative position (captured by the variable s_t in the model) falls, total liquidity falls. The liquidity-in-advance constraint then directly constrains consumption and output downward. Deflation is the only endogenous mechanism to rebuild real liquidity, but it works gradually and involves a protracted recession.

Q9. What monetary policy does the paper prescribe to neutralize the contractionary effects?

To avoid the contractionary liquidity effects of anticipated bond helicopter drops, the central bank must cut the interest rate on money and expand the money supply in a manner whose precise time profile depends on the timing of the fiscal shock. For an anticipated permanent bond-supply increase, the required monetary response involves gradually expanding the nominal money supply between announcement and implementation, followed by a discrete step decrease in nominal (and real) money at exactly the moment bond supply jumps up. This coordinated monetary expansion offsets the bond-price-driven compression of liquidity. The paper confirms this formally in Section IV (not fully extracted in the source text), with the conclusion that avoiding unwanted contractionary effects requires coupling fiscal bond issuance with specific, coordinated monetary actions.

Q10. How does the paper relate to fiscal dominance — and how does it differ?

The paper identifies a novel form of fiscal dominance in which monetary policy is compelled not to monetize the fiscal deficit but to stabilize government bond prices in order to protect aggregate demand and inflation. Traditional fiscal dominance (common in emerging markets) forces the central bank to print money to finance the deficit. Here, the mechanism is different: expected bond issuance drives down bond prices and compresses liquidity, so the central bank must intervene in bond markets — effectively buying newly issued bonds — to prevent deflationary recessions. An outside observer could mistake this for traditional monetization. The paper frames the Federal Reserve’s $1 trillion Treasury purchase program from mid-March 2020 onward as consistent with this bond-price-stabilization logic, citing Vissing-Jorgensen (2021) on the causal role of Fed purchases in driving down yields through acute liquidity provision.

Q11. What is the scope of the non-standard results?

The non-standard (neutral or contractionary) results apply specifically to bond-financed increases in government transfers to the private sector; money-financed fiscal expansion and bond-financed government consumption changes are not the focus and do not share these properties in the model. The authors explicitly note this caveat. However, they argue the exercise is policy-relevant because much of the fiscal response to both the 2008 Global Financial Crisis and the Covid-19 crisis took the form of sharp increases in government transfers financed by bond issuance. The model also assumes lump-sum taxes, so in the absence of liquidity effects Ricardian equivalence would obtain; all non-neutralities are driven entirely by the liquidity channel.

Key concepts

Liquidity-in-advance constraint : An analog of a cash-in-advance constraint in which the household must hold a weighted sum of real money balances and the real market value of bonds sufficient to finance current consumption; it always binds in the model’s equilibrium, so liquidity directly pins down output.

Price theory of money : The proposition (attributed to Keynes and labelled by Calvo 2012) that money is highly liquid partly because the nominal goods-price level is sticky, fixing the price of money in terms of goods; this insulates the real value of money from the anticipatory jumps that affect bond prices.

Bond helicopter drop : A government transfer to households financed by issuing long-term bonds (perpetuities), with no change in taxes or money supply; the term “helicopter drop of bonds” is used by the authors to parallel Friedman’s helicopter money but with bonds as the instrument.

Bond-price stabilization (non-traditional fiscal dominance) : The authors’ term for a situation in which expected fiscal bond issuance compresses bond-market liquidity and forces the central bank to expand money supply and cut the interest rate on money in order to stabilize bond prices and prevent contractionary effects, even though the central bank is not formally required to finance the deficit.

s_t (bond-to-money relative position) : A model variable defined as the log-deviation from steady state of the ratio of the real market value of bonds to real money balances; it captures the relative contribution of bonds to total portfolio liquidity and is the key endogenous state variable linking bond-price dynamics to aggregate demand.

Calvo-Phillips curve : The standard Calvo (1983) staggered-pricing supply side, used here to generate the inflation-output gap trade-off; in the paper’s notation, inflation dynamics satisfy π̇_t = δπ_t − κ(y_t − ȳ), where output gaps are driven by liquidity shortfalls rather than standard demand shocks.

Long-Term Debt and Short-Term Rates: Fixed-Rate Mortgages and Monetary Transmission

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

This paper uses instrumental-variable local projections (IV-LP) on an unbalanced panel of up to 35 countries over approximately two decades to establish two interconnected findings about fixed-rate mortgages (FRMs) and monetary policy. First, monetary policy affects mortgage type selection: a 100 basis point tightening increases the share of adjustable-rate mortgages (ARMs) in new originations by approximately 10 percentage points after one year, while easing generates the reverse shift toward FRMs. The mechanism is budget constraints: ARM rates move nearly one-for-one with policy rates while FRM rates respond by only about 0.5 percentage points per 100 bps, so after tightening the FRM-ARM spread narrows but both products become more expensive — households facing tighter budgets select the cheaper ARM option, irrespective of spread comparisons. Second, the prevailing stock composition of outstanding ARMs determines how strongly monetary policy transmits to real activity: for every additional percentage point of household debt held as ARMs, the same 100 bps policy change produces approximately 0.05 percentage points more impact on real private consumption at six quarters ahead, controlling for the level of household debt-to-GDP. A back-of-the-envelope calculation implies that the same 100 bps change induces a consumption response approximately 5 percentage points stronger in an economy with 100 percent ARMs versus one with only FRMs. These two findings jointly imply that FRMs create both path-dependency (past easing cycles populate the stock with FRMs, weakening future transmission) and state-dependency (current FRM prevalence determines how much a given rate change moves consumption and GDP) in monetary policy.

In depth

The paper draws on two data sources: flow data covering new mortgage originations in 27 countries and stock data on the outstanding mortgage composition in 35 countries, spanning approximately two decades of quarterly observations. A mortgage is classified as fixed-rate (FRM) if the contractual interest rate is fixed for 12 months or more from origination; below that threshold it is classified as adjustable-rate (ARM). This definition aligns with ECB and Eurostat conventions and is consistent across the panel, though note that some “fixed-rate” mortgages in the sample include hybrid products with initial fixed periods that eventually reprice. The FRM share in new flows (used in the path-dependency analysis, equation 2) captures how the composition of new originations responds to monetary policy. The FRM share in outstanding stock — expressed as a proportion of household debt-to-GDP (ARMdebt) — is the state variable in the state-dependency analysis (equation 3). Countries’ time-series for both measures display the expected patterns: in the long period of ultra-low rates following the GFC, the FRM share in stock increased substantially across the sample.

Q2. How are monetary policy shocks identified and why are information effects excluded?

Monetary policy shocks are constructed from Bloomberg high-frequency financial market surprises around central bank announcement windows, then orthogonalized with respect to the central bank’s private information component using the Bauer and Swanson (2023) procedure. The Bauer-Swanson orthogonalization removes the portion of policy surprises that is correlated with the central bank’s assessment of the economic outlook — the “Fed information effect” identified by Nakamura and Steinsson (2018). Without this purification, a policy surprise that partly reflects the central bank’s private negative news about growth would confound the identification: the estimated consumption response would reflect both the direct policy-rate effect and the information revelation, making it impossible to isolate the transmission mechanism through mortgage types. The first-stage Kleibergen-Paap Wald F statistics are 34 or above for the path-dependency regression (equation 2) and 12.9 or above for the state-dependency interaction regression (equation 3), satisfying standard relevance thresholds.

Q3. What is the path-dependency mechanism and what does Figure 3 show?

Figure 3 plots impulse responses of FRM rates, ARM rates, 10-year and 1-year government bond yields, the FRM-ARM spread, and the ARM share in new flows to a one percentage point policy rate change instrumented with the Bauer-Swanson-cleaned shocks. FRM rates respond by approximately 0.5 percentage points per 100 bps of policy change, similar to the response of 10-year government bond yields, with full reversion after about 4–6 quarters. ARM rates respond approximately one-for-one, similar to 1-year yields, also reverting after 4–6 quarters. Since ARM rates respond more than FRM rates, the FRM-ARM spread narrows by about 0.5 percentage points after a 100 bps tightening — making ARMs relatively cheaper compared to FRMs. Despite this narrowing of the spread (which should theoretically discourage ARM selection), the paper finds that ARM share in new flows increases significantly: a 100 bps tightening raises the ARM share by approximately 10 percentage points after one year, a large effect corresponding to about two thirds of a within-country standard deviation. The paper attributes this to budget constraints: even though the FRM-ARM spread narrows, both products become more expensive in absolute terms, and cash-constrained borrowers choose the cheaper option (ARM) to minimize initial monthly payments, rather than comparing relative spreads. The converse holds during loosening: as borrowing costs decline and budget constraints ease, borrowers show a revealed preference for the interest rate risk protection of FRMs, consistent with a general preference for payment certainty when affordability is not binding.

Q4. How does the mortgage stock composition affect monetary policy transmission (state-dependency)?

The state-dependency analysis (equation 3, Figure 4) regresses macroeconomic outcomes on the interaction of a policy rate change and the ex-ante ARM debt share (ARMs as a proportion of household debt-to-GDP), using country and quarter fixed effects with Driscoll-Kraay standard errors and IV identification. The left column of Figure 4 shows that the marginal effect of a 100 bps policy change on real private consumption increases by approximately 0.05 percentage points for each additional percentage point of ARMs in outstanding stock, a differential that becomes noticeable after about six quarters. The differential response for durables consumption appears earlier (around two quarters), while the real GDP differential is roughly half the consumption differential (about 0.02 percent per percentage point of ARM debt). The right column of Figure 4 separates the state variable into the pure ARM share and household debt-to-GDP by including both interaction terms in a horse-race specification. The paper finds that the ARM share (not the debt level) drives the transmission differences for real GDP and both measures of consumption, consistent with a cash-flow channel interpretation: it is interest rate resets on existing ARM contracts that affect disposable income flows and spending, not the debt level per se. Household debt-to-GDP is relevant for durables consumption, potentially reflecting wealth and collateral effects on credit-intensive spending categories. The 100 percent ARM versus 0 percent ARM back-of-the-envelope calculation implies a 5 percentage point consumption difference per 100 bps, corresponding exactly to one standard deviation in cumulative real private consumption changes at 6 quarters in this sample.

Q5. Why is the shift toward ARMs after tightening paradoxical given the standard relative pricing model, and what channels can explain it?

The standard framework predicts that borrowers choose FRMs when the FRM-ARM spread is low (ARMs relatively less attractive) and ARMs when the spread is high; a tightening that narrows the spread should therefore shift borrowers toward FRMs, not ARMs. The paper finds the opposite and offers two channels. First, a budget constraint channel: after tightening, both FRM and ARM rates rise in absolute terms, but ARMs remain cheaper at origination because they carry lower initial payments; liquidity-constrained borrowers facing higher total borrowing costs choose the cheaper option regardless of the spread direction, consistent with evidence in Andersen et al. (2023) that ARM adoption is more prevalent among liquidity-constrained borrowers. Second, a cost-minimization channel with short-run focus: some borrowers choose the product that minimizes current-period mortgage payments, not lifetime payments; after tightening, ARMs minimize the monthly payment even though they expose borrowers to future rate risk. The paper notes that the converse — FRM adoption after loosening despite rising FRM-ARM spreads — cannot be explained by short-run cost minimization and suggests a preference for rate certainty when affordability is non-binding.

Q6. Is the state-dependency effect asymmetric between tightening and loosening cycles?

The paper tests an asymmetric specification and finds that FRMs are a greater impairment to monetary transmission during tightening relative to loosening cycles, especially when free prepayment options are available. During tightening, a high FRM share means few borrowers face rate resets on their existing debt, so the cash-flow channel is weak; simultaneously, prepayment refinancing into new mortgages is unattractive (locking in a higher rate) so the existing FRM stock remains insulated. During loosening, a high FRM share means borrowers can refinance into lower FRM rates or into ARMs at lower cost, partially restoring the transmission channel. This asymmetry is consistent with findings in Berger, Milbradt, Tourre, and Vavra (2021) on mortgage prepayment and path-dependent monetary policy effects in the US, and suggests that the FRM-induced weakening of transmission is particularly binding precisely during contractionary cycles when central banks most need the transmission mechanism to be operative.

Q7. What are the implications for central bank transmission assessment and policy?

The two findings together imply that monetary policy transmission capacity is endogenous to the history of the policy cycle. A prolonged loosening phase (such as the post-GFC decade of ultra-low rates) shifts new originations toward FRMs, which accumulate in the outstanding stock; the resulting high FRM share means that subsequent tightening operates through a weakened transmission channel. The central bank’s policy instrument affects the transmission mechanism’s own strength. This endogeneity has at least two practical implications. First, central banks that have conditioned borrowers into expecting prolonged low rates may face amplified instrument-calibration uncertainty: the same 100 bps tightening has systematically weaker real effects in economies where prior easing locked in high FRM shares, requiring larger policy moves to achieve the same macroeconomic stabilization. Second, cross-country heterogeneity in the FRM-ARM mix — itself partly endogenous to the history of monetary policy — explains a significant portion of the observed heterogeneity in monetary policy transmission strength across countries, complementing structural explanations based on financial market depth, indebtedness levels, and household balance sheet composition.

Key concepts

fixed-rate mortgage (FRM): a mortgage with a contractual interest rate fixed for 12 months or more; holders are contractually insulated from subsequent policy rate changes, reducing the pass-through of monetary policy to household debt service costs through the cash-flow channel; in the paper’s framework, FRM prevalence is both a consequence of past policy (path-dependency) and a determinant of current transmission strength (state-dependency).

adjustable-rate mortgage (ARM): a mortgage where the interest rate resets with market rates (at intervals shorter than 12 months for the paper’s classification); holders feel policy rate changes immediately in their monthly payments, amplifying the cash-flow channel; the paper finds ARM share in new flows rises after monetary tightening due to budget constraint effects.

path-dependency: the property that the current effectiveness of monetary policy depends on the accumulated history of prior policy rate changes, through their effect on the outstanding mortgage stock composition; specifically, prolonged easing cycles generate high FRM shares that reduce future transmission potency.

state-dependency: the variation in monetary policy transmission strength with the prevailing share of ARMs in outstanding mortgage debt; the same policy rate change produces a consumption response approximately 5 percentage points larger in a 100 percent ARM economy than in a 100 percent FRM economy (per 100 bps), controlling for debt-to-GDP.

cash-flow channel of monetary policy: the mechanism by which changes in policy rates affect households’ disposable income through resets in the interest payments on their existing variable-rate debt; the dominant channel in the paper’s state-dependency results — ARM share (not debt level) drives transmission differences for consumption and GDP, consistent with income flow effects on spending propensity.

IV local projections (IV-LP): the estimation framework combining Jordà (2005) local projections — a flexible, model-free method for estimating impulse responses at multiple horizons — with instrumental variable identification using Bauer-Swanson-cleaned monetary policy shocks; used for both the path-dependency regressions (equation 2, ARM flow response) and the state-dependency regressions (equation 3, interaction with ARM stock).

Bauer-Swanson (2023) information effect correction: the procedure for removing the component of high-frequency monetary policy surprises that is correlated with the central bank’s private information about economic conditions; applied here to prevent the estimated transmission effects from conflating pure rate changes with information revelation about the macroeconomic outlook.

Marginal Propensity to Consume and Personal Characteristics: Evidence from Bank Transaction Data and Survey

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

Layer 1 — Overview

Research Question. This paper asks whether heterogeneity in the marginal propensity to consume (MPC) stems from temporary circumstances (e.g., transient wealth shocks that tighten liquidity) or persistent personal characteristics (e.g., high time discount rates or strong risk aversion that permanently shape saving behavior). Because liquidity constraints are endogenous — they can reflect either bad luck or impatient preferences — disentangling these two sources requires independently measured individual characteristics, which are not available in standard transaction datasets.

Data and Setting. The study combines two data sources drawn from Mizuho Bank, one of Japan’s three largest banks (approximately 24 million individual accounts). First, weekly bank account transaction data for January 2019 to November 2022 covering all outflows (ATM withdrawals, credit card debits, utility payments, interbank transfers) for the approximately 5,282 survey respondents. Second, a bespoke survey conducted in November–December 2022 among 400,000 randomly selected salary-receiving account holders (response rate 1.32%, yielding 5,282 usable observations). The survey elicits the Arrow–Pratt measure of absolute risk aversion, quantitative time discount rates for one-week, one-year, and ten-year horizons, self-reported liquidity constraints, homeownership, education, age, and gender, among other variables.

Three Income Shocks. MPC is estimated against three distinct income events: (1) the Japanese government’s Special Cash Payments (SCP) — a 100,000 JPY (approximately 800 USD) per-person lump-sum transfer during COVID-19, likely transitory, unexpected, and nearly randomly timed across municipalities due to administrative bottlenecks; (2) regular salary receipts (recurring, expected in both timing and amount); and (3) semi-annual bonus payments (received twice yearly, with timing known in advance but amount largely unknown — intermediate between SCP and salary in terms of expectedness).

Estimation Strategy. A two-way fixed effects regression with event-study leads and lags (windows of five weeks before and after each income event) is used to estimate consumption responses. Individual and week fixed effects absorb time-invariant heterogeneity and aggregate shocks (including COVID-19 emergency declarations). Standard errors are clustered at the individual level. For heterogeneity analysis, the income shock variable is interacted with individual characteristics from the survey (treated as proxies for persistent characteristics) and with time-varying log wealth and a liquidity constraint dummy (wealth below one-twelfth of annual income, proxying temporary circumstances).

Main Findings — Average MPC. Across all three income types, the on-impact MPC (week of receipt) is approximately 0.2: specifically γ₀ = 0.23 for the SCP (significant at 5%), 0.20 for salary, and 0.22 for bonus. When estimated jointly in a single regression, coefficients are γ_SCP = 0.21, γ_salary = 0.19, and γ_bonus = 0.21. This uniformity holds despite the sharply different properties of these shocks (transitory-unexpected vs. regular-expected vs. semi-known).

Main Findings — Heterogeneity. Significant heterogeneity in MPC is found primarily in the bonus subsample, where statistical power is greatest. The following cross-term coefficients are significant at the 5% level in the multivariate specification: (a) liquidity constraint dummy — positive and significant, indicating that individuals temporarily below one month’s income in deposits spend a larger fraction of their bonus, with a one standard deviation increase raising MPC by 0.094 (9.4 percentage points); (b) time discount rate (quantitative measure) — positive and significant, with a one standard deviation increase in impatience raising MPC by 0.084; (c) risk aversion (quantitative Arrow–Pratt measure) — positive and significant, conditional on controlling for wealth and liquidity, with a one standard deviation increase raising MPC by 0.031; (d) education — negative and significant irrespective of wealth/liquidity controls, with a one standard deviation increase in education reducing MPC by 0.041.

These magnitude estimates are sizable relative to the baseline MPC of approximately 0.2. For SCP and salary shocks, cross-term coefficients are uniformly insignificant at the 5% level, which the author attributes partly to smaller sample sizes and shorter observation windows for the SCP subsample.

Scope Conditions. The sample consists of Mizuho Bank account holders who receive salary payments directly into their Mizuho account, overrepresenting metropolitan areas and salaried workers relative to the national census. Wealth at Mizuho captures only deposits at that institution and excludes securities accounts, postal savings, and intra-household transfers. Age and gender do not yield significant cross-term coefficients in any specification; the self-reported survey measure of liquidity constraints (ability to cover one month’s income by drawing on savings, assets, or borrowing) is also insignificant, in contrast to the transaction-based liquidity constraint dummy.

In depth

Q1. Why is separating temporary circumstances from persistent characteristics important for MPC estimation?

Liquidity constraints — the standard proximate predictor of high MPC — are endogenous. An individual may be liquidity-constrained because of a temporary adverse income shock (bad luck) or because of persistently high impatience (high time discount rate) that leads to chronically low saving. If policy evaluation treats all constrained households symmetrically, it conflates these two very different channels. The paper follows Jappelli and Pistaferri (2020), Gelman (2021), and Aguiar, Bils, and Boar (2021) in arguing that both channels matter and that their relative contributions need empirical separation.

Q2. Why are Japanese bonuses particularly well-suited to identifying MPC heterogeneity?

Bonuses are paid semi-annually to most regular employees in Japan (accounting for roughly 15–30% of annual income), with timing known in advance but amount largely unknown until receipt. This intermediate nature — partially anticipated in timing but uncertain in magnitude — provides meaningful variation in consumption responses across individuals while maintaining a clean event-study design. The bonus subsample (3,722 individuals who received a bonus at least once) is also large enough to detect cross-term effects that are statistically insignificant in the SCP subsample (2,446 individuals) and in the salary analysis, likely due to greater statistical power.

Q3. How is the Arrow–Pratt measure of risk aversion constructed from the survey?

Respondents are asked whether they would purchase a lottery ticket at prize value Z = 100,000 JPY and price p = 10,000 JPY for varying winning probabilities α. The threshold α at which a respondent switches from accepting to rejecting identifies their risk attitude. The absolute risk aversion σ = −U’’/U’ is then calculated as (αZ² − 2αZp + p²) / (2(αZ − p)). This yields σ ranging from −4.5 (when α = 0.01, i.e., risk-loving) to 0.891 (when α = 1, i.e., refusing to buy even at a 90% win probability). Risk neutrality corresponds to σ = 0 (at α = 0.1).

Q4. How are time discount rates measured, and what is the range?

Respondents are asked the minimum amount X they would require to wait one week, one year, or ten years to receive a payment instead of receiving 100,000 JPY one week from now (using a one-week anchor to address hyperbolic discounting). The discount rate is calculated as r = X/100,000. The range is 0.01 (X = 100 JPY) to 100 (X = 10,000,000 JPY, i.e., would not wait even for 1,100,000 JPY in ten years). The unweighted average across one-week, one-year, and ten-year horizons is used as the composite discount rate in the multivariate specifications.

Q5. What is the transaction-based liquidity constraint dummy, and how does it differ from the survey-based measure?

The transaction-based dummy equals one if end-of-month deposits at Mizuho Bank (the previous month) are below one-twelfth of the individual’s annual income — i.e., if the individual holds less than one month’s equivalent income in liquid deposits. This is a time-varying measure. The survey-based measure asks respondents to self-report whether they could cover one month’s income by drawing on savings, selling assets, or borrowing. The transaction-based measure is significant at the 5% level in the bonus and salary heterogeneity regressions, while the survey-based measure is insignificant, indicating that the precise definition and data source of the liquidity constraint measure matters materially for detecting its effect on MPC.

Q6. What are the estimated on-impact MPC values for each income shock, and how stable are they across robustness checks?

The point estimates from the event-study regression (γ₀) are: 0.23 for SCP in the baseline sample (SCP recipients in 2020, N = 2,446 individuals), 0.20 for salary (all 5,282 survey respondents), and 0.22 for bonus (3,722 bonus recipients). In a robustness specification restricting to only year-2020 data for the SCP, γ₀ = 0.235; using cash withdrawals from ATMs as a proxy for consumption instead of total outflows, γ₀ = 0.162 for SCP. In a joint regression including all three income types simultaneously, γ_SCP = 0.21, γ_salary = 0.19, and γ_bonus = 0.21. The SCP MPC for the smaller second-wave subsample (200 individuals, 2021–22) is 0.104 and insignificant, consistent with insufficient statistical power rather than a structural difference.

Q7. Why is the similarity in MPC across the three shock types potentially surprising, and what does the paper say about it?

Standard theory predicts divergent MPCs: transitory unexpected windfalls (SCP) should have a higher MPC than permanent salary changes under the permanent income hypothesis, while Ricardian equivalence might reduce the MPC to fiscal transfers like the SCP if households anticipate future tax increases. The paper finds the MPCs are approximately equal (around 0.2 across all three types), and if anything the SCP MPC is slightly higher than the salary MPC. The paper acknowledges this uniformity without offering a structural explanation, using it primarily as a robustness check on the baseline estimate rather than a substantive puzzle to resolve.

Q8. Which personal characteristics are significantly associated with higher MPC, and in which income shock samples?

In the multivariate heterogeneity regression, significant cross-term coefficients at the 5% level are found exclusively in the bonus subsample (columns 5–6 of Table 6): the quantitative risk aversion measure (positive, coefficient 0.042–0.049), the quantitative discount rate (positive, coefficient 0.004), and education (negative, coefficient −0.034 to −0.037). The liquidity constraint dummy (transaction-based) is also positive and significant for bonuses. In the univariate robustness regressions (Table 7), the own-house dummy is negative and significant at 5% for bonuses (controlled and uncontrolled); discount rates for one-week and ten-year horizons are positive and significant at 5% for bonuses; risk aversion A (direct self-report) is negative and significant at 5% for SCPs in the uncontrolled specification.

Q9. Do age and gender matter for MPC heterogeneity?

No. In all specifications across all three income shock types, the cross-term coefficients on age and the male dummy are uniformly insignificant at the 5% level. The lack of significance for age and gender is noted as a notable result, since both are commonly used demographic proxies in heterogeneous agent models that assume they reflect economically meaningful differences in consumption behavior.

Q10. How does the paper quantify the economic magnitude of each significant heterogeneity factor?

Table 8 reports the product of each cross-term coefficient and the standard deviation of the corresponding variable. For the bonus subsample: a one standard deviation increase in the liquidity constraint dummy raises MPC by 0.094 (9.4 percentage points); a one standard deviation increase in the discount rate raises MPC by 0.084; a one standard deviation increase in risk aversion raises MPC by 0.031; and a one standard deviation increase in education reduces MPC by 0.041. All four magnitudes are described as sizable relative to the baseline MPC of approximately 0.2 (20%).

Q11. Why does the paper focus on bonuses for the heterogeneity analysis rather than the SCP?

The SCP events provide cleaner identification of transitory, exogenous income shocks (near-random timing due to municipal administrative bottlenecks, as documented by Kubota, Onishi, and Toyama 2021), but the subsample of SCP recipients is smaller (2,446 in 2020, 200 in the second wave), reducing statistical power for detecting heterogeneity in cross-term coefficients. The salary sample is large (5,282 individuals) but salaries are expected, recurring, and may partially update permanent income, complicating interpretation of cross-term estimates. Bonuses offer a balance: a relatively large subsample (3,722) and a partially unexpected income component, making them the most informative sample for heterogeneity analysis.

Q12. What are the main caveats and limitations the paper identifies?

Four caveats are noted. First, the personal characteristics from the survey — including time discount rates and risk aversion — are treated as exogenous, but they may themselves be endogenous to economic circumstances or short-term conditions at the time of the survey. Second, only Mizuho Bank deposits are observed; financial assets at other institutions (securities, postal savings) are missing, meaning the liquidity constraint measure understates true wealth for some respondents. Third, the sample is tilted toward metropolitan salaried workers and toward wealthier individuals compared to the full Mizuho customer base (median log wealth of 7.4 vs. 5.9 in Kubota et al. 2021). Fourth, the multiple-testing problem is acknowledged: with many cross-term tests conducted, some rejections of the null at the 5% level may be spurious.

Key Concepts

Marginal Propensity to Consume (MPC, on-impact). In this paper, MPC is operationalized as the coefficient γ₀ from the two-way fixed effects event-study regression — specifically, the fraction of an income shock spent during the same week the shock is received, estimated from total bank account outflows. This is a weekly, within-account measure, not a lifetime or annual consumption response.

Arrow–Pratt Absolute Risk Aversion (σ). A quantitative measure of risk preferences computed from the paper’s survey by eliciting the probability threshold α at which a respondent is indifferent between buying and not buying a lottery with prize Z = 100,000 JPY and price p = 10,000 JPY. Calculated as σ = (αZ² − 2αZp + p²) / (2(αZ − p)). Ranges from −4.5 to 0.891 in the sample, with σ = 0 indicating risk neutrality.

Time Discount Rate (r). Measured by asking respondents the minimum additional amount X (beyond 100,000 JPY) they would require to delay receipt by one week, one year, or ten years, with r = X/100,000. The paper uses the unweighted average of three horizon-specific rates as a composite measure. Ranges from 0.01 to 100 in the sample. Used as a proxy for impatience or myopia — a persistent personal characteristic.

Liquidity Constraint Dummy (transaction-based). A time-varying binary indicator that equals one if individual i’s end-of-month Mizuho Bank deposit balance in month t−1 is below one-twelfth of annual income at t−1 — i.e., less than one month’s equivalent income in liquid deposits. Distinguished in the paper from a survey-based self-report of liquidity constraints, which is found to be insignificant.

Special Cash Payment (SCP). The Japanese government’s COVID-19 pandemic transfer program, providing 100,000 JPY (approximately 800 USD) per person in 2020 (universal) and 100,000 JPY per child in 2021–22 (restricted to households with children under 18 and income below 9.6 million JPY annually). Used in this paper as a transitory, salient, and largely unexpected income shock because municipal administrative bottlenecks made the exact timing unpredictable and nearly random across households.

Two-Way Fixed Effects Event-Study Regression. The paper’s primary estimator, which includes individual fixed effects (controlling for time-invariant person-level heterogeneity) and week fixed effects (absorbing aggregate shocks such as COVID-19 emergency declarations and seasonal patterns). Event-study leads and lags (k = −5 to +5 weeks around each income receipt) allow pre-trend testing and tracing of the dynamic consumption response. Normalized to γ_{−1} = 0.

MPC Heterogeneity Cross-Term. A regression augmentation (equation 3 in the paper) in which the contemporaneous income shock X⁰_{it} is interacted with individual characteristic Z_{it}. The coefficient δ on this cross-term identifies how the MPC varies with Z — the marginal effect of characteristic Z on the MPC. Persistent characteristics (e.g., risk aversion, discount rate, education from the survey) and temporary circumstances (e.g., log wealth, liquidity constraint dummy from transaction data) are included as separate Z variables.

Market Regulation, Cycles, and Growth Dynamics in a Monetary Union

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

This paper develops a two-country currency union DSGE model with endogenous TFP growth and product and labor market frictions to assess how cross-country differences in market regulation affect long-run growth and business cycle dynamics. The central insight is that with endogenous growth, there is no reason to expect real income convergence within a monetary union: large shocks can lead to permanent changes in output and the real exchange rate through their effect on endogenous TFP, lifting the standard dichotomy between cycles and growth. Less regulated economies tend to have higher trend growth and recover faster from negative shocks because their institutional environment is more conducive to innovation and reallocation. Applied to the euro area financial and sovereign debt crisis, the model is consistent with the observed divergence of output and TFP paths between Northern and Southern member states, with the less reform-friendly Southern members experiencing higher inflation, lower employment, and disappointing TFP growth.

In depth

Q1. Why does endogenous growth break the convergence prediction?

With endogenous TFP growth, there is no reason to expect real income convergence within a monetary union because TFP growth depends on the institutional environment—including product and labor market regulations—which differs persistently across countries. In standard neo-classical models, capital flows toward lower-capital countries and convergence follows. But when TFP is endogenous and depends on regulations and innovation, countries with higher regulations face permanently lower TFP growth rates, and the absence of an exchange rate instrument prevents the usual adjustment mechanism from operating. The model thus provides a structural account of the non-convergence documented empirically for the euro area since 1999.

Q2. How do product and labor market regulations affect growth and cycle dynamics?

Product and labor market regulations affect both long-run trend growth (through their effect on steady-state innovation and TFP) and short-run dynamics (through their effect on how quickly economies adjust to shocks via factor reallocation). The paper documents empirically that less regulated euro area economies have higher R&D intensity and TFP growth rates. In the model, higher product market regulation reduces the incentive for firms to innovate and enter, while higher labor market regulation slows the reallocation of workers from declining to expanding sectors following a shock.

Q3. How do temporary shocks produce permanent output effects?

Temporary shocks—such as the risk premium shocks experienced by euro area countries during the financial and sovereign debt crisis—can lead to permanent reductions in the level of output and TFP through their effect on endogenous innovation and capital accumulation, producing hysteresis without any permanent shock to fundamentals. This mechanism lifts the standard dichotomy between cycles and growth: temporary financial disruptions that reduce investment and employment also reduce R&D and innovation, which lowers TFP permanently. The model thus provides a structural account of the ‘secular stagnation’ concerns following the euro area crisis.

Q4. What does the application to the euro area crisis show?

Applied to the euro area financial and sovereign debt crisis, the model is consistent with the observed divergence between Northern and Southern member states: the asymmetric risk premium shock hits less regulated Northern economies (which recover faster) and more regulated Southern economies (where output and TFP appear permanently lower) differently due to their different institutional environments. The model predicts that the divergence in output and TFP paths between Germany/France (back to pre-crisis trend) and Spain/Italy (on permanently lower paths) is consistent with the role of product and labor market regulation in mediating shock propagation, complementing the exchange rate inflexibility channel in standard currency union analyses.

Key concepts

endogenous TFP growth : TFP growth that depends on the institutional environment (product and labor market regulations) and on innovation decisions; key departure from standard DSGE models; breaks the cycle-growth dichotomy by allowing temporary shocks to permanently affect TFP levels. product market regulation (PMR) : regulations governing market entry, competition, and firm behavior in the product market; modeled here as affecting the incentive to innovate and enter new markets, thereby shaping steady-state TFP growth. labor market regulation (LMR) : regulations governing hiring, firing, and wage determination; modeled here as affecting the speed of labor reallocation following shocks, thereby shaping business cycle dynamics and recovery speed in the currency union. hysteresis : the persistence of shock effects on the long-run level of output or TFP beyond the duration of the shock itself; arises here through the effect of temporary demand contractions on endogenous innovation and TFP accumulation.

Misspecified Expectations among Professional Forecasters

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

Analyzing panel data from the U.S. Survey of Professional Forecasters (SPF, 1992Q1–2019Q4, 77 forecasters, 1,520 forecaster-quarter observations), Julio Ortiz finds that a “misspecified expectations” model — in which forecasters perceive an AR(2) data-generating process to be an AR(1), causing them to misperceive its underlying persistence — tends to outperform a noisy-information rational benchmark and two leading non-FIRE alternatives (overconfident and diagnostic expectations) when fit to forecast errors and revisions. The models are estimated by maximum likelihood and ranked using forecast-encompassing weights; for the baseline real GDP growth case, misspecified expectations earns the largest encompassing weight (0.539 vs. 0.462 for diagnostic, ~0 for rational and overconfident) and the highest log-likelihood. Across 14 macroeconomic variables, misspecified expectations provides the best fit for most series both in-sample and out-of-sample, though diagnostic expectations fits better for some (e.g., GDP deflator, industrial production, real residential investment) and rational expectations fits the unemployment rate best. The author argues misspecified expectations succeeds in part because its bias enters both the prediction and updating equations, producing overreaction to new information plus overextrapolation across horizons, which makes forecast errors longer-lived; he concludes it can serve as a “suitable approach” / useful benchmark to model professional-forecaster expectation formation, while emphasizing the results are specific to the context of professional forecasting and may not carry over to household or firm expectations.

In depth

Q1. What question does the paper address?

The paper undertakes a formal comparison of competing non-FIRE theories of expectation formation to move toward establishing a benchmark non-FIRE model in the context of professional forecasting. Ortiz motivates this with the observation that survey forecast errors are predictably correlated with real-time information — a violation of full-information rational expectations (FIRE) — but that, as noted in Reis (2020), the literature “has not yet settled on a benchmark non-FIRE model.” The paper offers “a partial answer to this question.”

Q2. What models are compared?

Four models are estimated: a noisy-information rational expectations baseline plus three biased non-FIRE models — overconfident expectations (Daniel et al., 1998), diagnostic expectations (Bordalo et al., 2020), and misspecified expectations (in the spirit of Fuster et al., 2010). All are embedded in a common noisy-information environment where the latent variable is unobservable and forecasters update via a Kalman filter from a noisy private signal. Overconfidence has forecasters misperceive their signal noise as smaller than it is; diagnostic expectations introduces a representativeness distortion ϕ > 0 generating overreaction to recent news; misspecified expectations has forecasters treat an AR(2) process as an AR(1).

Q3. What exactly is “misspecified expectations” in this paper?

Misspecified expectations is a model in which the underlying state follows an AR(2) process but forecasters treat it as an AR(1), so they misperceive the true persistence of the data-generating process. The author notes this version is “closest to natural expectations as modeled in Fuster et al. (2010),” with forecasters neglecting longer lags. Importantly, forecasters still understand the information structure. If the perceived persistence loads excessively onto the first lag, forecasters overextrapolate. The author flags three technical differences from Fuster et al. (2010): he does not model an AR(2) in levels with AR(1)-in-growth-rates forecasting; the perceived persistence is estimated from the data rather than defined as a function of the true autocorrelation parameters; and he does not define expectations as a weighted average of rational and naive AR(1) expectations.

Q4. What data and sample are used?

The estimation uses U.S. SPF panel data from 1992Q1 to 2019Q4, yielding 77 unique forecasters and 1,520 forecaster-quarter observations for the baseline. The 1992 start is chosen to avoid spanning different regimes and because the survey redefined output from GNP to GDP in 1992. The procedure requires unbroken observation sequences, so only each forecaster’s longest spell is kept, with a minimum spell length of eight quarters (because entry/exit may be non-random, per Engelberg et al., 2011). Real GDP growth is the baseline variable; 13 other macroeconomic variables are also estimated. Real-time forecast errors (not errors based on revised figures) are used, following the literature.

Q5. How are the models estimated and compared?

The models are estimated via a three-step maximum likelihood procedure, and their relative fit is compared using forecast-encompassing weights (West, 2001; Harvey et al., 1998; West, 2006), supplemented by AIC and a Vuong (1989) non-nested likelihood-ratio test. Step 1 estimates the fundamental process parameters (ρ₁, ρ₂, σ_w) from the macro time series and fixes them across models; step 2 estimates the signal-noise dispersion σ_v from the rational model and calibrates it across the other three; step 3 estimates each bias parameter (α_v, ϕ, ρ̂) by MLE on SPF data. This keeps fundamental and information parameters consistent across biased models so they are evaluated solely on the biases they generate, and makes identification transparent (notably, σ_v and α_v cannot be jointly identified in the overconfidence model). Encompassing weights are obtained from a constrained linear regression of realizations on model-based one-quarter-ahead forecasts, with weights summing to 1.

Q6. What are the baseline real GDP growth results?

For real GDP growth, the misspecified expectations model produces the highest log-likelihood and the largest encompassing weight, 0.539, versus 0.462 for diagnostic expectations and approximately 0.000 for both rational and overconfident expectations. The fundamental process estimates imply relatively low persistence (first-order autocorrelation ρ₁ ≈ 0.434, second-order ρ₂ ≈ −0.006). The estimated bias parameters are: overconfidence ≈ 0.72, diagnosticity ≈ 0.23, and perceived persistence ρ̂ ≈ 0.564. Because ρ̂ ≈ 0.56 exceeds the estimated ρ₁ ≈ 0.43, the misspecified model implies forecasters overestimate the first-order autocorrelation and neglect the partial reversal in the second lag, generating overreactions. The signal-to-noise ratio implied by the estimated private noise dispersion is σ_w/σ_v ≈ 1.09. AIC rankings (and BIC) do not change the ordering relative to the maximized likelihoods.

Q7. Does the result hold across other macroeconomic variables?

Across the 14 SPF macroeconomic variables, misspecified expectations provides the best in-sample fit for most series, but not all. Diagnostic expectations registers larger encompassing weights for certain series — the GDP deflator (0.771), industrial production (1.000), and real residential investment (0.624). Rational expectations provides the best fit for the unemployment rate (0.745) and housing starts (in-sample). For the bulk of the remaining variables (e.g., CPI 0.859, payroll employment 1.000, real consumption 0.777, real federal spending 1.000, real GDP 0.539, real nonresidential investment 1.000, real state/local spending 1.000, 3-month Treasury bill 0.713, 10-year bond 0.746), misspecified expectations carries the largest weight. Overconfident expectations “does not yield particularly large encompassing weights for any variable.”

Q8. Why does misspecified expectations fit better, and for which variables especially?

The author finds that, among variables exhibiting overreactions, misspecified expectations tends to offer a better fit for less persistent series, because the scope for it to generate overreaction (ρ̂ − ρ₁) is greater when ρ₁ is low. Unlike the alternatives, the persistence bias ρ̂ − ρ₁ can be positive or negative, allowing the model to account for both overreacting and underreacting variables; the alternative models cannot generate forecaster-level underreaction. Figure 2 plots the encompassing weight on misspecified expectations against the sum of autoregressive coefficients and suggests (with some exceptions) that less persistent variables have higher weight on misspecified expectations.

Q9. Does the model perform out of sample?

The misspecified expectations model also provides a better out-of-sample fit for more of the variables, estimated on 1992Q1–2005Q4 and evaluated on the latter half of the sample. However, out of sample diagnostic expectations now outperforms for the GDP deflator (0.987), industrial production (0.959), payroll employment (0.813), and real federal government expenditures (0.591); overconfident expectations outperforms for the 10-year government bond (0.653); and rational expectations outperforms for housing starts (0.502) and the unemployment rate (1.000). The author cautions that these results do not imply forecasters could improve their forecasts in real time, because the MLE observations include contemporaneous individual and consensus forecast errors that are not known to forecasters when they issue forecasts; for the same reason, the results are “not inconsistent with” Eva and Winkler (2023) on the poor out-of-sample performance of error-predictability regressions.

Q10. Could the apparent advantage of misspecified expectations just reflect learning?

The author argues that learning about the data-generating process does not appear to drive the relative model rankings in favor of misspecified expectations, based on two exercises. First, using the full pre-COVID sample (1968Q4–2019Q4) over 25-year rolling windows (three-year roll), the misspecified model outperforms diagnostic expectations in six of ten sub-samples and all models in five of ten, while diagnostic expectations wins four of ten — patterns that “do not indicate that learning over time favors misspecified expectations.” Second, splitting forecasters by “age”/tenure (a proxy for experience), misspecified expectations outperforms the others among experienced (above-median age) forecasters (encompassing weight 0.766, with overconfidence 0.234) and is dominant among inexperienced ones (1.000). The author concedes learning “is likely reflected in professional forecasts” but does not appear to drive the rankings.

Q11. What additional moments does misspecified expectations match?

Beyond overall fit, the author shows in the appendix that misspecified expectations matches five features of the data — overreaction, underreaction, overshooting, persistent disagreement, and updating behavior — and is the only model generating delayed overshooting. All three non-rational models generate individual-level overreaction (Bordalo et al., 2020 errors-on-revisions regression) and aggregate underreaction (Coibion-Gorodnichenko, 2015 consensus regression). But when simulating impulse responses, “only the misspecified expectations model generates a sign switch in the forecast error,” indicating delayed overshooting (Angeletos et al., 2020). The author reports “stronger evidence” favoring misspecified expectations on two further moments: it better generates persistent disagreement across horizons, and it better matches the relative weights forecasters place on priors versus news — because its bias also enters the prediction equation (not just the update equation), producing longer-lived errors.

Q12. What are the scope conditions and limitations the author stresses?

The author emphasizes that the results are specific to the context of professional forecasting and that the relative model rankings “may be different” for household or firm expectations, or for micro-level expectations rather than aggregate forecasts. He notes professional forecasters are arguably the most well-informed agents, so the literature has treated their predictions as informative about a lower bound on economy-wide information frictions and biases. The paper abstracts away from learning in the model setup and from theories that generate only underreaction. Models excluded from the comparison (e.g., imperfect memory, multi-frequency forecasting, asymmetric attention, learning) are set aside mainly because they cannot be flexibly nested into the common setting and would introduce additional parameters posing identification challenges.

Ortiz concludes that misspecified expectations “can serve as a suitable approach” / useful benchmark to model expectation formation among professional forecasters for a variety of macroeconomic aggregates, while framing this as only “a partial answer” to the search for a non-FIRE benchmark. He highlights a practical advantage: embedding this form of misspecified expectations into a quantitative model “only requires introducing two parameters into an otherwise standard model.” He also notes misspecification can arise either from a behavioral bias or because adopting parsimonious forecasting models is optimal (Branch and Evans, 2006; Pfajfar, 2013). A promising avenue for future research is whether evidence favors misspecified expectations in other settings.

Key concepts

Full-information rational expectations (FIRE): The benchmark in which forecast errors are uncorrelated with any information in the forecaster’s time-t information set; the orthogonality conditions it implies “tend to be violated in the data,” motivating non-FIRE models.
Misspecified expectations: The paper’s focal bias — the true state follows an AR(2) process, xₜ = ρ₁xₜ₋₁ + ρ₂xₜ₋₂ + wₜ, but forecasters treat it as an AR(1), xₜ = ρ̂xₜ₋₁ + uₜ, misperceiving its persistence; forecasters retain the correct information structure. The bias enters both the predict and update equations.
Persistence bias (ρ̂ − ρ₁): The gap between perceived AR(1) persistence and true first-order autocorrelation; positive values generate overextrapolation/overreaction, negative values generate underreaction, and its overreaction scope is larger when ρ₁ is low.
Overconfident expectations: Forecasters misperceive their private signal noise as smaller (σ̃_v = α_v σ_v, α_v ∈ [0,1]) than it truly is, placing excessive weight on new private information.
Diagnostic expectations: A representativeness-based distortion (Bordalo et al., 2020; Gennaioli-Shleifer, 2010) in which, with diagnosticity ϕ > 0, forecasters overweight outcomes representative relative to a “no news” reference scenario, generating overreaction to recent news.
Encompassing weight: The model-comparison metric — a weight wₖ from a constrained linear regression of realized one-quarter-ahead values on competing models’ forecasts, with weights summing to one; a larger weight indicates a better-fitting model.
Delayed overshooting: The Angeletos et al. (2020) pattern of initial underreaction followed by later overreaction to a shock; in this paper, only misspecified expectations produces the sign switch in the forecast-error impulse response that signals it.
Overreaction vs. underreaction: Individual-level overreaction is measured via the Bordalo et al. (2020) errors-on-revisions regression; aggregate/consensus-level underreaction via the Coibion-Gorodnichenko (2015) regression — the data exhibit both, and a successful non-FIRE model must reproduce both.

Mixing It Up: Inflation at Risk

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

This paper introduces a Bayesian Gaussian mixture density regression framework that estimates the complete forecast distribution of inflation — not just selected quantiles — and decomposes the entire risk outlook into contributions from individual economic predictors. The methodology accommodates multimodality, skewness, and fat tails without parametric restrictions, and allows construction of risk measures calibrated to the central bank’s own loss function rather than generic percentile-based measures. Applied to the recent U.S. inflation surge, the framework finds that post-pandemic inflation risk was primarily driven by the recovery of the U.S. business cycle and surging commodity prices, while adjustments in monetary policy contributed negatively — partially mitigating the increase in right-tail inflation risk — and credit spreads also offset some risk. The Gaussian mixture structure enables fast MCMC estimation and produces well-calibrated density forecasts across a range of macroeconomic variables.

In depth

Q1. What is the key methodological contribution relative to existing inflation-at-risk approaches?

Existing approaches to macroeconomic at-risk measures focus on specific quantiles of the forecast distribution — typically the 5th or 25th percentile — discarding information contained in the rest of the distribution; this paper redirects attention to the full forecast distribution while retaining the nonparametric flexibility of quantile regression. The Gaussian mixture density regression estimates a conditional distribution that is a weighted mixture of Gaussians, capturing multimodality, asymmetry, and fat tails simultaneously. The key innovation is decomposability: each predictor’s contribution to any region of the forecast distribution can be quantified, enabling a driver-level accounting of what generates tail risk in any given period.

Q2. What does the U.S. application reveal about the inflation surge?

The framework attributes the increase in right-tail U.S. inflation risk during 2021–2023 primarily to surging commodity prices and the recovery of the domestic business cycle, while monetary policy tightening contributed negatively — its effect partially offset the upward pressure from commodity and cycle drivers. Credit spreads also partially mitigated the risk. The decomposition implies that the dominant drivers of inflation risk were supply-side and aggregate-demand factors, and that monetary policy, when it tightened, reduced the right-tail risk as intended — providing quantitative support for the interpretation that policy was reactive but directionally correct.

Q3. How does the framework construct policy-relevant risk measures?

The framework allows weighting probability mass over the forecast distribution by any user-specified loss function, including asymmetric central bank preferences, yielding risk measures that integrate the full distributional information in proportion to the policymaker’s actual valuation of different inflation outcomes. A central bank that penalizes above-target inflation more heavily than below-target inflation (consistent with empirical evidence on CB loss functions) would weight the upper tail more, producing a risk statistic that is higher than a symmetric measure for the same distribution. This policy-preference-aligned risk measure could have provided a more accurate signal of the urgency of the 2021–2023 inflation risk than standard percentile measures.

Key concepts

inflation at risk : the quantile-based or distribution-based characterization of future inflation uncertainty; extended in this paper from a single quantile to the complete forecast distribution and its risk decomposition by driver.

density regression : a regression model in which the conditional distribution of the outcome — not just its mean or a specific quantile — is the object of estimation; the paper uses a Gaussian mixture density regression to capture non-standard distributional shapes.

risk decomposition : the attribution of shifts in the full forecast distribution to individual predictor variables; the paper’s key tool for identifying which economic factors drive right-tail inflation risk in any period.

CB-preference-aligned risk measure : a summary statistic constructed by weighting probability mass over the forecast distribution by the central bank’s loss function; captures asymmetric preferences and goes beyond standard percentile measures.

Monetary and Macroprudential Policy and Welfare in an Estimated Four‐Agent New Keynesian Model

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

This paper introduces a four-agent estimated New Keynesian DSGE model—comprising banked simple households, underbanked simple households, firm owners, and bank owners—to examine agent-specific and social welfare effects of monetary and macroprudential policy, estimated on U.S. quarterly data (1985Q1–2016Q4) via Bayesian methods. The model features two layers of endogenous default probability (for borrowers and banks), nominal, real, and financial frictions, and trend inflation and stochastic growth. The optimal bank capital requirement ratio (CRR) is estimated at 12.6%, which is 2.1% above Basel III’s 10.5%; increasing CRR up to approximately 12.2% raises welfare for all four agent types, though with smaller gains for credit-reliant simple households and firm owners. Countercyclical capital buffers benefit firm owners and bank owners with smaller gains for simple households. Coordinated monetary and macroprudential policy yields higher social welfare than non-coordinated policies.

In depth

Q1. Why does the paper use four agent types instead of the usual borrower-saver distinction?

The standard borrower-saver split lumps together all interest-earning agents—including both simple deposit-holding households and wealthy bank owners—so that macroprudential policies that shift surplus from borrowers to savers appear to benefit the simple household and the banker equally; the four-agent framework separates these groups and allows for heterogeneous welfare effects. Population shares are calibrated using Compustat and the Survey of Consumer Finances (firm owners and bank owners as shareholders of non-financial and financial firms) and the National Survey of Unbanked and Underbanked Households (underbanked simple households with very limited access to banking services).

Q2. What is the optimal CRR and how does it compare to existing benchmarks?

The optimal social CRR is estimated at 12.6%, which is 2.1% higher than Basel III’s 10.5%, 4.6% higher than Basel II’s 8%, and 3.6% higher than the 9% optimal CRR of Mendicino et al. (2019) who use a borrower-saver welfare framework. Increasing the CRR up to approximately 12.2% improves welfare for all four agent types, though unequally: simple households and firm owners who rely on credit see smaller gains. Above 12.2%, stricter CRR harms firm owners and simple households (tighter credit reduces activity), while bank owners continue to gain via higher capital income share until the CRR exceeds 25.9%, above which even bank owners are harmed as loans fall dramatically.

Q3. How do countercyclical capital buffers and loan loss provisions affect welfare by agent type?

Countercyclical capital buffers support firm owners and bank owners with smaller gains for the two simple household types; countercyclical loan loss provisions improve social welfare only for specific shocks and benefit underbanked simple households and firm owners at the expense of bank owners and banked simple households. The asymmetry reflects the different income streams: bank owners’ income derives primarily from loan returns and capital gains on bank equity, while underbanked simple households are most sensitive to credit availability. Loan loss provisions affect the timing of income recognition and loss absorption, generating distributional trade-offs that differ from those of capital requirements.

Q4. What are the gains from coordinating monetary and macroprudential policy?

Coordinating monetary and macroprudential policy yields higher social welfare than assigning each policy to an independent authority targeting its own objective, demonstrating that the interaction between interest rate policy and bank capital regulation matters for welfare outcomes. Investment shocks (27.41% of GDP growth variance) and financial risk shocks (~20%) are quantitatively important in this interaction. The model’s rich friction structure means that optimal monetary policy must account for how macroprudential policy changes the credit supply environment, and vice versa; failing to coordinate creates inefficiencies that coordinated policy avoids.

Key concepts

four-agent model : the model’s typology distinguishing banked simple households, underbanked simple households, firm owners, and bank owners; enables agent-specific welfare analysis of macroprudential policy with heterogeneous income streams and credit access. optimal capital requirement ratio (CRR) : the bank capital-to-assets ratio that maximizes social welfare; estimated at 12.6% in this model; 2.1% above Basel III’s current 10.5% requirement. countercyclical capital buffer (CCyB) : a macroprudential tool requiring banks to hold additional capital during economic expansions to be released in downturns; shown here to benefit firm owners and bank owners with smaller gains for simple households. dynamic loan loss provisions : a macroprudential tool requiring banks to build provisions against future expected losses during expansions; shown here to have welfare effects that depend on the source of the shock and to benefit different agent types than capital requirements.

Monetary Policy and the Drifting Natural Rate of Interest

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

This paper analyzes how monetary policy should respond to a long-run natural interest rate that can drift permanently — following a bounded random walk with upper bound 3 percent and lower bound 0 percent — when the zero lower bound (ZLB) on nominal interest rates is a binding constraint. The central result is that the long-run neutral rate (the real policy rate consistent with stable inflation in long-run equilibrium) should fall more than one-for-one with the long-run natural rate as the latter approaches zero, because the mere risk of future ZLB episodes — even when the economy is currently away from the ZLB — imparts a persistent downward bias on inflation expectations that can only be offset by maintaining a pre-emptive expansionary bias. Quantitatively, the model implies that the neutral rate should be zero as soon as the long-run natural rate falls to 75 basis points — well above the near-zero estimates prevailing in the late 2010s — and that the ZLB would bind one-third of the time under optimal policy when the natural rate fluctuates between 0 and 3 percent. Price level targeting with a 10-basis-point upward drift closely approximates optimal commitment policy and has the advantage of not requiring knowledge of the natural rate level.

In depth

Q1. What empirical fact motivates the model?

Empirical analyses of the long-run natural rate — the real interest rate prevailing over a long-run equilibrium in which nominal rigidities are absent — consistently find that it is time-varying in a manner best described by a random walk, meaning it can drift without reverting to a constant long-run level. The paper cites Holston, Laubach, and Williams (2017), Fiorentini et al. (2018), and Hamilton et al. (2016) as the main empirical references. Holston et al. (2017) place the long-run natural rate at between 0 and 1 percent in the U.S. and possibly slightly negative in the euro area as of 2016. The paper draws one central lesson: because the natural rate is time-varying and its future level is uncertain, a model with constant natural rate will give unreliable guidance for monetary policy, especially at low natural rate levels near zero.

Q2. What is the model and what are the key equilibrium concepts?

The paper embeds a new Keynesian model in which the long-run natural rate follows a bounded random walk with upper bound 3 percent and lower bound 0 percent, calibrated to post-WWII U.S. TFP data, and studies optimal monetary policy under commitment while imposing the zero lower bound. A critical distinction separates two notions of the long-run equilibrium interest rate: the “long-run natural rate” (denoted ¯r) is the real rate that would prevail in flexible-price equilibrium, determined by fundamentals outside the central bank’s control; the “neutral rate” (r*) is the real policy rate consistent with stable inflation in the long run, which the central bank operationally targets. The two coincide in standard models with constant ¯r, but diverge in this paper because ZLB risk drives a wedge between them.

Q3. What is the main theoretical result?

Under optimal commitment, the neutral rate r should fall more than one-for-one with the long-run natural rate ¯r — that is, the central bank should maintain a negative gap (r < ¯r) that widens as ¯r falls toward zero — because permanent downward movements in ¯r make future ZLB binding episodes permanently more likely, creating a persistent downward bias on inflation expectations that requires pre-emptive accommodation even in periods when the ZLB is not currently binding.** This result contrasts with the existing literature on optimal commitment at the ZLB, which has emphasized forward guidance — the promise to maintain low rates even after the economy recovers from a ZLB episode — as the primary stabilization tool. The paper shows that forward guidance alone is not sufficient when ¯r can permanently drift lower, because each downward drift permanently raises the probability of future ZLB episodes, reducing the central bank’s scope for fulfilling future inflation promises.

Q4. What are the quantitative implications?

The model implies that the neutral rate r reaches zero when the long-run natural rate ¯r is at 75 basis points — a level that was well above the near-zero estimates of ¯r prevailing at the end of the 2010s — and that the ZLB binds one-third of the time under optimal policy when ¯r fluctuates between 0 and 3 percent.* The 75 basis-point threshold means that a central bank operating in an environment where ¯r has declined to its estimated late-2010s levels would already be constrained to a neutral rate of zero under optimal policy. The one-third ZLB frequency is higher than what would be predicted by models with constant ¯r at typical calibrations, reflecting the permanent nature of ¯r shocks and their cumulative effect on the neutral rate.

Q5. What do the adjustment dynamics look like after a negative ¯r shock?

Following a permanent reduction in ¯r, the real policy rate adjusts gradually rather than immediately — remaining temporarily above the new long-run neutral rate during the transition — implying that monetary policy is contractionary along the adjustment path and that a permanent decline in ¯r is followed by a temporary disinflation before the economy settles at the new r.* This history-dependence of optimal commitment policy means the central bank does not immediately jump to the new, lower r* after a ¯r shock; it moves gradually, making the short-run policy stance more contractionary than the long-run position. The temporary disinflation is consistent with the general principle of history-dependence of optimal policy under commitment.

Q6. What role does price level targeting play?

Price level targeting variants — particularly a rule with an optimally chosen upward drift of 10 basis points — closely approximate the economic outcomes achieved under optimal commitment policy in the model, with the practical advantage that such rules do not require the central bank to know or estimate the current level of the long-run natural rate ¯r. The Eggertsson-Woodford (2003) price level target works well in models with constant ¯r by generating positive inflation expectations in the wake of deflationary ZLB episodes. Adding a small upward drift of 10 basis points strengthens this property under a drifting ¯r, because it provides additional buffer against the downward expectations bias that permanent ¯r drift generates. Under price level targeting rules, the neutral rate reaches the ZLB as soon as ¯r falls below 1 percent.

Key concepts

long-run natural rate (¯r) : the real interest rate prevailing over a long-run equilibrium in which nominal rigidities are absent; in this paper modelled as a bounded random walk with upper bound 3 percent and lower bound 0 percent, calibrated to post-WWII TFP data.

neutral rate (r)* : the real policy rate consistent with stable inflation in the long run; distinct from ¯r in this paper because ZLB risk drives a negative gap (r* < ¯r) that widens as ¯r approaches zero.

zero lower bound (ZLB) : the constraint that nominal policy rates cannot fall below zero; in this model the reason that permanent reductions in ¯r create a persistent downward bias on inflation expectations even when the ZLB is not currently binding.

expansionary bias : the paper’s finding that optimal commitment policy should maintain r* < ¯r — a pre-emptive accommodation away from the ZLB — to offset the downward bias on inflation expectations created by the risk of future ZLB episodes.

price level targeting : a monetary policy rule in which the central bank targets the price level rather than the inflation rate; shown in this paper to approximate optimal commitment policy and to have the practical advantage of not requiring knowledge of ¯r.

Monetary Policy, Employment Shortfalls, and the Natural Rate Hypothesis

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

This paper examines optimal monetary policy under discretion when the loss function is asymmetric — placing greater weight on employment shortfalls than on equivalently sized employment strength. The model satisfies the natural rate hypothesis (NRH): monetary policy is neutral in the long run, so persistent accommodation of above-potential activity raises inflation expectations without permanently boosting employment. The central paradox the paper establishes is that an asymmetric shortfalls-oriented loss function, despite its stated goal of reducing shortfalls, exacerbates them: the mechanism runs through the NRH expectation-adjustment channel, which creates an inflationary bias structurally analogous to the Barro-Gordon result. Mandating a central bank objective that is more symmetric than the social loss function — a conservative-in-asymmetry design — lowers both the frequency of activity shortfalls and the inflationary bias. As a corollary, the analysis implies that monetary accommodation of labor market strength requires justifications beyond the asymmetric costs of shortfalls, such as permanent effects of strong labor markets on economic potential.

In depth

Q1. How does the asymmetric loss function exacerbate employment shortfalls?

The mechanism runs through the natural rate hypothesis: under a loss function that places no weight on activity above potential, the optimal policy fully accommodates positive supply shocks by allowing above-potential output, but the NRH then raises the expectational baseline, making shortfalls more frequent as the perceived natural rate adjusts upward. Because the central bank treats above-potential activity as costless, it does not resist the accumulation of above-potential output in good states; expectations of future activity then rise, effectively moving the benchmark against which shortfalls are measured, and making shortfalls a more common outcome. The asymmetric policy thus generates a self-defeating dynamic: attempts to minimize shortfalls through accommodation of strength create an expectational environment in which shortfalls are more frequent.

Q2. How does the inflationary bias emerge?

The inflationary bias is structurally analogous to the Barro-Gordon (1983) time-inconsistency result: the central bank’s asymmetric desire to reduce shortfalls leads it to ease policy more aggressively than a symmetric loss function would warrant, and this tendency transmits into persistently higher inflation through the NRH expectations-adjustment channel. The classic Barro-Gordon mechanism operates through the desire to push output above its natural rate; here the analog is the desire to push activity above the shortfalls threshold. The paper’s model is constructed so that no Barro-Gordon bias exists in the baseline symmetric case, isolating the asymmetry as the sole source of the inflationary bias.

Q3. What policy prescription follows from the analysis?

The paper recommends mandating a central bank objective that is more symmetric than the social loss function, analogous to Rogoff’s (1985) conservative-central-banker result but applied to the dimension of asymmetry rather than the level of inflation aversion. A mandate that requires the CB to weight above-potential and below-potential activity more equally than society does lowers both the frequency and depth of shortfalls and reduces inflationary bias, improving welfare relative to a CB that faithfully implements the asymmetric social preference. The paper further shows that optimal policy under this design does not accommodate fluctuations from aggregate demand shocks, implying that accommodation of labor market strength requires other justifications — such as permanent productivity effects — not the shortfalls-cost asymmetry alone.

Key concepts

shortfalls asymmetry : the specification in which the central bank’s or social loss function places greater weight on employment below its natural rate than on equivalently sized employment above it; the paper’s central object of analysis.

natural rate hypothesis (NRH) : the assumption that monetary policy is neutral in the long run — persistent monetary accommodation does not permanently raise employment above its natural rate but does raise the price level; imposes the constraint that bounds the central bank’s ability to durably lower shortfalls.

inflationary bias : the systematic tendency of a central bank operating under a shortfalls-oriented asymmetric loss function to allow above-target inflation on average; emerges in this model via the NRH expectations-adjustment channel, analogous to but distinct from the Barro-Gordon result.

Monetary–Fiscal Policy Interactions When Price Stability Occasionally Takes a Back Seat

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

The paper builds a discrete-time DSGE model with Calvo sticky prices in which the public sector has two feedback rules that can hit corners, generating endogenous shifts between an “orthodox” regime and a “fiscally-dominant” regime. Fiscal policy sets the primary surplus as s̃_t = min(ϕb̃_{t−1}, s̄): the surplus tracks real debt with coefficient ϕ = 0.1 until the limit s̄ = 0.01 (1% of output in deviation from steady state; approximately 3% in level) binds. Monetary policy follows R̂_t = min(αp̂_t, R̄): a standard Taylor rule with coefficient α = 2.5 until the nominal interest rate cap R̄ ≈ 5% (annualized) is hit. When the surplus limit is slack — the orthodox regime — fiscal policy is locally passive and monetary policy is active in the sense of Leeper (1991). When the surplus limit binds — the fiscally-dominant regime — the central bank caps its policy rate to avoid aggravating fiscal stress, and price stability takes a back seat.

Calibration (Table 1): β = 0.995 (annual steady-state real rate ≈ 2%), σ = 1 (log utility), κ = 0.0093 (Calvo Phillips curve slope), η = 1 (inverse labor supply elasticity), θ = 10 (price elasticity of demand), ω = 0.8 (Calvo price-stickiness), α = 2.5, ϕ = 0.1, b/(4y) = 1 (100% debt-to-GDP), s̄ = 0.01, R̄ = 0.0074 in deviation from steady state (≈ 5% annualized), AR(1) coefficient ρ = 0.6, shock standard deviation σ_μ = 0.0016. The model is solved globally using a projection method to handle the kinks from the min operators.

In the fiscally-dominant regime, monetary policy is asymmetric: the central bank always lowers the rate for deflationary shocks but cannot raise it fully for large inflationary shocks (rate hits R̄). This stabilizes real debt in both shock directions while creating an asymmetric inflation response — inflation rises more in response to a positive cost-push shock than it falls for a negative shock of equal magnitude. This asymmetric profile is baked into agents’ expectations in all states of the world, including the orthodox regime, generating a systematic inflation bias that is increasing in the real value of government debt.

Simulation results (Table 2, based on 3,000 simulations of 1,000 quarters): the fiscally-dominant regime (surplus limit binding) occurs in 20% of periods, with an average duration of 3.6 quarters; the rate cap additionally binds in 10% of periods, with an average duration of 1.8 quarters.

Risky steady state (Table 3): The point to which the economy converges when transitory shocks have receded but agents fully internalize future regime-shift risk differs from the deterministic steady state: inflation is 27bp higher, output is 0.26pp lower, the real interest rate is 41bp higher, and the government debt-to-GDP ratio is 1.07pp higher. At the risky steady state the economy remains in the orthodox regime; all four effects stem from the inflation expectations channel.

Vicious-cycle mechanism: Higher debt raises the probability of fiscal dominance → larger inflation bias → higher real interest rate (the Taylor rule raises the nominal rate more than one-for-one with the inflation bias) → upward pressure on debt. The fiscal dominance risk is state-dependent: it increases with the cost-push shock and with the debt level (Figure 4).

Policy finding (Section 3.3 and Table 4): Because regime switches are endogenous, the central bank can reduce fiscal dominance risk by responding more moderately to inflation — lowering α from 2.5 to 1.5 — while still satisfying the Taylor principle (α > 1/β). A lower α attenuates the increase in debt servicing costs after an inflationary shock, requiring larger shocks to push the surplus limit to bind. Under α = 1.5: the fiscal dominance regime frequency falls to 0%; the risky steady-state inflation bias falls to essentially zero (0.01bp); inflation volatility falls from 1.93% to 1.89% — the volatility-reducing effect of avoiding fiscal dominance dominates the direct volatility-raising effect of a weaker response. At α ≈ 1.5, welfare (measured as the linear-quadratic loss −E[π̂² + λŷ²] with λ = κ/θ) is higher than at α = 2.5 (Figure 6). By contrast, under the benchmark configuration (no fiscal dominance risk), welfare falls monotonically as α declines.

Extension 1 — Distortionary taxation (Section 4.1): Replacing lump-sum taxes with a labor income tax (τL = 24%, cap = 25%) amplifies the mechanism. The risky steady-state inflation bias rises to 0.59pp; fiscal dominance occurs in 29% of periods; the rate cap binds in 16% of periods. The amplification reflects that the tax rate enters the Phillips curve, creating an additional cost-push channel when the tax cap binds.

Extension 2 — Passive monetary policy in the fiscally-dominant regime (Section 4.2): When the central bank switches to a passive rule with αF = 0.95 (rather than imposing a hard rate cap), the inflation bias is 0.23pp and fiscal dominance occurs in 15% of periods.

Scope conditions: The model features a representative household, a single cost-push shock, and lump-sum taxes in the baseline. All quantitative results are specific to the parameterization in Table 1, targeting 100% debt-to-GDP. Agents are assumed to have perfect knowledge of the central bank’s policy rule; in practice, a moderate α could be misinterpreted as abandoning the Taylor principle. The analysis is primarily conceptual; the paper notes that extending to a full-fledged multi-shock quantitative model is left for future work.

In depth

Q1. What are the two regimes in the model, and how do transitions occur?

The orthodox regime is characterized by an active central bank (α > 1/β, Taylor principle satisfied) and a passive fiscal authority (surplus responds to debt, ϕ ∈ (1−β, 1)); the fiscally-dominant regime arises when the fiscal surplus hits its upper limit s̄ = 0.01 and the central bank caps its nominal rate at R̄ ≈ 5% annualized to avoid deepening the fiscal stress. Transitions are driven entirely by the state of the economy: when real debt b̃_{t-1} crosses the threshold b̄ = s̄/ϕ from below following a sufficiently large inflationary cost-push shock, the surplus limit binds and the economy enters the fiscally-dominant regime. Exit occurs when a sequence of disinflationary shocks, together with the central bank’s rate cuts, lowers debt below the threshold. Both the entry and exit thresholds are determined by the structural parameters of the model, not set exogenously.

Q2. Why does fiscal dominance risk generate an inflation bias in the orthodox regime?

The key transmission channel runs through expectations: in the fiscally-dominant regime the central bank responds asymmetrically to shocks (always cutting for deflation, capped on the upside for large inflation), creating an asymmetric inflation distribution; agents rationally incorporate this skewness into their inflation expectations in all states — including the orthodox regime — pushing expected inflation above target; the Taylor rule then allows actual inflation to be persistently elevated because the response coefficient α = 2.5, while large, does not fully offset the expectations-induced inflation pressure. The upward inflation expectations shift appears in the forward-looking Phillips curve (equation 2): higher Etπ_{t+1} raises current inflation πt, and the Taylor rule’s response is insufficient to fully counteract the expectations-driven component of the inflation bias.

Q3. Why does the inflation bias increase with the debt level?

Higher beginning-of-period government debt reduces the buffer between current debt and the threshold b̄, so that any given realization of the cost-push shock has a higher probability of pushing debt over the threshold and triggering a shift to the fiscally-dominant regime next period; the larger this probability, the larger the expectations-driven inflation bias in the current period. This mechanism is illustrated in Figure 4, which shows the probability of fiscal dominance next period as an increasing function of the current cost-push shock (given debt near the risky steady state), and Figure 2, which plots the monotone increasing relationship between current debt and the inflation rate in both regimes.

Q4. How does the vicious cycle between inflation, interest rates, and debt operate?

The cycle works as follows: a larger inflation bias induced by higher debt triggers a stronger nominal interest rate response from the Taylor rule; in the orthodox regime this raises the real interest rate, which increases debt servicing costs and pushes real debt upward; higher debt in turn raises the probability of fiscal dominance, which amplifies the inflation bias in the next period. The cycle is self-reinforcing but not necessarily explosive in the baseline calibration — the model has a unique risky steady state at which these forces balance — but it does shift equilibrium outcomes permanently upward relative to the deterministic steady state: the real rate is 41bp higher, debt 1.07pp higher, and inflation 27bp higher at the risky steady state (Table 3).

Q5. Can the central bank break the cycle without abandoning price stability?

Yes: by lowering the Taylor rule coefficient from α = 2.5 to α = 1.5, the central bank reduces the increase in debt servicing costs after an inflationary shock, thereby making it less likely that the surplus limit binds; when the probability of fiscal dominance approaches zero, inflation expectations are anchored at the deterministic steady state and the inflation bias disappears. This works without violating the Taylor principle (α = 1.5 > 1/β ≈ 1.005) because the objective is not to tolerate more inflation at each point in time, but to reduce the regime-switch risk that is the source of the bias. Crucially, the central bank does not need to commit to any specific regime-change-contingent rule — modifying the response coefficient of the standard Taylor rule is sufficient.

Q6. Why does lower α also reduce inflation volatility, not just the bias?

In the regime-switching model there are two competing effects on inflation volatility when α falls: (i) a direct volatility-raising effect because a weaker rate response gives more room for cost-push shocks to move inflation, and (ii) a volatility-reducing effect because the fiscally-dominant regime — where inflation is amplified by asymmetric monetary policy — is less frequently visited. At α = 1.5, effect (ii) dominates: the standard deviation of annualized inflation falls from 1.93% (α = 2.5) to 1.89% (α = 1.5). This contrasts with the benchmark configuration (no fiscal dominance possible), where effect (i) always dominates and welfare falls monotonically with α.

Q7. What does distortionary taxation add to the baseline result?

When the government adjusts a labor income tax rate (τL capped at 25%, baseline 24%) instead of lump-sum taxes, the inflation bias is amplified to 0.59pp (versus 0.27bp in the baseline) and the fiscally-dominant regime occurs 29% of the time (versus 20%). The amplification comes from two sources: the labor tax rate appears directly in the New Keynesian Phillips curve (equation 9), so a binding tax cap generates an additional cost-push effect that raises inflation independently of the interest rate channel; and output is increasing in the debt level in the fiscally-dominant regime (because a higher debt level makes the rate cap more likely, raising output through the demand channel), which further increases the primary surplus through the tax base, partly offsetting the tax cap but complicating the fiscal dynamics.

Q8. How does the passive monetary policy extension compare to the baseline?

When the central bank switches to a passive rule αF = 0.95 in the fiscally-dominant regime (rather than imposing a hard nominal interest rate cap), the inflation bias at the risky steady state falls to 0.23pp and the fiscally-dominant regime occurs in 15% of periods — both improvements over the baseline (0.27bp, 20%), but the mechanism is somewhat different. Under the passive rule, there is no hard constraint on the interest rate, so the central bank can still raise rates to some extent in response to inflationary shocks in the fiscally-dominant regime, reducing the asymmetry in the inflation response. The rate cap extension (baseline) is the more extreme case in which the constraint is fully binding.

Q9. How does this paper differ from exogenous regime-switching models?

The key difference is that in this model the probability of a regime shift is not exogenous — it is a function of the current state (debt level, cost-push shock) and of the policy parameters (α, ϕ, s̄, R̄); this means the central bank can influence regime-change risk by changing its policy rule, which is not possible in models like Davig and Leeper (2006), Bianchi and Melosi (2017, 2019), or Bianchi and Ilut (2017) where switching probabilities are fixed Markov parameters. The ability of the central bank to manage regime-switch risk is the novel channel through which monetary policy can attenuate the inflation bias without abandoning price stability — a result that has no counterpart in models where the fiscal authority’s behavior is exogenous.

Key concepts

orthodox regime : the policy configuration in which the fiscal surplus limit is slack (s̃_t < s̄) and the central bank follows a standard Taylor rule (R̂_t = αp̂_t with α > 1/β); fiscal policy is passive and monetary policy is active in Leeper’s (1991) sense.

fiscally-dominant regime : the policy configuration in which the fiscal surplus limit binds (s̃_t = s̄) because the real value of government debt is sufficiently high, and the central bank caps its nominal interest rate at R̄ to prevent fiscal stability from deteriorating further; monetary policy becomes fiscally accommodative.

risky steady state : the point to which the economy converges when transitory shocks have receded but agents fully incorporate future regime-shift risk into their expectations; it differs from the deterministic steady state by an inflation bias of 27bp, a real interest rate premium of 41bp, an output shortfall of 0.26pp, and an additional 1.07pp of government debt (all in the baseline calibration).

inflation bias : the systematic elevation of equilibrium inflation above the price stability target that arises from the risk of future fiscal dominance episodes; it is increasing in the real value of government debt and is present even in periods when the economy is in the orthodox regime, because agents rationally incorporate fiscal dominance risk into their expectations.

endogenous regime switching : the feature of the model that distinguishes it from earlier regime-switching frameworks — the probability of a shift to the fiscally-dominant regime is a function of the current state of the economy (debt, cost-push shock) and of the policy parameters, so the central bank can influence regime-change risk through its choice of the Taylor rule coefficient.

vicious cycle : the self-reinforcing dynamic between debt, fiscal dominance risk, the inflation bias, and the real interest rate: higher debt raises fiscal dominance risk → larger inflation bias → higher real rate (via Taylor rule) → higher debt servicing costs → further upward pressure on debt.

On measuring the welfare cost of inflation

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

Measuring the welfare cost of inflation requires specifying a money demand function, a definition of money, and an approach to consumer surplus; existing estimates vary widely because these choices are not standardized. This paper advances the literature by applying neoclassical monetary demand theory that integrates the demand for money with the demands for consumption and leisure, using the Normalized Quadratic (NQ) flexible functional form that avoids imposing specific elasticity assumptions. The main contribution is to extend the Serletis and Xu (2021, 2023) framework to derive Hicksian (compensating variation) money demand functions from the NQ model and compare welfare cost estimates based on these against estimates from the Marshallian (consumer surplus) approach—a comparison not previously made within this integrated demand-system framework. The paper uses U.S. CFS Divisia monetary aggregates across multiple levels of monetary aggregation and finds that the two approaches yield internally consistent but quantitatively different welfare cost estimates, with the Hicksian compensating variation approach providing theoretically preferred measures that are robust across specifications.

In depth

Q1. What is the neoclassical demand system approach and how does it differ from earlier methods?

The Serletis-Xu framework integrates the demand for money with the demands for consumption goods and leisure in a joint utility maximization problem, estimating a flexible NQ functional form in a systems context rather than fitting a single-equation money demand specification. Earlier approaches—such as the log-log specification (Lucas 2000) or semi-log specification (Ireland 2009)—estimate a single money demand equation under a maintained functional form assumption and a fixed interest elasticity (often −0.5 as in the Baumol-Tobin model). The NQ approach, derived from the dual demand system of Diewert (1974), makes no assumption about the functional form of money demand and allows demand interactions among consumption goods, leisure, and money (as recommended by Abbott and Ashenfelter 1976 and Barnett 1979), which is necessary for correct welfare measurement when money is consumed jointly with other goods.

Q2. What is the distinction between the Marshallian and Hicksian approaches to measuring welfare cost?

The Marshallian (Bailey 1956) approach measures the area under the inverse money demand curve between the zero-inflation and positive-inflation nominal interest rates, which corresponds to consumer surplus but does not hold utility constant. The Hicksian (compensating variation) approach measures the income that must be given to the consumer to restore the same utility after the inflation increase as before—holding utility constant rather than income. The Hicksian approach is theoretically preferred because it measures the true welfare loss from inflation under standard consumer theory; the Marshallian approach can under- or over-estimate the true cost depending on income effects. The paper’s main contribution is to derive the Hicksian demands from the NQ model and compute the compensating variation, previously not done within this flexible-functional-form demand system framework.

Q3. What role do Divisia monetary aggregates play?

The paper uses CFS (Center for Financial Stability) Divisia monetary aggregates—which aggregate monetary assets using economic quantity indices that weight components by their monetary service flows—rather than simple-sum aggregates such as M1 or M2. Simple-sum aggregates treat all monetary assets as perfect substitutes regardless of yield differentials, introducing a substitution bias that misrepresents the quantity of monetary services; Divisia aggregates are theoretically consistent with the neoclassical demand system approach used here. The paper reports welfare cost estimates across multiple levels of monetary aggregation to assess sensitivity to the definition of money.

Q4. How do the results compare with the prior literature?

The paper’s estimates, while internally consistent with the NQ flexible form and Divisia aggregates, are in the range of prior estimates in the literature; the Hicksian compensating variation estimates differ from Marshallian consumer surplus estimates in ways consistent with theory, providing a more theoretically grounded benchmark. The wide range of estimates in the existing literature (discussed in the paper’s Table 1)—from the Lucas (2000) log-log model to the Ireland (2009) semi-log model—reflects sensitivity to functional form, money definition, data frequency, and methodology; the paper’s NQ framework addresses functional-form sensitivity while comparing the two surplus measures.

Key concepts

compensating variation (Hicksian welfare cost of inflation) : the income required to restore a consumer’s utility to its pre-inflation level after an inflation increase, holding utility constant; the paper’s main new estimate, derived from Hicksian money demand functions.

Normalized Quadratic (NQ) flexible functional form : a globally flexible functional form (Diewert and Wales 1988) used to approximate the consumer’s cost function without imposing restrictions on substitution elasticities; allows derivation of both Marshallian and Hicksian demand functions.

Divisia monetary aggregates : theoretically consistent monetary aggregates that weight monetary assets by their monetary service flows (user costs) rather than summing them with equal weights; CFS Divisia aggregates are used here as the measure of money.

Optimal Payment Arrangement in a Cash-Less Monetary Economy

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

This paper analyzes a payment arrangement in which monitoring technology can record and trace transfers and holdings of currency — but not of real resources — and shows this arrangement welfare-dominates traditional anonymous cash payments by allowing currency transfers among strangers that function as monetary loans. The abstract provides limited information about the paper’s quantitative findings or specific model structure; the summary reflects only what the abstract states.

In depth

Q1. What is the mechanism by which monetary loans improve welfare?

Traditional cash transactions among strangers are constrained by the inability to enforce deferred payment, since anonymous transactions leave no record; by recording currency transfers (though not real resource transfers), the monitoring technology converts cash transactions into recordable obligations, enabling currency loans and expanding the set of feasible intertemporal trades. A stranger can receive currency today and deliver it back in a future meeting, which is not possible in a purely anonymous cash economy. This expansion of the feasible transaction set is the source of the welfare gain over traditional cash payments.

Q2. What distinguishes this arrangement from other cashless payment models?

The key distinguishing feature is that only currency transfers and holdings are monitored — not real resource transfers — making this a partial recordkeeping environment that lies between fully anonymous cash and fully monitored digital transactions. This intermediate monitoring structure generates a distinct payment arrangement that the authors call a “cash-less monetary economy,” in which currency remains the medium of exchange but its circulation can be traced, enabling new forms of monetary credit among anonymous agents.

Key concepts

monetary loan : a currency transfer between strangers that is recorded by monitoring technology and creates a deferred repayment obligation; the key welfare-improving mechanism of this payment arrangement.

monitoring technology : the mechanism that records and traces currency transfers and holdings but not real resource transfers; the partial recordkeeping structure that enables monetary loans in this economy.

Outsourcing bank loan screening: The economics of third-party loan guarantees

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

Third-party loan guarantees—in which a fee-charging guarantor formally guarantees a bank loan and conducts its own due diligence on the borrower—are present in approximately 10% of Chinese bank loans and are required for most small and medium enterprise (SME) financing. This paper investigates their economic function using proprietary data from a large private loan guarantee firm and interviews with market participants. The paper systematically tests and rejects two leading alternative hypotheses: that guarantees circumvent interest rate caps via regulatory arbitrage (rejected because total loan payments never approach the cap in the data), and that guarantees primarily induce borrowers to self-select based on creditworthiness. The positive evidence points instead to a “second level of delegation of loan evaluation”: guarantors have private information about borrower quality beyond hard accounting data and collateral, screen bad loans effectively, and their pricing is consistent with the outsourced screening interpretation. This framework is analogous to Diamond’s (1984) delegated monitoring, but prior to loan origination rather than after.

In depth

Q1. Why are third-party loan guarantees prevalent in China’s SME lending market?

During the paper’s sample period, third-party loan guarantees are essentially a prerequisite for most SME loans in China, arising because banks face high costs of evaluating small borrowers with limited collateral and opaque financials; guarantors specialize in gathering soft information through site visits and examination of borrower books. The loan guarantee industry consists of a few large firms and many smaller ones; in exchange for a fee paid by the borrower and a pledge of collateral to the guarantor, the guarantor provides a formal credit guarantee to the lending bank. This is a transactional (not relationship-based) business.

Q2. How do the data reject the regulatory arbitrage and self-selection hypotheses?

The regulatory arbitrage hypothesis (that guarantees allow total payments to exceed the interest rate cap) is rejected cleanly because none of the loans in the sample have a total payment—interest plus guarantee fee—at or near the interest rate cap. The self-selection hypothesis (that guarantees induce only high-quality borrowers to apply, as in Thakor 1982) is rejected because: (i) only a small fraction of applications are accepted, suggesting the guarantor and bank do most of the selection rather than borrowers self-selecting; and (ii) the data show guarantors successfully screen out bad loans using private information, inconsistent with the borrower being the primary information-bearing party.

Q3. What is the positive evidence for the outsourced screening interpretation?

The guarantor has information about borrowers beyond hard accounting data and collateral—gathered from site visits and business-record examinations—and this private information is reflected in its risk assessments, which predict loan performance independently. Pricing of loans and guarantees in the data is consistent with a model in which the guarantor’s fee reflects its risk assessment (its private signal about borrower quality), and the bank’s interest rate reflects the residual risk after conditioning on the guarantor’s approval. A key empirical finding is that the correlation between bank loan rates and guarantor risk assessment is negative—when rates were higher in the economy, banks lent to safer credits, because high rates correlate with scarce credit in the sample—a pattern consistent with screening rather than adverse selection.

Q4. What are the broader implications for SME finance and financial intermediation theory?

The paper interprets third-party loan guarantees as a “second level of delegation of loan evaluation”—analogous to Diamond’s (1984) delegated monitoring (which occurs after loan origination) but occurring before—suggesting that the guarantor occupies a specialized information-gathering role that banks cannot efficiently internalize. This outsourcing of screening is potentially a more efficient organizational form than either direct bank screening (if banks face higher per-borrower costs) or government guarantees (which lack the performance incentives of private guarantors). The contrast with the CDS market (where AIG-style guarantors performed no serious checking or hedging) underscores that private guarantors with proper incentives can perform meaningful screening.

Key concepts

third-party loan guarantee : a contractual arrangement in which a fee-charging private guarantor formally guarantees a bank loan and bears the credit risk if the borrower defaults, having conducted independent due diligence on the borrower; the paper shows this functions as outsourced screening.

delegated screening (pre-loan) : the paper’s interpretation of the guarantor’s role as a second layer of delegation of loan evaluation before origination, analogous to Diamond’s (1984) delegated monitoring after origination; the guarantor has a comparative advantage in gathering borrower-specific soft information.

Passive Quantitative Easing: Bond Supply Effects through Lower Debt Issuance

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

The paper introduces the concept of “passive quantitative easing” (passive QE): a deliberate reduction in government debt issuance that lowers anticipated future bond supply and reduces long-term yields through the same supply channel as central bank asset purchases, without involving asset purchases or reserves creation. The authors develop a unified classification scheme for central bank balance sheet policies organized by their net effect on anticipated future bond supply, and show that the Danish government’s unexpected January 2015 debt halt — which removed approximately 29.9 billion DKK from the outstanding bond stock over roughly nine months — was followed by a two-day yield decline of approximately 25 basis points across the entire yield curve. Regression estimates controlling for concurrent ECB and SNB actions imply that the halt raised the safety premium on Danish bonds by 17–22 basis points and reduced the ten-year term premium by 37–70 basis points, with combined effects pointing to 54–92 basis points in lower yields relative to the counterfactual. The Danish episode ranks approximately on par with the Federal Reserve’s QE3 in the classification scheme, and the paper argues that passive QT — unexpectedly higher debt issuance — is contractionary through two additional portfolio balance channels not present in active QT and should be treated as an active policy tool rather than a neutral background condition.

In depth

Q1. What is “passive QE” and what distinguishes it from conventional QE?

The paper defines passive QE as a reduction in government debt issuance that lowers anticipated future bond supply, arguing this is functionally equivalent to central bank asset purchases in its effects on long-term yields, even though it involves neither asset purchases nor reserves creation. The supply-side equivalence holds because what matters for term premia and safe-asset premia is the anticipated future stock of bonds available to private investors: whether the central bank withdraws bonds via outright purchases or the government simply issues fewer new ones, the anticipated future supply declines, requiring downward adjustment in the compensation investors demand for duration risk and scarcity. The distinction from active QE is therefore operational rather than economic: passive QE leaves the central bank’s balance sheet unchanged, makes no reserve injection, and requires no fiscal–monetary coordination beyond the government’s own debt management decisions.

Q2. How do the authors classify central bank balance sheet policies?

The paper proposes a unified classification scheme that maps central bank balance sheet policies by their net effect on anticipated future bond supply, placing passive QE in the same stimulative category as active QE programs and ranking the Danish halt at approximately −0.0104 on this measure — nearly on par with the Federal Reserve’s QE3 at −0.0120. The scheme allows cross-country and cross-program comparisons of unconventional monetary policy actions by reducing them to a common currency of anticipated supply change. The classification also distinguishes passive QT from active QT: the paper argues that passive QT (higher-than-anticipated issuance) is more contractionary than active QT of equal magnitude because higher issuance also reduces safe-asset scarcity value and shifts duration risk back to the market through two additional portfolio balance channels.

Q3. What does the Danish debt halt episode show?

The January 30, 2015 announcement by Denmark’s debt management office that it would halt new government bond issuance for the remainder of the year was unexpected and was followed within two trading days by a yield decline of approximately 25 basis points across the entire yield curve. The halt lasted roughly nine months and reduced the outstanding Danish government bond stock by approximately 29.9 billion DKK. The reaction is interpreted as evidence that market participants immediately revised down their expectations of future bond supply, compressing the compensation required for holding duration risk and raising the relative value of the now-scarcer safe assets.

Q4. What do the regression estimates imply?

Controlling for the concurrent SNB and ECB announcements in January 2015, the authors’ regression estimates imply that the Danish halt raised the safety premium on Danish bonds by 17–22 basis points and reduced the ten-year term premium by 37–70 basis points, pointing to a combined reduction in bond yields of 54–92 basis points relative to the counterfactual without the halt, measured over the halt period. The term-premium decline is interpreted as consistent with supply-induced portfolio balance effects: fewer bonds requiring lower duration-risk compensation. The safety-premium increase is consistent with safe-asset scarcity effects: a tighter supply of high-quality government bonds raising their relative scarcity value. These two channels are identified separately in the yield decomposition and estimated to be independently significant.

Q5. How does the paper treat passive QT?

The paper argues that passive QT — a higher-than-anticipated level of government debt issuance — is not a neutral background condition but an active contractionary force, and potentially more contractionary than active QT of equal magnitude through two additional portfolio balance channels. The argument is that higher issuance reduces safe-asset scarcity value and directly shifts duration risk from the central bank to the market, while active QT (central bank balance sheet reduction) lacks these two additional channels. This implies that fiscal authorities’ debt issuance decisions carry monetary policy implications that are not captured in frameworks treating issuance as a non-monetary decision.

Key concepts

passive QE : a deliberate reduction in government debt issuance that lowers anticipated future bond supply and reduces long-term yields through supply effects; the paper treats it as functionally equivalent to central bank asset purchase programs despite involving no asset purchases or reserves creation.

passive QT : higher-than-anticipated government debt issuance; the paper treats it as an active contractionary tool, potentially more contractionary than active QT of equal magnitude, because it triggers two additional portfolio balance channels.

safety premium : the premium on high-quality safe assets such as government bonds reflecting their scarcity value; in the Danish halt episode this rose as supply tightened.

term premium : the component of a long-term bond yield compensating investors for bearing duration risk; in the Danish halt episode this fell as anticipated future bond supply declined.

classification scheme : the paper’s taxonomy of central bank balance sheet policies organized by their net effect on anticipated future bond supply, allowing cross-program comparisons including passive QE and passive QT.

Danish debt halt : the January 30, 2015 announcement by Denmark’s debt management office of a halt to new government bond issuance for the remainder of the year, used as the natural experiment to test the passive QE hypothesis.

Payment Flows, Bank Lending, and Central Bank Digital Currencies

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

This paper examines how the degree of user anonymity built into a central bank digital currency (CBDC) affects bank lending decisions and what this implies for the optimal design of CBDC anonymity. “Anonymity” in the paper’s sense is the lender’s inability to discern whether a borrowing entrepreneur is diverting funds—a moral hazard problem that arises because CBDC transactions, if unobservable to lending banks, prevent the screening that banks currently perform using deposit (card-based) transaction records. In a signaling model where entrepreneurs choose a payment instrument to influence bank refinancing decisions, moderate CBDC anonymity is shown to produce an inefficient pooling equilibrium in which both high- and low-quality borrowers choose CBDC, preventing banks from screening. To avoid this pooling inefficiency, CBDC anonymity should be set either low—making CBDC less attractive to entrepreneurs seeking to obscure diversion—or high—discouraging bank lending through CBDC entirely—with high anonymity optimal when CBDC significantly benefits sales, and low anonymity otherwise. Competition between bank deposits and CBDC may impede the implementation of the low-anonymity optimum.

In depth

Q1. How is “anonymity” defined, and why does it create a conflict between entrepreneurs and banks?

“Anonymity” is defined as the lender’s inability to discern an entrepreneur’s actions that enable fund diversion, and it creates a conflict because entrepreneurs may prefer anonymity (which allows diversion) while banks prefer observability (which enables screening for loan refinancing). The paper is motivated by the example of Square (Square Loans), which uses point-of-sale transaction data to screen firms for refinancing decisions; a switch to a more anonymous payment instrument removes this data, worsening the bank’s adverse selection problem. When a CBDC is issued, central banks face a design choice over how visible CBDC transaction data are to lending banks, and this design choice has real consequences for credit allocation.

Q2. What is the inefficient pooling equilibrium under moderate anonymity?

Under moderate CBDC anonymity, both high- and low-quality entrepreneurs choose CBDC, producing a pooling equilibrium in which the bank cannot distinguish project quality and cannot make screening-based refinancing decisions—an outcome that is inefficient. The pooling failure occurs because moderate anonymity is simultaneously attractive enough for low-quality types (enabling diversion) and for high-quality types (due to CBDC’s sales benefits), so neither type’s payment choice reveals useful information. The bank, unable to screen, must make refinancing decisions based on prior beliefs alone.

Q3. What is the optimal anonymity policy and when should each level apply?

Optimal CBDC anonymity should be either low or high but not moderate: specifically, it should be high when CBDC significantly benefits sales—because under those conditions bank lending through CBDC should be designed away—and low otherwise, to preserve the bank’s ability to screen by observing CBDC transaction records. Under low anonymity, CBDC is made unattractive to entrepreneurs seeking to obscure fund diversion, allowing the separating equilibrium to be restored. However, competition between deposits and CBDC may prevent the implementation of the low-anonymity optimum, because deposits offer entrepreneurs an already-monitored alternative.

Q4. What is the scope of the model?

The model is presented in the context of firm borrowing, with entrepreneurs of privately known project quality choosing payment instruments that signal type to the lending bank, but the paper notes the model can be relabeled for consumer finance by interpreting consumers as borrowers repaying from future income. The key friction is moral hazard through fund diversion enabled by anonymity; the results apply to any setting where a payment intermediary’s transaction records affect a lender’s refinancing decision. This working paper version presents theoretical results without empirical estimates of magnitudes.

Key concepts

CBDC anonymity : as defined in this paper, the lender’s inability to discern whether a borrowing entrepreneur is diverting funds, parameterized by the degree to which CBDC transaction records are visible to the lending bank; contrasted with deposit (debit card) payments, which offer limited anonymity because the bank can observe the full transaction record.

fund diversion : an entrepreneur’s action of redirecting loan proceeds for private benefit rather than productive use, facilitated by higher anonymity because the bank cannot detect the action when transaction records are obscured.

pooling equilibrium : an equilibrium in which both high- and low-quality entrepreneurs choose the same payment instrument, preventing the bank from inferring project type and making efficient refinancing decisions impossible.

separating equilibrium : an equilibrium in which high- and low-quality entrepreneurs choose different payment instruments, allowing the bank to condition its refinancing decision on the revealed type signal.

Policy Biases in a Model with Labor‐Market Frictions

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

Layer 1 — Overview

Research Question

Dennis and Kirsanova ask whether shocks to labor-market matching efficiency and worker bargaining power pose a significant problem for monetary policy, and whether the inability to commit (discretion versus commitment) generates important stabilization bias in a model with labor-market matching frictions. They also examine how several popular simple monetary policy rules perform in response to these and other shocks.

Model and Methodology

The paper develops a fully nonlinear DSGE model featuring: (1) a goods market characterized by monopolistic competition and Rotemberg-style quadratic price-adjustment costs; and (2) a labor market characterized by a constant-returns-to-scale matching function (Mortensen-Pissarides) and Nash bargaining over wages and hours worked. Because the flex-price equilibrium is inefficient — owing to both monopolistic competition and the matching friction — a linear-quadratic approximation is not valid for the discretionary policy problem, and the authors solve the model using Smolyak sparse-grid methods with Chebyshev polynomial basis functions.

The model is calibrated to quarterly U.S. data. Key parameter values include: discount factor β = 0.99 (annualized real interest rate ≈ 4 percent), elasticity of substitution across goods ε = 11 (steady-state markup of 10 percent), price-adjustment cost φ = 80, quarterly separation rate δ = 0.12, job-finding rate f = 0.65 (delivering an employment rate close to 0.94 and an unemployment rate near 5.95 percent in steady state), elasticity of matching function with respect to unemployment ξ = 0.72, and workers’ mean bargaining power equal to ξ = 0.72 (satisfying the Hosios condition at steady state). Five AR(1) shocks are included: aggregate technology (persistence 0.95, standard deviation 0.008), matching efficiency (persistence 0.80, standard deviation 0.032), bargaining power (persistence 0.80, standard deviation 0.028), consumption preference (persistence 0.70, standard deviation 0.006), and elasticity of substitution (persistence 0.85, standard deviation 0.12).

Main Findings

The central finding is that optimal monetary policy — whether conducted under commitment (Ramsey) or discretion — is highly efficient at responding to labor-market shocks, producing impulse responses that closely replicate the flex-price equilibrium for real variables. Specifically, in response to matching efficiency shocks and bargaining power shocks, the commitment and discretionary equilibria both track the flex-price equilibrium closely for output, consumption, employment, tightness, and the real wage.

Discretion generates a pronounced inflation bias of approximately 1.82 percent per annum — large but not implausible — but does not generate a meaningful stabilization bias for the class of shocks studied (technology, matching efficiency, bargaining power, and consumption preference). The one exception is the elasticity of substitution shock (analogous to a markup shock in linearized models): for this shock, the impulse responses under discretion diverge noticeably from those under commitment, revealing a discretionary stabilization bias — consistent with conventional New Keynesian results.

Regarding simple rules, strict inflation targeting (SIT) performs closely in line with commitment and discretion for all shocks. The two Taylor-type rules — one responding to inflation and output growth, the other to inflation and the unemployment rate — generate substantially greater volatility in inflation and the nominal interest rate relative to optimal policy. The unemployment-gap Taylor rule is the worst performer among the three simple rules; nevertheless, all three simple rules produce household welfare outcomes close to those under optimal monetary policy. The suboptimality of the simple rules is most evident in nominal variables, particularly inflation and the nominal interest rate, and less evident in real variables — though labor-market inefficiencies under the Taylor-type rules do emerge in response to matching efficiency and bargaining power shocks, with hours worked and the real wage deviating noticeably from flex-price outcomes.

The probability of encountering the zero lower bound is, for all policies considered, considerably less than 0.5 percent across one million simulated observations, suggesting that ZLB concerns are not material for the shocks under study.

Scope Conditions

These results hold within the context of a model with a fixed labor force (no participation margin), balanced-budget fiscal authority, no capital accumulation, and Nash bargaining over both wages and hours. The Hosios condition is satisfied at steady state (though the authors report that relaxing it has little effect on results). The analysis abstracts from the zero lower bound constraint when solving the model.

In depth

Q1. What is the Hosios condition and what role does it play in this model?

The Hosios condition requires that workers’ bargaining power equal the elasticity of matches with respect to unemployment in the matching function (ξ = 0.72). When the condition holds, bargaining is efficient in the sense that the decentralized search equilibrium replicates the social planner’s allocation. The authors impose it at steady state (mean bargaining power & = ξ = 0.72) so that the flex-price equilibrium is distorted only by monopolistic competition, not by inefficient search. The authors state they also analyzed versions where the Hosios condition does not hold and found it had little effect on results.

Q2. How are matching efficiency shocks transmitted through the economy, and how does optimal policy respond?

An improvement in matching efficiency raises the rate at which vacancies are filled and the unemployed find jobs, increasing employment from existing vacancy and unemployment levels. Employment rises, unemployment falls, labor market tightness increases, and the real wage rises. Firms substitute toward more workers (extensive margin) and away from hours-per-worker (intensive margin), so hours worked per employee decline even as aggregate hours rise. Both commitment and discretion track the flex-price equilibrium closely for all these real variables. Some difference is visible in inflation: under discretion the real wage rises by more than under commitment, pushing real marginal costs and inflation higher in the short run.

Q3. How does a bargaining power shock affect the economy under optimal monetary policy?

An increase in worker bargaining power shifts the match surplus toward workers, raising real wages and hours worked per employee. Firms, receiving a smaller surplus share, post fewer vacancies and hire fewer workers, leading to a decline in employment, a fall in labor market tightness, and a rise in unemployment. The employment decline is large enough to lower household income, goods production, and aggregate consumption. Under both commitment and discretion, the real economy tracks the flex-price equilibrium closely. Notable differences between commitment and discretion appear in inflation: under discretion, the inflation response on impact is larger and more persistent than under commitment, and monetary policy tightens more aggressively (higher nominal rate) under discretion.

Q4. What is the key difference between the commitment and discretionary equilibria, and why is stabilization bias mostly absent?

Commitment (Ramsey) policy differs from discretionary policy primarily in the level of inflation, not in the dynamics of the real economy. Discretion generates an inflation bias of approximately 1.82 percent per annum. However, the impulse responses for real variables (output, consumption, employment, tightness, real wage) under commitment and discretion are very similar to each other and to the flex-price equilibrium for four of the five shocks. This indicates that forward guidance — which commitment provides and discretion does not — is not an important factor in this model’s response to these shocks. The intuition is that the economy’s fluctuations in response to matching efficiency and bargaining power shocks are largely efficient, so the central bank needs only to avoid creating additional distortions, which both commitment and discretion achieve.

Q5. What distinguishes the elasticity of substitution shock from the other shocks in terms of policy performance?

The elasticity of substitution shock behaves similarly to a markup shock in linearized models: an increase in substitutability reduces firms’ monopolistic power, lowers the price markup, raises output and consumption, increases hours worked, posted vacancies, employment, and the real wage. For this shock, the impulse responses under discretion diverge noticeably from those under commitment — the decline in inflation is larger and more persistent under discretion than under commitment, and the nominal interest rate response differs in sign across policies. This is the only shock in the model for which a meaningful discretionary stabilization bias is evident, consistent with conventional wisdom from linearized New Keynesian models that markup shocks generate stabilization bias.

Q6. How do the three simple rules compare with optimal policy for labor-market shocks?

Strict inflation targeting (SIT) behaves similarly to commitment and discretion and hence closely replicates the flex-price equilibrium for all five shocks. The two Taylor-type rules — one responding to inflation and output growth (parameterized with φ_π = 2.5, φ_y = 0.5/4) and one responding to inflation and the unemployment rate (φ_π = 2.5, φ_u = 1.5/4) — both generate substantially more volatility in inflation and the nominal interest rate relative to optimal policy. The unemployment-gap Taylor rule generally results in inflation moving more in response to shocks and in the economy returning more slowly to baseline, making it the worst-performing simple rule. However, all three simple rules produce welfare outcomes close to those under optimal policy; the suboptimality of the Taylor-type rules is most evident in nominal rather than real variables.

Q7. Does the zero lower bound (ZLB) pose a concern under any of the policies studied?

Based on simulating one million observations from each model, the unconditional probability of encountering the ZLB is very small — well below 0.5 percent — for all policies considered. The commitment policy has a ZLB probability of approximately 0.077 percent, reflecting its near-zero average inflation. Discretion’s positive inflation bias of 1.82 percent reduces the ZLB probability to approximately 0.001 percent. The Taylor-type rules — especially the unemployment-gap rule (ZLB probability approximately 0.296 percent) — have higher probabilities than discretion, though these remain very small. These results suggest that for the shocks analyzed, violations of the ZLB are extremely unlikely.

Q8. What are the steady-state and stochastic simulation mean outcomes, and how do they compare across regimes?

The deterministic steady-state unemployment rate is approximately 5.95 percent, rising slightly to a mean of 6.04 percent in the stochastic flex-price economy. The stochastic means for output, consumption, employment, and the real wage are all slightly below their deterministic steady states across all regimes, because in the absence of capital households respond to increased volatility by substituting away from labor toward leisure (precautionary leisure) rather than precautionary saving. Mean outcomes for real variables under discretion (e.g., output mean ≈ 0.3730, unemployment mean ≈ 6.025 percent) and commitment (output mean ≈ 0.3729, unemployment mean ≈ 6.028 percent) are very similar to each other and to the flex-price means (output mean ≈ 0.3728, unemployment mean ≈ 6.038 percent). The key difference is in inflation: commitment delivers near-zero mean inflation (≈ 0.00043 percent annually) while discretion delivers ≈ 1.82 percent annually.

Q9. Why is a nonlinear solution method used, and what does this allow the paper to capture that log-linearized approaches cannot?

The nonlinear solution is required because the flex-price equilibrium is not efficient (monopolistic competition and the matching friction both create distortions), so the discretionary policy problem cannot be formulated as a linear-quadratic problem. The nonlinear approach allows the paper to analyze both level biases (the steady-state inflation bias) and stabilization biases (the dynamic response to shocks) in a unified framework — something that log-linearization around the efficient steady state would preclude. Related papers by Furlanetto and Groshenny (2016) and Zhang (2017) focus on log-linearized models and the natural rate of unemployment; this paper focuses instead on optimal policy and policy biases.

Q10. What role does the consumption preference shock play, and how does it differ from the other shocks?

The consumption preference shock is the only shock in the model that acts somewhat like a demand shock. A one standard deviation increase raises the utility obtained from consumption, leading households to increase consumption and hours worked (at a slightly lower real wage), which induces firms to post more vacancies and raise employment. Most of the labor market response comes through higher hours rather than higher employment. Both commitment and discretionary policy cope well with this shock — the real economy closely tracks the flex-price equilibrium — because the shock has relatively little impact on inflation (inflation declines slightly due to lower real marginal costs from the lower real wage). The nominal interest rate rises because the increase in the real interest rate (driven by households’ desire to borrow) more than offsets the decline in inflation.

Key Concepts

Matching efficiency shock: A stochastic shock to the parameter mt in the constant-returns-to-scale matching function Mt = mt * u_t^xi * v_t^(1-xi), which governs the overall rate at which unemployed workers and posted vacancies are matched. A decline in mt reduces the number of matches formed at any given levels of unemployment and vacancies, raising unemployment and reducing employment. The paper treats this as an empirically relevant shock motivated by evidence of a sustained decline in aggregate matching efficiency during the Great Recession.

Discretionary inflation bias: The tendency for a central bank conducting policy without the ability to commit to produce systematically higher inflation than would occur under a commitment (Ramsey) regime. In this model, discretion generates an annualized inflation rate of approximately 1.82 percent, while commitment produces near-zero average inflation. This reflects the time-inconsistency problem (Kydland and Prescott, 1977; Barro and Gordon, 1983) arising from the interaction of monopolistic competition and price stickiness.

Stabilization bias: A distortion that arises under discretionary policy, in which the central bank’s inability to commit leads it to respond to shocks in a manner that departs from optimal commitment responses, producing suboptimal dynamics for real variables in addition to the inflation bias. In this paper, stabilization bias is found to be largely absent for matching efficiency, bargaining power, technology, and consumption preference shocks, but is present for the elasticity of substitution shock.

Hosios condition: The condition, derived in Hosios (1990), that efficient decentralized search-and-matching equilibrium requires workers’ bargaining power to equal the elasticity of matches with respect to the unemployment rate (ξ). In the paper’s notation: & = ξ. When the condition holds, the flex-price equilibrium replicates the social planner’s allocation in the labor market; deviations cause either excessive or insufficient vacancy posting.

Labor market tightness (θ): Defined as the ratio of vacancies to unemployed searchers, θt = vt/ut. When tightness is high, the labor market is tight and firms have difficulty filling vacancies (low job-filling rate q(θ)) while workers find jobs easily (high job-finding rate f(θ)). Tightness is the key state variable linking vacancy posting decisions by firms to employment dynamics and wage bargaining outcomes.

Bargaining power shock: A stochastic shock to the worker’s share of the Nash bargaining surplus (&t), which follows an AR(1) process. The Hosios condition holds at steady state but is violated when the shock is realized. A positive shock shifts surplus from firms to workers, raising real wages, depressing vacancy posting, and reducing employment, while a negative shock has the reverse effect.

Rotemberg price-adjustment cost: A quadratic cost φ/2 * (π_t)^2 * y_t paid by firms when they change prices, creating price stickiness without the “menu cost” lumpiness of Calvo pricing. This creates a role for monetary policy and generates a nonlinear Phillips curve. The coefficient φ is set to 80, based on the estimate in Ireland (2001).

Flex-price equilibrium: The benchmark equilibrium in which prices are fully flexible and bargaining is efficient (Hosios condition satisfied exactly). In this equilibrium there is no role for monetary policy over the price-adjustment margin, and the economy responds to shocks in a manner that is efficient conditional on the remaining frictions (monopolistic competition and the matching friction). The paper uses deviations of commitment and discretionary outcomes from this benchmark to measure the efficiency of optimal monetary policy.

Redemption Fees and Gates in the Lab

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

Layer 1: Overview

This paper uses laboratory experiments to evaluate the effectiveness of two liquidity management tools — redemption fees and redemption gates — in reducing runs on money market funds (MMFs), explicitly accounting for preemptive run behavior where investors withdraw before a fee or gate is triggered to avoid being harmed by its imposition. The experimental design is based on a Diamond–Dybvig framework modified following Engineer (1989), in which four investors must decide whether to withdraw before learning their own liquidity type (patient or impatient), generating a setting where preemptive runs are theoretically possible even without fear of fund default. Three treatments are compared: a laissez-faire baseline, a gates treatment (withdrawals suspended after cash reserves are exhausted), and a fees treatment (a redemption fee charged on withdrawals once cash reserves are exhausted). Across 15-period session halves, redemption fees produce significantly lower withdrawal rates than both the baseline and gates treatments, with the gap emerging primarily after the first ten periods as participants adapt to the tool; gates, contrary to the theoretical prediction that they reduce the risk factor of the no-run equilibrium, do not lower withdrawal rates relative to the baseline — and in the full-session analysis, gates actually generate significantly higher withdrawal rates than the baseline, consistent with preemptive runs accelerating when investors fear losing access to their funds. The overall finding is that neither tool eliminates fund fragility, but fees offer a modest and delayed stabilizing effect while gates are counterproductive, lending empirical support to the SEC’s 2023 regulatory shift away from gates and toward fees in MMF regulation.

In depth

Q1. What is the experimental design and why does it explicitly study preemptive runs?

The experiment models a fund with four investors, each holding a demandable claim worth 1 ECU in period 1; the fund holds 2 ECUs in cash and a project that pays 2R ECUs in period 2 if allowed to mature but only 1 ECU if liquidated early, and investors must make their period-1 withdrawal decision before learning whether they are impatient (need period-1 funds) or patient (can wait), mirroring the Engineer (1989) setup where preemptive runs arise from the risk of being locked in rather than from fundamental insolvency concerns. The key feature is that an investor who expects fees or gates to be imposed faces an incentive to withdraw early to avoid either losing access (gates) or paying a fee (fees) at precisely the moment their liquidity need arises, which is exactly the preemptive run mechanism observed empirically during the COVID-19 MMF turmoil of spring 2020. Investors are sequentially asked whether they wish to withdraw in a random order without observing others’ choices, and they learn their type only in the evening of period 1 after having already made the morning withdrawal decision. In the treatment with gates, the fund suspends payouts entirely once its 2 ECU cash reserve is exhausted (i.e., after two withdrawals), forcing the third and fourth investors to wait for period 2 regardless of their type. In the treatment with fees, the fund charges a redemption fee on the third and fourth period-1 withdrawals instead of suspending them.

Q2. How does the theoretical risk factor framework generate the paper’s main hypothesis?

The paper uses the concept of the “risk factor of the no-run equilibrium” — defined as the probability p at which an investor becomes indifferent between staying invested and withdrawing when all other investors stay with probability p — to rank the three treatments by their predicted effectiveness: fees should generate the lowest risk factor and thus the highest tendency toward the no-run equilibrium, followed by gates, with the baseline highest. Fees dominate gates on the risk factor because fees still permit withdrawal in period 1 (albeit at a cost), meaning an impatient investor who remained invested can still access funds when needed, whereas under gates an impatient investor who is locked out has no recourse. This additional flexibility of fees means that the downside of remaining invested is smaller under fees than under gates, making the no-run equilibrium relatively more attractive under fees. The paper’s design tests whether this theoretical ranking carries through to actual investor behavior in the lab, where cognitive limitations, learning dynamics, and strategic uncertainty may produce deviations from the prediction.

Q3. What are the main experimental results on withdrawal rates?

Pooled over the first 15 periods of the first session halves (where no spillovers from prior experience occur), withdrawal rates are 30.3% in the baseline, 31.7% in gates, and 27.6% in fees; proportion tests confirm that fees produce significantly lower withdrawal rates than both baseline and gates at the 5% level, but no significant difference is found between baseline and gates — gate withdrawal rates are actually slightly higher than the baseline, contradicting the directional hypothesis. In the robustness check using both session halves (full 30 periods), the pattern sharpens: overall withdrawal rates are 30.3% (baseline), 33.4% (gates), and 25.4% (fees), with gates now significantly higher than baseline (p = 0.000) as well as significantly higher than fees, indicating that gates actively encourage preemptive withdrawal rather than deterring it. Withdrawal rates in the fees treatment exhibit a distinctive time pattern: they start higher than the other treatments in the first 5 periods (the Fees × Period interaction in the regression is negative and significant, while the main Fees coefficient is positive and significant, indicating an initially elevated but steeply declining trajectory), with the fee benefit materializing only from period 11 onward — consistent with the European Commission’s (2023) observation that European MMF investors more familiar with fees show less preemptive behavior than U.S. investors.

Q4. What does the regression analysis reveal about the treatment effects and dynamics?

Random-effects panel linear probability models of the binary withdrawal decision confirm that the fees treatment produces a significantly negative trend (Fees × Period coefficient negative and statistically significant) while the baseline shows no time trend and gates show no significant deviation from baseline trends, and that prior round experience — specifically the number of withdrawal requests in the immediately preceding round — is a strong positive predictor of withdrawal (approximately 6 percentage points per additional prior-round withdrawal request), while longer-run experience before the last round carries no significant predictive power. The inclusion of individual-level controls in Model (4) shows that higher risk tolerance is associated with significantly lower withdrawal rates (a surprising finding relative to prior experimental literature, which the authors suggest may reflect the preemptive nature of the decision making risk tolerance relevant through attitudes toward liquidity timing risk rather than through classic strategic risk). The regression analysis confirms that gates’ ineffectiveness is not explained by observable participant characteristics: the gates dummy is never significant and the gates-period interaction is not significantly different from the baseline, ruling out the possibility that session-level composition differences drive the null result for gates.

Q5. Does switching regulatory regime across session halves generate behavioral change?

Switching from the baseline to fees in the second session half produces a significant reduction in withdrawal rates in the final 5-period block consistent with Hypothesis 2, and switching from fees to gates in the second half produces a significant increase in withdrawal rates in the final 5-period block; however, switching from baseline to gates and from gates to fees produce no significant differences between session halves at the 5% level. The modest switching effects suggest that the fee benefit takes time to emerge regardless of prior regime experience — a finding consistent with the general pattern that fee effectiveness materializes only after participants have had multiple rounds of exposure. This regime-switching analysis also rules out a strong order effect as an explanation for the observed fee benefit: the fee advantage over baseline is present even when comparing within the same session halves and is not driven by participants carrying in stabilizing prior knowledge from the fees treatment.

Q6. What are the regulatory implications and how do the findings connect to the 2020 MMF turmoil?

The experimental findings directly inform the ongoing regulatory overhaul of MMF liquidity management tools, supporting the SEC’s 2023 decision to move away from gates toward mandatory swing pricing (which functions similarly to a fee) as the primary tool for U.S. MMFs, and providing micro-level behavioral evidence for why the 2014 fees-and-gates provisions failed to prevent the spring 2020 MMF runs even though they were in force. The preemptive run mechanism is empirically identified in the lab as a real and substantial phenomenon: withdrawal rates in the first round are if anything higher under fees than under the baseline, and the fee benefit only consolidates after participants have repeatedly experienced the tool, suggesting that investor familiarity is necessary for fee effectiveness — a condition that was likely not met in 2020. The finding that gates actively worsen run propensity in the full-session analysis provides the starkest regulatory implication: gates may be self-defeating by compressing investors’ effective option to wait, creating a focal first-mover advantage that accelerates exactly the run the gate is meant to stop.

Key Concepts

preemptive run : a run in which investors withdraw from a fund before their immediate liquidity need arises, driven by the strategic risk that fees or gates will be imposed at the exact moment they need liquidity; modeled here following Engineer (1989) and experimentally documented as a significant behavioral phenomenon that undermines both fees and gates.

risk factor of the no-run equilibrium : a measure based on risk dominance (Harsanyi and Selten 1988) defined as the probability p at which an investor becomes indifferent between withdrawing and remaining when all others stay with probability p; lower risk factor means the no-run equilibrium is more robust to coordination failure, and the paper predicts fees < gates < baseline in this ranking.

redemption gate : a liquidity management tool that suspends fund withdrawals once cash reserves are depleted, theoretically preventing fire sales but experimentally found to be ineffective and potentially counterproductive due to the preemptive run incentive it creates for investors who fear losing access to their funds.

redemption fee : a liquidity management tool that charges a cost on fund withdrawals during periods of redemption stress, internalizing liquidation losses into the withdrawing investor’s payoff; experimentally found to significantly reduce withdrawal rates relative to both baseline and gates, but only after a learning period of approximately 10 periods.

Redistributive Policy Shocks and Monetary Policy with Heterogeneous Agents

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

Layer 1 — What this paper finds and why it matters

Governments in emerging market and developing economies (EMDEs) routinely intervene in agricultural markets — procuring grain and redistributing it to poor households — in response to food price shocks or expanded food security mandates (India’s 2013 National Food Security Act is the leading example). This paper asks how monetary policy should respond to such “redistributive policy shocks,” and what those shocks do to sectoral inflation and the consumption distribution between rich and poor households. The authors build a two-sector (agriculture with flexible prices; manufacturing with sticky prices), two-agent (Ricardian rich; rule-of-thumb poor) New Keynesian DSGE model, calibrated to India, that extends the TANK framework of Debortoli and Gali (2018) to two sectors and introduces explicit government procurement and redistribution. They show that a redistributive policy shock raises aggregate inflation and the output gap but also raises poor consumption and aggregate welfare, because the subsidy-in-kind effect on poor households more than offsets the decline in rich consumption and the inflationary pressure. They further show that consumer heterogeneity matters for whether monetary policy responses to various shocks raise or reduce aggregate welfare: in models with a flexible-price agricultural sector, contractionary monetary shocks produce larger deflation but smaller declines in real consumption relative to one-sector benchmarks, so the welfare cost of monetary contraction is lower than standard NK models imply.

In depth

Q1. What is a “redistributive policy shock” and how does the model capture it?

A redistributive policy shock is a sudden increase in the fraction of government-procured agricultural output that is redistributed to poor households. In the model, the government taxes rich (Ricardian) households via lump-sum levies each period, uses those proceeds to purchase agricultural output at the open market price, and then redistributes a fraction φ_t of the procured quantity to poor households as an in-kind subsidy. The remaining fraction goes into a buffer stock. The shock to redistribution is modeled as a positive innovation to φ_t (AR(1) process), distinct from a shock to the procurement quantity Y^P_{A,t} itself. Because the in-kind transfer reduces the effective price paid by the poor for agricultural goods — the poor face an effective price of (1 − λ_t)P_{A,t} — the redistributive shock operates as a proportional price subsidy on agriculture consumption for the poor, even though the quantity is what the government directly controls.

Q2. What are the two types of households and how do they differ?

Rich households are Ricardian (forward-looking) and hold one-period risk-free bonds; poor households are rule-of-thumb consumers who do not save. Both types consume goods from both the agricultural and manufacturing sectors according to Cobb-Douglas indices, but they differ in three ways. First, poor households have a higher budget share for agricultural goods (δ_P > δ_R), consistent with Engel’s Law. Second, the inverse of the intertemporal elasticity of substitution (IES) is higher for the poor (σ_P > σ_R), following Atkeson and Ogaki (1996) estimates for Indian household data; this means the poor are less willing to substitute consumption across time and respond differently to real wage changes. Third, rich households have both labor income and dividend income from monopolistically competitive manufacturing firms, while poor households have only labor income.

Q3. What happens to inflation and consumption when a positive agricultural productivity shock hits?

A positive agricultural productivity shock leads to a decline in inflation, a rise in the output gap, and higher consumption for both rich and poor households. Because the agriculture sector has flexible prices, a positive productivity improvement lowers agricultural prices immediately, reducing the terms of trade (the relative price of agriculture to manufacturing). Aggregate CPI inflation falls. The rise in agricultural output increases real income for both household types, raising consumption and aggregate welfare. These dynamics are compared to the Aoki (2001) representative-agent two-sector benchmark.

Q4. What are the aggregate and distributional effects of a positive redistributive policy shock?

A procurement-and-redistribution shock raises aggregate inflation, the output gap, and poor consumption, while lowering rich consumption; aggregate welfare rises because the redistribution effect dominates. The mechanism has two parts. First, the government procures additional agricultural output at the market price, financed by higher lump-sum taxes on the rich; this reduces rich consumption. Second, the redistributed grain lowers the effective price of the agricultural good for the poor, raising poor consumption through a “redistribution effect.” Because poor households spend a higher share of income on the agricultural good than rich households, and because the poor receive a fraction of their agricultural consumption for free, market demand for the agricultural good in the open market is less than it would be without redistribution. Consequently, the inflationary impact of the procurement shock is substantially lower in the two-agent model than in the Aoki representative-agent model (where there is no redistribution to dampen open-market demand).

Q5. How does consumer heterogeneity alter the transmission of a contractionary monetary policy shock?

In models with a flexible-price agricultural sector, a contractionary monetary shock produces a larger deflation but a smaller decline in consumption and smaller welfare losses than in single-sector or representative-agent benchmarks. A rise in the nominal interest rate induces intertemporal substitution of consumption, reducing aggregate demand and the aggregate price level. This deflationary effect is amplified when a flexible-price sector is present alongside the sticky-price sector, because agricultural prices can fall immediately. However, the same flexible-price sector means that real interest rates rise by less (compared to an all-sticky-price economy), so the reduction in rich and poor consumption is also smaller. The paper compares this to three benchmarks: the simple one-sector one-agent NK model (Gali 2015, Chapter 3), the Debortoli-Gali (2018) one-sector two-agent model, and the Aoki (2001) two-sector one-agent model. The welfare losses from monetary contraction are lower in the two-sector models (the authors’ framework and Aoki’s) than in the one-sector models.

Q6. How does the model differ from its three main benchmark frameworks?

The model merges the two-sector production structure of Aoki (2001) with the TANK distributional structure of Debortoli and Gali (2018), and adds explicit government procurement and redistribution — none of the benchmarks have all three features. Relative to Aoki: the paper adds poor/rich heterogeneity, different IES parameters, and the government redistribution mechanism. Relative to Debortoli-Gali: the paper adds an agricultural flexible-price sector and the redistribution shock, and assumes complete markets (Debortoli-Gali assumes incomplete markets; their model is treated as an approximation). Relative to Gali (2015, Chapter 3): the paper adds both a second sector and household heterogeneity. The three differences from the simple NK benchmark in the Dynamic IS and NKPC equations are: (i) the presence of a terms of trade channel, (ii) heterogeneous agents with different IES parameters and budget shares, and (iii) redistribution policy that shifts the effective price index of the poor.

Q7. What role do terms of trade play in the model’s transmission mechanism?

The terms of trade between agriculture and manufacturing (T_t = P_{A,t}/P_{M,t}) is a central transmission variable that affects both aggregate consumption and inflation. Aggregate CPI inflation can be decomposed as π_t = δ_R·π_{A,t} + (1 − δ_R)·π_{M,t} = δ_R·ΔT_t + π_{M,t}, so movements in the terms of trade feed directly into headline inflation. Total agricultural and manufacturing consumption both depend on T_t, rich consumption C_{R,t}, and poor consumption C_{P,t} through equations (22) and (23). A rise in the terms of trade (higher relative agricultural prices) makes the consumption basket of the poor more expensive because they spend a larger share of income on agricultural goods, inducing them to reduce agricultural purchases. This terms-of-trade channel is absent from one-sector benchmarks and is a key reason the paper’s framework generates different aggregate dynamics than Debortoli-Gali.

Q8. What is the welfare metric used, and what is the paper’s welfare conclusion?

Welfare is defined to depend on aggregate consumption in the standard fashion, and the paper’s central welfare conclusion is that consumer heterogeneity matters for whether monetary policy responses to shocks raise or reduce aggregate welfare. For a redistributive policy shock, aggregate welfare rises despite higher inflation, because the gain in poor consumption (driven by the subsidy) exceeds the loss in rich consumption and the distortionary cost of inflation. For a contractionary monetary shock, welfare losses are smaller in the two-sector framework than in single-sector frameworks, because the flexible-price agricultural sector moderates the real interest rate increase and limits the consumption decline. The paper does not report specific numerical welfare loss figures in the portion of text available in this source extract.

Key concepts

Redistributive policy shock : in this paper’s usage, a positive shock to the fraction (φ_t) of government-procured agricultural output that is redistributed to poor households as an in-kind subsidy; distinct from a procurement level shock. Modeled as an AR(1) process on φ_t.

TANK (Two-Agent New Keynesian) model : a tractable heterogeneous-agent NK framework with exactly two household types — Ricardian (forward-looking, hold bonds) and rule-of-thumb (hand-to-mouth, do not save) — that Debortoli and Gali (2018) showed provides a good approximation to the aggregate dynamics of a full HANK model.

Rule-of-thumb (hand-to-mouth) consumers : households that maximize static utility subject to a static budget constraint, consuming all current income each period. In this model, the poor are rule-of-thumb consumers with only labor income and no bond holdings.

Effective price of agriculture for the poor : P’{A,t} = (1 − λ_t)P{A,t}, where λ_t is the fraction of poor agricultural consumption provided for free via the redistributive subsidy. The poor face a price index P’t = {(1−λ_t)P{A,t}}^{δ_P} · P_{M,t}^{1−δ_P}, which differs from the rich price index.

Terms of trade (TOT) : T_t = P_{A,t}/P_{M,t}, the relative price of the agricultural good to the manufactured good. Changes in TOT affect the sectoral composition of consumption for both household types and transmit through the Dynamic IS and NKPC equations.

Intertemporal elasticity of substitution (IES) : 1/σ_K for household type K. The paper assumes σ_P > σ_R (poor have lower IES than rich), following Atkeson and Ogaki (1996) estimates for Indian household data; this differential drives asymmetric labor supply responses to real wage changes.

Procurement shock : a shock to the quantity Y^P_{A,t} of agricultural output the government procures each period, modeled as a separate AR(1) process from the redistribution-fraction shock. Together, the procurement level and redistribution fraction determine the total subsidy received by poor households.

Regulating Credit Lines in the Presence of Fire‐Sale Externalities

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

This paper provides a contract-theoretic rationale for the special liquidity regulation of bank credit lines—a form of lending that has received little attention in the regulatory literature despite being the most important source of firm liquidity risk management. In the model, banks choose pre-arranged funding (committed before drawdowns accumulate) and ex-post funding (raised as drawdowns occur) to finance firms’ liquidity needs through credit lines. In states with high liquidity needs, banks cannot raise sufficient ex-post funding to meet all drawdowns and renege on some credit lines, forcing liquidations. Because each additional liquidation depresses the equilibrium liquidation value for all liquidated firms—a pecuniary externality—competitive banks choose insufficient pre-arranged funding in the private equilibrium. A minimum requirement on bank pre-arranged funding per committed (undrawn) funds in credit lines restores constrained efficiency, despite making credit lines more costly; welfare improves because more firms receive funding in high-liquidity states. The optimal regulatory ratio is increasing in the frequency of high-liquidity-need states, the value lost in liquidation, and the sensitivity of liquidation values to forced sales, and decreasing in the premium on pre-arranged funding.

In depth

Q1. Why can banks not fully meet credit line drawdowns in high liquidity need states?

In high liquidity need states, where many firms simultaneously draw on their credit lines, the revenues that banks receive from credit lines (interest payments and fees from the small share of firms that need no drawdown) shrink relative to the total drawdown demand, and the resulting shortfall cannot be fully met through ex-post funding raised from new investors because bank revenues are the collateral for such funding. The model captures the systemic nature of correlated liquidity shocks: when drawdowns are idiosyncratic, banks can cross-subsidize from non-drawing firms and raise ex-post funding easily; when drawdowns are highly correlated, these cross-subsidy revenues vanish and ex-post funding is insufficient, making pre-arranged funding essential for maintaining credit line insurance.

Q2. What is the pecuniary externality and why does it lead to under-provision of pre-arranged funding?

When a bank reneges on a credit line and the borrowing firm is liquidated, the forced sale of the firm’s assets depresses the equilibrium liquidation value—a fire-sale externality that reduces the payoff for all other firms being liquidated simultaneously; competitive banks do not internalize this negative spillover because, individually, each bank takes liquidation prices as given, leading the private equilibrium to feature too little pre-arranged funding and too frequent reneging relative to the constrained social optimum. This is a classic pecuniary externality (Lorenzoni 2008): the externality does not operate through a technological channel but through prices (liquidation values), so it is invisible to competitive agents who treat prices as parametric.

Q3. How does the minimum liquidity requirement on credit lines restore efficiency?

A minimum requirement mandating that banks hold a specified amount of pre-arranged funding per committed (undrawn) credit line funds induces competitive banks to internalize the social value of additional pre-arranged funding—namely, that more pre-arranged funding reduces the number of liquidated firms and raises equilibrium liquidation values—and thereby implements the constrained planner’s solution. This regulatory tool resembles the Basel III LCR (which requires banks to hold liquid assets equal to 5%-30% of undrawn credit lines, depending on the type of credit facility) and the NSFR (which requires stable funding equal to at least 5% of undrawn credit lines); the paper provides the first theoretical justification for precisely this type of regulation for credit lines and characterizes how the optimal ratio depends on economic fundamentals.

Q4. What are the determinants of the optimal regulatory ratio?

The optimal minimum pre-arranged funding requirement per committed funds in credit lines is higher when: (1) the premium on pre-arranged over ex-post funding is lower (making additional pre-arranged funding less costly at the margin); (2) high-liquidity-need states are more frequent (making the insurance value of pre-arranged funding higher in expectation); (3) liquidations are more costly (larger welfare losses per uninsured firm); and (4) liquidation values are more sensitive to the number of liquidations (a steeper fire-sale externality). This comparative statics result is policy-relevant: it implies that the Basel III framework’s one-size-fits-all approach to credit line liquidity ratios cannot be optimal across jurisdictions with different economic fundamentals, and national authorities should calibrate requirements to local conditions.

Key concepts

credit line pre-arranged funding : bank funding committed before credit line drawdowns accumulate; provides insurance against high-liquidity-need states by ensuring the bank can meet drawdowns even when ex-post funding is insufficient; corresponds to equity-like stable funding in Basel III terminology. fire-sale pecuniary externality on liquidation values : the depression of equilibrium firm liquidation values caused by simultaneous forced sales when many firms are liquidated after banks renege on credit lines; not internalized by competitive banks, leading to under-provision of pre-arranged funding in the private equilibrium. optimal credit line liquidity requirement : a minimum ratio of pre-arranged funding to committed (undrawn) credit line funds that restores constrained efficiency by internalizing the fire-sale externality; shown to be an increasing function of the frequency of high-liquidity-need states, liquidation costs, and liquidation-value sensitivity.

Riding the Housing Wave: Home Equity Withdrawal and Consumer Debt Composition

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

Layer 1 — Overview

Research Question

This paper investigates how rising house prices affect the composition of household debt portfolios in Sweden during 2010–2014. Specifically, the authors ask whether homeowners who experience housing wealth gains use home equity withdrawals to substitute relatively expensive unsecured consumer (non-mortgage) debt with cheaper collateralized mortgage debt — a form of debt re-optimization — and what individual and policy factors drive this behavior.

Data and Methodology

The study uses a monthly individual-level panel dataset sourced from Upplysningscentralen (UC), the Swedish credit bureau, covering approximately 4.8 million individuals (62 percent of the Swedish adult population) from July 2010 to July 2014. The UC data captures approximately 80 percent of total household credit volume and 97 percent of household mortgage loans. Parish-level house price indices come from Valueguard, and municipality-level education data come from Statistics Sweden. The empirical analysis draws on a random sample of approximately 150,000 individuals, of whom 81,667 (81 percent) are classified as homeowners — defined as individuals holding a mortgage throughout the entire sample period.

The primary identification strategy uses renters as a control group for homeowners in a difference-in-differences (DiD) framework, exploiting the variation in local (parish-level) house price growth. Because Sweden’s rental market is heavily regulated and uses a queuing allocation system, the rent-versus-own decision is largely exogenous to individual wealth, making renters a credible counterfactual for homeowners. The authors also use two instrumental variables to address endogeneity of house price growth: (1) historical house price volatility at the municipal level from 1981–2005 (the “Palmer instrument”), and (2) a “building-friendly” instrument measured as the share of municipal planning appeals overruled by county authorities, derived from Sweden’s 2013 National Board of Housing survey. A difference-in-difference-in-differences (DDD) approach is employed to examine the role of DTI constraints and financial literacy. Home equity withdrawals are identified as increases in outstanding mortgage balances of at least SEK 20,000, after excluding cases where the equity was used to purchase a new property.

Main Findings

Total debt and mortgage growth: A one percentage point increase in local house prices is associated with an increase of SEK 959.1 in total household debt for homeowners relative to renters, driven primarily by mortgage growth. This effect is robust to instrumental variable estimation.
Debt re-optimization — unsecured loans: Conditional on withdrawing home equity in month t, homeowners reduce their outstanding unsecured consumer loan balances by 53.5 percent in the following month (t+1). This is large relative to the U.S. benchmark of 16.7 percent reported in Bhutta and Keys (2016). The average reduction in unsecured loan balances across all equity withdrawers is SEK 9,624 per withdrawal event, while credit card debt declines by only SEK 73.3 — an economically negligible amount. For equity withdrawers who had pre-existing unsecured loan balances and actively repaid them, outstanding unsecured loans fell by SEK 55,040 — nearly six times the full-sample average. For this subsample, 17.7 percent of the total withdrawn home equity was applied to unsecured loan repayment (versus 2.98 percent for the full sample of equity withdrawers).
Credit card debt: The effect of equity withdrawal on credit card balances is not statistically significant. This reflects the institutional feature that credit cards in Sweden are used primarily as payment instruments within a 30–45 day interest-free grace period, not as a credit facility. Swedish credit card outstanding balances average only 16 percent of a debtor’s monthly disposable income, compared to 201 percent in the U.S.
Heterogeneity by homeowner type: The debt re-optimization finding is specific to equity withdrawers. House traders increase non-mortgage debt alongside mortgage debt. Amortizers show neither effect at meaningful scale. The substitution between unsecured loans and mortgage debt is not observed for non-withdrawing homeowners.
DTI and financial literacy: The debt re-optimization effect is strongest for borrowers with above-median DTI ratios residing in municipalities with above-median education levels (used as a proxy for financial literacy). Borrowers in this high-DTI, high-literacy group paid down approximately SEK 10,000 more in unsecured loans after a home equity withdrawal than high-DTI borrowers in low-literacy areas. A larger fraction of their withdrawn equity was also directed toward unsecured loan repayment.
Macroprudential policy: The introduction of an 85 percent LTV cap in October 2010 is associated with an increase in non-mortgage debt, particularly unsecured consumer loans, by both existing equity withdrawers and new mortgage borrowers. For new mortgagors entering after the LTV cap, the ratio of unsecured loans to mortgage debt increased by 1.68 percentage points, consistent with borrowers using unsecured loans to fund the required 15 percent downpayment. The debt re-optimization behavior itself (i.e., paying back unsecured loans with withdrawn equity) was found to persist both before and after the LTV cap introduction, with no statistically significant difference between regimes.
Interest rates: Both the probability and the size of home equity withdrawal are negatively correlated with the mortgage rate and positively correlated with the spread between the unsecured loan rate and the mortgage rate. During the sample period, mortgage rates averaged between 2.5 and 3 percent, while unsecured loan rates were on average two to three times higher.

Scope Conditions

The results are specific to Sweden during a housing boom period (2010–2014), under interest-only floating-rate mortgages with full recourse, and in the context of a tightly regulated rental market that makes the renter vs. owner distinction largely exogenous. The re-optimizing behavior requires actively rising house prices to generate the equity needed for withdrawal; the authors note this strategy is fragile if house prices were to decline. Swedish households increased their total debt levels even while re-optimizing its composition, raising financial stability concerns.

In depth

Q1. What exactly is “home equity withdrawal” in the Swedish institutional context, and how does it differ from the U.S.?

A: In Sweden, home equity withdrawal occurs exclusively by increasing the existing outstanding mortgage balance against an updated home valuation; there are no HELOCs, home equity loans, or cash-out refinancing products as in the U.S. Households must pass a credit check and comply with the 85 percent LTV limit (post-October 2010). Some banks require a minimum withdrawal of SEK 100,000. Fixed transaction costs include a bank administration fee (around SEK 700 for apartment owners) and a fixed fee to the building association (around SEK 750), making the process cheap but not costless.

Q2. How do the authors identify home equity withdrawal events in the data?

A: An equity withdrawal event for individual i in month t is defined as a positive change in outstanding mortgage balance greater than SEK 20,000 (approximately the average monthly disposable income), conditional on no simultaneous change in residential address, property type, or acquisition of a second property. This threshold is applied to avoid measurement error from minor rounding or bank adjustments. After applying all exclusion criteria, the authors identify 46,499 equity withdrawal events over the sample period.

Q3. What is the identification strategy for isolating the causal effect of house prices on debt portfolios?

A: The primary identification uses renters as a control group in a DiD framework. Because Sweden’s heavily regulated rental market (with queuing systems and rents far below market rates) makes the rent-vs-own decision largely exogenous to individual wealth, renters experience the same local economic conditions as homeowners but cannot access the equity-based financing channel. The key identifying assumption is that unobserved local economic shocks — which may jointly drive house prices and credit demand — affect renters and homeowners similarly. Two IVs are used as robustness checks: historical municipal house price volatility (1981–2005) and a “building-friendly” regulation index.

Q4. What is the first-stage strength of the Palmer instrumental variable?

A: The estimated coefficient on the historical house price volatility instrument in the first-stage IV regression is 0.00022 and is statistically significant at the 1 percent level. The first-stage F-statistic is 38.41, which exceeds conventional weak-instrument thresholds, confirming that historical volatility is a strong predictor of current house price growth across municipalities.

Q5. Why is credit card debt not reduced by equity withdrawals in Sweden, even though it carries higher interest rates than unsecured loans?

A: Credit cards in Sweden function predominantly as payment instruments within a 30–45 day interest-free grace period rather than as actual credit facilities. Average outstanding credit card balances amount to only 16 percent of debtors’ monthly disposable income (versus 201 percent in the U.S. during the same period), and balances are typically repaid in full at month-end. Because cardholders are not accruing significant interest on their balances, there is no financial incentive to extinguish credit card debt using withdrawn home equity.

Q6. How is the 2.98 percent figure for equity used in debt repayment to be interpreted?

A: Across all home equity withdrawers (including those who have no pre-existing unsecured loans), the average share of the total amount withdrawn that is applied to unsecured loan repayment in the following month is 2.98 percent. This low average reflects that the majority of homeowners do not hold outstanding unsecured consumer loans and therefore have no debt to repay. When the sample is restricted to equity withdrawers who both held outstanding unsecured loans before the withdrawal and actively repaid some portion in the following month, the repayment share rises to 17.7 percent of the withdrawn amount.

Q7. What is the DDD specification used to identify the roles of DTI and financial literacy, and what do the triple interaction terms reveal?

A: The DDD specification interacts the equity withdrawal indicator with a high-DTI dummy (above-median DTI at the individual level in the current month) and a high-financial-literacy dummy (municipality’s share of post-secondary educated residents above the national median in that year). The triple interaction term (EquityWithdrawal × HighDTI × HighLit) is negatively significant at approximately −SEK 9,913 to −9,966 (in thousands, i.e., around −SEK 10,000) in the unsecured loan repayment regression. This implies that, conditional on withdrawing equity, borrowers with both high DTI and high financial literacy municipality background reduced their unsecured loans by roughly SEK 10,000 more than high-DTI borrowers in low-literacy areas.

Q8. How does the introduction of the 85 percent LTV cap in October 2010 affect non-mortgage debt?

A: Comparing a three-month window before and after October 2010, the authors find that: (a) before the LTV cap, changes in household debt did not respond significantly to house price growth for any debt type; (b) after the LTV cap, all debt types — including unsecured consumer loans — increased significantly in areas with higher cumulative house price growth. The interaction term between house price growth and the post-LTV dummy is positively significant for non-mortgage debt, driven by unsecured loans. For new mortgage borrowers, the ratio of unsecured loans to mortgage debt increased by 1.68 percentage points after the LTV cap, consistent with constrained borrowers using blanco (unsecured) loans to fund the mandatory 15 percent downpayment.

Q9. Does the LTV cap affect the debt re-optimization behavior (i.e., the use of withdrawn equity to repay unsecured loans)?

A: The authors find that equity withdrawers reduce unsecured loans both before and after the LTV cap introduction. The interaction terms between the LTV dummy and equity withdrawal indicators (both dummy and size) are not statistically significant, indicating that the debt re-optimization behavior per se — the channel of using withdrawn equity to pay down non-mortgage debt — was not materially altered by the macroprudential tightening. The authors caution that the very short pre-cap period (only three months of data from July to September 2010) limits statistical power for this comparison.

Q10. What is the role of interest rate spreads in driving equity withdrawal decisions?

A: Both the probability of withdrawing equity and the size of the withdrawal are negatively correlated with the prevailing mortgage rate and positively correlated with the spread between the unsecured loan rate and the mortgage rate. This implies that equity withdrawal is more common and larger in magnitude when mortgages are cheaper or when the relative cost premium on unsecured lending is higher — consistent with the debt re-optimization motive. Results for the interest rate analysis are reported in Appendix B.2.

Q11. How do the results differ across homeowner subgroups (equity withdrawers, house traders, amortizers)?

A: Among equity withdrawers: mortgage increases and unsecured loan decreases are both statistically significant (debt re-optimization). Among house traders: mortgage increases significantly and non-mortgage debt also increases (no substitution — they borrow across all categories to finance property purchases). Among amortizers: changes in both mortgage and non-mortgage debt are smaller in magnitude and primarily reflect active principal repayment rather than refinancing activity. The substitution between unsecured and mortgage debt is thus exclusive to equity withdrawers.

Q12. What is the overall change in Swedish house prices and aggregate debt during the sample period?

A: The house price index rose by 20 percent between July 2010 and July 2014, with particularly strong appreciation after January 2012 following a mild dip in the second half of 2011. Over the same period, aggregate mortgage balances of homeowners increased by 16 percent. Aggregate non-mortgage debt also increased, though from a much smaller base. In the cross-sectional regression, a one percentage point increase in house prices is associated with an SEK 926.7 increase in total individual debt (4 percent of average house value of SEK 21,500 per percentage point).

Q13. What are the robustness checks and do they alter the conclusions?

A: The following robustness checks are reported: (1) redefining equity withdrawers as those who withdrew exactly once (Tables A4–A6); (2) restricting equity withdrawers to those withdrawing SEK 20,000–100,000 to exclude potential house traders; (3) using alternative house price growth windows of 12, 24, and 48 months (Tables A7–A9); (4) using the “building-friendly” regulation IV (Tables A2–A3); (5) supplementary time-series panel regressions (Appendix B.1). All robustness checks yield qualitatively consistent results, with the substitution from unsecured loans to mortgages preserved across specifications.

Q14. What are the financial stability implications the authors identify?

A: Despite the debt re-optimization behavior, total indebtedness among Swedish equity withdrawers does not decline — they increase their mortgage balances more than they reduce unsecured loans. Swedish average household DTI is approximately double that of the U.S. (OECD, 2022). The authors note that if house prices were to fall, homeowners relying on equity withdrawal for debt restructuring would lose access to this financing channel and face the full cost of high-interest unsecured debt. Additionally, the circumvention of the LTV cap through unsecured loan substitution raises financial stability concerns because it concentrates households in more expensive, unprotected debt.

Key Concepts

Home Equity Withdrawal (Sweden-specific): The act of increasing an existing outstanding mortgage balance against a revalued home, which is the only channel for equity extraction in Sweden. Unlike the U.S., there are no HELOCs, home equity loans, or cash-out refinancing products. Subject to the 85 percent LTV cap introduced in October 2010 and a minimum threshold (SEK 100,000 at some banks).

Debt Re-optimization: The behavior by which homeowners substitute relatively expensive unsecured consumer debt with cheaper collateralized mortgage debt during a housing boom, using the proceeds of home equity withdrawal to repay unsecured loans. In the paper’s usage, this implies a deliberate, financially sophisticated portfolio adjustment — not merely passive debt accumulation.

Blanco Loans (Unsecured Consumer Loans): Unsecured personal loans in Sweden (referred to as “blanco” loans in Swedish). These carry interest rates historically two to three times higher than mortgage rates. In the Swedish context, they are used both as consumer finance and — especially after the 85 percent LTV cap — as a source of downpayment funds. They are the primary non-mortgage debt instrument that equity withdrawers pay down.

Loan-to-Value (LTV) Cap: The macroprudential regulation introduced by the Swedish Financial Supervisory Authority in October 2010, limiting mortgage debt (including home equity withdrawals) to 85 percent of the property’s market value. This applied both to new mortgage originations and to existing mortgagors increasing their mortgage balance. In the paper, this is treated as an exogenous policy event against which behavioral responses are measured.

Financial Literacy Proxy (Municipal Education Level): Because individual-level financial literacy data are unavailable, the paper uses the share of a municipality’s residents with post-secondary education in a given year as a municipality-level proxy for financial literacy. Municipalities above the national median in this share are classified as high-literacy areas. The classification can change year to year.

Debt-to-Income (DTI) Ratio: The ratio of an individual’s total outstanding debt to annual disposable income, used in the paper as a measure of financial constraint. A borrower is classified as “high DTI” if their DTI exceeds the cross-sectional median for all borrowers in that month. High-DTI borrowers in the paper’s sample tend to be younger, have larger mortgages, and have more unsecured loan balances.

Interest-Only Floating-Rate Mortgage: The predominant Swedish mortgage structure during the sample period. Most mortgages are effectively three-month floating-rate contracts with no amortization requirement (until June 2016), making Swedish borrowers more sensitive to short-term interest rate movements than borrowers in fixed-rate amortizing mortgage systems. This institutional feature means that increases in home equity during the sample period derived almost entirely from house price appreciation rather than principal repayment.

Self-Fundamentals, Cross-Fundamentals, and Exchange Rate Predictions

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

This paper proposes incorporating both self-fundamentals (the macroeconomic conditions of the two economies in a given currency pair) and cross-fundamentals (the macroeconomic conditions of other major economies, motivated by third-country effects) into exchange rate forecasting. A Mallows model averaging approach optimally combines predictions from multiple fundamental sub-models. The approach significantly outperforms the random walk benchmark for one-month-ahead exchange rate predictions, with both self- and cross-fundamentals contributing independently to forecast accuracy. The paper also reports economically meaningful investment profits from a strategy exploiting the forecasts in currency and bond markets.

In depth

Q1. What are cross-fundamentals and why do they improve forecasts?

Cross-fundamentals are macroeconomic variables from economies outside the bilateral currency pair — motivated by Berg and Mark’s (2015) theory of third-country effects, which shows that trade patterns, interest rate differentials, and capital flows create bilateral exchange rate linkages beyond the direct bilateral relationship. By including cross-country macro indicators alongside bilateral fundamentals, the model captures information that bilateral-only models discard. The paper finds both self- and cross-fundamentals contribute independently to forecast accuracy, confirming that third-country effects are empirically relevant beyond their theoretical motivation.

Q2. How does Mallows model averaging improve forecasts relative to single models?

Rather than selecting a single exchange rate fundamental model, Mallows model averaging assigns optimal weights to multiple sub-models by minimizing a criterion that balances in-sample fit and model complexity, avoiding the model-uncertainty problem that plagues individual exchange rate forecasting models. No single fundamental model robustly predicts exchange rates, but a weighted combination that allows each model’s information to contribute in proportion to its predictive power significantly outperforms both individual models and the random walk at one-month horizons.

Key concepts

self-fundamentals : macroeconomic variables of the two economies forming a bilateral currency pair; the standard ingredient of exchange rate forecasting models.

cross-fundamentals : macroeconomic variables of major economies outside the bilateral pair; the paper’s novel addition, motivated by third-country effects, that improves exchange rate forecasts.

Mallows model averaging : an optimal linear combination of forecasts from multiple sub-models minimizing a Mallows-type criterion; used to aggregate self- and cross-fundamental information without requiring a single correctly specified model.

Taylor Rule Deviations Across Horizons: A Practical Tool for Monetary Policy

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

Layer 1 — Overview

Research Question

The paper addresses a fundamental limitation of the standard Taylor rule as a monetary policy stance gauge: the rule is defined solely for the overnight federal funds rate (FFR) and cannot assess stance across the maturity spectrum of the yield curve. This limitation becomes acute when the FFR hits its effective lower bound (ELB) and the Federal Reserve resorts to unconventional monetary policy (UMP) instruments—quantitative easing and forward guidance—that are explicitly intended to influence longer maturities. The authors ask: can the Taylor rule idea be extended across the yield curve horizon to produce a maturity-specific monetary policy stance measure that remains informative even during ELB episodes?

Methodology and Data

The paper proposes the “Taylor rule yield curve,” which extends the original Taylor rule to points in time in the future horizon (maturities of 1 through 10 years). The Taylor rule expected rate at maturity h is defined as the average of h annual one-period-ahead Taylor-rule-implied short-term rates, each computed from professional forecasters’ expectations of inflation and the output gap h years ahead. The market counterpart is the Overnight Index Swap (OIS) rate for the corresponding maturity. The “Taylor rule deviation” (TRD) at maturity h is then the difference between the Taylor rule expected rate and the market OIS rate at that maturity—interpretable as the average expected monetary policy stance from the current period through h years ahead.

Data sources: inflation and GDP growth forecasts from Consensus Economics (1–5 years ahead, and 6–10 year average); output gap forecasts constructed using Congressional Budget Office potential output estimates; natural rate of interest estimates from Holston, Laubach, and Williams (2017) available from the Federal Reserve Bank of New York; FFR, core CPI inflation, and GDP growth from FRED; OIS rates from Bloomberg (available from 2002/Q1). Two Taylor rule coefficient sets are examined: the “original” rule (α = 0.5, β = 0.5) and the “balanced” rule (α = 0.5, β = 1.0), with the balanced rule as baseline. An inertia parameter of ρ = 0.85 (quarterly) is assumed, implying annual persistence of approximately 0.52. The sample period runs from 2000/Q1 to 2018/Q4 for the Taylor rule yield curve itself, and from 2002/Q1 to 2017/Q4 for OIS-based TRD analysis.

Main Findings

First, the estimated Taylor rule expected rate curves show that after the onset of the Global Financial Crisis (GFC), the balanced-rule Taylor rate dropped completely below zero for all maturities up to 10 years. During 2008/Q4, the Taylor rule expected rate curve lay approximately 2–3 percentage points below the market rate curve across maturities, reflecting excessively tight market expectations relative to what the Taylor rule framework implied. By 2011/Q4, the market OIS curve fell below the Taylor rule expected rate curve for maturities beyond 4 years—indicating that explicit and forceful forward guidance (the August 2011 FOMC statement committing to “exceptionally low levels for the federal funds rate at least through mid-2013”) had driven market rates below the Taylor-implied accommodative path at the long end.

Second, VAR analysis for the sample period 2002–2017 shows that TRDs at both 2-year and 10-year maturities generate statistically significant impulse responses: positive TRD shocks—indicating a tighter-than-Taylor monetary policy stance—cause both the output gap and inflation to decrease. Importantly, this result holds during the ELB period when the FFR gap and shadow policy rate gap do not yield theoretically consistent impulse responses; in the 2002–2017 subsample, both the FFR gap and the shadow rate gap produce perverse (positive) responses of output and inflation to a tightening shock, presumably because the ELB binds and UMP operates outside the overnight rate. The OIS rates per se (without the Taylor rule expected rate subtracted) show mostly muted and statistically insignificant impulse responses in the same VAR framework. Granger causality tests (62 observations) confirm that TRDs Granger-cause OIS rates for both 2-year (F-statistic = 4.579, p = 0.014) and 10-year (F-statistic = 7.734, p = 0.001) maturities, while the reverse direction is not rejected in either case, highlighting TRDs’ informational superiority over raw OIS rates.

Third, TRDs for 2-, 5-, and 10-year maturities are positively correlated with the VIX in the same quarter (R² values of 0.34, 0.37, and 0.35 respectively), whereas the FFR gap is negatively correlated with the VIX (R² = 0.22). This positive TRD–VIX relationship holds during both ELB (2008/Q1–2015/Q3) and non-ELB subperiods, suggesting TRDs serve as a proxy for risk appetite in financial markets—with a loose-relative-to-Taylor monetary stance associated with lower risk aversion.

Fourth, a stylized New Keynesian model with anticipated future shocks to the Taylor rule (interpreted as “news shocks”) provides theoretical support. When agents learn of a future expansionary Taylor rule shock, they revise upward their expectations of future output and inflation, which—through consumption smoothing (Euler equation) and forward-looking pricing (New Keynesian Phillips curve)—produce contemporaneous expansionary effects. An extended model with habit formation, backward-looking price-setters, and interest rate smoothing generates hump-shaped and persistent IRs consistent with the empirical patterns. Simulations on model-generated data confirm that the TRD measure, but not the future interest rate or contemporaneous rate deviation, recovers statistically significant and correctly signed impulse responses in the VAR.

Scope Conditions

The methodology requires data on professional forecasters’ expectations of output and inflation at multi-year horizons, limiting applicability to countries for which such forecast data exist. Term premium components of OIS rates are excluded from the analysis, which the authors note may make estimates of forward guidance impact conservative. The analysis is confined to the United States for the period 2000/Q1–2018/Q4.

In depth

Q1. What is the precise mathematical definition of the Taylor rule deviation (TRD) at horizon h, and how does it differ from the conventional FFR gap?

A: The TRD at maturity h is defined as the difference between the market OIS rate at h-year maturity and the Taylor rule expected rate at that maturity. The Taylor rule expected rate is the average (across years k = 1 to h) of the Taylor-rule-implied short-term interest rates expected k years ahead, where each expected rate uses professional forecasters’ projections of inflation and the output gap at that horizon, together with the current natural rate of interest (assumed unchanged). The conventional FFR gap is the deviation of the overnight FFR from the contemporaneous Taylor rule rate—a scalar at a single point in time. The TRD generalizes this to any maturity: it equals the average expected monetary policy stance (accommodative or tight relative to Taylor) from the current period through h years ahead, capturing the cumulated sum of anticipated and unanticipated disturbances to the Taylor rule.

Q2. Why does the FFR gap fail as a monetary policy stance indicator during the ELB period, and why does the shadow rate gap not resolve this failure?

A: When the FFR hits the ELB, it is pinned near zero regardless of how accommodative the Federal Reserve’s actual policy intentions are; any further intended easing through forward guidance or quantitative easing is not reflected in the overnight rate’s level or its deviation from the Taylor rule. The authors show (Figure 8a, 2002–2017 subsample) that in a three-variable VAR with output gap, inflation, and FFR gap, a positive FFR gap shock generates increases in both output and inflation—the opposite of theoretically expected contractionary effects—because the ELB constrains the FFR while UMP operates through longer maturities. The shadow policy rate (Wu and Xia, 2016) drops below zero during the UMP period and conceptually summarizes the entire yield curve’s accommodation in a single synthetic overnight rate. However, Figure 8b shows that replacing the FFR with the shadow rate leaves the perverse VAR impulse responses qualitatively unchanged in the 2002–2017 subsample, because a single short-term summary rate cannot isolate the maturity-specific information that the TRD captures.

Q3. What does the VAR analysis reveal about TRDs’ ability to capture monetary policy effects at the ELB, and does the maturity of TRD matter?

A: For the 2002–2017 sample period (Figure 9a), VAR impulse responses with the TRD replacing the FFR gap show that a positive TRD shock causes statistically significant decreases in both the output gap and inflation—the theoretically expected contractionary response. This result holds for both 2-year and 10-year TRDs. The fact that the 10-year TRD also produces this correct result indicates that TRDs at long maturities can capture the stance reflected in forward guidance, which explicitly targets expectations about the future course of monetary policy well beyond overnight. The output gap response is quantitatively larger in magnitude than the inflation response across both maturities (figure axis ranges suggest output gap peaks at roughly ±1.0% versus inflation at ±0.2%), consistent with the theoretical model’s prediction that the output gap is more responsive to contemporaneous effects while inflation responds to both current and expected future conditions.

Q4. What is the role of the output gap component versus the inflation component in driving TRD changes?

A: Figures 6 and 7 decompose period-by-period first differences of TRDs into their output gap and inflation contributions for both 2-year and 10-year maturities. The output gap component is the main determinant of changes in TRDs across both maturities, reflecting the substantially volatile outlook on economic growth—especially around the GFC. The inflation component has a considerably smaller contribution, and this difference is even more pronounced for 10-year maturities than for 2-year maturities, reflecting the fact that professional forecasters’ inflation expectations change much less at longer horizons than near-term GDP growth expectations.

Q5. What does the Granger causality analysis reveal about the informational content of TRDs relative to OIS rates?

A: Table 1 reports Granger causality tests using 62 observations. For 2-year maturities, the null that TRD 2Y does not Granger-cause OIS 2Y is rejected at the 5% level (F = 4.579, p = 0.014), while the null that OIS 2Y does not Granger-cause TRD 2Y is not rejected (F = 0.999, p = 0.375). For 10-year maturities, the null that TRD 10Y does not Granger-cause OIS 10Y is rejected at the 1% level (F = 7.734, p = 0.001), while the reverse null is not rejected (F = 0.843, p = 0.436). This unidirectional causality—TRDs leading OIS rates but not vice versa—implies that TRDs contain information about future OIS rate movements not already embedded in current OIS rates, making TRDs informationally superior to raw OIS rates for assessing monetary policy stance.

Q6. How do TRDs relate to VIX, and does this relationship depend on whether the economy is at the ELB?

A: Figures 10 and 11 document that TRDs for 2-, 5-, and 10-year maturities are positively correlated with the VIX in the same quarter (R² values of approximately 0.34, 0.37, and 0.35 for 2Y, 5Y, and 10Y TRDs respectively), meaning that a tighter-than-Taylor monetary policy stance (positive TRD) is associated with higher market risk aversion. By contrast, the FFR gap shows a negative correlation with the VIX (R² = 0.22), the opposite sign. The same positive TRD–VIX correlation is observed when current TRDs are plotted against VIX four quarters later, though the R² values are smaller (ranging from approximately 0.04 to 0.05). Critically, Figure 11 shows that dividing the 2002/Q1–2017/Q4 sample into ELB (2008/Q1–2015/Q3) and non-ELB periods, the positive correlation between the 5-year TRD and VIX holds during both subperiods (R² = 0.37 for ELB current quarter, R² = 0.41 for ELB four quarters ahead), demonstrating that TRDs’ relationship with risk appetite is not an artifact of the ELB environment.

Q7. What does the theoretical New Keynesian model contribute, and what is the mechanism by which anticipated future Taylor rule shocks affect current macroeconomic variables?

A: The paper embeds anticipated future shocks to the Taylor rule (news shocks) in a stylized New Keynesian model with Euler equation, New Keynesian Phillips curve, and Taylor rule. When a one-period-ahead expansionary monetary policy shock (εh,t for h=1) is announced at time t, agents expect expansionary effects in period t+1 (higher output gap and inflation). Through consumption smoothing in the Euler equation, expected higher output in t+1 raises current consumption and thus current output. Through forward-looking pricing in the NKPC, expected higher future inflation raises current inflation. Analytically, the coefficients on the one-period-ahead shock (c_{1,y} and c_{1,π}) satisfy the same signs as the contemporaneous shock coefficients (c_{0,y} and c_{0,π}), confirming the contemporaneous impact. The model shows that for the inflation rate, the future shock has larger impact than the contemporaneous shock (|c_{1,π}| > |c_{0,π}|) because inflation responds to both current and future output gap in the NKPC; for the output gap, the future shock has smaller impact (|c_{1,y}| < |c_{0,y}|) because higher expected inflation raises the nominal interest rate via the Taylor rule’s endogenous feedback, partially offsetting the expansionary effect on current output.

Q8. How do simulations on model-generated data validate the VAR methodology for identifying TRD effects?

A: Figure 17 uses simulated data from the model with inertia (200 periods, corresponding to 50 years) to compare three interest rate measures in a three-variable VAR (output gap, inflation, interest rate measure): (i) the average future interest rate (I), (ii) the contemporaneous interest rate deviation (ε_{0,t}), and (iii) the H-period TRD with H = 8. When the future interest rate I is used, the identified monetary policy shock produces impulse responses with the opposite sign relative to the structural model, because the VAR captures reverse causality between the interest rate and the state of the economy. When the contemporaneous rate deviation ε_{0,t} is used, responses have the intended sign but are not statistically significant, because future anticipated shocks are not materialized in the current period’s rate. When the TRD is used, the identified shock generates statistically significant responses with the correct sign, validating TRD as the appropriate measure for capturing the effects of anticipated future monetary policy shocks in an empirical VAR framework.

Q9. How does the Taylor rule yield curve behave at specific historical episodes, and what do these patterns reveal about monetary policy stance?

A: During 2008/Q4, the Taylor rule expected rate curve (balanced rule) lay approximately 2–3 percentage points below the market OIS curve across all maturities, reflecting that markets expected a much faster policy normalization than the Taylor rule implied given the economic collapse—indicating excessively tight market expectations. By 2011/Q4, after successive rounds of forward guidance, the market OIS curve fell below the Taylor rule expected rate curve for maturities beyond 4 years, with the balanced-rule Taylor expected rates remaining negative for maturities up to 3 years. By 2013/Q4, mid- and long-term market expected rates were roughly aligned with Taylor rule expected rates. In 2015/Q4, when the Fed hiked for the first time post-GFC (while the Taylor rule short-term rate was still negative), the market curve almost perfectly matched the Taylor rule expected curve for maturities beyond one year. In 2017/Q4, the Taylor rule expected rate curve exceeded the market curve by approximately 0.5–1 percentage points, suggesting continued expansionary stance even after policy rate normalization began.

Q10. How robust are the results to the choice between the original and balanced Taylor rule specifications?

A: Robustness checks (Figures 12–14) compare results under the original rule (α = 0.5, β = 0.5) versus the baseline balanced rule (α = 0.5, β = 1.0). The original rule generates smaller fluctuations in Taylor rule expected rates, reflecting its lower coefficient on the more volatile output gap. However, the overall trajectories do not change significantly. The main qualitative difference emerges in 2011/Q4 and 2013/Q4: the balanced rule implies Taylor expected rates are negative for 1–3 year maturities (indicating the ELB was still binding even relative to medium-term Taylor-implied paths), while the original rule produces all-positive Taylor expected rates for these periods. For 2008/Q4, 2009/Q4, 2015/Q4, and 2017/Q4, both specifications yield similar pictures, and the central conclusions about TRDs’ macroeconomic relevance and relationship with risk appetite are robust to the specification choice.

Key Concepts

Taylor Rule Yield Curve: The paper’s proposed extension of the standard Taylor rule from the overnight federal funds rate to all points in the future yield curve horizon (1 through 10 years). For maturity h, it is the average of h annual Taylor-rule-implied expected short-term rates, each calculated using professional forecasters’ h-years-ahead projections of inflation and the output gap plus the current estimate of the natural rate. Not a market instrument but a model-derived benchmark yield curve representing the “neutral” rate at each horizon.

Taylor Rule Deviation (TRD): The gap between the market OIS rate at maturity h and the corresponding Taylor rule expected rate—that is, the deviation of market expectations from what the Taylor rule framework implies should prevail at that horizon. A positive TRD indicates market rates are above the Taylor-implied rate (tighter-than-neutral stance); a negative TRD indicates easier-than-neutral stance. The TRD at maturity h equals the average of expected monetary policy stance residuals from the current period through h years ahead.

Effective Lower Bound (ELB): The floor to which a central bank can reduce the nominal policy rate before further cuts become infeasible or counterproductive. In the paper’s empirical context, the FFR ELB episode for the United States runs from 2008/Q1 to 2015/Q3. During this period, the standard FFR gap and shadow rate gap measures fail to produce theoretically consistent VAR impulse responses.

Taylor Rule Expected Rate: The paper’s specific construct: the average of Taylor-rule-implied future short-term interest rates at each year of maturity, computed from professional forecasters’ consensus projections of inflation and output gap at multi-year horizons. Distinct from any market rate; serves as the “neutral” benchmark at each maturity against which OIS rates are compared.

Balanced vs. Original Taylor Rule: Two coefficient specifications used in the paper. The “original” rule (Taylor, 1993) sets the inflation gap coefficient α = 0.5 and the output gap coefficient β = 0.5. The “balanced” rule (Taylor, 1999) sets α = 0.5 and β = 1.0, placing greater weight on output stabilization; the paper uses the balanced rule as its baseline on the grounds that it better reflects the Federal Reserve’s dual mandate in recent years.

Anticipated Future Taylor Rule Shocks (News Shocks): Shocks to the Taylor rule that are known to agents at time t but materialize in a future period t+h. Following Laséen and Svensson (2011) and Del Negro et al. (2012), the paper embeds these in a New Keynesian model to show that anticipated future expansionary policy has contemporaneous expansionary effects through consumption smoothing and forward-looking pricing—the theoretical mechanism underpinning why TRDs at longer maturities affect current macroeconomic outcomes.

Risk-Taking Channel via TRD: The paper’s finding that TRDs for 2-, 5-, and 10-year maturities are positively correlated with VIX (R² ≈ 0.34–0.37 in the same quarter), holding in both ELB and non-ELB periods. A positive TRD (tighter-than-Taylor stance) corresponds to higher market risk aversion as measured by VIX, enabling TRDs to serve as a maturity-specific measure of risk appetite in financial markets—in contrast to the FFR gap, which shows the opposite (negative) correlation with VIX.

The Effects of an Aging Population on the Structure of Bank Assets and Liabilities

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

Using 2001-2022 annual data on U.S. commercial and savings banks matched with county-level demographic data, this paper shows that banks operating in areas with older populations—measured by the deposit-weighted proportion of seniors (individuals over 65) in the counties where the bank has branches—issue more retail deposits and less wholesale funding, pay relatively lower retail deposit rates with greater stickiness across maturities, and experience smaller deposit withdrawals when market interest rates rise. On the asset side, these banks hold significantly more securities and fewer loans (particularly small business and residential mortgage loans) with longer maturities, substantially raising their asset-liability maturity gap. These findings are consistent with a lifecycle model in which seniors demand risk-free retail deposits as an investment vehicle while exhibiting lower borrowing demand, combined with the localization of banks’ deposit-taking and lending. The paper instruments for a bank’s senior exposure using projected county-level senior population shares constructed from historical state-level fertility rates and county-level cohort change rates by race and sex, mitigating concerns about endogenous bank location relative to contemporaneous economic conditions.

In depth

Q1. How is a bank’s exposure to seniors measured, and why is this measure preferred?

A bank’s ’exposure to seniors’ is defined as the deposit-weighted senior population share of all counties where the bank operates branches, using each county’s deposits at that bank as weights; this measure is preferred because it captures the bank’s actual demographic exposure to older depositors while accounting for the relative importance of each local market to the bank. The paper instruments for this measure using projected county-level senior population shares derived from historical demographic data (state-level fertility rates by race, historical county-level cohort change rates by race and sex), which are orthogonal to the contemporaneous economic conditions that could cause population migration and confound the results.

Q2. How does senior exposure affect retail deposit rates and stickiness?

Banks with greater senior exposure pay significantly lower interest rates on retail time deposits, and the spread between an equivalent-maturity competitive market rate and the bank’s retail deposit rate widens by more as market rates rise, indicating greater deposit rate stickiness; this effect is especially pronounced at longer maturities (24- and 60-month CDs), where seniors’ preference for deposits as an investment vehicle rather than a transaction account gives banks greater market power. Moreover, these banks’ deposits are less likely to be withdrawn when the Federal Funds Rate rises, despite lower and slower-adjusting deposit rates, consistent with seniors’ lesser sensitivity to interest rate differentials (limited recall in monitoring rates, as in Kahn, Pennacchi, and Sopranzetti 1999).

Q3. How does senior exposure affect the composition and maturity of assets?

Banks exposed to more seniors hold significantly more securities and fewer loans—particularly small business loans and residential mortgages—and choose securities and loans with much longer maturities, which substantially raises their asset-liability maturity gap. The lifecycle model predicts this: in markets with older populations, the demand for loans is lower (seniors are net savers, and local businesses benefit from greater labor supply in younger areas), leaving the bank’s retail deposit surplus to be invested in securities. The long-maturity asset allocation is supported by the bank’s stable retail deposit base, which is less sensitive to market rate movements (increasing the effective duration of deposits beyond their stated maturity).

Q4. What are the macroeconomic implications as populations age?

The paper’s findings predict economically important changes in banks’ future asset-liability structures as U.S. populations age: aggregate bank loan-to-asset ratios should decline, security-to-asset ratios rise, retail deposit shares increase, wholesale funding shares decrease, and the banking system’s aggregate asset-liability maturity gap should widen—with corresponding implications for banks’ interest rate risk exposure and the transmission of monetary policy through the bank lending channel. The demographic shift is projected to continue: the U.S. share of the population over 65 is predicted to reach 22% by 2050, while the EU’s share is projected at 28% and China’s share of those over 60 is projected at 40% in 2050, making these dynamics relevant across advanced economies.

Key concepts

bank exposure to seniors : the deposit-weighted proportion of individuals over age 65 in the counties where a bank has branches; the paper’s key explanatory variable, capturing how much of the bank’s deposit base is drawn from an older population. deposit rate stickiness : the slower adjustment of retail deposit rates to changes in equivalent-maturity competitive market interest rates; greater stickiness implies a widening of the deposit rate spread as market rates rise; found here to be more pronounced for banks with higher senior exposure. asset-liability maturity gap : the difference between the bank’s asset average maturity and its deposit average maturity; measures the bank’s exposure to interest rate risk; found here to be significantly larger for banks with higher senior exposure due to longer-maturity assets and stable retail deposit funding.

The Effects of Regulatory Office Closures on Bank Behavior

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

Using closures of U.S. bank regulatory offices between 2002 and 2013 as difference-in-differences shocks to the physical proximity between supervisors and the community banks they oversee, the paper asks whether a decentralized network of local supervisory offices produces safer banks. The authors first show closures are not predicted by the risk or performance of the supervised banks — offices near a regional main office with falling workload are the ones shut — which supports treating closures as plausibly exogenous to affected banks. Following a closure, banks previously supervised by the closed office increase total lending by about 6-10% and tilt toward riskier loans (e.g., commercial real estate), and overall risk-taking as measured by the Z-Score rises by roughly 19-32% of the sample mean, with larger increases in distance to the new office associated with riskier policies. Banks affected before the 2008-09 financial crisis subsequently exhibited more bad loans, higher charge-offs, and higher failure rates during the crisis. Examining channels, the authors find affected banks report lower and less timely loan-loss provisions (and more income-increasing provisions, making balance sheets more opaque), increase dividend payouts, and see lower risk-adjusted returns on assets — which they read as evidence that proximity lets supervisors enforce timelier provisioning, restrain payouts, and share expertise. On balance the authors interpret the results as implying that geographical proximity reduces informational frictions in supervisory monitoring and leads to more stable banks — that is, the monitoring-benefit view dominates the regulatory-capture view on average.

In depth

Q1. What is the paper’s research design and identification strategy?

The paper uses a difference-in-differences design built on closures of FDIC, Federal Reserve, and OCC regulatory offices from 2002 to 2013, comparing banks that lost their supervising office to nearby banks in the same county supervised by a different office. Because U.S. banks in the same geographic area may be supervised by one of three federal regulators, within a county where an office closed only banks supervised by that closed office should be affected, while similarly located banks supervised by another office serve as controls exposed to the same local economic conditions. The analysis draws on a hand-collected data set mapping regulatory office locations and focuses on community banks, which are tied to local markets and served by traveling rather than in-house examiners. The tightest specifications include county-quarter, regulatory-office-quarter, and bank fixed effects, and the authors report parallel pre-trends and, using a timing-effects model, effects that appear only after closures and not before.

Q2. Are office closures plausibly exogenous to the affected banks?

The authors report that office closures are unrelated to the risk, performance, assets, or loans of the banks the office supervised; instead, offices closest to a regional main office experiencing a falling workload are the ones closed. They read this as the reasons for closure residing with banks outside the closed office’s immediate vicinity and reflecting a rebalancing of supervisory resources within regions, which they argue alleviates reverse-causality concerns that poor bank performance could drive both office closures and subsequent higher risk-taking.

Q3. What happens to bank lending and risk-taking after a regulatory office closes?

Following a closure, affected banks increase total lending by 6-10% and increase overall risk-taking as measured by the Z-Score by 19-32% of the sample mean, directing new lending toward riskier loan categories such as commercial real estate. In addition, larger increases in physical distance to the new supervising office are associated with riskier policies, which the authors interpret as evidence that proximity alleviates informational frictions in collecting information from and communicating with banks. The paper reports that its analysis does not provide clear evidence that treated banks hold more capital after office closures.

Q4. Do these changes have consequences for bank fragility?

Banks affected by office closures prior to the 2008-09 financial crisis subsequently exhibited more bad loans, higher charge-offs, and were more likely to fail during the crisis. The authors present this as evidence that the additional lending and risk-taking following closures was not benign, and read it, collectively, as support for the view that a decentralized supervisory structure — by keeping supervisors proximate — leaves banks less fragile.

Q5. Through what channels does proximity appear to operate?

The authors examine three nonmutually exclusive channels — provisioning practices, payouts, and supervisory expertise — and report evidence consistent with each. On provisioning, affected banks report both lower and less timely loan-loss provisions and make greater use of income-increasing provisions, which leads to more opaque balance sheets. On payouts, affected banks significantly increase their dividend payouts to shareholders. On expertise, risk-adjusted returns on assets for affected banks decrease after closures, which the authors read as consistent with proximate supervisors advising banks toward more efficient risk-taking. They interpret the combined evidence as proximity reducing informational frictions in supervisory monitoring.

Q6. How do the authors position their contribution and interpret the findings overall?

The authors state that, to the best of their knowledge, they are the first to use regulatory office closures to study how geographical networks of offices matter for bank supervision, and they interpret their results as indicating that the monitoring-benefit view dominates the regulatory-capture view on average. They emphasize that both views — that proximity aids monitoring and that proximity risks capture — can operate simultaneously, so the empirical question is which dominates; the finding of riskier, more fragile banks after supervisors move farther away implies proximity’s monitoring benefits dominate. The paper frames the policy-relevant implication as: geographical proximity reduces informational frictions in supervisory monitoring and leads to more stable banks.

Key concepts

Regulatory office closure : the shutting of a local supervisory office of the FDIC, Fed, or OCC, used here as a shock that increases the physical distance between a community bank and its supervisor while leaving the bank’s regulator and the applicable rules unchanged.

Decentralized supervisory structure : the arrangement whereby a unified body of banking regulation is enforced through geographically dispersed networks of local supervisory offices, intended to give supervisors easier access to local (especially soft) information about banks.

Monitoring-benefit (proximity) view : the hypothesis that physical proximity lowers the cost of collecting soft information and communicating supervisory expectations, enabling supervisors to enforce safer bank policies.

Regulatory capture view : the alternative hypothesis that proximity to supervised banks can undermine monitoring, because closer contact fosters social/communal ties or career concerns that lead supervisors to cater to bank interests.

Loan loss provisions (LLPs) : accounting charges intended to reflect the expected future losses on a bank’s loan portfolio; under-provisioning can flatter short-term liquidity and performance while masking inadequate capital, and the paper finds affected banks report lower and less timely LLPs.

Z-Score : the accounting-based measure of bank risk the paper uses; the paper reports that overall risk-taking, as measured by the Z-Score, increases by 19-32% of the sample mean for banks affected by office closures.

Community banks : smaller banks tied to local markets and served by traveling rather than in-house examiners — the sample the paper focuses on.

Key concepts

Community banks : smaller banks tied to local markets and served by traveling rather than in-house examiners — the sample the paper focuses on.

The Liquidity of the Government Bond Market — What Impact Does Quantitative Easing Have? Evidence from Sweden

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

This paper uses transaction-level bond data under MiFID I and II to measure five dimensions of Swedish government bond market liquidity during the Riksbank’s QE program (2015–2020) and identifies two offsetting effects: a demand effect, whereby outright purchases temporarily improve liquidity on the day of a transaction, and a scarcity (holding) effect, whereby the accumulated stock of central bank holdings persistently reduces liquidity. Across all five liquidity measures — Turnover (TURN), Turnover Ratio (TR), Yield Impact (YI), Market Efficiency Coefficient (MEC), and Volume-Adjusted Imputed Volatility (VAIV) — the scarcity effect is statistically significant and negative for all five, while the demand effect is positive and significant for four of five. Quantitatively, the scarcity effect is five times larger than the demand effect at average holding levels, and is nonlinear: both effects are near zero when the Riksbank’s holding share is below 40 percent of outstanding bonds, but the scarcity effect on transaction costs (YI) is approximately four times larger when holdings exceed that 40 percent threshold. The Swedish Debt Management Office’s Securities Lending Facility (SLF) partially mitigates the scarcity effect on two of five measures (YI and VAIV) but not on volume-based measures.

In depth

Q1. What are the five liquidity measures and how are they constructed from MiFID transaction data?

The paper derives five measures from 316,413 filtered dealer-to-client and dealer-to-dealer transactions (out of 802,102 raw transactions) covering Swedish nominal government bonds from 2015 to 2020 under MiFID I and II reporting obligations. Tightness is captured by Yield Impact (YI), defined as the price change per trade divided by time to maturity — higher YI signals lower transaction costs per unit of duration. Immediacy and breadth are captured by Turnover (TURN, total volume traded weekly) and Turnover Ratio (TR, volume as a fraction of outstanding). Resilience is captured by Market Efficiency Coefficient (MEC) and Volume-Adjusted Imputed Volatility (VAIV): MEC compares return variance over long and short horizons — a ratio near one signals efficient absorption of order flow; VAIV measures price volatility after adjusting for volume, so that higher VAIV signals less efficient price formation per unit of trading. These five dimensions track different aspects of market quality and do not always move together, which is why using a single measure would miss the full picture.

Q2. What is the demand effect of QE purchases, and how large is it relative to the scarcity effect?

The demand effect captures the temporary improvement in liquidity on the week of a central bank purchase, measured by the coefficient on the contemporaneous Riksbank purchase variable; it is positive and significant for four of the five measures (TURN, TR, YI, and VAIV), but not for MEC. In the baseline regression (Table 3, Panel 1), a one standard deviation increase in outright purchases increases YI by approximately 4.4 standard deviations. However, this is a one-time event: the coefficient on purchases captures the effect at time t only, and the paper confirms that liquidity in the subsequent week is not significantly affected by prior purchases. By contrast, the scarcity (holding) effect from accumulated bond stock is persistent: at average holding levels of approximately 36 percent of outstanding, the holding variable decreases YI by 0.15 basis points from an average level of around 1.17 basis points per transaction. The scarcity effect is therefore approximately five times larger than the demand effect at these holding levels, and lasts as long as the central bank holds the bonds — effectively until maturity.

Q3. What is the nonlinearity in the scarcity effect and how is the 40 percent threshold identified?

The threshold is identified from a bond-by-bond analysis of the Debt Management Office’s Securities Lending Facility (SLF) usage: both the volume and volatility of SLF activity increase significantly when the Riksbank’s holding share crosses approximately 40 percent of outstanding for a given bond, indicating that market participants seek alternative sources of bond supply precisely at that concentration level. The paper re-estimates the baseline model on two subsamples — bonds with holding below 40 percent and bonds with holding above 40 percent. Below the threshold, neither the demand effect nor the scarcity effect is significant for most measures (all purchase coefficients become insignificant except MEC, which turns negative; all holding coefficients are insignificant except TR which turns negative). Above the threshold, the demand effect strengthens (intuition: with fewer free-float bonds, the marginal impact of a purchase on liquidity is amplified), and the scarcity effect on YI is approximately four times larger than in the baseline. Volume-based turnover measures (TURN and TR) do not show significant scarcity effects above the threshold, suggesting that the scarcity effect concentrates on transaction costs and price efficiency rather than traded volumes when the holding share is large.

Q4. Does the Securities Lending Facility offset the scarcity effect?

The SLF coefficient is consistently positive across all five measures, and statistically significant for YI and VAIV in the baseline, suggesting the facility partially restores liquidity by lending bonds to market makers when the central bank’s holdings reduce free-float supply. However, the SLF does not significantly improve the volume-based measures (TURN and TR), and the effect is only detectable above the 40 percent threshold for turnover measures. The paper orthogonalizes SLF volumes against the Holding variable (to address the 50 percent pooled correlation between them) and finds no material change in the holding coefficients. The interpretation is that the SLF provides a buffer against scarcity-driven deterioration in transaction costs and price efficiency, but it does not fully restore pre-QE liquidity levels when holding shares are high. The paper also notes that the SLF may set a floor for short-term market interest rates relative to the policy rate, partially offsetting QE’s effect on yields — a second-order consideration for the liquidity analysis but relevant for the broader QE transmission mechanism.

Q5. Why does bond market liquidity not respond to QE announcements?

The paper tests whether QE announcement dates predict liquidity improvements and finds that they do not: liquidity responds only to actual purchases, not to forward-looking price adjustments at announcement. This contrasts with asset prices, which are forward-looking and respond immediately to announced changes in the expected path of central bank asset holdings. Bond market liquidity depends on the physical quantity of bonds available for trading, which changes only when purchases are executed, not when they are anticipated. This asymmetry has a policy implication: policymakers cannot exploit an announcement effect to improve market liquidity in advance of purchases, and the liquidity costs of QE (the scarcity effect) accumulate gradually over the purchase period rather than being front-loaded at announcement.

Q6. How robust are the results to time aggregation, time fixed-effects, outliers, and alternative specifications?

The baseline results are robust across six groups of robustness checks. (1) Time aggregation: results are materially unchanged at monthly frequency. (2) Time fixed-effects: switching from month FE to year FE or to no FE (replacing FE with macroeconomic controls including VIX, business confidence, money market premium, 5–2 year yield spread, debt-to-GDP, and the ESMA sovereign bond liquidity index) does not change the sign or significance of the demand and scarcity coefficients. (3) Outliers: winsorizing or truncating at the 5th and 95th percentile preserves the main results despite removing 10–18 percent of observations. (4) SLF specifications: orthogonalizing SLF volumes against Holding, normalizing by total outstanding rather than free float, and lagging up to four periods do not materially change results. (5) Inflation-linked bonds: including inflation-linked bonds (which are less liquid than nominal bonds) amplifies both effects as expected. (6) The paper also checks that the threshold of 40 percent is not driven by threshold choice: results at alternative thresholds (both lower and higher) are consistent in direction.

Q7. What is the broader implication for QE program design?

The results imply that QE programs face a liquidity-yield tradeoff: large-scale asset purchases that achieve meaningful yield compression must reach holding concentrations that materially impair government bond market liquidity, and this impairment is nonlinear and accelerates once concentration exceeds approximately 40 percent of outstanding per bond. For central banks designing future purchase programs, the threshold suggests a natural limit on per-bond concentration, consistent with the ECB’s 33 percent issuer limit for its own purchase programs. The paper also highlights the role of complementary facilities: the SLF partially offsets the scarcity effect on transaction costs, suggesting that security lending programs are a useful adjunct to large-scale asset purchases. The finding that the scarcity effect persists as long as holdings are maintained — rather than reverting when purchases stop — implies that balance sheet normalization (quantitative tightening) may be needed to restore liquidity, not merely a pause in purchases.

Key concepts

demand effect: the temporary improvement in government bond market liquidity on the day of a Riksbank outright purchase, reflecting the positive price impact of incremental buyer demand; positive and significant for four of five liquidity measures, but transitory (does not persist to the following week).

scarcity effect (holding effect): the persistent deterioration in government bond market liquidity caused by the accumulated stock of bonds held by the Riksbank, which reduces free-float supply available to market participants; negative and significant for all five measures, five times larger than the demand effect at average holding levels, and nonlinear — concentrated and amplified when holding share exceeds 40 percent of outstanding.

Yield Impact (YI): a transaction-cost measure of tightness defined as the price change per trade divided by time to maturity; higher YI indicates lower transaction costs per unit of duration; the paper’s primary measure for quantifying the demand and scarcity effects.

Market Efficiency Coefficient (MEC): a resilience measure comparing return variance over long and short horizons; a ratio near one signals efficient absorption of order flow; the measure for which the demand effect is not positive and significant in the baseline, suggesting QE purchases may temporarily disrupt price efficiency rather than improve it.

Securities Lending Facility (SLF): the Swedish Debt Management Office’s bond-lending program that lends government bonds to market makers against collateral; partially offsets the scarcity effect on transaction costs (YI, VAIV) but not on volume-based measures (TURN, TR), and its activity accelerates when Riksbank holdings exceed 40 percent.

free-float supply: the quantity of a government bond available for trading in the secondary market after subtracting the central bank’s holdings; the mechanism through which the scarcity effect operates — lower free-float reduces order book depth and increases transaction costs.

The Role of Remittances and FDI for the Current Account: The Case of Cambodia

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

This paper builds and estimates a small open economy real-business-cycle (SOE-RBC) model for Cambodia augmented with two non-standard external-sector shocks — net unilateral transfers (remittances and government grants) and net foreign direct investment — in addition to the standard shocks of transitory productivity, permanent productivity, and world interest rate. Estimated on annual Cambodian data over 1993–2018 using Bayesian Markov Chain Monte Carlo, the model shows that FDI and unilateral transfers together account for approximately 50 percent of the variance in Cambodia’s current account-to-output ratio (approximately 27 percent for FDI and 23 percent for unilateral transfers), substantially exceeding the combined contribution of productivity and world-interest-rate shocks. The estimated model tracks the observed current account path with a correlation of 0.93 and a measurement error of only 4.1 percent, compared to a measurement error of 58 percent and correlation of 0.80 when FDI and unilateral transfers are omitted. Applied to the COVID-19 scenario (1 percentage point drop in transitory productivity, 2 percentage point drop in the FDI-to-output ratio, and 8 percentage point drop in unilateral transfers-to-output), the model predicts the current account-to-output ratio will fall to approximately −14 percent in 2020, closely matching the World Bank’s forecast of −14.1 percent.

In depth

Q1. Why does a standard SOE-RBC model fail to explain Cambodia’s current account, and what does the paper add?

A standard SOE-RBC model with only transitory productivity, permanent productivity, and world interest rate shocks leaves 58 percent of the variance in Cambodia’s current account-to-output ratio unexplained and achieves only a 0.80 correlation with the observed series, because it omits two empirically large and persistent external financing flows — FDI (which averaged around 11 percent of GDP over the sample) and net unilateral transfers (remittances and grants) — that directly affect both the capital account and saving behavior in a developing country with shallow domestic capital markets. The paper follows Chang and Fernández (2013), who establish that world interest rate and transitory productivity shocks matter more than permanent productivity for business cycles in emerging markets, and extends that framework specifically for a low-income developing economy where external capital inflows are a primary driver of investment and consumption rather than an auxiliary shock. FDI is modeled as an exogenous shock to the net-FDI-to-output ratio with its own AR(1) process, and it enters the model with a direct spillover onto permanent productivity growth (parameter γ, with a posterior mean of 0.08), capturing the technology-diffusion channel of FDI.

Q2. What is the model structure and what shocks does it incorporate?

The model is a two-good SOE-RBC framework with Cobb-Douglas production (F = a_t K^α h^(1-α)) where output growth is driven by a stationary transitory productivity level a_t and a non-stationary permanent productivity trend g_t; households maximize utility over consumption and leisure with CRRA preferences (σ = 2) and discount factor β = 0.96, subject to a budget constraint linking consumption, capital accumulation (with quadratic adjustment costs, calibrated posterior mean φ = 15.76), foreign borrowing, and two external inflow variables: net unilateral transfers (NT) and net FDI. The world interest rate R_t is the product of the world risk-free rate R*_t and a country-specific spread S_t that depends negatively on expected future productivity, introducing an endogenous risk-premium channel. The working-capital requirement θ (posterior mean 0.50) requires firms to pre-finance a fraction of the wage bill at the current period interest rate, creating a financial-accelerator-like amplification of world interest rate shocks. The complete list of five structural shocks is: transitory productivity (σ_a), permanent productivity growth (σ_g), world interest rate (σ_R), unilateral transfers (σ_nt), and FDI (σ_fdi). The model is estimated in log-differences of Y, C, and I and in levels of TB/Y, CA/Y, NT/Y, and FDI/Y.

Q3. What does the variance decomposition show and how does it allocate current account variation across shocks?

Table 3 shows that for the current account-to-output ratio, FDI and unilateral transfers together account for approximately 50 percent of variance (~27 percent for FDI and ~23 percent for unilateral transfers), while transitory productivity and world interest rate shocks together account for the bulk of the remainder; permanent productivity growth (σ_g) contributes negligibly to CA/Y variance; the measurement error in CA/Y (σ_CA) is approximately 4.12 percent, indicating the model fits the current account data very closely. The paper notes that “the shocks of world interest rate and transitory productivity play more important roles than the shock of permanent productivity growth in explaining macroeconomic fluctuations,” consistent with Chang and Fernández (2013) and the standard SOE-RBC finding. For output, consumption, and investment, transitory productivity and world interest rate shocks dominate (each accounting for roughly 30–50 percent of variance across the macro aggregates). The FDI shock plays a comparable role to the interest rate shock for output fluctuations, reflecting that FDI inflows to Cambodia are large enough to function as a de facto external financing channel. A model without FDI and transfers (Appendix Table A1) shows that measurement error in CA/Y rises to 58.31 percent, confirming the quantitative importance of the two additional shocks.

Q4. How do impulse responses to the five shocks illuminate the current account dynamics?

A positive transitory productivity shock of 1 percent causes output, consumption, and investment to expand on impact, but the expansion in domestic absorption (C + I) exceeds that of output because the persistence of the shock (ρ_a = 0.91) leads consumption-smoothing households to borrow against higher expected future income, producing a current account deterioration of approximately 1 percentage point on impact — consistent with a temporary boom financed by current account deficits. A positive world interest rate shock reduces consumption and investment by roughly 1 percentage point on impact as borrowing costs rise and firms reduce the wage-bill they pre-finance; trade balance and current account improve initially (~1 percentage point) as domestic absorption falls more than output, but then deteriorate as the higher interest payment on the accumulated debt stock (with persistence ρ_R = 0.87) pushes the current account below its steady state after period 1. A positive FDI shock raises consumption and investment while keeping output unchanged on impact, deteriorating the current account by approximately 1 percentage point; because FDI raises permanent productivity growth (γ > 0), the accumulation of capital eventually raises output so that the current account gradually recovers toward its steady state, but domestic absorption remains above output due to the joint persistence of FDI and productivity (ρ_fdi = 0.87, ρ_g = 0.72). A positive unilateral transfer shock has a negligible impact on consumption, investment, and output (magnitudes below 0.06 percent) because the shock is low-persistence (ρ_nt = 0.15) and consumption-smoothing households save most of the windfall; however, the transfer improves the current account by its full magnitude (~1 percentage point) essentially one-for-one by definition.

Q5. How well does the model fit the historical current account trajectory and what does the shock decomposition reveal about phases of Cambodian development?

The estimated model produces a time-series of fitted current account-to-output ratios with a 0.93 correlation with the observed data and only 4.1 percent measurement error; the model initially over-predicts by about 5 percentage points (due to uncertainty about initial conditions), but then closely tracks the observed trajectory of deficits averaging roughly −11 percent of GDP from the mid-1990s through 2018. The shock decomposition (Figure 5) shows that FDI and unilateral transfers dominate the current account in the earlier part of the sample (mid-1990s to mid-2000s), while transitory productivity shocks contribute more in the later period (post-2010) — a pattern the authors interpret as consistent with the stylized fact that capital inflows drive growth in early-stage development, while productivity improvements become the primary driver as the economy matures. The world interest rate shock contributes relatively little throughout the sample, suggesting that Cambodia’s current account dynamics are primarily driven by supply-side (FDI-productivity linkages) and income-transfer channels rather than by global borrowing-cost variation.

Q6. What does the COVID-19 scenario exercise predict and what is the model’s forecasting accuracy?

Combining simultaneous shocks calibrated to IMF and World Bank 2020 projections for Cambodia — a 1-percentage-point drop in transitory productivity (consistent with a World Bank projection of 1 percent GDP contraction), a 2-percentage-point drop in the FDI-to-output ratio (World Bank 2020 forecast), and an 8-percentage-point drop in unilateral transfers-to-output (reflecting IMF’s Sayeh and Chami 2020 estimate of 20 percent or more remittance decline plus EU EBA trade preference suspension) — the model predicts the current account-to-output ratio will fall to −14 percent in 2020, essentially identical to the World Bank’s external forecast of −14.1 percent. The three shocks propagate differently: the productivity drop temporarily improves the current account by approximately 2 percentage points as domestic absorption contracts more than output, but then worsens it in 2021 as output falls and consumption reverts; the FDI drop similarly has a transient current-account-improving effect before the productivity-growth channel drags output down; the transfer drop has an essentially one-to-one negative effect on the current account (8 percentage points lower) that quickly reverses. The combined prediction of −14 percent, coinciding with the World Bank’s external forecast, is presented as validation of the model’s out-of-sample performance.

Q7. What is the role of the endogenous vs. exogenous discount factor, and why does it matter?

The paper tests whether specifying the discount factor as endogenous (depending on lagged consumption as in Schmitt-Grohé and Uribe 2003, to ensure stationarity of net foreign assets) versus exogenous materially affects the current account dynamics, and finds it does not — the discount factor specification is immaterial for explaining Cambodian current account fluctuations because FDI and unilateral transfers, which dominate the variance decomposition, are exogenous to the household’s saving-patience parameter that the discount factor governs. This result simplifies model specification choices for similar small open economy applications: the patience assumption matters for long-run external position dynamics in models where standard RBC shocks dominate, but loses its influence when there are large direct external financing flows. The finding extends to the working capital parameter θ, which also does not significantly alter the current account dynamics despite affecting the transmission of world interest rate shocks to investment and output.

Q8. How does this paper contribute relative to existing SOE-RBC literature and what are its limitations?

The key contribution relative to Aguiar and Gopinath (2007), García-Cicco et al. (2010), and Chang and Fernández (2013) is to demonstrate quantitatively that for very low-income developing countries where FDI and remittances are large relative to GDP, the standard SOE-RBC shock triplet (transitory productivity + permanent productivity + world interest rate) is misspecified and will systematically fail to fit current account data; adding the two external financing shocks reduces the CA/Y measurement error from 58 percent to 4 percent, a quantitatively enormous improvement. A limitation noted by the paper is that the working paper version (MPRA 108489) covers only Cambodia over 1993–2018, so cross-country generalizability to other developing economies with large FDI and remittance flows (e.g., Bangladesh, Nepal, Vietnam) is not formally established; the model is also log-linearized around the steady state, which may miss non-linear dynamics during extreme events like the COVID-19 shock. Additionally, FDI is treated as an exogenous process despite the literature on FDI determinants suggesting it responds endogenously to domestic institutional quality, trade policy, and productivity trends.

Key Concepts

SOE-RBC (small open economy real-business-cycle) model : a dynamic stochastic general equilibrium model in which a small economy takes world prices and interest rates as given; households maximize lifetime utility by choosing consumption, investment, and foreign borrowing; the current account emerges as the net change in the foreign debt position; log-linearized around the steady state and solved via perturbation methods.

Bayesian Markov Chain Monte Carlo (MCMC) estimation : a method for estimating the posterior distribution of structural parameters by combining prior beliefs with the likelihood of observing the data; the paper uses prior distributions from Chang and Fernández (2013) for most parameters and Cambodian data for the AR(1) coefficients of the new shocks; parameters with posterior means significantly different from priors (at the 10 percent level) are highlighted in Table 2.

variance decomposition : the share of variance in each endogenous variable attributable to each exogenous shock at the business-cycle horizon; computed from the estimated model’s spectral density; in this paper, used to quantify the relative importance of FDI and unilateral transfers relative to productivity and interest rate shocks for the current account.

unilateral transfers (NT) : net flows of income from abroad that do not require repayment, including workers’ remittances from Cambodian migrants abroad and official government grants from donor countries; modeled in the paper as an exogenous shock to the NT-to-output ratio with AR(1) persistence ρ_nt = 0.15 (low persistence).

FDI productivity spillover (γ) : the elasticity of permanent productivity growth with respect to the FDI-to-output ratio; estimated to be 0.08 (posterior mean), reflecting the hypothesis that FDI brings technology transfer and know-how that raises Cambodia’s total factor productivity trend; the FDI shock thus affects the current account both directly (through the capital account) and indirectly (through the productivity channel).

working capital requirement (θ) : the fraction of the wage bill that firms must borrow in advance at the current period’s interest rate; estimated at 0.50 (posterior mean), implying that world interest rate shocks are amplified through a financial-accelerator mechanism in which higher borrowing costs reduce labour demand and output, beyond the standard intertemporal substitution channel.

country-specific spread (S_t) : the risk premium Cambodia pays above the world risk-free rate, modeled as a decreasing function of expected future productivity; captures the tendency of developing countries to face higher borrowing costs when growth prospects weaken, creating a pro-cyclical external financing condition.

The Welfare and Distributional Consequences of Corporate Tax Cuts in Open Economies

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

Layer 1: Overview

This paper uses an open-economy heterogeneous-household model with incomplete markets to evaluate the welfare and distributional consequences of the U.S. Tax Cuts and Jobs Act (TCJA) of 2017 — which reduced the U.S. corporate tax rate from 35 to 21 percent — both within the U.S. and in affected trading partners. The model features three economies (the U.S., a small open economy calibrated to Canada, and the rest of the world), free capital flows, progressive income taxes, and idiosyncratic uninsurable labor income shocks generating empirically realistic wealth Gini coefficients (0.80 for the U.S., 0.70 for Canada). Three main results are established. First, the TCJA is regressive in the U.S. — under a permanent cut, the bottom 5 percent of U.S. households by wealth experience welfare losses of 0.10–0.26 percent of lifetime consumption, while the top 1 percent gain 0.92 percent — and generates an even more regressive outcome in trading partners, where approximately the bottom 80 percent of the small open economy’s wealth distribution experience welfare losses averaging 1.28 percent at the bottom decile against gains of 2.57 percent at the top. Second, whether U.S. wealth-poor households benefit depends critically on the persistence of the tax cut: under a permanent cut, households above approximately the bottom 5 percent of the U.S. wealth distribution gain (driven by wage increases from capital inflows), but under an anticipated partial reversal from 21 to 28 percent after 7 years, approximately the bottom 75 percent of U.S. households experience welfare losses because the temporary wage gain is dominated by a persistent increase in the public debt burden. Third, when the small open economy reciprocates by matching the U.S. corporate tax reduction to 21 percent, the domestic distributional consequence reverses: all wealth quintiles in the small open economy gain (Table 5, Panel B shows gains of 0.52–1.19 percent across all groups), with the gain being roughly progressive within the SOE — a result driven by the wage increase from capital inflows exceeding the financing cost, which falls primarily on the wealth-rich through higher top marginal tax rates.

In depth

Q1. What is the model structure and how are the three economies connected?

The paper extends the Aiyagari (1994) incomplete-markets heterogeneous-household model to an open-economy setting with three countries — the U.S., a small open economy (SOE) modeled as Canada, and the rest of the world (ROW) modeled with Canadian parameters — linked by free capital flows that equalize after-tax returns to capital across countries: (1 − τc^US)r^US = (1 − τc^SOE)r^SOE = (1 − τc^ROW)r^ROW = r^b. Households in each economy face idiosyncratic uninsurable productivity shocks (three states: low s₁ = 0.167, medium s₂ = 0.839, high s₃ = 5.087, with a persistent Markov transition matrix following Domeij and Heathcote 2004) and save in internationally traded capital and government bonds, subject to borrowing constraints calibrated to match wealth Gini coefficients. The fiscal rule follows Bohn (1998) with the residence-based tax revenue responding to the debt-to-GDP ratio to ensure stationarity, and the top marginal tax rate τ₁ adjusts endogenously when corporate tax revenues change (consistent with Mertens and Montiel Olea 2018’s evidence on tax instrument choice). The SOE size is 10 percent of the U.S., enabling the paper to capture the asymmetric spillover mechanism by which U.S. corporate tax policy creates large distributional consequences abroad without generating offsetting fiscal adjustments in the SOE.

Q2. What are the distributional effects of the permanent TCJA in the U.S. and SOE?

Under a permanent reduction from 35 to 21 percent in the U.S. corporate tax rate, the average U.S. welfare gain is +0.146 percent of lifetime consumption, but this masks a strongly regressive distribution: households in the bottom 5 percent of the U.S. wealth distribution experience welfare losses of −0.045 to −0.101 percent, while those in the top 1 percent gain +0.920 percent, with gains monotonically increasing through the wealth distribution above the 5th percentile; in the SOE, the average welfare effect is −0.392 percent, and the losses are far larger and more broadly distributed, with approximately the bottom 80 percent (up to the 75th–95th percentile boundary) experiencing losses ranging from −0.582 to −1.282 percent while the top 1 percent gains +2.566 percent (Table 3). The mechanism for the U.S. involves capital inflows that raise wages (benefiting labor-income-reliant poor households at least partially) offset by increased tax burden from debt accumulation; in the SOE, capital outflows depress wages more severely, and wealth-rich households in the SOE gain even more than their U.S. counterparts because SOE households face no increase in their domestic tax burden to finance the U.S. corporate tax cut, making the SOE spillover a “free lunch” for SOE capital owners.

Q3. Why does the permanence of the tax cut matter for lower-wealth U.S. households?

When the TCJA is anticipated to be partially reversed — from 21 percent back to 28 percent after 7 years — households in approximately the bottom 75 percent of the U.S. wealth distribution experience welfare losses averaging from −0.091 to −0.259 percent; under a permanent cut only approximately the bottom 5 percent suffer losses, so the reversal shifts the crossover point from the 5th to the 75th percentile of the wealth distribution (Table 4, Panel A). The mechanism is that under a temporary tax cut the capital inflow is short-lived and so the wage increase is limited in duration, while the increase in U.S. government debt is persistent — because the government finances the cut through debt issuance and the debt level remains elevated even after the reversal from 21 to 28 percent, the resulting higher tax burden on labor income persists and dominates the temporary wage benefit for wealth-poor households who primarily earn labor income. This result has a direct policy implication: the distributional case for extending or making permanent the TCJA’s corporate rate reduction is much stronger than for a time-limited cut, because the wage-raising channel — the main argument for the cut’s benefits to workers — operates only persistently.

Q4. What happens when the small open economy reciprocates with its own corporate tax cut?

When the SOE reduces its corporate tax rate to match the U.S. at 21 percent (from 38 percent) simultaneously with the TCJA, all wealth groups in the SOE experience welfare gains (Table 5, Panel B shows average gains of +0.524 to +1.190 percent across wealth groups), with the distributional effect being progressive within the SOE: the incremental gain from reciprocation compared to not reciprocating is +1.807 percent for the bottom 1 percent of the SOE wealth distribution and −1.376 percent for the top 1 percent (Table 5, Panel C). The reason the SOE reciprocation is progressive is that the capital inflow triggered by the SOE’s cut raises wages across the SOE (benefiting labor-income-reliant poor households), while the financing cost of the cut — through debt accumulation and the eventual increase in top marginal tax rates — falls disproportionately on wealthy households. The paper notes this result depends on the SOE’s small size: because the SOE is only 10 percent of the U.S., its corporate tax cut creates a better investment opportunity for all global capital owners but the financing cost falls entirely on SOE residents, creating a distributional asymmetry between who benefits (all capital owners globally) and who pays (SOE income-rich households domestically).

Q5. How does the model fit the pre-TCJA data and what are the calibration targets?

The model closely matches its calibration targets: capital-to-output ratios of 2.50–2.52 (target 2.50), debt-to-GDP ratios of 0.827–0.882 (targets from Jordà-Schularick-Taylor 2017), and wealth Gini coefficients of 0.82 for the U.S. (target 0.80, from Budría-Rodríguez et al. 2002) and 0.71 for the SOE (target 0.70, from Brzozowski et al. 2010); and generates an untargeted prediction that the U.S. is a net borrower and Canada a net lender, consistent with data (Table 2, Panel B). The discount factors are calibrated to β^US = 0.968 and β^SOE = 0.969 to match the capital-output ratio, and the borrowing constraints are set at ψ = −1.65 for the U.S. and ψ = −0.88 for the SOE/ROW to match their respective wealth Gini coefficients. The model abstracts from terms-of-trade effects (consistent with Hanson et al. 2021’s evidence that US-Canada terms of trade are unaffected by US corporate tax changes) and aggregate uncertainty beyond corporate tax changes, and the SOE is set at 10 percent of the U.S. economy by population size.

Q6. How do the results change under alternative fiscal financing assumptions?

The key qualitative results — regressivity of the TCJA in the U.S. and its greater regressivity in the SOE — are robust across alternative fiscal financing assumptions: when the corporate tax cut is financed by immediately increasing the residence-based tax (χ = 1) rather than by debt (χ = 0 in the baseline), the losses at the bottom of the U.S. distribution become larger (approximately the bottom 70 percent lose rather than the bottom 5 percent), and when progressivity of the income tax (τ₃) rather than the top marginal rate (τ₁) adjusts, the additional tax burden falls more on wealth-poor households, making the cut even more regressive. The SOE reciprocation result is also robust: Appendix C.3 shows that financing the SOE corporate tax cut through increases in the residence-based tax (χ^SOE = 1) reduces the welfare gains for all SOE households but preserves the progressive distributional pattern within the SOE, while appendices C.1–C.2 show that the results are linear in the size of the SOE’s tax cut (at 30 and 18 percent, the distributional pattern is similar in direction).

Key Concepts

open-economy Aiyagari model : the paper’s framework — an extension of the Aiyagari (1994) incomplete-markets model with heterogeneous households and idiosyncratic uninsurable labor shocks to an international setting with free capital flows — used to capture how corporate tax changes distribute welfare across the wealth distribution in multiple countries simultaneously.

consumption equivalent variation : the proportional change in lifetime consumption required to make a household in the counterfactual no-TCJA economy as well off as in the economy with the TCJA; the welfare metric used in Tables 3–5, measured in percent of lifetime consumption, conditional on wealth and productivity state at the time of implementation.

TCJA persistence channel : the mechanism by which the distributional effect of the corporate tax cut for lower-wealth U.S. households depends on whether the cut is permanent: a permanent cut sustains capital inflows and wage gains long enough to dominate the increased tax burden, while a temporary cut leaves only a persistent debt overhang with limited wage benefits, turning even the bottom 75 percent of U.S. households into net losers.

SOE reciprocation progressivity : the finding that a small open economy that matches the U.S. corporate tax reduction achieves a progressive domestic distributional outcome because the wage increase from capital inflows benefits all households but the financing cost (through higher top marginal tax rates) falls mainly on the wealthy; this mechanism is size-dependent and reverses the regressivity that the U.S. cut generates domestically.

Unequal and Unstable: Income Inequality and Bank Risk

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

This paper documents that U.S. metropolitan statistical areas with higher income inequality have a larger share of failed banks, higher average bank default probabilities, and greater dispersion of bank risk, using cross-sectional regressions across 178 MSAs and 5,543 banks over 2000–2019 with the Gini coefficient measured from the 2006 American Community Survey. A move from the 25th to the 75th percentile of the Gini distribution (0.429 to 0.460) is associated with a 0.124 percentage point higher share of failed banks, a large effect relative to the 0.3 percent mean failure rate in the sample. To account for these patterns, the paper builds a general equilibrium model in the Allen and Gale (2000) tradition in which banks compete to lend to households that differ by income and finance housing purchases with mortgages; competition and deposit insurance together induce some banks to lend to low-income (subprime) households at rates that carry negative expected present value, creating a segment of endogenously risky banks that fail with positive probability in the bad state. Income inequality expands the subprime borrower pool both directly — by shifting more households below the endogenous income cutoff — and indirectly — by raising the equilibrium cutoff itself via higher housing prices — leading to a larger share of risky banks. A key counterfactual result is that if deposit insurance premiums fully reflected bank-specific risk (eliminating risk-shifting), all banks would be safe regardless of the income distribution, isolating risk-shifting as the necessary friction.

In depth

Q1. What is the empirical design, and what does the data show?

The paper uses a cross-sectional dataset at the MSA level, covering 178 MSAs with 5,543 commercial and savings bank headquarters over 2000–2019, regressing several measures of bank risk on the Gini coefficient measured from the 2006 ACS (one-year survey) while controlling for MSA-level income, population, urbanization, and year fixed effects in panel extensions. Bank failure is the primary risk measure: the share of bank headquarters that failed (FDIC-confirmed failure dates, excluding 2008–2009 TARP years to avoid ambiguity about government support) is regressed on the Gini coefficient. Additional risk measures — banks’ predicted probabilities of default (from a logit model trained on financial ratios) and z-scores — are used to confirm that the Gini result is not driven entirely by crisis-period observations. The paper finds significant positive relationships between the Gini and: (i) the share of failed banks (Panel A), (ii) the risk of the most-risky banks per MSA (Panel B), (iii) average bank risk (Panel C), and (iv) the dispersion of bank risk across banks in the MSA (Panel D). Robustness checks use 3-year survey Gini coefficients, the income share of the top 5 percent as an alternative inequality measure, and panel regressions with MSA-level clustering; results are qualitatively unchanged. Poverty (share of households below the poverty line) is not significantly associated with bank risk, distinguishing inequality from the level of the lower tail.

Q2. What is the theoretical framework and what agents populate the model?

The model is a two-date (0 and 1) general equilibrium model with a continuum of households heterogeneous in income and a continuum of ex-ante identical, risk-neutral bankers; households finance housing purchases at date 0 with mortgage loans that are repaid at date 1, and bankers can choose at date 0 to operate a safe bank (solvent in both states) or a risky bank (insolvent in the bad state with probability q). Housing is produced by competitive firms with increasing marginal cost, so the equilibrium housing price P_0 is an increasing function of aggregate housing demand. Deposits are insured (explicitly or implicitly), and banks are subject to a minimum capital requirement (maximum leverage ratio ρ). The cost of bank capital exceeds the cost of deposits, so all banks lever to the maximum. Each bank’s cost of managing its balance sheet is quadratic in balance sheet size, which pins down individual bank size and allows a clean characterization of how many risky vs. safe banks exist in equilibrium.

Q3. What is the key sorting result between banks and borrowers (Proposition 1 and 2)?

In equilibrium, there is an endogenous income cutoff y such that households with income above y are prime borrowers served by safe banks at undistorted interest rates r_u(y), and households with income below y* are subprime borrowers served by risky banks at a uniform risk-shifting interest rate r_rs; crucially, subprime loans carry negative expected net present value because competition among risky banks drives r_rs below the break-even rate for a safe bank (Corollary 1).** The risk-shifting interest rate r_rs is lower than the undistorted rate for low-income borrowers because a risky bank only internalizes the loan payoff in the good state (where it is solvent) and benefits from the deposit insurance subsidy in the bad state (where it defaults and the fund covers depositor losses). Risky banks are therefore willing to lend at below-NPV rates, and competition among them drives r_rs to equality with their marginal cost conditional on survival. Safe banks rationally refuse to enter the subprime segment because they internalize the expected loss in the bad state. The clientele of safe and risky banks do not overlap in equilibrium.

Q4. How does income inequality affect the proportion of risky banks?

Income inequality raises the share of risky banks through two reinforcing channels: a direct channel that shifts a larger mass of households below the fixed cutoff y, expanding the subprime borrower pool, and an indirect channel that moves the cutoff y upward (because inequality raises the equilibrium housing price P_0, which in turn raises the default rate among any given income level, making more households effectively subprime) — under convex housing demand (plausible if n(y) is concave below a poverty-line income ymin), both channels reinforce each other.** Numerically, with a log-normal income distribution calibrated to the observed Gini range of 0.35–0.55, the model generates a monotone positive relationship between the Gini coefficient and (i) the proportion of risky banks, (ii) average bank default probability, and (iii) dispersion of bank default probabilities — matching the empirical patterns from Section 2. A Pareto income distribution produces a steeper relationship, suggesting the result is robust to distributional assumptions. The proportion of risky banks in Proposition 2 equals the subprime housing demand divided by the sum of subprime and weighted prime demand, and is therefore a smooth function of the income distribution H.

Q5. Why is risk-shifting — not borrower riskiness — the necessary friction?

Proposition 3 shows that if deposit insurance premiums fully reflected each bank’s individual default probability (i.e., if risk-shifting were not feasible), all banks would choose to be safe even when the income distribution places many households with high default rates below y, because a risky bank would have to pay higher deposit rates to attract insured deposits and would be unable to extract a competitive advantage from subprime lending.* The proposition isolates risk-shifting as a necessary condition: without it, the income distribution has no effect on bank risk. This result directly connects to Keeley’s (1990) observation that bank risk reflects the option value of limited liability plus deposit insurance. It also implies that policies that make deposit insurance premiums bank-risk-sensitive (such as risk-based FDIC premiums) could substantially mitigate the inequality–bank-risk nexus, though the paper notes that empirical evidence suggests current risk-based premiums do not fully internalize bank-specific risk.

Q6. How does housing supply elasticity interact with the inequality–bank-risk relationship?

When housing supply is inelastic (high marginal cost c_1), a mean-preserving spread in income raises the equilibrium housing price P_0 substantially, which raises the subprime cutoff y sharply via the indirect channel — and for very high values of c_1, this can actually push the cutoff above the top of the income distribution, putting all households into the prime segment and reducing the share of risky banks.* This asymmetry means that in regions with very inelastic housing supply (e.g., coastal urban areas with strict zoning), higher inequality may be associated with fewer risky banks because the high housing price forces even low-income households to borrow at rates where a safe bank is marginally competitive. Conversely, in regions with elastic housing supply, the indirect channel is weak and the direct channel dominates, so higher inequality unambiguously raises bank risk. The paper characterizes this interaction numerically using Figure 4, noting that the perverse (negative) relationship is theoretically possible but considered less empirically relevant in practice.

Q7. What are the model’s extensions and robustness?

The paper discusses four extensions that leave the central mechanism intact: (i) ex-ante heterogeneous banks, in which risky banks specialize in subprime mortgages and also finance risky firms; (ii) risk-weighted capital requirements, which permit risk-shifting as long as risk weights are not fully calibrated to bank-specific risk; (iii) a firm sector, in which risky banks serve risky small firms in addition to subprime households; and (iv) housing speculation by high-income households, which amplifies the risky-bank segment by creating additional demand for negative-NPV mortgages. In extension (iv), the high-income speculator demands a risky mortgage even though speculator income is above y*, creating an additional channel through which inequality can generate bank risk beyond the subprime-borrower mechanism. The discussion also addresses the baseline model’s assumptions about flat deposit rates and homogeneous bankers, arguing that relaxing either would introduce quantitative but not qualitative changes to the central sorting result.

Q8. What does the paper contribute relative to the literature on bank risk and inequality?

The paper’s empirical contribution is to document a robust cross-sectional positive relationship between income inequality and bank failure rates at the MSA level, a relationship that is not driven by poverty (the lower tail per se), is present for multiple bank-risk measures, and survives including the crisis years 2008–2009 in the bank-risk measures (though significance weakens). On the theory side, the contribution relative to the Cairo-Sim (2018) monetary policy and inequality work and the Allen-Gale (2000) rational bubbles framework is to endogenize the sorting of banks and borrowers into safe/risky pairs in response to the income distribution, and to show that this sorting — not borrower riskiness per se — generates the empirical bank-risk gradient. The model is purposefully simple (one period, no dynamics, no aggregate shock heterogeneity) to make the mechanism transparent; the authors acknowledge that a dynamic model with time-varying inequality might generate additional predictions about the timing of bank failures relative to inequality trends.

Key Concepts

subprime cutoff y* : the endogenous income level that separates prime (income above y*) from subprime (income below y*) borrowers; determined in equilibrium as the income level at which the undistorted mortgage rate for a safe bank equals the risk-shifting rate charged by a risky bank; shifts in response to the equilibrium housing price.

risk-shifting interest rate (r_rs) : the mortgage rate that a risky bank is willing to accept on a subprime loan, determined by the condition that the bank earns zero profit conditional on the good state (survival), without internalizing the loss imposed on the deposit insurance fund in the bad state; in the paper’s equilibrium, r_rs is uniform across all subprime borrowers.

undistorted interest rate (r_u(y)) : the mortgage rate that a safe bank requires from a household with income y, determined by the full expected return on the loan across both good and bad states; increasing in y because lower-income households have higher default rates in the bad state.

negative NPV subprime loans : mortgage loans to households with income below y* that carry a negative expected present value when the deposit insurance cost is internalized; attractive only to risky banks that do not internalize the bad-state payoff, and not to safe banks that must break even in expectation.

Allen-Gale (2000) rational bubbles framework : a one-period general equilibrium model in which banks lend to asset purchasers using deposit insurance, creating a wedge between private and social returns on risky assets; this paper adapts that framework to a mortgage/housing market with a continuous income distribution to generate endogenous bank sorting and an inequality channel.

direct vs. indirect channel of inequality : the direct channel (region A in Figure 2) operates by shifting more households below the existing cutoff y* as the income distribution spreads; the indirect channel (region B) operates by raising y* itself through higher equilibrium housing prices; both channels reinforce each other when housing demand is convex in income (n(y) convex below the poverty line).

deposit insurance subsidy : the implicit transfer from the deposit insurance fund to risky banks in the bad state; risky banks pay the same deposit rate as safe banks despite imposing expected losses on the fund, creating the wedge that makes subprime lending attractive to risky banks and not to safe banks.

Journal of Money, Credit and Banking | Macro Paper Warehouse

A Model of Post-2008 Monetary Policy

Layer 1: Overview

In depth

Q1. What is the core modeling innovation relative to the basic New Keynesian model?

Q2. Why does the model deliver determinacy and avoid the NK ZLB pathologies?

Q3. What exactly are the three (four) facts the model targets, and which mechanism handles each?

Q4. What are the two key conditions for QE to be nearly non-inflationary, and how sensitive are the results?

Q5. How is the central spread calibrated given the shadow rate is unobservable, and why is that a limitation?

Q6. How does the liquid-government-bond extension reconcile non-satiation with T-bill rates below the IOR rate?

Q7. What does the model imply for monetary-policy normalization and Neo-Fisherian effects?

Q8. What does the model say about the floor system and the Taylor principle?

Q9. What robustness checks support the determinacy result?

Q10. How does this paper relate to and differ from closely related prior work?

Q11. What are notable caveats the authors themselves raise?

Key Concepts

Banks of a Feather: The Informational Advantage of Being Alike

Layer 1: Overview

In depth

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

Q2. How do the authors separate supply effects from demand effects?

Q3. How do they rule out that lenders are just reacting to their own correlated portfolio quality?

Q4. What are the main mechanisms, and how are they distinguished empirically?

Q5. What heterogeneity is documented?

Q6. What robustness checks and additional analyses are run?

Q7. How does this paper relate to and differ from closely related prior work?

Q8. What are the policy implications and their scope conditions?

Q9. What are the key caveats the authors themselves flag?

Key Concepts

CBDC as Imperfect Substitute to Bank Deposits: A Macroeconomic Perspective

Layer 1: Overview

In depth

Q1. What is the model’s identification/derivation strategy, since this is a theoretical paper rather than an empirical one?

Q2. Why does the introduction of CBDC leave the deposit rate and bank lending unchanged in this model?

Q3. What are the three welfare channels and how is each maximized?

Q4. What does seigniorage look like as a function of the CBDC rate, and what do Propositions 1-2 say?

Q5. What heterogeneity / cross-country variation does the paper document?

Q6. What robustness / alternative-parameter checks are run (Table 3)?

Q7. How does this paper relate to and differ from the closest prior work?

Q8. What are the main caveats and scope conditions on the welfare results?

Q9. Is cash incorporated, and does it change the conclusions?

Key Concepts

Does the Phillips Curve Lie Down as We Age?

Layer 1: Overview

In depth

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

Q2. How is the age effect distinguished from an income effect?

Q3. What are the two channels behind the age-elasticity gap, and how are they separated?

Q4. Why does a lower elasticity flatten the Phillips curve mechanically in the model?

Q5. Doesn’t the Calvo model undercut the result, since elasticity doesn’t enter its Phillips-curve slope?

Q6. What does the quantitative exercise actually compute, and what are its limits?

Q7. What heterogeneity is documented beyond the age gradient?

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 robustness checks and caveats does the paper provide?

Key Concepts

Estimating the Interest Rate Trend in a Shadow Rate Term Structure Model

In depth

Q1. What are the two key modeling innovations?

Q2. Why use the full yield curve rather than a few selected maturities?

Q3. What are the main empirical findings about the interest rate trend?

Q4. What is the relationship between term premiums and inflation uncertainty?

Key concepts

Financial Fragility and the Fiscal Multiplier

Layer 1: Overview

In depth

Q1. What is the new mechanism (“channel”) the paper identifies, and how does it differ from prior crowding-out stories?

Q2. What are the three terms in the analytical decomposition of the lending response (equation 9)?

Q3. How is the contribution of each ingredient (maturity vs. sovereign risk) quantified?

Q4. Why does implementation timing matter, and what is the mechanism?

Q5. What heterogeneity / dimensions of variation are documented?

Q6. What is the identification/estimation strategy, and what are its limitations?

Q7. How is sovereign default modeled, and does default actually hit bank net worth in equilibrium?

Q8. What robustness checks are run (Appendix E)?

Q9. How does the paper relate to and differ from closely related prior work?

Q10. What are the three main policy recommendations and their scope conditions?

Q11. Why can the cumulative multiplier be negative even though the direct spending effect is positive?

Key Concepts

Financial Stability with Fire Sale Externalities

Layer 1: Overview