E50 | Macro Paper Warehouse

A Theory of Supply Function Choice and Aggregate Supply

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

Research Question

Modern macroeconomic models of aggregate supply universally restrict firms to price-setting — committing to a price and supplying whatever quantity the market demands. Flynn, Nikolakoudis, and Sastry ask: what happens if instead firms choose any supply function, a mapping that describes the price charged at each quantity of production? The paper develops the first general-equilibrium, macroeconomic theory of supply function choice and characterizes its implications for the slope of aggregate supply, monetary non-neutrality, and time-varying inflation-output tradeoffs.

Methodology

The paper proceeds in two stages. In partial equilibrium, a single monopolistic firm with constant-returns-to-scale technology and constant-elasticity demand faces log-normal uncertainty about demand shifters, the aggregate price level, real marginal costs, and the stochastic discount factor. The firm chooses a non-parametric supply function — any implicit mapping f(p,q) = 0 — to maximize expected real profits. The paper shows that supply function choice is equivalent to conditioning price-quantity decisions on the realized nominal demand state z = ΨP^η. The authors prove (Theorem 1) that the optimal supply function is endogenously log-linear: log p = α₀ + α₁ log q, where the inverse supply elasticity α₁ is characterized in closed form.

In general equilibrium, the authors embed supply function choice in an otherwise standard monetary business cycle model (in the tradition of Woodford 2003a and Hellwig and Venkateswaran 2009), featuring a representative household demanding differentiated goods, a money supply following a random walk with time-varying volatility, and idiosyncratic shocks to productivity, wages, and demand. They guess and verify a log-linear equilibrium and derive a scalar fixed-point equation for the equilibrium supply elasticity (Theorem 3).

For quantification, the authors calibrate structural parameters (η = 8 from Hottman et al. 2016 scanner data; γ = 0.11 from Gagliardone et al. 2023 Belgian firm data; κ^M = 0.29 calibrated to match an average aggregate supply slope of 0.11 from Hazell et al. 2022) and estimate time-varying uncertainty via a GARCH model of quarterly US data on GDP growth, inflation, and real marginal cost growth from 1960 Q1 to 2024 Q4. Idiosyncratic demand uncertainty is set proportional to aggregate TFP uncertainty using the proportionality factor R = 6.5 from Bloom et al. (2018).

Main Findings

Optimal supply function. The optimal firm-level supply function is log-linear with inverse supply elasticity α₁ determined by the relative variances and covariances of demand, the price level, and real marginal costs. Three comparative statics drive the macroeconomic results: (1) higher idiosyncratic demand uncertainty (σ²_Ψ) flattens the supply function toward price-setting, because a fixed price insulates profit markups against demand variation; (2) higher price-level uncertainty (σ²_P) steepens the supply function toward quantity-setting, because setting a fixed quantity allows relative prices to adjust; (3) lower price elasticity of demand (less elastic demand, more market power) flattens the supply function, conditional on a sufficient condition that holds in US data whenever η > 2.5.

From micro supply to aggregate supply. With fixed log-linear supply functions, the economy has a unique log-linear equilibrium with an AD/AS representation (Theorem 2). The slope of aggregate supply ε^S_t depends on ω₁ (the transformed inverse supply elasticity), κ^M (firms’ signal precision about the money supply), γ (income effects), and η (demand elasticity). Aggregate supply is maximally elastic — money is as non-neutral as possible — if and only if firms are pure price-setters (ω₁ = 0). Aggregate supply is perfectly inelastic — money is neutral — if and only if firms are quantity-setters (ω₁ = 1/η). A lower elasticity of demand flattens aggregate supply through general equilibrium strategic complementarities, a prediction opposite to the New Keynesian model.

Equilibrium supply slope and its determinants. The equilibrium ω₁ solves a fixed-point equation (Theorem 3) in which macroeconomic uncertainty shapes firms’ optimal supply functions, which in turn shape macroeconomic dynamics. Under the special case of balanced strategic interactions (ηγ = 1), the slope of aggregate supply has a clean closed form depending only on the ratio ρ_t = σ_{ϑ,t}/σ^M_{t|s} (idiosyncratic demand uncertainty relative to posterior monetary uncertainty). Critically, the equilibrium supply slope is invariant to the overall level of uncertainty — only the composition of uncertainty matters (Proposition 3). Even vanishingly small uncertainty can generate any level of monetary non-neutrality depending on uncertainty composition.

Quantitative results — United States over time. The model’s estimated slope of aggregate supply shows sharp variation since 1960. The slope is relatively flat and stable during the 1960s, the Great Moderation (1991–2007), the Great Recession (2008–2019), and the recovery from the Great Recession. It spikes dramatically during the 1970s oil crisis and the post-Covid inflation of the 2020s. Compared to Ball and Mazumder (2011), the model qualitatively matches the steepening during 1973–1984 (+58% in the model) vs. the data’s +175%, and a subsequent flattening of −25% vs. −32% in the data during 1985–2007. Compared to Cerrato and Gitti (2022), the model accounts for approximately 4/5 of the steepening between the pre-Covid and post-Covid periods (+112% model vs. +145% data). For the Hazell et al. (2022) comparison, the model accounts for approximately 1/2 of the estimated flattening from 1978–1990 to 1991–2018.

Quantitative results — Cross-country. Using OECD annual data from 1960–2019, the model’s predicted slope of aggregate supply is not positively correlated with the average level of inflation across countries. For countries with the highest inflation rates, the model predicts a negative slope of aggregate supply, driven by very high correlation between price-level uncertainty and real marginal cost uncertainty. The model-predicted slope correlates positively with the reduced-form regression coefficient of inflation on real output growth across countries, even after instrumenting for demand. This predictive power is over and above what can be explained by the level or volatility of inflation alone.

Scope Conditions

All results are derived under log-normality of uncertainty, which ensures the log-linear structure of optimal supply functions. The quantification relies on GARCH-estimated uncertainty and treats idiosyncratic demand uncertainty as proportional to aggregate TFP uncertainty. The model abstracts from microeconomic nominal price stickiness (though the authors show in Appendix B that Calvo-style sticky prices can be incorporated). The baseline model requires the equilibrium condition on firm beliefs to be consistent (rational expectations). Multiple equilibria of the scalar fixed-point are possible in principle, bounded by at most five log-linear equilibria (Proposition 2).

Q&A

Q1: What is wrong with assuming price-setting or quantity-setting as a primitive restriction on firm behavior?

A: Price-setting and quantity-setting are two isolated, generically non-optimal points in the larger space of supply functions. Corollary 2 establishes that price-setting is optimal only in the limit as idiosyncratic demand uncertainty becomes unboundedly large (σ²_Ψ → ∞), while quantity-setting is optimal only in the limit as price-level uncertainty becomes unboundedly large (σ²_P → ∞). In a macroeconomic environment where both sources of uncertainty are present in comparable magnitudes, both extreme policies perform poorly and the analyst who imposes either inadvertently restricts firms’ strategies in ways that have large macroeconomic consequences — for example, making money neutral under quantity-setting even when information frictions are present, or making the slope of aggregate supply invariant to demand elasticity under price-setting.

Q2: What is the formal equivalence between supply function choice and conditioning on realized demand?

A: The firm’s problem of choosing a supply function f(p,q) = 0 ex ante is mathematically equivalent to choosing a price-quantity plan (p(z), q(z)) indexed by the nominal demand state z = ΨP^η (Equation 4 in the paper). After the supply function is set, the firm produces where the supply function intersects the demand curve, which pins down the market-clearing outcome as a function of z. Choosing the supply function ex ante is therefore the same as choosing z-contingent prices and quantities without any parametric constraint. This links the model to rational expectations equilibrium in the spirit of Lucas (1972): firms use the demand for their product as a noisy signal to update beliefs and set their optimal price and quantity in response to realized demand conditions.

Q3: How is the optimal inverse supply elasticity α₁ derived, and what is the 2SLS interpretation?

A: Because the optimal supply function allows the firm to set a z-contingent price, the first-order condition at each realized demand state z = t equates expected marginal revenue and expected marginal cost (Equation 7). Under log-normality, this yields a log-linear relationship log p = α₀ + α₁ log q. The elasticity α₁ equals the ratio (d log p / d log z) / (d log q / d log z) = Cov[log z, log p**] / Cov[log z, log q**], where p** and q** are the full-information optimal price and quantity (Equation 9). This is formally equivalent to a 2SLS regression: the firm estimates how its optimal price should change with its optimal quantity, using the nominal demand state z as an instrument for the optimal quantity. The supply function is steep if nominal demand strongly predicts movements in the full-information optimal price (large reduced-form coefficient); it is flat if nominal demand primarily predicts movements in the full-information optimal quantity (large first-stage coefficient).

Q4: How do uncertainty and demand elasticity shape the firm’s optimal supply function in partial equilibrium?

A: Three key comparative statics apply when the supply function is upward-sloping. (1) Greater price-level uncertainty (σ²_P increases) steepens α₁ toward quantity-setting: not knowing competitors’ prices makes aggressive dynamic pricing attractive because it allows the firm’s relative price to adjust ex post. (2) Greater idiosyncratic demand uncertainty (σ²_Ψ increases) flattens α₁ toward price-setting: demand uncertainty favors a fixed price to keep the markup over real marginal costs constant, accommodating demand with quantity variation. (3) A lower price elasticity of demand (more market power, lower η) flattens α₁: more market power reduces the cost of setting the “wrong” price, reducing the benefit of dynamic pricing. Corollary 1 provides a sufficient condition — σ_{M,P} ≥ 0, 2ησ_{M,P} + σ_{M,Ψ} ≥ σ_{P,Ψ}, and α₁ ≥ 0 — under which ∂α₁/∂η > 0, implying greater market power flattens supply; the paper verifies this condition holds in US data whenever η > 2.5.

Q5: How does the model generate an aggregate supply and demand representation from supply function choices?

A: Theorem 2 establishes that, given any fixed log-linear supply functions with slope ω₁,t, there is a unique log-linear equilibrium. In this equilibrium, the price level and real output are jointly determined by an aggregate demand curve — shifting with the money supply but not productivity — and an aggregate supply curve — shifting with productivity but not the money supply. The inverse elasticity of aggregate supply is ε^S_t = γ(κ^M_t + ω₁,t(η − 1/γ)(1 − κ^M_t)) / ((1 − ω₁,t η)(1 − κ^M_t)), derived from aggregating firm-level pricing decisions. The slope depends on ω₁,t (micro supply), κ^M_t (signal precision about money), γ (income effects), and η (demand elasticity). An aggregate demand shock of ∆ log M raises the price level by ε^S_t ∆ log M / (ε^D_t + ε^S_t) and raises real output by ∆ log M / (ε^D_t + ε^S_t), where ε^D_t = γ is the inverse elasticity of aggregate demand.

Q6: What is the equilibrium fixed-point equation and why can there be multiple equilibria?

A: Theorem 3 shows that the equilibrium transformed inverse supply elasticity ω₁,t solves a quintic polynomial fixed-point equation (Equation 29) that depends on the variances of idiosyncratic demand shocks (σ²_ϑ,t), posterior uncertainty about productivity (σ^A_{t|s}), and posterior uncertainty about money (σ^M_{t|s}). Multiple equilibria can arise because of a self-reinforcing feedback: if firms set steep supply functions, prices respond more to demand, which raises price-level volatility, which in turn makes quantity-setting more attractive, further steepening supply functions. Proposition 2 establishes existence of at least one log-linear equilibrium and at most five. Idiosyncratic productivity and factor price uncertainty do not enter the fixed-point equation because the variance of real marginal costs per se does not affect optimal supply function choice — only the covariance of marginal costs with demand and the price level matters.

Q7: What determines the slope of aggregate supply in the special case of balanced strategic interactions (ηγ = 1)?

A: Under ηγ = 1 — where strategic complementarities from relative price effects exactly offset strategic substitutabilities from aggregate consumption effects — the slope of aggregate supply has the closed-form expression ε^S_t = γ(κ^M_t / (1 − κ^M_t))(1 + 1/(γ²ρ²_t κ^M_t)) where ρ_t = σ_{ϑ,t}/σ^M_{t|s} is the ratio of idiosyncratic demand uncertainty to posterior monetary uncertainty (Corollary 5). Aggregate productivity uncertainty drops out entirely because firms do not use the demand state to infer aggregate productivity when strategic interactions are balanced. As ρ_t → ∞ (idiosyncratic demand dominates), the slope converges to the price-setting value γκ^M_t/(1 − κ^M_t). As ρ_t → 0 (monetary uncertainty dominates), the slope goes to infinity, corresponding to quantity-setting and monetary neutrality.

Q8: What is the role of total uncertainty versus the composition of uncertainty?

A: Proposition 3 establishes a striking invariance result: if all standard deviations in the economy are scaled by a common factor λ > 0, the equilibrium supply elasticity and slope of aggregate supply are unchanged. The equilibrium outcomes depend only on the ratios of different sources of uncertainty, not their absolute magnitudes. This sharply distinguishes the model from menu-cost models, in which any increase in uncertainty unambiguously raises the benefit of price adjustment and steepens aggregate supply. A corollary is that idiosyncratic productivity uncertainty has no effect on the slope of aggregate supply in the supply function model, whereas it would steepen aggregate supply in Golosov-Lucas menu-cost models. Moreover, even a vanishingly small level of uncertainty can generate any level of monetary non-neutrality, because the equilibrium supply elasticity is discontinuous at zero uncertainty (ε^S_t (0) = {∞} while ε^S_t (λ) is bounded for any λ > 0).

Q9: How does market power (demand elasticity) affect the slope of aggregate supply, and why does this differ from the New Keynesian prediction?

A: In the supply function model, a lower elasticity of demand (more market power, lower η) flattens aggregate supply by reducing general-equilibrium strategic complementarities. When other firms raise their prices following a demand shock, a given firm faces higher relative demand; the strength of this effect is parameterized by η. With supply functions (ω₁,t ≠ 0), this relative demand increase generates an additional price response, so higher η steepens aggregate supply. Crucially, this effect is exactly zero if and only if firms are pure price-setters (ω₁,t = 0) — meaning the prediction that market power affects aggregate supply is absent from price-setting models. This is the opposite of the New Keynesian prediction: in Woodford (2003b) with decreasing returns to scale, a higher elasticity of demand (less market power) steepens the Phillips curve, because more elastic demand amplifies the quantity response to price changes and thereby the marginal cost response to nominal cost shocks.

Q10: How does the model rationalize the steepening of aggregate supply in the 1970s and 2020s?

A: The GARCH estimates of macroeconomic uncertainty show abrupt increases in inflation uncertainty during the 1970s oil crisis period and after the Covid-19 shock in the 2020s. In the model, a spike in aggregate price-level uncertainty (σ²_P increases) causes firms to choose steeper supply functions — closer to quantity-setting — endogenously. This steepens the aggregate supply curve so that demand shocks have larger nominal effects and smaller real effects. Quantitatively, relative to the base period, the model predicts a steepening of +58% during 1973–1984 and +112% during 2021–2023. The empirical comparisons are +175% (Ball and Mazumder 2011, 1973–1984) and +145% (Cerrato and Gitti 2022, 2021–2023). The model thus accounts for the direction and rough order of magnitude of both episodes but not their full extent. The quarterly time series of model-implied ε^S_t has a correlation of 0.93 with one-quarter-ahead inflation uncertainty and 0.62 with the quarterly level of inflation.

Q11: How does the cross-country evidence help distinguish the model from alternatives based on the level of inflation?

A: The cross-country analysis uses OECD data from 1960–2019 to construct country-level model-implied slopes of aggregate supply using the same structural parameters (η = 8, γ = 0.11, κ^M = 0.29) and country-specific GARCH uncertainty estimates from a one-lag VAR. The key finding is that the model-implied slope is not positively predicted by average inflation across countries (Panel A of Figure 5) — in fact, for the highest-inflation countries such as Chile, Israel, and Mexico, the model predicts a negative slope of aggregate supply, reflecting high correlation between price-level uncertainty and real marginal cost uncertainty. By contrast, the model-implied slope correlates positively with the reduced-form regression coefficient of inflation on real output growth (Panel B), and this positive correlation is also found using a model-derived instrument isolating exogenous monetary variation. This implies that relative uncertainties, not the mean or volatility of inflation per se, help account for cross-country heterogeneity in inflation-output tradeoffs beyond the predictions of Ball et al. (1988).

Q12: How can supply functions be integrated into larger linearized macroeconomic models?

A: Section 4.5 provides a general framework. For any model in which firms face a demand function q_it = d(p_it, z^D_it) and a value function V(p_it, q_it, z^V_it), log-linearization around a deterministic steady state yields an optimal pricing rule ˆp_it = ω₁,it ˆz^D_it (Equation 35) for some scalar ω₁,it determined by the covariance structure of the linearized model. The coefficients ω₁,it enter the standard representation of aggregate dynamics (McKay and Wolf 2023) through the ideal price index ˆP_t = ∫₀¹ ˆp_it di. The additional “rational expectations” restriction is that ω₁,it must be consistent with the equilibrium law of motion for prices. The paper argues that supply functions can thereby be embedded in the broad class of linearized DSGE models used for quantitative work, including models with decreasing returns, monopsony, endogenous markups, sticky prices, investment, and quality choice.

Q13: What are the implications of supply function choice for monetary policy discretion?

A: The model implies a thorny tradeoff for monetary policymakers. If a central bank wishes to maintain discretion — the ability to surprise private agents — this increases firms’ uncertainty about the money supply (higher σ²_M). Under balanced strategic interactions (ηγ = 1), greater posterior monetary uncertainty (σ^M_{t|s}) lowers the ratio ρ_t = σ_{ϑ,t}/σ^M_{t|s}, which flattens the aggregate supply curve (reduces ε^S_t) and thereby increases the real effect of monetary surprises. However, this also endogenously induces firms to set steeper supply functions — closer to quantity-setting — so that the aggregate supply curve steepens in response to the greater price-level uncertainty generated by such an environment. The paper therefore concludes that maintaining monetary policy discretion may be, at least partially, self-defeating.

Inverse supply elasticity (α₁): The percentage by which a firm increases its price in response to a one percent increase in production, characterizing the slope of the firm’s optimal supply function. It is endogenously log-linear and determined by the ratio of covariances relating the nominal demand state to the firm’s optimal price vs. optimal quantity under full information — formally equivalent to a 2SLS coefficient using nominal demand as an instrument.

Supply function: A mapping f(p, q) = 0 describing the locus of prices and quantities a firm commits to, as an implicit function over price-quantity pairs. Unlike price-setting (f depends only on p) or quantity-setting (f depends only on q), the general supply function allows prices to vary with realized demand, nesting both polar cases as limits of extreme uncertainty.

Nominal demand state (z): The composite variable z = ΨP^η that indexes the demand curve. Firms observing their own output market clearing can use z as a noisy signal for inference about the aggregate price level, real marginal costs, and monetary conditions. The supply function is formally equivalent to conditioning price-quantity choices on z.

Slope of aggregate supply (ε^S): The inverse elasticity of the aggregate supply curve in the AD/AS representation, measuring the relative within-period response of the price level versus real output to an aggregate demand shock. It depends on the slope of firm-level supply functions (ω₁) interacted with the information precision about the money supply (κ^M) and income effects (γ).

Transformed inverse supply elasticity (ω₁): The reparameterization ω₁ = α₁/(1 + ηα₁), where α₁ is the firm-level inverse supply elasticity and η is the price elasticity of demand. ω₁ = 0 corresponds to price-setting; ω₁ = 1/η corresponds to quantity-setting. The equilibrium value of ω₁ solves a fixed-point equation that maps macroeconomic uncertainty back into firms’ optimal supply function choices.

Balanced strategic interactions (ηγ = 1): A parametric special case in which strategic complementarities from aggregate demand externalities (parameterized by η) exactly offset strategic substitutabilities from wage pressure (parameterized by 1/γ). Under this condition, the slope of aggregate supply has a closed-form solution that depends only on the relative uncertainty about idiosyncratic demand vs. the money supply.

Relative uncertainty sufficient statistic (ρ_t): The ratio σ_{ϑ,t} / σ^M_{t|s}, measuring firms’ uncertainty about idiosyncratic demand shocks relative to posterior uncertainty about the money supply. Under balanced strategic interactions (ηγ = 1), ρ_t is the single sufficient statistic determining the equilibrium slope of aggregate supply. As ρ_t → ∞ (idiosyncratic demand uncertainty dominates), firms converge to price-setting and aggregate supply flattens; as ρ_t → 0 (monetary uncertainty dominates), firms converge to quantity-setting and aggregate supply becomes vertical.

Invariance to total uncertainty: A key property of the model: the equilibrium slope of aggregate supply is invariant to the overall scale of uncertainty (Proposition 3). Only the composition of uncertainty across idiosyncratic vs. aggregate sources and demand vs. productivity shocks matters. This distinguishes the model from menu-cost models, in which any increase in uncertainty raises the benefit of price flexibility and steepens aggregate supply regardless of uncertainty composition.

Are Inflationary Shocks Regressive? A Feasible Set Approach

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

Layer 1 — Overview

Research Question. The paper asks whether inflationary shocks are regressive, and demonstrates that the answer depends critically on the source of the shock. A single aggregate inflation statistic conceals radically different distributional consequences depending on whether inflation is driven by an oil supply contraction or by expansionary monetary policy.

Framework. The authors develop a “feasible set approach” grounded in the envelope theorem. They show that the first-order money-metric welfare effect of any macroeconomic shock on a household is summarized by the present discounted value of changes to five components of the household’s budget constraint: (1) consumption prices, (2) wage income, (3) asset dividends, (4) asset prices, and (5) government transfers. Because the envelope theorem implies that endogenous substitution responses are not welfare-relevant to a first order, no assumption about the utility function’s form or the economy’s general equilibrium structure is required. The framework is valid for generic stationary shocks that do not directly shift household preferences.

Empirical Strategy. The welfare formula requires two inputs: (i) impulse response functions (IRFs) for all prices, dividends, wages, and unemployment, estimated using internal-instrument SVAR methods applied to two identified shocks — the Kanzig (2021) oil supply news shock (instrumented by oil futures surprises around OPEC announcements) and the Gertler-Karadi (2015) monetary policy shock (instrumented by fed funds futures surprises in 30-minute windows around FOMC announcements) — and (ii) cross-sectional data on consumption bundles, labor income, and asset portfolios from the CEX, CPS, SCF, and SIPP for three education groups (high school or less, some college, college-educated) across the full lifecycle. The baseline cross-section uses 2019 data. Shocks are normalized to produce comparable aggregate inflation responses: a 10% WTI oil price increase and a 25 basis point decline in the one-year Treasury yield each generate roughly 15–16 basis points of CPI-U inflation on impact, rising to approximately 34–35 basis points after two quarters.

Main Findings. Oil supply contractions are regressive and monetary expansions are progressive, and this divergence is primarily driven by the asset price channel, not the consumption price or labor income channels.

For the 10% oil supply shock: middle-aged households with high school education or less must be paid approximately $870 (around 2% of annual consumption) to be made whole relative to their pre-shock utility; college-educated middle-aged households, by contrast, gain the equivalent of approximately $833 (1.1% of annual consumption). Younger college-educated households (still net equity accumulators) gain around $572.

For the 25 basis point monetary rate cut: low-education households approximately break even (net welfare effect near $23), while middle-aged college-educated households must be paid approximately $4,051 (around 5.5% of annual consumption) to restore their pre-shock utility. Older college-educated households must be paid approximately $851.

Why asset prices dominate. Oil supply contractions reduce equity prices (S&P500 falls approximately 2% one year post-shock) and depress dividends (approximately 82 basis points), while leaving house prices and bond prices largely unaffected. Because middle-aged college-educated households are the primary accumulators of equities, they benefit from the price decline (cheaper future accumulation), making oil shocks progressive through this channel — but regressive overall once the consumption and labor income channels (both mildly regressive) are included. Monetary expansions do the opposite: equity prices rise approximately 3 percentage points on impact, house prices rise approximately 1.5% after three years, and dividends increase. These asset price increases hurt those in the accumulation phase — disproportionately middle-aged college-educated households — creating a progressive distributional pattern.

Consumption and labor income channels. Both shocks generate disproportionate inflation in motor fuel and fuel and utilities, and low-education households spend a larger share of their budget on these goods, making the consumption channel mildly regressive for both shocks. The labor income channel differs sharply: oil shocks raise unemployment (approximately 0.15 log points for low-education households two years post-shock) and reduce weekly earnings by 0.2–0.6 log points, mildly harming low-education workers; monetary expansions reduce unemployment (approximately 0.83 log points for low-education workers one year post-shock) and similarly benefit low-education households through the labor market, pushing toward progressivity.

Scope conditions. Results apply to short-run first-order welfare effects of identified stationary macroeconomic shocks (four-year horizon). The framework does not incorporate uncertainty shocks, preference shocks, or the role of hedging motives in portfolio choice. Results concern policy shocks rather than policy rules.

Robustness. Qualitative conclusions hold across six alternative specifications: incorporating borrowing constraints (with or without empirical death rates), adjusting for unemployment insurance replacement rates (approximately 6% true average replacement rate), allowing for log-linear trends in no-shock choices, and dropping aggregate CPI controls from IRF estimation.

Layer 2 — Q&A

Q1: What is the “feasible set approach” and how does it differ from prior work on inflation incidence? A: The feasible set approach measures welfare effects through changes in the household’s entire budget constraint — consumption prices, wage income, asset dividends, asset prices, and government transfers — rather than focusing on any single channel. Prior work either examined the Fisher channel (net nominal positions), or consumption price heterogeneity, or labor income responses in isolation. The key insight is that the envelope theorem implies substitution responses are not welfare-relevant to a first order, so the money-metric welfare change is simply the discounted sum of changes in the five budget constraint components evaluated at pre-shock choices, without requiring knowledge of the utility function’s form or the economy’s general equilibrium structure.

Q2: Why is the asset price channel — rather than consumption prices — the dominant channel in both shocks? A: Asset holdings are large relative to annual consumption (net worth averages $1.5 million for college-educated and $260,000 for high-school-educated households in 2019), so even modest percentage movements in asset prices generate large dollar welfare effects. By contrast, the budget shares on the goods most responsive to both shocks (motor fuel, fuel and utilities) are relatively modest, so the consumption channel, while mildly regressive, is quantitatively small relative to the portfolio channel. The portfolio channel accounts for roughly 0.5% of consumption gains for middle-aged college-educated households under the oil shock, while the consumption channel produces losses of only about 0.1% for college-educated and 0.25% for low-education households.

Q3: How does the direction of the equity price response differ between oil and monetary shocks, and why does this create opposite distributional effects? A: An oil supply contraction reduces equity prices (approximately 2% decline one year post-shock) and dividends (approximately 82 basis points decline), while a monetary expansion raises equity prices (approximately 3 percentage points on impact, approximately 4% higher after four quarters) and increases dividends. The welfare effect of asset price changes falls on those who trade the asset, not those who merely hold it at a constant level: middle-aged college-educated households are the primary net accumulators of equity, so falling prices benefit them (they can buy more cheaply) while rising prices hurt them. This is the principal reason oil shocks appear progressive through the portfolio channel — but regressive overall — while monetary expansions are regressive through the portfolio channel and progressive overall.

Q4: What are the precise welfare numbers for oil supply shocks by education group (baseline, ages 22–65)? A: From Table 3 (baseline row, lifecycle-weighted averages for ages 25–65): households with high school or less experience a welfare loss of approximately $798; those with some college experience a loss of approximately $816; and college-educated households experience a welfare gain of approximately $494. These numbers reflect the sum of the consumption, labor income, portfolio, and transfer channels over a 16-quarter horizon, discounted at the one-year Treasury yield.

Q5: What are the precise welfare numbers for monetary policy shocks by education group (baseline, ages 25–65)? A: From Table 3 (baseline row): households with high school or less experience a small welfare gain of approximately $23; those with some college experience a welfare loss of approximately $1,278; and college-educated households experience a welfare loss of approximately $3,055. These losses for college-educated households are driven overwhelmingly by rising equity and house prices that raise the cost of planned asset accumulation.

Q6: How does the life cycle interact with the distributional incidence of both shocks? A: There is substantial heterogeneity within education groups across the life cycle because asset accumulation and decumulation patterns are age-dependent. Under oil shocks, younger college-educated households (who are net equity accumulators) gain approximately $572, middle-aged college-educated households gain approximately $833, while older college-educated households lose approximately $69 (because they hold large equity positions and lose dividend income). Under monetary shocks, middle-aged college-educated households lose the most (approximately $4,051) because they are simultaneously accumulating equities and housing, both of which become more expensive. Older college-educated households lose less (approximately $851) because rising dividends on existing holdings partially offset the asset price cost. Low-education households are approximately flat across the life cycle under monetary shocks.

Q7: How does the consumption channel compare across education groups and across the two shocks? A: The consumption channel is mildly regressive for both shocks, but of similar absolute magnitude across the two shocks because both generate similar inflation in motor fuel and fuel and utilities — the goods with the largest price response. Low-education households spend a larger share on motor fuel and fuel and utilities; as a result, they lose approximately 0.25% of consumption from the consumption channel under the oil shock, compared with less than 0.1% for college-educated households. For monetary shocks, the consumption channel affects all household types roughly equally in proportional terms.

Q8: How does the labor income channel differ between oil and monetary shocks across education groups? A: Oil shocks raise unemployment disproportionately for low-education workers (approximately 0.15 log point increase after two years, roughly 0.68 standard deviations, compared with near-zero response for college-educated workers) and reduce weekly earnings by 0.2–0.6 log points across groups. Monetary expansions reverse this: a 25 basis point rate cut reduces log unemployment by approximately 0.83 log points for low-education workers and approximately 1.96 log points for college-educated workers after one year, with limited response in conditional wages. Thus the labor income channel pushes toward regressive incidence for oil shocks and toward progressive incidence for monetary expansions, though in both cases it is quantitatively smaller than the portfolio channel.

Q9: What is the role of housing in the portfolio channel? A: Housing behaves simultaneously as a durable consumption good and a financial asset. A house price increase raises welfare for households planning to decumulate (sell) housing (primarily older households) through the portfolio channel, but also raises the implicit rental cost for those who use housing — a negative consumption-side effect. Monetary expansions raise house prices by approximately 1.5% after three years. College-educated households accumulate housing at a faster rate and earlier in the life cycle than low-education households, making them more exposed to the cost of rising house prices during the accumulation phase. This amplifies the progressive pattern of monetary shocks through the portfolio channel.

Q10: How does the paper handle the dual role of durable goods (vehicles and housing)? A: Durable goods are treated as both a consumption good and a financial asset. The utility-relevant consumption price of a durable is proportional to the price times the depreciation rate per unit of use, capturing the “implicit rent” of ownership. On the asset side, the durable enters the portfolio channel like a zero-dividend financial asset. This allows the framework to correctly attribute, for example, that a rise in house prices hurts net accumulators (through the portfolio channel) while also raising the implicit cost of housing services (through the consumption channel), rather than treating house price appreciation as an unambiguous welfare gain for homeowners.

Q11: What happens to the main conclusions when borrowing constraints are introduced? A: Incorporating net worth constraints (with either constant or empirical death rates) dampens the portfolio channel for young and middle-aged college-educated households, because rising asset prices relax borrowing constraints for these households, partially offsetting the welfare cost of more expensive accumulation. Under constant death rates with borrowing constraints, college-educated households’ oil shock welfare gain falls from +$494 to +$76; under empirical death rates, it becomes a loss of -$394. For monetary shocks, the college-educated loss falls from -$3,055 to -$1,718 (constant death rate) or -$1,036 (empirical death rates). Despite these quantitative changes, the qualitative conclusion — oil shocks are regressive, monetary expansions are progressive — holds across all specifications.

Q12: What is the implication of these findings for the policy interaction between oil shocks and monetary tightening? A: If the monetary authority responds to oil-price-induced inflation with unexpected interest rate increases, it may exacerbate the distributional consequences of the initial oil shock. An oil supply contraction is already regressive (harming low-education households through consumption prices and labor market effects); a disinflationary monetary tightening would additionally harm low-education households through the labor income channel (higher unemployment, lower wages) while partially benefiting college-educated households through lower asset prices. The paper notes this policy interaction as noteworthy, while cautioning that the results concern identified policy shocks rather than policy rules.

Q13: How are the two shocks calibrated to be comparable? A: The oil shock is normalized to a 10% increase in WTI crude oil prices (approximately one standard deviation of monthly oil price growth). The monetary shock is normalized to a 25 basis point decline in the one-year Treasury yield — chosen because it generates approximately the same aggregate CPI-U inflation response as the oil shock (approximately 15–16 basis points on impact, rising to approximately 34–35 basis points after two quarters). This normalization allows the paper to attribute the different distributional outcomes to the source of inflation rather than to differences in the aggregate inflation magnitude.

Q14: What role does the transfer channel play, and for whom? A: The transfer channel is small relative to the other three channels for the vast majority of working-age households, because transfer income is less than $100 per month for most households under age 65. Social Security payments — the bulk of transfer income — are explicitly indexed to the CPI; the paper models them as moving with CPI with a one-year lag. The transfer channel exclusively benefits older households (those receiving Social Security), and its quantitative effect is modest even there. Transfer income is more than 20 times smaller than labor and asset income for prime-age households of all education groups.

Key Concepts

Feasible set approach. The paper’s organizing framework, in which the first-order welfare impact of a macroeconomic shock is measured by how the shock changes the household’s budget constraint (consumption prices, wage income, asset dividends, asset prices, and government transfers) evaluated at the household’s pre-shock choices. Substitution responses are not welfare-relevant to a first order by the envelope theorem.

Money-metric welfare gain. The willingness-to-pay measure used throughout: the welfare change from a shock divided by the household’s marginal utility of consumption at time zero, expressed in time-zero dollars. Interpreted as an equivalent variation — the amount the household must be paid or would give up to be indifferent to receiving the shock. Used because it places households with very different utility functions on a common dollar scale.

Portfolio channel. The component of the welfare formula capturing the effect of asset price and dividend changes on household welfare. Asset price changes are welfare-relevant only for households that trade (accumulate or decumulate) the asset: rising prices benefit sellers and harm buyers; falling prices benefit buyers and harm sellers. This is distinct from the “Fisher channel” in prior literature, which focuses on net nominal positions rather than on which households are in the accumulation versus decumulation phase.

Internal instrument SVAR. The time-series estimation procedure used throughout: the pre-estimated identified shock series (oil supply news or monetary policy surprise) is included as a variable ordered first in a recursive structural VAR for each outcome variable. This separates shock identification (using the published instruments and controls from Kanzig 2021 and Gertler-Karadi 2015) from IRF estimation for each outcome variable, allowing the use of the full available sample for each outcome series.

Oil supply news shock (Kanzig 2021). An identified supply shock to oil markets, constructed from changes in oil price futures in tight windows around OPEC production announcements. Used to capture exogenous cost-push inflation driven by supply constraints rather than demand.

Monetary policy shock (Gertler-Karadi 2015). An identified demand-side shock, constructed from federal funds rate futures surprises in 30-minute windows around FOMC announcements, instrumented into a monetary SVAR. Captures exogenous interest rate cuts that generate aggregate demand expansion and inflation.

Borrowing constraint wedge. An additional term that appears in the welfare formula when households face net worth constraints. Proportional to the Lagrange multiplier on the net worth constraint, it discounts future periods more heavily when constraints bind, and adds a term for the welfare value of relaxed constraints when asset prices rise. Identified from deviations from perfect consumption smoothing using CEX lifecycle consumption data.

Consistent Evidence on Duration Dependence of Price Changes

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

Layer 1 — Overview

Research Question. This paper asks two related questions. First, can one develop a robust, distribution-free estimator for the discrete-time mixed proportional hazard (MPH) model of duration with unobserved heterogeneity? Second, what does that estimator reveal about the shape of the hazard of price changes, the role of heterogeneity in shaping aggregate price dynamics, and the distinction between regular price changes and sales?

Methodology. The authors develop a linear generalized method of moments (GMM) estimator for the discrete-time MPH model, building on identification results in Honoré (1993). The model specifies that the probability a price spell ends at duration t, conditional on surviving to t, equals the product of a product-specific frailty parameter θ (unobserved, fixed over time) and a common baseline hazard bt. The estimator exploits repeated price spells per product via moment conditions that are linear in bt, making estimation and inference straightforward. It accommodates right- and left-censored data, competing risks, and spell-specific observable characteristics, without requiring any parametric assumption on the frailty distribution. The estimator is consistent as the number of products grows, even with a short time dimension. A Hansen-Sargan J-test of overidentifying restrictions and a test of the monotone-average-type prediction are also developed.

The estimator is applied to two datasets: (1) IRI weekly store data (2001–2011), covering 30 product categories and more than 21 million products, yielding 684,919,778 pairs of durations; and (2) Online Micro Price data from Cavallo (2018), comprising approximately 250,000 products at daily frequency.

Main Findings with Quantitative Magnitudes.

Baseline hazard and heterogeneity. In the pooled IRI data, the Kaplan-Meier hazard is steeply declining throughout the entire range from 2 to 60 weeks. In contrast, the estimated baseline hazard is roughly constant until week 4 and then declines only modestly, with a noticeable spike at week 52. The ratio of the Kaplan-Meier hazard to the baseline hazard — the average type, E[θ|t] — drops by approximately 60 percent within the first 20 weeks, and continues to decline, reaching roughly 0.3 of its initial value after one year. This decomposition reveals substantial unobserved heterogeneity that accounts for a large fraction of the observed decline in the Kaplan-Meier hazard.

Implications for structural models. The finding of a decreasing baseline hazard is inconsistent with canonical state-dependent pricing models (Golosov and Lucas, 2007), which predict an increasing hazard, conditional on a given firm’s type. The decreasing baseline hazard is instead broadly consistent with time-dependent pricing models, though not with a constant-hazard (Calvo, 1983) specification.

Monetary policy impulse response. In a calibrated time-dependent pricing model with strategic complementarity (α = 0, 0.5, 0.95), the aggregate price level dynamics in the estimated heterogeneous-firm MPH economy are close to those of a homogeneous-firm economy that uses the Kaplan-Meier hazard as the common price-change hazard. The homogeneous-firm approximation is substantially closer to the MPH economy than a Taylor (1979, 1980) staggered-contract economy with the same Kaplan-Meier hazard, particularly when strategic complementarity is strong (α = 0.95). The Calvo economy provides a poor approximation due to its exponential (constant-speed) price convergence structure.

Regular versus temporary price changes. Using the competing-risks extension with spell-specific observables — classifying spells by whether they start and end with a price increase (+) or decrease (−) — the authors separately estimate four baseline hazards. The baseline hazard for consecutive price increases (b++t) is relatively flat, especially for the first 6 weeks, then flat until week 45, with a spike near one year, consistent with price-plan models. The baseline hazard for reversals (particularly b−+t, price decreases followed by price increases, associated with sales) is steeply declining. The J-test statistics are substantially lower for price trends (J++ = 3,920; J−− = 3,401) than for reversals (J+− = 8,737; J−+ = 7,910), and markedly lower than the pooled-model J = 10,498, indicating that the MPH structure fits regular price changes considerably better than sales.

Scope Conditions. Results are conditional on weekly store-level price data for mostly packaged consumer goods (30 IRI product categories). The analysis focuses on price spells of at least 2 weeks to avoid spurious duration-one spells from mid-week price changes. The maximum duration examined is 60 weeks. The comparison of estimation methods relies on the IRI data only; the Online Micro Price data confirm weekly decision-making through a spike in the daily hazard every 7 days. Comparisons with maximum likelihood estimates show that GMM recovers more heterogeneity (average type declines to 0.37 at 6 months by GMM versus 0.48 by continuous-time MLE), and that time aggregation explains most of the discrepancy between the two methods.

Layer 2 — Q&A

Q1. What is the mixed proportional hazard (MPH) model as used in this paper, and what does the estimator identify?

A1. The MPH model specifies that the hazard that a price spell ends at duration t, conditional on surviving to t, equals θ·bt, where θ is a product-specific frailty parameter drawn from an unknown distribution G and bt is a baseline hazard common to all products. The estimator, which is linear in bt, identifies the baseline hazard up to a multiplicative constant using moment conditions derived from repeated spell data, without restricting the shape of the frailty distribution. Identification relies on comparing the joint survival probabilities of two consecutive spells for the same product and exploits the symmetry implied by the MPH structure across spells.

Q2. How does the Kaplan-Meier hazard relate to the baseline hazard, and what does this relationship imply about heterogeneity?

A2. The paper proves that the Kaplan-Meier hazard Ht equals bt times E[θ|t], the mean frailty among spells surviving to duration t. Because higher-type products (those with a higher propensity to change prices) exit the pool of surviving spells earlier, E[θ|t] is strictly decreasing in t — a form of dynamic selection. The ratio Ht/bt, normalized to 1 at the start, falls to approximately 0.4 by week 20 in the pooled IRI data and to approximately 0.3 after one year, documenting that a large share of the decline in the Kaplan-Meier hazard reflects heterogeneity rather than structural negative duration dependence.

Q3. What does the estimated baseline hazard imply about structural models of price setting?

A3. A decreasing baseline hazard is inconsistent with the canonical state-dependent model of Golosov and Lucas (2007), in which a firm’s hazard of price change is increasing in the time since the last change, because larger deviations from the desired price accumulate with duration. The decreasing baseline hazard is instead consistent with time-dependent pricing models and with price-plan models where within-plan switches are costless. The mild spike at week 52 in the baseline hazard is consistent with Taylor-type annual pricing rules.

Q4. What is the approximate aggregation result for monetary policy, and how quantitatively accurate is it?

A4. In the time-dependent pricing model without strategic complementarity (α = 0), the impulse response of the aggregate price level to a monetary shock in a heterogeneous-firm economy is exactly the same as in a homogeneous-firm economy whose single firm uses the Kaplan-Meier survival function. This extends Carvalho and Schwartzman (2015) to an approximation in the case with strategic complementarity (α = 0.5 and α = 0.95). Numerically, the path of aggregate prices in the estimated MPH economy is close to that in the homogeneous-firm Kaplan-Meier economy, and substantially closer to it than to the Taylor-contract economy — the difference is most pronounced at horizons beyond about half a year when α = 0.95, where the Taylor economy shows notably slower initial convergence and faster later convergence relative to the MPH and homogeneous economies.

Q5. How do the paper’s results differ from those obtained using maximum likelihood estimation of the continuous-time MPH model?

A5. The GMM estimator recovers substantially more heterogeneity than maximum likelihood (MLE) applied to the continuous-time model with continuous records (assumed gamma frailty). The average type falls from 1 to 0.37 at six months under GMM, versus only 0.48 under MLE. The authors investigate two sources of this discrepancy: the assumed frailty distribution family (gamma) and time aggregation. They conclude that time aggregation is quantitatively more important in the IRI weekly data — that is, the continuous-time MLE approach fails to properly account for the discrete nature of the data-generating process, leading it to understate heterogeneity and recover a steeper baseline hazard.

Q6. How does the paper distinguish regular price changes from sales without directly observing a sales flag?

A6. The competing-risks extension classifies each spell by whether it starts with a price increase or decrease (observable characteristic χ ∈ {+, −}) and by whether it ends with a price increase or decrease (competing risk ρ ∈ {+, −}). Price trends — spells where the direction is the same at both the start and end (++ or −−) — are interpreted as regular price changes; price reversals (especially −+, i.e., price decrease followed by increase) are associated with sales. This approach is consistent with the statistical model used for estimation, avoids the bias from simply dropping suspected sales spells before estimation, and allows the MPH structure to hold only for the risks of interest even if it fails for others.

Q7. How well does the MPH model fit regular price changes versus sales?

A7. The J-test of overidentifying restrictions yields test statistics of J++ = 3,920 for consecutive price increases and J−− = 3,401 for consecutive price decreases, compared with J = 10,498 for the pooled model and J+− = 8,737 and J−+ = 7,910 for the reversal hazards. All rejections are at conventional significance levels (critical value 1,749 at 5%), but the rejection is substantially milder for price trends than for price reversals. For individual product categories, the model cannot be rejected for 8 categories (out of 30) for b++ and 21 categories for b−−, suggesting the MPH structure is a much better description of regular price changes than of sales.

Q8. What role do one-week price spells play in the data, and why are they excluded?

A8. In the IRI data, prices are measured as the ratio of weekly revenue to quantity, so a price change occurring mid-week generates a spurious price spell of duration one week. If all spells including one-week spells are retained, the autocorrelation of spell durations is only 0.029 in levels and even negative (−0.042) in logs, which is inconsistent with a mixture model. Once one-week spells are excluded, the autocorrelation rises to 0.235 in levels and 0.233 in logs, and is stable when two-week spells are also excluded (0.248 and 0.256). The paper therefore sets the lower duration bound at T̲ = 2 weeks.

Q9. What does the daily Online Micro Price data add relative to the weekly IRI data?

A9. The daily data reveal a sharp spike in the price-change hazard every seven days, suggesting that even when prices are observed daily, the decision to change prices is made at the weekly frequency. This justifies the use of a discrete-time model with a one-week period. The estimates from daily and weekly aggregations of the same data are broadly similar, though weekly data recovers somewhat less heterogeneity than daily data. Aggregating IRI weekly data to monthly frequency understates heterogeneity even more, confirming that frequency matters for measuring heterogeneity.

Q10. What are the computational advantages of the GMM estimator relative to maximum likelihood?

A10. Because the moment conditions are linear in the baseline hazard bt, the GMM estimator is obtained in closed form, making estimation fast and inference straightforward. On the pooled IRI sample, GMM estimation (including standard errors) required 70 minutes on a machine with 60 GB memory, whereas the maximum likelihood estimator required 15 hours on a machine with 256 GB memory and failed entirely on the 60 GB machine. The GMM approach also avoids the need to specify the frailty distribution family and guarantees a global solution (proved by the identification result), whereas the likelihood function is non-linear in bt and may have multiple local maxima.

Q11. What is the shape of the b++ baseline hazard for regular price increases, and what models does it support?

A11. The baseline hazard for spells starting and ending with a price increase (b++) is decreasing during the first 6 weeks — dropping by almost 50% — and then flat until approximately week 45, with a pronounced spike at around one year. This shape is consistent with price-plan models (Eichenbaum, Jaimovich, and Rebelo, 2011) with Calvo-type switching between plans, where within-plan changes are costless and the hazard of between-plan switching is approximately constant. The annual spike is consistent with Taylor-type pricing. Approximately 76.8% of complete spells starting after a price increase last at most 6 weeks.

Key Concepts

Baseline hazard (bt). The component of the MPH hazard that is common to all products and may vary arbitrarily with elapsed duration t. It represents structural duration dependence — the tendency for a given product to be more or less likely to change price as a function of how long its current spell has lasted — net of heterogeneity. It is identified only up to a multiplicative constant.

Frailty parameter (θ) / frailty distribution (G). The product-specific scaling factor in the MPH model, fixed over all spells for a given product, that captures permanent unobserved differences in price-change frequency across products. The paper treats G as a nuisance parameter and does not require a parametric assumption on its shape. A higher θ means the product has a higher baseline propensity to change its price.

Average type (E[θ|t]). The mean frailty parameter among spells that have survived to at least duration t. Because high-type products change price earlier and exit the pool of surviving spells first, the average type is provably strictly decreasing in t under the MPH model. It is measured as the ratio of the Kaplan-Meier hazard to the baseline hazard, and its rate of decline measures the importance of dynamic selection.

Kaplan-Meier hazard (Ht). The probability that a randomly drawn spell ends at duration t, conditional on having lasted at least t periods. It mixes together structural duration dependence (captured by bt) and dynamic selection (captured by changes in the average type). It can be estimated without imposing the MPH structure, requiring only stationarity of the duration process.

Competing risks. The framework in which a price spell can end for multiple distinct reasons — here, ending with a price increase or a price decrease — each with its own hazard function. The paper’s GMM approach allows the MPH structure to hold for only a subset of risks and observables, without imposing any structure on the remaining risks.

Price trends vs. price reversals. A classification of spells based on the direction of the surrounding price changes. Price trends are spells where the direction of the price change at the start and end of the spell is the same (++ or −−), interpreted as regular price changes. Price reversals are spells where the direction switches (e.g., −+, a price decrease followed by a price increase), associated with sales and other temporary price changes.

Strategic complementarity in pricing (α). The degree to which a firm’s target price responds to the average price set by other firms. Parameterized by α ∈ [0, 1), where α = 0 yields the exact aggregation result (only the Kaplan-Meier hazard matters) and higher α increases aggregate price stickiness by making firms reluctant to deviate from the average price when few others are adjusting.

Dynamic selection. The mechanism by which the composition of the pool of surviving price spells shifts toward lower-type (more price-sticky) products as duration increases, because higher-type products change price sooner and exit the pool. This is the source of the gap between the steeply declining Kaplan-Meier hazard and the more modestly declining baseline hazard.

Firm Quality Dynamics and the Slippery Slope of Credit Intervention

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

Crises have cleansing effects—low-quality firms face greater financial shortfalls and invest less than high-quality firms—but public credit support dampens these effects by reducing financing cost differentials, distorting the firm quality distribution downward and reducing total productivity. This trade-off between preserving output capacity and distorting quality determines the optimal size of intervention. The distortionary effects are self-perpetuating: a downward bias in quality necessitates interventions of greater scale in future crises, implying further distortions—a “slippery slope.” The distortions are amplified by expectations: because low-quality firms expect underpriced government funding in future crises, their Tobin’s q is biased upward, leading them to overinvest even in normal times, while high-quality firms may underinvest. A low interest rate environment exacerbates the distortionary effects because the low yield on savings discourages firms from accumulating precautionary internal liquidity against crises.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What are the cleansing effects of crises and how does credit intervention dampen them?

Crises have cleansing effects because low-quality firms face tighter financial constraints and have lower Tobin’s q, causing them to invest less than high-quality firms; public credit support reduces this differential, preserving overall production capacity but distorting the quality distribution downward. The model follows the limited-commitment literature (Kehoe-Levine, Kiyotaki-Moore, Rampini-Viswanathan): firms differ in productive capital quality that also serves as collateral. Government intervention is valued because the government has superior enforcement ability compared to private investors, but its credit support cannot be perfectly priced by quality—due to informational limits or political constraints—so it pulls financing costs of high- and low-quality firms closer together, dampening the cleansing mechanism.

Q2. What is the “slippery slope” mechanism?

The slippery slope arises because the downward bias in the quality distribution induced by one intervention necessitates larger interventions in future crises, generating a ratchet toward ever-larger public credit support. After intervention, high-quality firms accumulate capital less rapidly than they would absent intervention, while low-quality firms’ capital shares remain higher than in the laissez-faire equilibrium. The resulting lower aggregate productivity means that future crises are more severe in terms of output loss, requiring a larger optimal intervention, which in turn further distorts the quality distribution.

Q3. How do expectations of future intervention amplify the distortions?

Because low-quality firms expect underpriced credit support in future crises, their Tobin’s q is biased upward, motivating them to overinvest even in normal times; simultaneously, high-quality firms may underinvest because their Tobin’s q may fall below the first-best level. The self-perpetuating distortion thus operates through both the crisis-time reallocation channel and the pre-crisis investment channel, amplifying the divergence from the efficient allocation relative to a setting with no anticipation effects.

Q4. Why does a low interest rate environment exacerbate the distortionary effects?

A low interest rate environment exacerbates the distortionary effects of credit intervention because the low yield on savings discourages high-quality firms from accumulating precautionary internal liquidity against crises, causing them to invest less in crises and requiring a greater scale of credit support. Low-quality firms, expecting underpriced government funding, have even less incentive to self-insure through savings when interest rates are low, further worsening the quality distribution. The paper’s findings echo cautions against ultra-low interest rates (Brunnermeier and Koby, 2018; Quadrini, 2020) by providing a distinct mechanism operating through firm quality dynamics.

Q5. Can intervention be welfare-improving despite the distortions?

The paper shows that when carefully designed, intervention can improve welfare even though it generates distortionary effects on the firm quality distribution—the trade-off between preserving production capacity and distorting quality determines the optimal size of intervention. This framing does not suggest intervention should be avoided, but that its optimal scale requires balancing the quantity-preserving benefit against the quality-distorting cost. The paper previously circulated as “The Distortionary Effects of Central Bank Direct Lending on Firm Quality Dynamics.”

Key concepts

cleansing effect of crises : the tendency for crises to reduce the investment of low-quality firms relative to high-quality firms through tighter financial constraints, reallocating capital toward higher-productivity uses; credit intervention dampens this by reducing the financing cost differential. slippery slope of intervention : the self-perpetuating dynamic in which intervention-induced downward distortion of the quality distribution necessitates larger interventions in future crises, generating a ratchet toward ever-larger public credit support. credit mispricing : the inability of public credit support to differentiate financing costs by firm quality, arising from informational limits or political constraints on discriminatory treatment; the proximate source of the quality-distribution distortion.

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.

Layer 2 — Q&A

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.

Q2: What share of 2-year yield variation do the three shocks each explain over the full sample?

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.

Political Pressure on the Fed

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

This paper combines a hand-collected archival data set of over 800 personal interactions between U.S. Presidents and Federal Reserve officials from 1933 to 2016 with a narrative structural VAR to identify shocks to political pressure on the Fed and quantify their macroeconomic effects. The identification strategy exploits the well-documented Nixon-Burns episode of 1971—corroborated by Nixon Tapes recordings and Burns’s personal diary—as a narrative restriction that the spike in personal interactions that year was driven primarily by a political pressure shock rather than by economic conditions. Political pressure shocks are found to (i) increase inflation strongly and persistently, (ii) lead to statistically weak negative effects on activity, (iii) contribute to inflationary episodes outside the Nixon era, and (iv) transmit differently from standard expansionary monetary policy shocks because political pressure can be publicly observed, generating a stronger direct effect on inflation expectations. Quantitatively, increasing political pressure by half as much as Nixon, sustained for six months, is estimated to raise the price level by more than 8%.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the narrative identification strategy and how is the Nixon-Burns episode exploited?

The identification strategy imposes that the spike in President-Fed personal interactions in 1971 is mainly driven by a political pressure shock, exploiting the well-documented fact that Nixon pressured Burns to ease monetary policy in the run-up to his 1972 re-election. Recordings from the “Nixon Tapes” and Burns’s personal diary corroborate this interpretation: Burns wrote that “the President will do anything to be reelected” and that Nixon urged him to “start expanding the money supply.” Romer and Romer (2004) estimated large easing shocks to monetary policy prior to Nixon’s re-election, contrasting with a large systematic tightening after it, further supporting that Burns eased in response to the pressure. Narrative evidence from Johnson’s pressure in the 1960s is additionally used to strengthen the identification.

Q2. What does the new data on President-Fed personal interactions show?

The paper hand-collects over 800 personal interactions between U.S. Presidents and Fed officials from the historical daily schedules made available by the Presidential Libraries from Franklin D. Roosevelt (1933) through Barack Obama (2016). The average interaction lasts 53 minutes; 36% are one-on-one; 11% occur on weekends; 16% are in social settings such as dinners; 92% involve the Fed Chair and 8% other Fed officials. There is large variation across administrations: President Nixon interacted with Fed officials 160 times, while only 6 interactions occurred under Clinton. These interactions arise endogenously in response to economic conditions, which is why narrative identification is needed to isolate the political pressure component.

Q3. What are the estimated macroeconomic effects of political pressure shocks?

Political pressure shocks are found to increase inflation strongly and persistently, to have statistically weak negative effects on activity, and a pressure shock half as large as Nixon’s sustained over six months is estimated to raise the price level by more than 8%. The weak activity effect distinguishes these shocks from standard demand expansions; the mechanism operates more through expectations channels than through aggregate demand, consistent with the public observability of political pressure on the central bank. The evidence also suggests political pressure shocks contributed to inflationary episodes in periods beyond the Nixon era.

Q4. Why do political pressure shocks transmit differently from conventional monetary policy easing shocks?

Political pressure shocks transmit differently from standard expansionary monetary policy shocks primarily because political pressure on the Fed can be publicly observed, which generates a stronger direct effect on inflation expectations than a private Fed decision to ease. The paper finds a stronger effect of political pressure shocks on inflation expectations relative to the activity effect, consistent with this channel: when the public observes that the President is pressuring the central bank, expected inflation rises even before the Fed acts on that pressure.

Key concepts

President-Fed personal interactions : face-to-face or telephone contacts between U.S. Presidents and Federal Reserve officials recorded in historical presidential daily schedules 1933–2016; used as a noisy observable proxy for political attention to the Fed, from which a political pressure shock series is extracted via narrative restrictions.

political pressure shock : an exogenous, structurally identified shock to the intensity of political influence on Fed policy, isolated using a narrative SVAR restriction that the 1971 Nixon-Burns spike in interactions was driven by political pressure rather than economic conditions.

narrative identification : an approach that imposes sign or zero restrictions on a structural VAR at specific historical episodes known from external archival evidence to be driven predominantly by a particular structural shock; here used to exploit the Nixon-Burns and Johnson-Fed pressure episodes.