Inflation | Macro Paper Warehouse

Did the US Really Grow Out of Its World War II Debt?

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

Layer 1: Overview

Research question and motivation. The fall in the US federal debt-held-by-the-public/GDP ratio from a postwar peak of 106% in fiscal year 1946 to a trough of 23% in 1974 is widely cited (Elmendorf-Mankiw, Krugman) as evidence that an economy “grows out of” debt because the GDP growth rate exceeds the interest rate on government debt (r < g). That narrative underpins the modern view (Blanchard 2019; Furman-Summers 2020) that high public debt “may have no fiscal cost.” Acalin and Ball ask how much of the postwar debt decline was genuinely due to growth exceeding undistorted real interest rates, versus three other factors: primary budget surpluses, the Fed’s 1942-1951 interest-rate peg before the Fed-Treasury Accord, and surprise inflation.

Method and data. The authors simulate counterfactual debt/GDP paths from the standard debt-dynamics identity D_t = (1+i_t)D_{t-1} - P_t, starting from the actual 1946 debt level and holding nominal GDP fixed at its historical path. They build three counterfactuals: (i) “primary balance” (set primary surplus to zero each year); (ii) “adjusted interest rate” (remove distortions from both the peg and surprise inflation); and (iii) “combined” (both), whose path is driven purely by r* - g, the undistorted real rate minus growth. A key innovation is measuring the “reverse maturity structure” — the fractions of currently outstanding debt issued in each past year — using Hall-Payne-Sargent (2018) data for 1942-1960 and CRSP thereafter. They construct a term structure of inflation expectations from one-year (Livingston, SPF) and ten-year (FRB/US) survey data, and estimate undistorted peg-era real rates from ex-ante real rates on securities issued in 1952-1961. T-bills and TIPS are assumed unaffected by inflation surprises (conservative). Debt is par value, held by the public, by fiscal year.

Main quantitative findings. In the combined counterfactual, debt/GDP falls only to 74% in 1974 (vs. 23% actual); the individual counterfactuals give 40% (primary balance) and 51% (adjusted rate) in 1974. Of the actual 83-point fall (106 to 23), 51 points are explained by surpluses plus rate distortions, decomposed as 17 points from surpluses alone, 28 from rate distortions alone, and 6 from their interaction; only 32 points (the fall to 74%) reflect growth net of undistorted rates. Extending to the present, the combined counterfactual ratio starts rising in 1980, dipping to 70% in 1979 before climbing to 84% in 2022 — only 22 points below the 1946 level of 106. Over the full 76 years, undistorted growth alone would have cut debt/GDP by just 22 points. The post-1979 reversal reflects a sign change in r* - g: average r* rose from 2.3% (1947-1979) to 2.8% (1980-2022) while average g fell from 3.5% to 2.6%. The estimated undistorted real-rate term structure is 1.7% (1yr), 2.2% (5yr), 2.5% (10yr), 2.7% (30yr).

Mechanisms and implications. Primary surpluses averaged 1.1% of GDP over 1947-1974 (peaking at 6.3% in 1948), then turned to persistent deficits. The peg (caps of 0.375% on bills to 2.5% on 30-year bonds) combined with post-1946 inflation surges (CPI averaging 7.1% in FY1947-1951) produced deeply negative ex-post real rates; the aggregate interest-rate adjustment x_t reached 13 points in 1947 and 8 points in 1951. Policy implication: the distortions are unlikely to recur (no peg/price controls planned, Fed committed to low inflation, shorter average maturity — down from 4.4 years in 1951 to 2.2 years in 2022 — blunts inflation’s effect), so substantially reducing today’s 97% (FY2022) ratio will likely require primary surpluses, which CBO projections suggest are not forthcoming.

In depth

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

There is no causal identification in the econometric sense; the strategy is an accounting simulation of the debt-dynamics identity under counterfactual interest rates and primary balances, holding nominal GDP (and real GDP and undistorted real rates) fixed at historical values. Threats: (1) the undistorted peg-era real rates are unobserved and must be guessed from 1952-1961 ex-ante real rates; (2) the reverse maturity structure (weights w) is held at historical levels even though higher counterfactual debt would alter issuance; (3) general-equilibrium feedback is ignored — higher counterfactual debt would raise real rates and crowd out capital, lowering GDP, both of which would push debt/GDP even higher, so the authors interpret their paths as LOWER BOUNDS; (4) pre-1943 debt is not adjusted for surprise inflation because long-term expectations data do not exist before 1943, which the authors argue biases against finding a large inflation role.

Q2. How are the effects of the peg and surprise inflation distinguished, and can they be separated?

The adjusted-interest-rate scenario removes both jointly. The authors state it would be difficult to separate them cleanly because that requires measures of expected inflation during the peg period (1942-1951), and there are no data on long-term inflation expectations before 1951 or short-term expectations before 1947 (start of Livingston). For post-1952 debt, the surprise-inflation adjustment is pi_t minus the expectation formed when the security was issued; for peg-era debt the adjustment is the gap between the ex-post real rate and the assumed undistorted real rate.

Q3. What is the decomposition relative to Hall and Sargent (2011)?

Hall-Sargent decompose the 1946-1974 debt/GDP change into r-g and primary surpluses but do not ask how interest-rate distortions shape r-g. Replicating their approach (Table 2A), the authors attribute -48.1 points to r-g and -29.6 points to primary surpluses (the terms sum to -78 points, less than the actual -82.9 because of the debt-dynamics residual). The paper’s extension (Table 2B) splits the -48.1 r-g contribution into only -11.7 points from r*-g (undistorted) and -36.3 points from the distortion r-r*, with surpluses still -29.6. So most of the apparent ‘growth out of debt’ was actually interest-rate distortion.

Q4. Why do the Table 2 surplus contributions differ from the Table 1 scenario differences?

In Table 2 surpluses contribute -29.6 points, larger than the 17-point effect implied by the Table 1 difference between actual 1974 debt/GDP and the primary-balance scenario. The reason is an interaction: eliminating surpluses raises the debt path d_{t-1}, which magnifies the r-g term, so additional debt is partly eroded by r-g. The authors call the Figure 7 / Table 1 scenario paths the more precise representation.

Q5. How do the findings reconcile with Blanchard’s (2019) claim that r < g since 1979?

The authors find r > g on average since 1979 (even in the primary-balance counterfactual with actual ex-post rates), so debt/GDP would rise. The difference from Blanchard is purely measurement: (1) they use the government’s interest payments on outstanding debt — the rates set at issuance — whereas Blanchard uses current market yields (a weighted average of 1- and 10-year Treasury rates), which since 1979 have been lower because rates trended down; (2) the authors use pre-tax rates while Blanchard uses after-tax rates. Figure A.11 confirms: with the authors’ measure debt/GDP rises 1979-2022; with Blanchard’s pre-tax market yields it rises then falls back near its 1979 level; with his after-tax rates it falls significantly. The authors argue the rate paid by the government is the relevant one for the debt-dynamics identity, and that a natural baseline assumes debt has no net effect on tax revenue (so pre-tax rates apply).

Q6. What is a notable nuance about the post-1979 period in the primary-balance counterfactual?

The post-1979 rise in debt/GDP is LARGER in the primary-balance counterfactual (19 points, from 34% to 53%) than in the combined counterfactual (14 points). This is because inflation surprises since 1979 have on average been negative (post-Volcker disinflation, actual below expected), raising ex-post real rates and thus debt/GDP. It confirms that actual r has exceeded g since 1979.

Q7. What robustness checks are run?

(1) Undistorted peg-era real rates shifted by +/-0.5% and +/-1% across the whole term structure: 1974 combined debt/GDP ranges from 67% (-1%) to 81% (+1%) around the 74% baseline; 2022 ranges from 78% to 91% around 84% (Table A.2). (2) Pre-1962 interest measured by net interest times 1.1; using net interest directly gives 73% in 1974 and 83% in 2022 vs. 74% and 84% baseline. (3) The debt-dynamics residual epsilon (mainly Treasury cash balances) is held at historical values; setting it to zero gives a combined counterfactual of 78% in 1974 and 77% in 2022, showing the residual contributed -0.19% GDP/year on average over 1947-1974 and +0.25% over 1975-2022. (4) Term-structure shape assumptions and the GDP-deflator-vs-CPI expectation-error approximation are checked in the Appendix as reasonable.

Q8. What heterogeneity across the debt structure matters?

The reverse maturity structure is central: the share of debt with reverse maturities above five years peaked at 48% in 1951 (long-term WWII bonds), then fell, fluctuating between 10% and 25% from 1975-2022; average reverse maturity fell from 4.4 years in 1951 to 2.2 years in 2022. Shorter maturity means inflation surprises erode less debt — a reason later inflation surprises had smaller effects than the 1940s-1970s ones. T-bills (assumed unaffected by surprise inflation since rolled over at adjusting rates) and TIPS (post-1997, indexed) are excluded from the inflation-surprise adjustment. Non-marketable debt fell from 23% of total in 1960 to 3% in 2022; its reverse maturity structure is assumed constant after 1960.

Q9. What are the timing/measurement complications?

Unit is fiscal year (July-June before FY1977, October-September after), creating a ‘Transitional Quarter’ in Q3 1976 requiring special handling. Inflation is GDP-deflator growth. Pre-1970 deflator expectations are proxied from Livingston CPI forecasts assuming equal expectation errors for CPI and deflator. Ten-year expectations before 1968 are fitted from one-year expectations via a regression (1968-1997) with a negative coefficient (-1.549) on the change in smoothed one-year expectations, capturing long-term expectations lagging short-term moves.

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

Because the postwar debt reduction came largely from one-off distortions (the peg with price controls, and surprise inflation) unlikely to recur — and the Fed is committed to low inflation while shorter average maturity weakens inflation’s erosive power — economic growth alone is unlikely to resolve the current ~97% (FY2022) ratio. Substantial reduction will probably require primary surpluses, which CBO projects will not occur under current policy (large primary deficits forecast for three decades). Scope conditions: results are lower bounds (GE crowding-out omitted); they depend on the assumed undistorted real-rate term structure; the 2021-2022 inflation surge is again temporarily reducing debt/GDP.

Key Concepts

Dispersion Over the Business Cycle: Passthrough, Productivity, and Demand

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

Layer 1: Overview

Carlsson, Clymo, and Joslin use Swedish manufacturing firm-level microdata for 1998–2013 to separately identify and characterize the cyclical behavior of physical productivity (TFPQ) shocks and demand shocks at the firm level, two forces that are observationally equivalent under the standard CES-demand benchmark. The paper’s central contribution is threefold: it documents new empirical facts about dispersion cyclicality, estimates a non-constant-elasticity (non-CES) demand curve directly from firm-level price and quantity data, and embeds those estimates into a quantitative heterogeneous-firm model to study the aggregate consequences of each type of dispersion shock.

The data combine four Swedish register sources: the Företagens Ekonomi (FEK) survey for bookkeeping variables; the Industrins Varuproduktion (IVP) survey for 8-digit product-level price and quantity data used to construct firm-level price indices; the Konjunkturstatistik för Industrin (KFI) survey for quarterly capacity-utilization data; and additional investment deflators. The unbalanced panel contains 3,181 unique manufacturing firms and 15,044 firm-year observations. TFPQ is measured using a Cobb-Douglas value-added production function with factor utilization adjustment; factor elasticities are estimated via cost shares at the 2-digit sector level, yielding an average labor share of 0.735.

Demand is estimated using the Gopinath-Itskhoki-Rigobon (GIR) flexible demand curve, which nests CES as the limiting case. TFPQ innovations instrument for price in a second-order approximation, following Foster, Haltiwanger, and Syverson (2008). The main-sample estimates yield theta = 2.94 (average elasticity) and eta = 4.27 (super-elasticity), both significant at the 1% level. The second-order price term is statistically significant at the 5% level in all three samples, decisively rejecting CES. These estimates imply that a 5% price increase raises the demand elasticity from 2.94 to 3.74, while a 5% price reduction reduces it to 2.42, creating a “real rigidity” in the sense of Ball and Romer (1990): raising price loses many customers while lowering it gains few.

Incomplete passthrough of TFPQ shocks is a central empirical finding. OLS estimates yield beta_z = -0.124; first-difference estimates yield -0.097. Even in the subsample of firms that adjusted all product-level prices in a given year, TFPQ passthrough remains near -0.10, ruling out Calvo or menu-cost price stickiness as the sole driver. Longer-horizon (two- and three-year) first-difference regressions produce similar estimates, ruling out Rotemberg gradual adjustment as well. The non-CES demand curve alone implies a static-optimal passthrough of theta/(theta + eta) = 3/(3 + 4.3) = 41%, so real rigidity explains most of the incompleteness even before accounting for adjustment costs. Demand shocks pass through to prices at a rate of 0.209-0.235, a non-zero result rationalized in the quantitative model by input adjustment costs.

On cyclicality of dispersion, both TFPQ and demand shock dispersion are countercyclical, but demand dispersion rises by more and is more robust across recession episodes. In 2009 (the Great Recession), the IQR of demand shock growth was 56% above its non-recession average, while the IQR of TFPQ shock growth rose 36%. Sales dispersion rose 58% (IQR) in 2009. A semi-structural variance decomposition shows that demand shocks account for 63% of average sales growth dispersion and approximately 80% of its increase in 2009; TFPQ dispersion contributes only marginally to sales dispersion because the TFPQ variance is shrunk by a factor of roughly 25 on its way to sales growth through the chain of low passthrough and demand elasticity. Demand accounts for about 50% of average price growth dispersion and 40% of its cyclical increase in 2009; TFPQ accounts for about 10% of price dispersion on average.

The quantitative heterogeneous-firm model extends Bloom (2009) and Bloom et al. (2018) to continuous time with both TFPQ and demand shocks, non-CES demand (theta = 3, eta = 4.3 from the estimates), and non-convex input adjustment costs on a composite scale factor covering both capital and labor. The resale loss kappa = 0.3565 is taken from Bloom et al. (2018). The model is calibrated to match IQRs of 0.2 for TFPQ and demand shock log-changes in the low-uncertainty state, consistent with pre-crisis Swedish data. For the high-uncertainty state, the calibration targets the Great Recession peaks: a 30% rise in TFPQ dispersion (sigma_z(2) = 1.38 sigma_z(1)) and a 60% rise in demand dispersion (sigma_epsilon(2) = 1.90 sigma_epsilon(1)), reflecting the empirical finding that demand dispersion increases more.

A simulated transition to the high-uncertainty state causes aggregate output to fall by 3.5%. Decomposing into the Bloom (2009) “volatility effect” (realized shocks drawn from the high-dispersion distribution, firms believe low) and “uncertainty effect” (firms believe high, shocks drawn from low distribution), the paper finds both effects are negative in the non-CES model, in sharp contrast to Bloom (2009) where the volatility effect is positive (the Oi-Hartman-Abel effect). Non-CES demand amplifies the total output decline by approximately 40% relative to the CES model (peak fall 2.5% vs. 1.75%), primarily by reversing the sign of the volatility effect. Increased demand dispersion drives almost all of the first-year output decline and the majority of the uncertainty effect; TFPQ dispersion is the main driver of the negative volatility effect via markup dispersion. The inaction rate among firms jumps from 50% to 95% on impact of the uncertainty shock, then recovers within one year. TFPQ uncertainty induces little wait-and-see behavior because firms optimally adjust inputs by only 23% of the TFPQ shock size (versus 200% under CES), so uncertainty about TFPQ translates mainly into markup uncertainty. Demand uncertainty triggers strong wait-and-see behavior because demand directly maps one-for-one into desired input use.

In depth

Q1. What is the paper’s core identification strategy for separating TFPQ and demand shocks, and what are the main threats?

The authors identify TFPQ from a utilization-adjusted Cobb-Douglas value-added production function, then estimate demand using TFPQ innovations as instruments for price. TFPQ innovations are valid instruments because they shift marginal cost without directly shifting demand, tracing out the demand curve. The utilization adjustment (from the KFI managerial survey) is critical: without it, demand shocks that reduce utilization would appear as negative TFPQ shocks, biasing demand elasticity estimates upward and breaking instrument validity. The paper validates the adjustment by showing that firms reporting ‘insufficient demand’ exhibit 15% lower utilization on average, and 23% lower during the Great Recession. A second threat is quality change in firm-level prices; the authors address this with (a) robustness using the Eslava et al. (2023) CUPI quality-adjusted price index and (b) a single-product-firm subsample. Demand and passthrough results are similar across all three price index approaches. The within-firm focus (demeaning by firm and sector-year fixed effects throughout) mitigates cross-sectional comparability issues but limits misallocation-level analyses analogous to Hsieh and Klenow (2009).

Q2. How is the non-CES demand curve identified, and what exactly does the super-elasticity parameter eta measure?

The GIR demand curve is q = (1 - eta * log p)^(theta/eta). A second-order approximation around the firm’s average price yields log q = -theta * p_hat - (etatheta/2) * p_hat^2 + fixed effects + epsilon, where p_hat is the firm’s demeaned log relative price. Regressing real sales on p_hat and p_hat^2, instrumented by demeaned TFPQ and its square, recovers theta = -b1 and eta = 2b2/b1. Because p_hat is demeaned at the firm level, the estimates capture within-firm nonlinearity in the price-sales relationship, not cross-sectional heterogeneity in elasticity levels. The parameter eta is the ‘super-elasticity’: it measures how much the demand elasticity itself changes with the price. When eta > 0, a firm that raises its price faces an increasingly elastic demand curve (loses customers rapidly), and one that lowers its price faces a less elastic curve (gains customers slowly). The estimated eta = 4.27 in the main sample is roughly half the value of 10 studied (but not estimated) in Klenow and Willis (2016) and larger than the approximately 2 used in Berger and Vavra (2019).

Q3. How does the paper distinguish the ‘volatility effect’ from the ‘uncertainty effect’ in the quantitative model?

Following Bloom (2009), the paper simulates two counterfactuals. The uncertainty effect holds shocks drawn from the low-dispersion distribution (s=1) but lets firms believe that the high-uncertainty state (s=2) has arrived; this isolates the precautionary wait-and-see channel. The volatility effect draws shocks from the high-dispersion distribution (s=2) but lets firms believe they are in the low-uncertainty state; this isolates the direct effect of realizing more extreme shocks on aggregate output. In the non-CES model, both effects are negative. The uncertainty effect is dominated by demand uncertainty because demand shocks directly affect desired input use one-for-one, so uncertainty about future demand creates strong incentives to pause investment. TFPQ uncertainty induces little wait-and-see behavior because the optimal scale adjustment to a TFPQ shock is only 23% of the shock magnitude (vs. 200% under CES). The volatility effect is dominated by TFPQ dispersion because realized TFPQ shocks generate markup dispersion via incomplete passthrough, creating misallocation. Under CES, the volatility effect from TFPQ is positive (OHA effect: convex output-productivity relationship); non-CES demand makes the output-productivity relationship concave for eta large enough, flipping the sign.

Q4. What mechanism makes TFPQ passthrough so low in both the data and the model?

Two mechanisms operate. First, non-CES demand itself: when eta > 0, raising price increases the demand elasticity, and lowering price decreases it. This means the benefit to revenue from a price cut (following a productivity gain that reduces costs) is muted because the firm gains fewer customers than under CES. The static optimal passthrough is theta/(theta + eta) = 3/(7.3) = 41%. Second, non-convex input adjustment costs further reduce passthrough by making firms reluctant to change their scale in response to TFPQ shocks. In the model, the investment threshold is nearly flat across a wide range of TFPQ values (shown in Figure 6, left panel), reflecting that optimal scale barely responds to productivity. Together these mechanisms reproduce TFPQ passthrough of 20-30% in model-simulated data vs. 10-24% in the actual data, both far below the CES benchmark of 100%. The paper also verifies that low passthrough persists in the subsample of flexible-price firm-years, ruling out sticky prices as the primary driver.

Q5. Why does demand shock dispersion, rather than TFPQ dispersion, dominate the variance decompositions of sales and price growth?

The contribution of TFPQ dispersion to sales dispersion is (1-theta)^2 * beta_z^2 * Var(z). With beta_z = -0.097 and theta = 2.99, the TFPQ variance is shrunk by approximately (1-2.99)^2 * (0.097)^2 = 4 * 0.0094 ≈ 0.04, so only about 4% of TFPQ variance propagates to sales variance. This extremely small multiplier reflects two successive attenuation steps: low TFPQ passthrough to prices (beta_z^2 ≈ 0.01) and a small price-to-sales elasticity. Demand shocks, by contrast, affect sales directly through the demand curve without a price intermediary: the contribution is ((1-theta)*beta_epsilon + 1)^2 * Var(epsilon). With beta_epsilon = 0.209 and theta = 2.99, the multiplier is ((1-2.99)*0.209 + 1)^2 = (1 - 0.416)^2 = 0.34, about eight times larger than for TFPQ even though both shocks have similar variance. The cyclical increase is even more skewed toward demand because demand dispersion rises by 56% vs. 36% for TFPQ in 2009.

Q6. How does the paper relate to TFPR dispersion, and what does it say about using TFPR as a sufficient statistic?

TFPR = p * z. For arbitrary passthrough, TFPR growth = beta_epsilon * delta_epsilon + (beta_z + 1) * delta_z. Because passthrough from both shocks is incomplete, TFPR growth reflects a mixture of both underlying shocks. The paper shows via a variance decomposition of TFPR that TFPQ is the main driver of TFPR growth dispersion—accounting for roughly 60% on average—because low passthrough means prices move little, leaving TFPQ changes to dominate TFPR. However, this finding obscures the importance of demand shocks for aggregate outcomes: demand dispersion is the dominant driver of sales growth dispersion and wait-and-see behavior, yet TFPR growth dispersion mostly reflects TFPQ. A researcher relying on TFPR dispersion to infer uncertainty would correctly detect productivity uncertainty but would miss the more cyclically important demand uncertainty channel.

Q7. How do the Oi-Hartman-Abel (OHA) and wait-and-see mechanisms work differently under non-CES vs. CES demand?

Under CES demand, sales of each firm are s = z^(theta-1) * exp(epsilon), and aggregate output is E[z^(theta-1)] which is convex in z, so a mean-preserving spread in TFPQ raises aggregate output (OHA effect). Under the estimated non-CES parameters (theta=3, eta=4.3), the approximate relationship yields output proportional to z^0.82, which is concave, so a mean-preserving spread in TFPQ reduces aggregate output. The mechanism is that under non-CES demand, TFPQ shocks pass through incompletely to prices and thus create markup dispersion: high-productivity firms have high markups, low-productivity firms have low markups, and the resulting misallocation reduces total output even relative to a social planner who would set p=mc. For wait-and-see: under CES, optimal input adjustment to a TFPQ shock equals (theta-1) times the shock, which is 200% for theta=3; under non-CES with eta=4.3, it is only (theta^2/(theta+eta) - 1) * shock = 0.233 * shock = 23%. This means firms adjust scale very little in response to TFPQ uncertainty, dampening the wait-and-see channel for TFPQ. TFPQ uncertainty then causes uncertainty about markups, which is costly but does not trigger large investment adjustments.

Q8. What role do adjustment costs play, and how robust are the results to the structure of those costs?

Non-convex adjustment costs on a composite firm-scale factor x = k^alpha * l^(1-alpha) create an inaction region: firms neither invest nor disinvest until shocks are sufficiently large. In the low-uncertainty state, the model generates a yearly inaction rate of 25.4% (consistent with pre-crisis Swedish data showing roughly 15%). When uncertainty rises, the inaction region widens, the inaction rate jumps to 95% on impact, and firms let their scale shrink via depreciation. The baseline calibration uses the resale loss kappa = 0.3565 from Bloom et al. (2018). The paper also calibrates kappa to the Swedish inaction rate (kappa = 0.1165), which delivers qualitatively identical dynamics but a smaller amplitude recession (1.7pp vs. 3.5pp output fall). The paper also solves a version with adjustment costs only on capital (as in Bachmann and Bayer, 2013): the wait-and-see effect is dampened but the qualitative results hold—demand uncertainty still dominates TFPQ uncertainty in driving wait-and-see, and non-CES demand still reverses the sign of the OHA effect.

Q9. What is the role of the price wedge and time-varying passthrough?

The passthrough equation residual (price wedge, tau) captures price changes unexplained by TFPQ and demand shocks. It could reflect un-modeled shocks (e.g., financial constraints, as Gilchrist et al. (2017) document for Sweden), markup decisions, or measurement error. The price wedge makes a meaningful contribution to both average sales/price dispersion and to the rise in 2009. Time-varying passthrough is also documented: TFPQ passthrough is countercyclical (more negative in recessions), while demand passthrough is procyclical (falls in recessions when firms receive more extreme idiosyncratic demand shocks). Redoing the variance decomposition with year-by-year passthrough estimates makes demand’s contribution to sales dispersion in 2009 even larger, because firms adjust prices less to demand shocks during the recession, leaving more of the demand shock impact in sales.

Q10. What heterogeneity is documented across industries and firm types?

Sectoral demand elasticity estimates from the pooled 22-sector sample yield an average theta of 3.89 and median of 2.73 for the linear CES model; for the non-linear model, average theta is 3.26 and average eta is 7.42, with substantial positive skew. The median non-linear eta of 5.37 is larger than the pooled estimate of 4.27, indicating the pooled estimate is pulled down by some sectors with smaller deviations from CES. Key empirical results (greater cyclicality of demand dispersion, incomplete TFPQ passthrough) hold within each major sector and across balanced panels, the single-product subsample, and the CUPI price-index sample. Time-varying passthrough is also found to be systematically higher by about 25% in the post-2008 period compared to the pre-2008 period, suggesting a structural shift in how demand shocks transmit to prices, though the paper does not investigate the source of this change.

Q11. What robustness checks are run on the demand and passthrough estimates?

Demand estimation robustness: (1) piece-wise linear specification (elasticity of 2 below average price, 4 above average price, significant at 0.1% level); (2) balanced panel; (3) excluding the Great Recession; (4) using Statistics Sweden firm identifiers instead of authors’ own; (5) CUPI price index; (6) single-product firms; (7) sector-by-sector estimation; (8) including firm and sector-year fixed effects directly in the nonlinear regression (rather than pre-demeaning). All exercises confirm statistically significant eta and broadly similar theta. Passthrough robustness: (1) OLS vs. IV (lagged shocks) vs. first-differences; (2) balanced panel; (3) single-product subsample; (4) two-period lagged instruments (beta_z = -0.294, beta_epsilon = 0.249); (5) flexible-price subsample; (6) longer-horizon (two- and three-year) first differences for TFPQ. Corroboration: TFPQ innovations are positively associated with reported process innovations in Eurostat CIS data (7% greater TFPQ growth for process innovators); negative demand shocks are correlated with managers reporting ‘insufficient demand’ in KFI data (8% lower demand growth).

Q12. How does this paper differ from and relate to Bloom (2009) and Bloom et al. (2018)?

Bloom (2009) and Bloom et al. (2018) model a single composite firm-level shock (implicitly TFPR) in a CES-demand economy, finding that uncertainty shocks reduce output through wait-and-see behavior but generate a positive volatility effect (OHA) that partly offsets the uncertainty effect. The present paper adds two departures: (1) it separates TFPQ and demand shocks and shows they have distinct empirical and aggregate implications; (2) it replaces CES demand with an estimated non-CES demand curve. Departure (2) reverses the OHA effect, amplifying the total output decline by around 40% relative to the CES model. Departure (1) shows that the uncertainty channel operates primarily through demand, while TFPQ operates primarily through the volatility channel. The quantitative model uses the same non-convex adjustment cost structure and calibration approach as Bloom et al. (2018) to ensure comparability. The paper also relates to Bachmann and Bayer (2013) and Mongey and Williams (2017), who find smaller aggregate effects with adjustment costs only on capital; the present paper notes that adjustment costs on both capital and labor are needed for large wait-and-see effects, but qualitative conclusions are unchanged with capital-only costs.

Q13. What are the policy and theoretical implications of the findings?

First, policies aimed at reducing firm-level demand uncertainty (e.g., demand stabilization, aggregate demand management) have larger aggregate output effects than policies addressing productivity uncertainty, because demand uncertainty triggers wait-and-see investment behavior while TFPQ uncertainty is largely absorbed in markups without changing investment much. Second, TFPQ dispersion is still harmful but through misallocation: policies that reduce markup dispersion induced by productivity differentials can raise aggregate output without requiring reduced dispersion per se. Third, the finding that TFPR dispersion is a poor proxy for demand shock dispersion has implications for how researchers use TFPR as a measure of misallocation or uncertainty: it conflates two distinct forces with different aggregate implications. Fourth, the estimated super-elasticity provides a data-disciplined input for calibrating models with real rigidities, directly relevant for the Ball-Romer nominal non-neutrality question—higher real rigidities amplify the output effects of monetary policy shocks. The authors flag this as a natural extension. The scope conditions are: Swedish manufacturing, annual data 1998-2013, partial equilibrium model (aggregate price level exogenous), firms with matching price and utilization data (large-firm bias).

Q14. What additional findings are documented regarding the cyclicality of other firm-level variables?

Beyond TFPQ and demand dispersion, the paper documents that dispersion of sales growth, price growth, labor, intermediate goods, and capacity utilization are all countercyclical. The IQR of sales growth was 58% above the non-recession average in 2009 and 9% above in 2001; the IQR of price growth was 83% above in 2009 and 5% above in 2001. The one notable exception is investment, which displays procyclical dispersion (less dispersed during the Great Recession). The paper also documents that roughly 30% of firms report insufficient demand at all their plants in the survey data; average capacity utilization is 88% with median 91% and standard deviation of 14.1%; and about 25% of firm-year observations involve utilization at or above 100%.

Key Concepts

Physical total factor productivity (TFPQ): Firm-level quantity productivity: output per unit of inputs, measured from a utilization-adjusted Cobb-Douglas value-added production function. Distinct from revenue TFP (TFPR = p*z) because it abstracts from demand conditions and price-setting. In this paper, TFPQ is estimated within firm over time using the cost-share approach and a capacity-utilization correction from managerial survey data.

Demand shock (epsilon): The idiosyncratic component of a firm’s demand curve that captures its ability to sell more (or fewer) units at a given price in a given year, reflecting changes in customer base size or customers’ willingness to pay. Estimated as the residual from the GIR demand curve after controlling for firm fixed effects, sector-time fixed effects, and the firm’s own price.

Non-CES demand curve / super-elasticity (eta): A demand specification adapted from Gopinath, Itskhoki, and Rigobon (2010) in which the demand elasticity is not constant but rises with the firm’s price. The parameter eta (estimated at 4.27 in the main sample) governs how fast the elasticity rises with the price: when eta > 0, firms gain few customers by cutting price (elasticity falls as price falls) and lose many customers by raising price (elasticity rises as price rises). This is the source of ‘real rigidity’ that makes incomplete TFPQ passthrough optimal.

Incomplete TFPQ passthrough: The empirical finding that firms reduce their prices by far less than one-for-one in response to a productivity gain (estimated beta_z = -0.097 to -0.124, far from the CES benchmark of -1). The paper attributes this primarily to non-CES demand real rigidity (which implies an optimal static passthrough of only 41% given the estimated parameters) and secondarily to adjustment costs.

Oi-Hartman-Abel (OHA) effect: The positive ‘volatility effect’ in standard CES-demand uncertainty models: because output is a convex function of TFPQ under CES, a mean-preserving spread in productivity raises aggregate output (lucky firms expand more than unlucky firms contract). The paper overturns this result by showing that with non-CES demand (eta sufficiently large), the output-productivity relationship becomes concave, so TFPQ dispersion reduces aggregate output via markup misallocation.

Wait-and-see channel: The mechanism by which uncertainty about future shocks causes firms with non-convex input adjustment costs to pause investment: firms prefer to remain inactive and let inputs depreciate rather than invest or disinvest, at the risk of having to pay an irreversibility cost if the shock turns out to have been in the opposite direction. In this paper, this channel is driven primarily by demand uncertainty because demand shocks determine how many units a firm can sell and hence its desired input level; TFPQ uncertainty does not trigger strong wait-and-see behavior because the optimal scale response to TFPQ shocks is small under non-CES demand.

Markup dispersion / misallocation: Dispersion across firms in the ratio of price to marginal cost, arising in this paper from incomplete TFPQ passthrough: firms with high productivity set high markups rather than passing through productivity gains as price cuts. The resulting wedge between prices and marginal costs means that resources are misallocated (too little output at high-productivity firms relative to the social optimum), reducing aggregate output. This is the channel through which TFPQ dispersion harms the aggregate economy in the model.

Price wedge (tau): The residual from the passthrough regression: the component of firm price changes unexplained by the estimated TFPQ and demand shocks. Interpreted as capturing un-modeled shocks (financial constraints, markup adjustments) and potentially measurement error. The price wedge makes a meaningful contribution to both average sales/price dispersion and to the Great Recession increase in dispersion.

Forecasting with Feedback

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

Layer 1: Overview

This paper develops a strategic model of point forecast production in environments where the forecast itself influences the outcome being predicted — what the authors call “forecasting with feedback.” The canonical example is Federal Reserve staff (Greenbook) inflation forecasts: these forecasts guide FOMC interest rate decisions, and those rate decisions in turn affect realized inflation. The central theoretical claim, proved formally, is that even a forecaster with purely quadratic (mean-squared-error) loss will optimally produce biased forecasts in such environments, provided there is some uncertainty about how strongly the decision maker (DM) will react to the forecast. This finding offers a third interpretation of observed forecast biases — beyond the two dominant explanations in the prior literature, namely forecaster irrationality and asymmetric loss functions.

The model has three components. First, an outcome equation: y_{t+1} = theta_t + a_t + epsilon_{t+1}, where theta_t is a private signal (the state of the economy) observed only by the forecaster, a_t is the DM’s action, and epsilon_{t+1} is unforecastable noise. Second, a DM reaction function: a_t = x_t * [y_T - E(theta_t | f_t)], analogous to a Taylor rule, where y_T is a known target, and x_t is a strength-of-reaction multiplier drawn from a distribution with mean mu and variance tau^2; x_t is the DM’s private information. Third, the forecaster minimizes expected squared error, anticipating the DM’s endogenous response. The model is linear and closed-form solutions are derived.

The key mechanism is a bias-variance tradeoff. Because the DM’s action responds to the forecast, the variance of the realized outcome itself becomes a function of the forecast. When the DM’s reaction strength x_t is uncertain (tau^2 > 0), this variance-of-outcome term is not trivially minimized by an unbiased forecast. The forecaster reduces outcome volatility by attenuating the sensitivity of the forecast to the state — shrinking the forecast slope toward zero relative to what an unbiased forecast would require — at the cost of introducing systematic bias. When tau^2 = 0 (no uncertainty about the DM’s reaction), the forecaster can perfectly anticipate and correct for the DM’s response, and the optimal forecast is unbiased. Feedback alone, without uncertainty, does not produce bias.

The paper derives equilibrium forecasts in a Perfect Bayesian Equilibrium where the DM holds correct (rational) beliefs about the forecasting rule. Key analytical results include: (i) the equilibrium exists when tau^2 <= 1/4; (ii) the equilibrium conditional bias equals [(1 - sqrt(1 - 4*tau^2))/2] * (theta_t - y_T), which changes sign depending on whether the state is above or below the target — the forecaster gravitates toward the target; (iii) the Mincer-Zarnowitz (MZ) regression slope (the slope from regressing realized outcomes on forecasts) can be large and positive, close to zero, or even negative, depending on mu and tau^2; (iv) when mu = 1 (the DM on average fully closes the gap to the target), the equilibrium MZ slope is exactly zero for any tau^2 value.

The paper motivates these results with two documented empirical patterns in Greenbook 4-quarter-ahead inflation forecasts from 1980q1 to 2019q4. First, using 40-quarter rolling windows, bias in Greenbook forecasts is persistent but sign-changing over time — a pattern consistent with the model’s prediction that the sign of bias tracks whether the state theta_t is above or below the inflation target y_T. Second, the MZ slope (from 40-quarter rolling-window regressions) hovers near unity in the mid-1980s through early 1990s, returns to unity by the late 1990s, then drops sharply to significantly negative territory by the mid-2000s, before becoming indistinguishable from zero in the final portion of the sample — a pattern consistent with the model’s prediction that the MZ slope shifts radically with changes in mu and tau^2. Both facts are computed using the last revision of the GDP deflator.

The policy and methodological implications are significant. Standard forecast rationality tests (Mincer-Zarnowitz regressions, bias tests) are designed to detect irrationality or asymmetric loss, but in feedback environments these same test statistics can indicate “failure” even when the forecaster is fully rational under quadratic loss. Studies conducting rationality tests or estimating loss functions must either explicitly assume away feedback (and justify that assumption) or account for the feedback mechanism.

In depth

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

The paper is primarily theoretical: it derives closed-form equilibrium forecasting rules and forecast statistics from first principles within a stylized game-theoretic model. There is no econometric identification exercise. The Greenbook evidence is descriptive and motivational — rolling-window bias estimates and MZ slope estimates are presented as stylized facts consistent with the theory, not as causal identification. The main caveat the authors themselves make is that the model is not claimed to be an exclusive or exhaustive explanation of the documented GB forecast patterns. Inflation forecasting is complex, and many other factors (learning, structural breaks, regime changes in monetary policy, data revisions) could contribute to the observed patterns. The authors explicitly disclaim any claim to exclusivity.

Q2. What is the core mathematical mechanism, and how does uncertainty play a necessary role?

The forecaster’s MSE decomposes into a conditional variance term and a squared-bias term: MSE = Var[a*(f_t) | theta_t] + bias^2(f_t | theta_t) + sigma^2. The critical insight is that when x_t (the reaction-strength multiplier) is uncertain, the variance of the DM’s action — and hence of the outcome — depends on the level of the forecast itself. Specifically, Var[a*(f_t) | theta_t] = tau^2 * (y_T - f_t/c + b/c)^2. So choosing a larger or smaller forecast changes not just the bias term but also the variance term. The optimal resolution of this tradeoff requires an attenuated (biased) forecast slope. When tau^2 = 0 (no uncertainty), the variance term vanishes entirely and the forecaster can correct for feedback in full by solving a fixed-point problem, producing an unbiased forecast. The paper explicitly proves (taking limits as tau^2 to 0 in the bias and MZ slope formulas) that both return to zero and one respectively, confirming that uncertainty is a necessary condition for bias.

Q3. What is the equilibrium concept and what are its properties?

The equilibrium is a linear Perfect Bayesian Equilibrium (PBE). The DM conjectures that the forecast is a linear function f_t = b + c*theta_t, uses that conjecture to form expectations E(theta_t | f_t) = (f_t - b)/c, and chooses her action optimally. Equilibrium requires that the DM’s conjectured intercept and slope (b, c) coincide with those actually used by the forecaster. The paper shows (Corollary 1) that such a linear PBE exists when tau^2 <= 1/4, and that the equilibrium is fully revealing — the DM can learn the true state theta_t from the forecast because the forecast is a one-to-one function of the state. Two linear equilibria exist: the paper focuses on the Pareto-preferred one (lower forecaster loss, lower absolute bias), which is also the one whose limit as tau^2 approaches 0 corresponds to the natural optimal forecast.

Q4. What sign and magnitude patterns does the equilibrium bias exhibit?

From Corollary 2(a), the conditional equilibrium bias is: E(y_{t+1} - f_t^dagger | theta_t) = [(1 - sqrt(1 - 4tau^2)) / 2] * (theta_t - y_T). The multiplier (1 - sqrt(1 - 4tau^2))/2 is always positive (for tau^2 in (0, 1/4]), so the sign of the bias is determined entirely by the sign of (theta_t - y_T). When theta_t > y_T (state above target), bias is positive — the forecaster underpredicts, shrinking the forecast toward the target. When theta_t < y_T, bias is negative — the forecaster overpredicts, again gravitating toward the target. This sign-change mechanism, driven by changing economic conditions relative to a fixed target, is cited as consistent with the persistent but sign-changing bias observed in Greenbook inflation forecasts from 1980 to 2019.

Q5. What does the model predict about the Mincer-Zarnowitz slope, and how variable can it be?

From Corollary 2(b), the MZ slope in equilibrium is a highly nonlinear function of mu and tau^2. Figure 3 in the paper (discussed in the text) shows that the slope can be large and positive, positive but close to zero, negative, or even very steeply negative, for different combinations of mu and tau^2. A key special case: when mu = 1 (DM fully closes the gap to target on average), E(y_{t+1} | f_t^dagger) = y_T for all values of the forecast, giving an MZ slope of exactly zero and intercept equal to y_T. The authors note that when mu is close to 1 and tau^2 is small, even small deviations of mu from unity can produce large positive or negative MZ slopes. The model can thus account for the dramatic shift in the GB MZ slope documented in the paper — from around unity in the 1980s-1990s, to significantly negative territory in the mid-2000s, to approximately zero thereafter.

Q6. What is the relationship between the DM’s reaction function and the Taylor rule, and how is it microfounded?

The DM’s reaction function is a_t* = x_t * [y_T - E(theta_t | f_t)], directly analogous in spirit to a Taylor rule (Taylor, 1993). Online Appendix A provides a formal microfoundation: if the DM minimizes a quadratic loss in (y_{t+1} - y_T)^2 plus a quadratic adjustment cost w_t * a_t^2 — where w_t is a private, randomly drawn adjustment cost parameter — then the optimal action is precisely a_t* = x_t * [y_T - E(theta_t | f_t)] with x_t = 1/(1 + w_t). This microfoundation connects the model to the literature on central bank optimal control and provides a rational justification for the reaction function structure used throughout the paper.

Q7. How does this paper relate to and differ from the Crawford-Sobel (1982) cheap talk model?

The paper borrows the sender-receiver communication game structure from Crawford and Sobel (1982), with the forecaster as sender and the DM as receiver. However, it departs in two important ways. First, in Crawford-Sobel, the sender’s payoff depends only on the state and the action, not directly on the message (the forecast). In this paper, the forecast enters the forecaster’s loss function directly through the outcome equation (y = theta + a + epsilon, and the forecast determines a which determines y which enters the loss), making it a model of ‘costly talk’ in the sense of Kartik, Ottaviani, and Squintani (2007). Second, in standard communication games the realized outcome is exogenous — the DM’s action affects only her own payoff but not the variable being forecast. Here, the DM’s action causally determines the realized outcome that the forecaster was trying to predict. This feedback causality is absent in the standard setup and is the source of the paper’s novel results.

Q8. How does this paper relate to Bernanke and Woodford (1997)?

Bernanke and Woodford (1997) also study professional inflation forecasts and monetary policy in a rational expectations equilibrium framework, and raise the question of whether an informative equilibrium exists — concluding it may not. This paper differs in three respects: it assumes the forecaster has private information (state theta_t) that the DM cannot directly observe; it works in an environment with uncertainty about the DM’s reaction (x_t is random); and rather than focusing on equilibrium existence, it derives the statistical properties of equilibrium forecasts — the bias formula, MZ regression coefficients — which Bernanke and Woodford do not. The authors describe their work as providing ’the first formal treatment of the statistical properties of forecasts’ in feedback environments.

Q9. What heterogeneity and parameter sensitivity is documented?

The paper documents sensitivity of forecast properties to mu (mean policy reaction strength) and tau^2 (variance of policy reaction strength). The DM’s average aggressiveness mu affects both the sign and magnitude of the MZ slope: for cautious DMs (mu near 0.1), the equilibrium MZ slope is relatively close to unity; for aggressive DMs (mu near 1), the slope can flatten toward zero; for moderate but increasing mu (with tau^2 above a threshold of approximately 0.05), the slope flattens monotonically. A higher tau^2 at given mu generally attenuates the slope toward zero, but the relationship is nonlinear. When mu is precisely one, the MZ slope is exactly zero regardless of tau^2. The equilibrium bias magnitude scales with [(1 - sqrt(1 - 4*tau^2))/2], which increases in tau^2. The sign of bias is determined by the direction of (theta_t - y_T). The paper does not present cross-sectional or time-series panel heterogeneity — the parametric sensitivity analysis in Figure 3 constitutes the heterogeneity exercise.

Q10. What robustness checks are run for the Greenbook empirical patterns?

The authors state (in a footnote) that the documented patterns — persistent but sign-changing bias in 4-quarter-ahead GB inflation forecasts from 1980q1 to 2019q4 — are robust to using the second release of the GDP deflator rather than the last release. The main results use the last release. The choice of 40-quarter (10-year) rolling window is applied uniformly for both the bias plot and the MZ slope plot. No additional robustness checks (alternative window lengths, alternative forecast horizons, formal structural break tests) are explicitly documented in the paper, though the authors cite Rossi and Sekhposyan (2016), who use formal rationality tests and confirm that GB forecast rationality breaks down around 2005 — consistent with the pattern the authors document via the rolling MZ slope.

Q11. What does the model say about the forecaster’s inability to commit, and could commitment help?

In the baseline model, the forecaster cannot commit to a fixed forecasting rule ex ante because the state theta_t is not directly observable by the DM. The authors note in Section 3.3 that modeling forecasters with commitment is a straightforward extension, and that commitment can actually increase forecaster welfare in equilibrium. However, this extension is not formally developed in the paper. The intuition is that if the forecaster could credibly commit to a more informative forecast rule, the DM could react more precisely, reducing the variance of outcomes; but without commitment, the strategic equilibrium involves an attenuated (biased) forecast.

Q12. What are the implications for forecast rationality tests and loss function estimation?

The paper’s central methodological warning is that standard forecast rationality tests (MZ regression tests for zero intercept and unit slope; bias tests) and loss function estimation exercises are contaminated in environments with policy feedback. If feedback is present and x_t is uncertain, a fully rational forecaster with quadratic loss will produce forecasts that fail standard rationality tests — showing nonzero bias, non-unit MZ slopes (potentially even negative), and forecast errors correlated with the forecaster’s own information. Researchers conducting such tests must either: (a) explicitly assume no feedback applies (and justify this assumption in their specific application), or (b) carefully model the feedback mechanism and account for it. Studies that interpret GB forecast irrationality (e.g., Rossi and Sekhposyan 2016) or asymmetric loss (e.g., Capistran 2008) as the explanation for observed GB forecast properties may be confounded by the feedback mechanism identified in this paper.

Q13. What are the conditions under which a linear equilibrium does or does not exist?

From Corollary 1 and Remark 3 following it: a linear PBE exists if and only if tau^2 <= 1/4. When tau^2 > 1/4, the forecaster always wants to attenuate the slope more than the DM expects, so no fixed-point equilibrium in linear strategies exists. The paper also notes a sufficient condition for equilibrium existence: if the support of x_t is contained in [0, 1] (the DM never overreacts and never underreacts by more than half), then tau^2 <= 1/4 is automatically satisfied and an equilibrium always exists. Two linear equilibria exist when tau^2 <= 1/4, but the paper focuses on the Pareto-preferred one, which has lower forecaster loss, lower absolute bias, and a natural limiting behavior as tau^2 approaches 0.

Q14. What scope conditions limit the applicability of the results?

Several scope conditions are made explicit: (1) The outcome equation is linear; nonlinear outcome determination would change quantitative results but the feedback mechanism would persist qualitatively. (2) The model is a single-period (point-in-time) game, not a multi-period learning model — it does not analyze how beliefs about mu and tau^2 evolve over time. (3) The independence assumption between x_t and theta_t is a benchmark; if policy aggressiveness varies with economic conditions, additional effects arise. (4) The focus on linear equilibria rules out non-linear forecasting strategies. (5) The results apply to unconditional forecasts (where the forecaster anticipates the DM’s response); conditional forecasts (conditioned on a pre-specified action) behave differently. (6) The empirical Greenbook evidence is illustrative, not a formal test of the model — the authors explicitly state they do not claim their model provides an exclusive explanation of GB forecast properties.

Key Concepts

Forecasting with feedback: A forecasting environment in which the DM’s action — taken in response to the forecast — causally affects the realized value of the variable being forecast, so that the forecast influences its own target outcome. Distinguished from no-feedback environments (e.g., weather forecasting) where decisions made on the basis of the forecast do not affect the outcome.

Unconditional forecast: A forecast that anticipates and factors in the expected response of the decision maker to the forecast itself, rather than being conditioned on a pre-specified (potentially counterfactual) action. The paper’s model produces unconditional forecasts; conditional forecasts (conditioned on a given policy path) are a distinct and narrower concept.

Bias-variance tradeoff (in feedback forecasting): The tradeoff that arises when the DM’s reaction to the forecast is uncertain: a less informative (attenuated) forecast reduces the variance of the outcome (by inducing a less volatile policy action) but introduces systematic bias. The optimal forecast under quadratic loss resolves this tradeoff by attenuating the forecast slope below what an unbiased forecast would require, producing an optimally biased forecast.

Reaction function (DM’s): The rule by which the decision maker translates a forecast into a policy action: a_t* = x_t * [y_T - E(theta_t | f_t)], analogous to a Taylor rule. The multiplier x_t captures the strength of the policy response and is drawn from a distribution with mean mu and variance tau^2; it is the DM’s private information and a key source of the forecaster’s uncertainty.

Mincer-Zarnowitz (MZ) regression: The linear regression of the realized outcome on the forecast: y_{t+1} = alpha + beta * f_t + error. Under the canonical null of rational forecasting with quadratic loss and no feedback, the intercept alpha should be zero and the slope beta should be one. The paper shows that under optimal forecasting with feedback, alpha and beta can take a wide range of values, including negative beta, even when the forecaster is rational.

Equilibrium forecast slope (c-dagger): The slope of the linear forecasting rule in Perfect Bayesian Equilibrium, given by c^dagger = (1/2) - mu + sqrt(1 - 4*tau^2)/2. This slope is less than one and can be negative depending on mu and tau^2, reflecting the attenuation of the forecast toward the policy target that arises from the bias-variance tradeoff under uncertain DM reactions.

Greenbook (GB) inflation forecasts: Inflation forecasts produced by Federal Reserve staff (now called Tealbook forecasts), used as empirical motivation in the paper. The paper documents two stylized facts for 4-quarter-ahead GB forecasts from 1980q1 to 2019q4: (i) persistent but sign-changing bias in rolling 40-quarter windows, and (ii) a dramatic shift in the rolling MZ slope from approximately unity in the 1980s-1990s to significantly negative in the mid-2000s and approximately zero in the final part of the sample.

Policy feedback (as a confound for rationality tests): The paper’s use of this term to describe the mechanism by which the presence of feedback invalidates the standard interpretation of forecast rationality test outcomes: a forecaster who is fully rational (quadratic loss, no private agenda) and operating in a feedback environment will systematically produce forecasts that fail standard MZ-based rationality tests, not because of irrationality or asymmetric loss, but because of the optimal bias-variance tradeoff induced by uncertain policy reactions.

Identifying the Impact of Inflation Expectations

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

Layer 1: Overview

Branch (2022) asks whether subjective consumer inflation expectations causally raise the inflation rate — a question whose empirical answer has been elusive despite its central role in New Keynesian theory and central bank communication. The identification problem is acute: expectations are endogenous by construction, and the standard approach of estimating a Phillips curve with aggregate data produces estimates biased sharply downward by endogeneity. OLS regressions of regional inflation on regional mean expectations, controlling for unemployment, lagged inflation, and region and time fixed effects, yield a slope of only 0.069 (Table 2 context; Figure 1b), far below the theoretical prior of near-unity pass-through.

The paper’s empirical strategy exploits a key fact: different demographic groups consume heterogeneous bundles of goods, so their inflation expectations differ systematically and reflect their own basket’s price movements. Using roughly 273,000 individual responses from the University of Michigan Survey of Consumers spanning 1978:1–2022:5, Branch classifies respondents into 160 demographic groups defined by sex, age (five categories), education (four levels), marital status, and parental status. The panel covers four U.S. Census regions, producing dimensions T = 528 months, N = 4 regions, and G = 160 groups. Regional inflation is measured from BLS CPI series for all urban consumers.

The identification strategy is a shift-share (Bartik) instrument: for each region-month, the predicted regional inflation expectation is the population-weighted average of each demographic group’s national-level average inflation expectation, where the weights are the group’s share of the region’s population. Two share measures are used: (i) the January 1978 Current Population Survey (CPS78) distribution, which is time-invariant and plausibly exogenous to subsequent inflation shocks; and (ii) contemporaneous Michigan survey shares. The leave-one-out variant is the preferred construction. The instrument is relevant — first-stage F-statistic of 52.4 (significant at 0.1%) — and the Durbin-Wu-Hausman test rejects OLS consistency at the 1% level (statistic = 8.074).

Main 2SLS estimates: using Michigan survey shares, a 1 percentage point increase in a region’s expected inflation raises regional inflation by 0.33 percentage points (significant at 5%; Table 2). Using CPS78 shares, the estimate rises to 0.55 percentage points (significant at 1%; Table 2). After applying the split-sample jackknife bias correction for finite-sample bias in the small-N/large-T panel, the estimates increase slightly to 0.36 and 0.60 respectively (Table 3). The paper characterizes the 60 basis point estimate as its “preferred” figure. Both are substantially above the OLS estimate of 0.069 and represent a lower bound: because time fixed effects absorb cross-regional spillovers, the aggregate pass-through is likely stronger, with the paper arguing that after accounting for spillovers the effect is plausibly in the range of 1.0–1.6, consistent with the Calvo- and Taylor-model predictions of Werning (2022), who shows pass-through should lie in [1/2, 1] or above.

Sectoral decomposition reveals that the expectation effect is concentrated in non-durable goods prices (coefficient 1.74, significant at 1%; Table 7) and commodities more broadly (1.29, significant at 1%; Table 7), with no statistically meaningful effect on durables (−0.10, insignificant) and only marginal positive effects on services (0.22, marginally significant). Among services, the effect is somewhat larger when housing services are excluded.

A key finding on expectations horizons: when both one-year-ahead and five-to-ten-year-ahead expectations are simultaneously instrumented using their respective Bartik shift-shares, only the short-run (one-year) expectation retains a significant positive effect on inflation. The long-horizon coefficient is small in absolute value, negative in sign, and statistically insignificant in both the joint and standalone specifications (Tables 10 and 12). After conditioning on aggregate macroeconomic factors captured by time fixed effects, long-run inflation expectations have no independent causal role in the regional inflation rate.

Identification heterogeneity: using the Rotemberg weight decomposition of Goldsmith-Pinkham, Sorkin, and Swift (2020), the identifying variation derives primarily from younger, married consumers with at least a high school degree — specifically those aged 18–34 (Michigan instrument) or 25–49 (CPS78 instrument). The group-specific treatment effects (βg) for these heavily weighted groups are positive and significantly above 1. Temporally, the heaviest identification weights fall on the Great Inflation and Volcker disinflation (1978–82), the Great Recession (2007–09), and the post-pandemic inflation episode (2021–22). The impulse response function shows a significant contemporaneous positive effect of expectations on inflation that mean-reverts cyclically within approximately 12 months, though confidence bands are wide at longer horizons.

In depth

Q1. What is the core identification strategy and what makes it plausible?

The strategy is a differential-exposure quasi-experiment using a Bartik (shift-share) instrument. For each Census region and month, the instrument is the population-weighted average of each demographic group’s national-level mean inflation expectation, with weights equal to that group’s share of the region’s population. The key identifying assumption has two parts: (1) demographic groups have heterogeneous consumption baskets, so their inflation expectations reflect the prices in their own basket; and (2) the distribution of demographic groups across regions is exogenous to unobserved shocks driving regional inflation (as opposed to being exogenous to regional price levels, which is a weaker and separately justified claim). Plausibility is supported by the CPS78 shares having no predictive power for the other covariates of inflation over the sample, and by using a leave-one-out instrument construction to avoid mechanical correlation.

Q2. What are the main threats to identification and how does the paper address them?

The principal threat is that regional demographic composition could be endogenous to regional inflation rather than merely to regional price levels. The paper argues identification requires only exogeneity to the change in prices (inflation), not to the level. The empirical check is that CPS78 beginning-of-period shares show no statistically or economically significant correlation with the other regressors that predict regional inflation. A second threat is that groups may sort into regions based on economic conditions correlated with inflation. The paper argues the channel runs through demand from heterogeneous baskets rather than supply-side sorting. A third threat is weak instruments: this is addressed by first-stage F = 52.4. Fourth, survey measurement concerns (re-interview selection bias, outliers, endogenous prompting thresholds) are addressed through a battery of alternative specifications (first-time respondents only, outlier removal, CPS vs. survey shares, lagged shares, alternative CPI measures).

Q3. Why are OLS estimates biased downward and by how much?

OLS is biased because inflation expectations are endogenous — they move with the same shocks driving inflation, so OLS conflates the causal effect with reverse causation and omitted-variable bias. The OLS estimate from the panel regression with region and time fixed effects is approximately 0.069 (Figure 1b). The 2SLS estimates using the Bartik instrument range from 0.33 to 0.55, roughly five to eight times larger than OLS, confirming substantial downward bias. The Durbin-Wu-Hausman test confirms OLS inconsistency at the 1% level.

Q4. What heterogeneity across demographic groups is documented?

Women consistently report higher inflation expectations than men, particularly outside the high-inflation 1970s episode. Older respondents (50+) receive small Rotemberg identification weights, meaning their expectations contribute little to the identifying variation. Younger groups (18–34 under Michigan shares; 25–49 under CPS78 shares), married, with at least a high school education are the groups whose expectations drive the regional cross-sectional identification. The group-specific causal effects (βg) for these heavily weighted groups are uniformly positive and significantly above 1.0, ranging roughly from 1.38 to 1.91 in the top-10 groups. College-educated groups receive higher weight under the CPS78 instrument, while the Michigan shares instrument weights high school and college groups more evenly.

Q5. What is the sectoral decomposition of the inflation expectations effect?

Table 7 estimates separate 2SLS regressions for components of the CPI. Non-durable goods prices respond most strongly (coefficient 1.74, significant at 1%). Commodities broadly (which include non-durables and durables) also show a large effect (1.29, significant at 1%). Durable goods prices show no meaningful effect (−0.10, statistically insignificant). Services show only a marginal positive effect (0.22, marginally significant at 10%). Among services, the effect is somewhat stronger when housing services are removed. These results are consistent with prior findings that consumer grocery and non-durable prices most directly influence and reflect household inflation expectations.

Q6. What do the long-run expectations results show and what is the interpretation?

The Michigan survey’s PX5 question elicits 5-to-10-year ahead inflation expectations. Constructing a shift-share Bartik instrument for these long-horizon expectations and including both short- and long-run instruments simultaneously, the second-stage coefficient on long-horizon expectations is small (−0.023 to −0.037 in the joint specification, Table 10), negative, and statistically insignificant in all specifications. When long-horizon expectations alone are instrumented, the second-stage coefficient is 0.005 to 0.034 (Table 12), positive but still insignificant. The interpretation is that, after controlling for time fixed effects (which capture aggregate macroeconomic factors), long-run expectations have no independent causal role in regional inflation outcomes. Only short-run (one-year ahead) expectations matter. The first stage confirms the long-run instrument is relevant for long-run expectations but orthogonal to short-run expectations.

Q7. What robustness checks are reported and what do they find?

Table 8 reports four alternative specifications, all using Michigan survey shares: (1) ‘small’ — removing survey responses with absolute values above 25% — gives a coefficient of 0.66 (significant at 1%), larger than baseline, though the paper does not prefer this because large expectations may have real behavioral effects; (2) ‘first-only’ — using only first-time respondents and dropping the 40% re-interviewed — yields a coefficient of 0.58, still positive though the standard error rises and significance falls; (3) ‘state-CPI’ — replacing the BLS regional CPI with state-level CPIs aggregated as in Hazell et al. (2022) — gives 0.33 (significant at 5%), very close to the Michigan-shares baseline; (4) ’lag Michigan shares’ — instrumenting with 12-month lagged survey shares — gives 0.53 (significant at 5%), bracketed between the two baseline estimates. The jackknife bias correction (Table 3) slightly raises estimates to 0.36 and 0.60 for the two instruments.

Q8. What does the impulse response function show?

Using local projections (Jordà 2005) to estimate a 2SLS impulse response function, a shock to inflation expectations produces a significant positive contemporaneous effect on regional inflation. The response is cyclical and mean-reverting, returning to near zero within approximately 12 months. Confidence intervals are wide in subsequent quarters, so the analysis cannot rule out lingering effects, but the central estimates suggest the impact dissipates within about a year. The paper notes that the lack of strong persistence may reflect the specific U.S. inflation history and suggests extending the analysis to countries with more volatile or persistent inflation histories.

Q9. How does this paper relate to the New Keynesian Phillips Curve literature?

The standard approach to measuring expectations’ impact on inflation is to estimate a NKPC with an instrument for expectations under rational expectations. Mavroeidis, Plagborg-Moller, and Stock (2014) document that this approach faces severe identification and weak-instrument problems. Branch’s approach avoids these issues by not assuming rational expectations, not requiring an explicit model of expectations formation, and using a shift-share instrument whose validity rests on cross-sectional demographic heterogeneity rather than time-series moment conditions. The theoretical model in Section 3.1 permits non-rational expectations and nests ‘anticipated utility’ or ‘steady-state learning’ (Evans and Honkapohja 2001; Woodford 2013) as the simplifying assumption. The estimated regional coefficients are below but potentially consistent with Werning’s (2022) theoretical range of [1/2, 1] for Calvo and Taylor pricing models once spillovers are accounted for.

Q10. How does the paper relate to the literature on household-level inflation heterogeneity?

The paper builds on Hobijn and Lagakos (2005), who show households consume different bundles, and Kaplan and Schulhofer-Wohl (2017), who find two-thirds of cross-household inflation variation stems from paying different prices for the same goods. D’Acunto, Malmendier, Ospina, and Weber (2021) establish that grocery store prices directly influence household inflation expectations. Branch takes these findings as given — they motivate the identifying assumption that expectations reflect basket-specific prices — and focuses on the downstream question of whether those expectations causally raise actual inflation outcomes. Earlier work on heterogeneous expectations by Branch (2004, 2007) using Michigan survey data, finding time-varying heterogeneity across forecasting rules, is also directly referenced.

Q11. What does the Rotemberg weight decomposition reveal about the source of identifying variation?

The Bartik estimate is a weighted average of 160 just-identified group-specific estimates. Goldsmith-Pinkham, Sorkin, and Swift (2020) show the weights (αg) measure each group’s contribution to the overall estimate and sensitivity to bias from that group’s potential endogeneity. Tables 4–5 list the top-10 weighted groups: under CPS78 shares, these are predominantly 25–49-year-olds, mostly college-educated, seven of ten married with children. Under Michigan shares, the top groups are even younger (mostly 18–24), with at least a high school degree, almost all married without children. Table 6 shows men receive slightly higher aggregate weight than women (0.53–0.57 vs. 0.43–0.47), and those aged 50+ contribute less than 15% of total weight. Figure 11 shows temporal variation: the heaviest-weighted periods are the late-1970s Great Inflation and Volcker disinflation, the Great Recession (2007–09), and the post-pandemic episode (2021–22).

Q12. What are the policy implications and their scope conditions?

The paper provides empirical support for central bank attention to short-run consumer inflation expectations: a 1 percentage point increase in one-year-ahead regional expectations causally raises regional inflation by 0.33–0.55 basis points (lower bound, since spillovers are excluded). Accounting for cross-regional aggregate effects raises the likely total pass-through to above one, validating the central bank emphasis on anchoring short-run expectations. However, the null finding for long-run (5-to-10-year) expectations — controlling for aggregate time effects — suggests that ‘anchoring long-run expectations’ may not independently prevent near-term inflation above and beyond its correlation with short-run beliefs. The scope conditions are important: the estimates come from U.S. Census regions over 1978–2022, so applicability to countries with persistently high or hyper-inflation is uncertain. The identifying variation is concentrated in high-volatility inflation episodes, suggesting potential nonlinearities in the expectations-to-inflation mapping. The empirical strategy also does not capture general equilibrium feedback from realized inflation back to expectations.

Q13. What are the data limitations and survey design concerns the paper acknowledges?

Five limitations of the Michigan survey are acknowledged: (1) whether surveys elicit genuine expectations rather than attitudes; (2) the rotating panel structure, with roughly 40% of respondents re-interviewed after six months, creates potential selection bias if more accurate forecasters are likelier to re-participate; (3) declining telephone response rates threaten representativeness; (4) the survey prompts respondents reporting ‘unreasonable’ expectations, with the threshold endogenously tied to recent inflation history; (5) the question wording asks about ‘prices going up’ rather than ‘aggregate U.S. inflation’, making the measure closer to consumption-basket-specific expectations — which the paper treats as a feature rather than a flaw for its identifying assumption. The paper addresses concerns (1)–(4) through alternative specifications (first-time-only respondents, outlier removal, CPS vs. survey shares). The geographic dimension is limited to four Census regions because finer location identifiers are unavailable for a long panel.

Key Concepts

Shift-share (Bartik) instrument for expectations: In this paper, the instrument for regional inflation expectations is constructed by interacting each demographic group’s national-level mean inflation expectation (the ‘shift’) with that group’s population share in the region (the ‘share’). The resulting weighted average predicts how much regional expectations would be elevated purely by the region’s demographic composition reacting to aggregate group-level expectation shocks, isolating variation plausibly orthogonal to region-specific inflation supply shocks.

Differential exposure quasi-experiment: The identification design exploits the fact that U.S. Census regions have different demographic compositions, giving them differential exposure to aggregate shocks in group-specific inflation expectations. Regions with a higher share of a group whose expectations are rising will see a larger predicted increase in regional expectations than regions with a lower share of that group, independent of region-specific factors — this cross-regional contrast is the source of causal identification.

Rotemberg weights: Following Goldsmith-Pinkham, Sorkin, and Swift (2020), the Bartik 2SLS estimate is decomposed as a weighted sum of 160 just-identified group-specific estimates, where the weight αg for group g measures the sensitivity of the overall estimate to potential endogeneity in group g’s share. Groups with large αg drive identification and are the groups most important to probe for exogeneity. In this paper, the heaviest-weighted groups are younger, married consumers with at least a high school degree.

Anticipated utility / steady-state learning: The paper’s theoretical model allows for non-rational subjective expectations. Firms and households are modeled as ‘anticipated utility’ maximizers (Woodford 2013) who adjust expectations over time (’learning’) but assume for current decisions that expected inflation will remain at its present rate — termed ‘steady-state learning’ by Evans and Honkapohja (2001). This assumption implies future prices evolve along a linear trend from current expectations, yielding a tractable closed-form link between current expectations and the sector-specific price-setting equation.

Heterogeneous consumption baskets as identification: The paper’s core identifying assumption is that different demographic groups consume different bundles of goods across sectors, so their inflation expectations reflect the price changes in their own basket rather than a common aggregate signal. This basket heterogeneity is what makes group-level expectations differ systematically and allows the shift-share instrument to generate exogenous variation in regional inflation expectations.

Lower bound interpretation of regional estimates: The 2SLS estimates capture only the regional (within-country, across-region) effect of expectations on inflation, because time fixed effects absorb cross-regional spillovers — if expectations rise in one region, the increased demand for traded goods spills into other regions and raises their prices too. The paper argues the regional estimates are therefore a lower bound on the aggregate pass-through from expectations to overall U.S. inflation, consistent with the stronger aggregate correlation seen in Figure 1a.

Long-run expectations nullity: The paper’s extension finds that 5-to-10 year inflation expectations, instrumented with their own shift-share Bartik and included alongside the one-year instrument, have no statistically or economically significant causal effect on regional inflation once time fixed effects control for aggregate factors. This result implies that, conditional on short-run expectations and macroeconomic controls, long-horizon expectations carry no independent causal information for the current inflation rate.

Increasing Inventories: The Role of Delivery Times

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

Layer 1: Overview

This paper documents and explains a previously unreported reversal in U.S. manufacturing inventory trends: after a 25-year secular decline, inventories-to-sales ratios have been rising steadily since 2005. The central claim is that this reversal is driven by the rise of global sourcing, which lengthens and makes more volatile the delivery times of inputs, compelling firms to hold larger buffer stocks. The paper combines new empirical evidence with a calibrated quantitative model to attribute 81% of the post-2005 inventory rise to global sourcing.

The research question is timely: while the efficiency gains from global sourcing are well-documented, the risk implications—particularly for inventory behavior—have received scant attention. The inventory trend reversal itself was previously undocumented. The average U.S. manufacturing firm held 1 month and 4 days of sales as inventories at the lowest point in December 2005; by end of 2019, firms were holding an additional 12 days of sales as inventories. This reversal is present across all NAICS three-digit manufacturing industries (except Paper Manufacturing), all inventory types (finished goods, materials/supplies, work-in-process), public firm data from Compustat, and in the manufacturing sectors of Australia, Canada, Japan, and South Korea. Within inventory types, intermediate-input inventories show the steepest decline and rise, directly implicating input sourcing decisions.

Contemporaneously, the share of foreign inputs in U.S. manufacturing production rose from 13.3% in 1997 to 16.5% in 2018, with approximately 3 percentage points of that increase attributable to inputs from China. The distance traveled by imports rose at an average annual rate of 6% from 1995 to 2018 across the U.S. and four peer countries. Since roughly 80% of Chinese imports arrive via ocean and take approximately 25–35 days in transit (with around 30% of shipments arriving more than one day late), the shift toward Chinese inputs materially increases both the mean and the variance of delivery times. Cross-industry regressions confirm the link: a 10% increase in foreign inputs is associated with a 7% rise in intermediate-input inventories (controlling for industry value added).

To quantify the causal role of delivery times, Carreras-Valle builds a dynamic partial-equilibrium model of final-good firms that source both domestic and foreign inputs, stock inventories, and face iid firm-specific demand shocks. The key methodological innovation is a tractable formulation of stochastic delivery times: a random fraction λ of the ordered inputs arrives within the period and can be used for production, while the remainder arrives in the following period. This setup nests as special cases the fixed one-period lag used in prior literature, while permitting calibration to observed lead-time distributions and enabling comparative statics across the full distribution of delivery times. The model features CES aggregation of domestic and foreign inputs (elasticity σ = 0.8, from Boehm, Flaaen, and Pandalai-Nayar 2017), Cobb-Douglas technology with an input share α = 0.63 (from BEA Input-Output Tables), and monopolistic final-good producers.

The model is calibrated to 1992 U.S. manufacturing and then subjected to two observed trends: (i) a technology channel—decreasing mean and variance of domestic delivery times, calibrated to ISM lead-time data (mean 35 days in 1992, declining thereafter); and (ii) a trade channel—a falling relative price of foreign inputs, calibrated to match the 3 percentage point rise in the Chinese input share, implying an approximately 1% average annual decline in the foreign-to-domestic input price ratio. The model generates the full U-shaped inventory trend as an untargeted prediction, accounting for 50% of the 1992–2004 decline (data: −2.3% per year; model: −1.2% per year) and 81% of the 2005–2018 rise (data: +1.2% per year; model: +1.0% per year).

A key structural decomposition reveals that the total inventory rise is driven entirely by foreign inventories (rising at +1.5% per year), which more than offset the continuing decline in domestic inventories (−0.5% per year). Firms require both channels: the technology channel alone produces initial decline but no subsequent rise; the trade channel alone generates a monotone increase that misses the initial decline. Further, the model decomposes inventory incentives into demand risk (the interaction of positive delivery times with demand volatility) and delivery-time risk (the variance of λ). Demand risk accounts for most of the level of inventories; delivery-time risk accounts for the growth in inventories over time—especially important as firms shift toward foreign inputs subject to frequent delays.

The model also characterizes an aggregate efficiency-volatility tradeoff from globalization. Comparing an economy with the 2018 share of foreign inputs (16%) to one fixed at the 1992 share (13%), output rises 13.9% and the price level falls 2.6% in the more globalized economy, but the standard deviation of prices rises 9.7% and the standard deviation of output rises 12.3%. The share of firms experiencing stock-outs rises from 8% to 12%. Even with higher inventories, firms cannot fully insure against the amplified demand risk, so price and output volatility rise. Results are robust to alternative values of the demand elasticity (ε = 1.5, 4), the input substitution elasticity (σ = 0.6, 0.8, 1.5), and storage costs (δ = 5%, 7.5%, 15%).

In depth

Q1. What is the core identification strategy for the empirical relationship between foreign inputs and inventories, and what are the main threats?

The paper uses panel regressions of log inventories on log imported inputs with industry and year fixed effects, covering NAICS three-digit manufacturing industries from 1997 to 2018. The industry fixed effects absorb time-invariant industry characteristics that correlate with both import intensity and inventory needs; year fixed effects absorb common macro trends. The main threat is omitted variables that are industry-time varying: for instance, a demand boom that simultaneously induces firms to import more and stock more could generate a spurious correlation. The author partially addresses this by controlling for value added, showing the elasticity falls from 0.59 to 0.35 for total inventories (and from 0.72 to 0.42 for input inventories) but remains positive and significant. The author also presents results separately for inputs from China specifically, where a 10% increase in Chinese inputs is associated with 2–5% higher inventories (Table 1, columns 7-8), and replicates results with three independent data sources (WIOD, OECD I-O Tables, U.S. Census end-use classification), all showing consistent findings.

Q2. What is the main mechanism by which delivery times raise inventory holdings, and how does it differ from the delivery-time risk mechanism?

The primary mechanism is demand risk exposure: because firms must order inputs before demand is realized, and because a share of the order only arrives in the following period, longer delivery times reduce a firm’s ability to respond to the current period’s demand shock using new orders. Firms therefore hold buffer inventories to bridge the gap. This mechanism operates even when delivery times are positive but deterministic (the dashed line in Figure 15), and it accounts for most of the level of inventories. The secondary mechanism is delivery-time risk: since the fraction λ that arrives is itself stochastic, firms also hold inventories to insure against low-λ realizations (input shortfalls). Delivery-time risk contributes less to the level of inventories but accounts for a disproportionate share of the growth in inventories over time, because growth accelerates as firms shift toward foreign inputs—subject to more frequent ocean-shipping delays—come to dominate the input mix. The model separates the two by running a scenario with deterministic but positive delivery times (demand risk only) against the full stochastic model.

Q3. How does the paper model delivery times, and what is novel about this approach relative to the literature?

The paper introduces a tractable stochastic delivery-time specification in which a firm-specific iid fraction λ drawn from an input-specific log-normal distribution G_i(μ_λ, σ_λ) arrives within the period and is available for production, while (1−λ) of the order arrives at the start of the next period and is added to the following period’s inventory. The literature had largely assumed a fixed deterministic one-period lag (all inputs arrive exactly one period later). One exception is Alessandria, Kaboski, and Midrigan (2010b), who model a binary probability-of-arrival (either the entire order arrives now or next period); Carreras-Valle’s formulation allows a stochastic share to arrive, which accommodates heterogeneous delivery time distributions across inputs and enables direct calibration to observed lead-time data from ISM and Freightos. This flexibility permits the paper to match different mean and variance profiles for domestic versus foreign inputs and to study how marginal changes in the delivery-time distribution affect sourcing and inventory choices.

Q4. What data sources are used, and how are the key variables constructed?

Inventory and sales data come from the U.S. Census Bureau’s Manufacturers’ Shipments, Inventories, and Orders (M3) survey, matched to NAICS three-digit industries (monthly, 1992–2018; petroleum sector NAICS 324 excluded). Firm-level inventory data are from WRDS Compustat. Imported input shares by country of origin are constructed from U.S. Census Bureau import data (retrieved from Schott 2008), apportioned using BEA Input-Output Tables following the BEA’s own import-matrix methodology: the share of imports from country i used as inputs in industry j is assumed proportional to country i’s share of total U.S. imports in that sector. This is robust to using WIOD and OECD I-O tables. Domestic delivery times are from the ISM Manufacturing PMI, adjusted to remove foreign transit times using Chinese transit data, then smoothed with the Hodrick-Prescott filter. Foreign delivery times are calibrated to Freightos ocean-shipping data for the U.S.–China route (25 days to West Coast, 35 days to East Coast, combined average 30 days plus 35 days domestic transit). Distance of imports uses CEPII Gravity dataset population-weighted distance weighted by dollar value of imports by origin country.

Q5. How does the model generate the inventory trend as an untargeted moment, and what does it miss?

The model is calibrated to match only two 1992 moments (the level of input inventories over output and the share of foreign inputs in 1992). The time path of inventories from 1992 to 2018 is then entirely untargeted. Given the estimated paths of domestic delivery times (declining from ISM data) and the relative price of foreign inputs (declining at roughly 1% per year to match the observed import share), the model generates a U-shaped inventory trend qualitatively and quantitatively similar to the data. The main shortcoming is timing: the model’s inventory reversal begins around 2003, two years ahead of the 2005 reversal in the data. The author attributes this gap to China’s WTO accession in 2001 feeding into the model’s trade channel immediately, whereas in reality adjustment lags and other factors may have delayed the full inventory response. The model accounts for 50% of the initial decline and 81% of the subsequent rise, leaving room for other forces including changes in demand volatility (e.g., rising trade-policy uncertainty, Amazon’s market penetration), improvements in inventory-storage technology, and the low-interest-rate environment.

Q6. What heterogeneity is documented across industries and types of inventories?

The inventory trend is present across all NAICS three-digit manufacturing industries except Paper Manufacturing (NAICS 322, which represents only 3% of total manufacturing inventory). Import-intensive industries show the largest growth in inventories: sorting industries into terciles by average imported-input intensity (1997–2018), the most import-intensive group shows the largest decline and the sharpest subsequent rise in both total and intermediate-input inventories. Among the three inventory types, intermediate-input inventories (materials/supplies + work-in-process) show the steepest decline and steepest rise, consistent with sourcing decisions being the primary driver. Finished-goods inventories also rise but less sharply. The cross-sectional slope between imported-input intensity and inventories is 0.3 for total inventories and 0.9 for intermediate-input inventories. The trend is also present in four other countries’ manufacturing sectors (Australia, Canada, Japan, South Korea), with the distance of imports rising at 6% per year on average across these countries, suggesting the phenomenon is a global consequence of globalization.

Q7. What are the robustness checks?

The paper presents extensive robustness. For the empirical inventory trend: the U-shaped pattern holds when including the petroleum and coal sector (NAICS 324), when excluding the transportation sector (NAICS 336), and using the long-horizon NBER-CES Manufacturing Industry Database from 1958 (annual, 6-digit NAICS). The positive relationship between imported inputs and inventories is robust to using WIOD, OECD I-O Tables, and the U.S. Census end-use classification as alternative data sources, and appears consistently in both cross-sectional and time-series regressions. For the quantitative model: the inventory trend is robust to alternative values of the final-good elasticity of substitution (ε = 1.5 and 4), the domestic/foreign input substitution elasticity (σ = 0.6, 0.8, 1.5), and storage costs (δ = 5%, 7.5%, 15%). The qualitative proposition that inventories increase with delivery times is proved formally for the full multi-input model (Appendix C), not just for the simplified one-input version.

Q8. How does this paper relate to and differ from the closest prior work on inventories?

The paper builds directly on Khan and Thomas (2007) and Alessandria, Kaboski, and Midrigan (2010a) for the theoretical framework of inventories in general equilibrium. It departs from both by introducing stochastic and heterogeneous delivery times rather than a fixed one-period lag. The earlier literature on the inventory decline (Ohno 1988 just-in-time; Feinberg and Keane 2006; Dalton 2013; Shirley and Winston 2004; Li and Li 2013; Cui and Li 2018) focused exclusively on the downward trend attributed to improvements in transportation and information technology. This paper is the first to document the reversal and to introduce a model that accommodates both the decline and the subsequent rise through opposing forces. The inventory-import nexus has been documented in firm-level data for Chilean firms (Alessandria, Kaboski, and Midrigan 2013) and Indian firms (Khan and Khederlarian 2020), but this paper is the first to show the relationship across U.S. manufacturing industries and to tie it explicitly to China’s WTO accession and the delivery-time channel. It also contributes to the global supply chain risk literature (Baldwin and Freeman 2022) by quantifying inventories as the instrument firms use to absorb that risk.

Q9. What does the efficiency-volatility tradeoff finding imply for policy, and what are its scope conditions?

The model’s key aggregate implication is that globalization—access to cheaper foreign inputs—raises output and lowers prices on average, but simultaneously raises macroeconomic volatility because longer delivery times amplify demand shocks. Specifically, moving from the 1992 to the 2018 import share raises average output 13.9% and lowers the average price level 2.6%, but raises price volatility by 9.7% and output volatility by 12.3%. The share of firms in stock-out (constrained) rises from 8% to 12%. This tradeoff is not negated by the endogenous inventory response: firms do hold more inventories with globalization, but optimal inventory holdings leave some demand states unmet because insuring fully against all demand shocks is prohibitively costly. Policy implications are cautionary: reshoring or restricting imports to reduce delivery-time risk would reduce volatility but at the cost of lower average output and higher prices. The scope conditions are important: the model abstracts from labor reallocation, firm entry/exit, foreign-firm productivity dynamics, and consumer welfare under price variability. The calibration is to U.S. manufacturing 1992–2018, and the foreign input price trend is modeled as a single composite (China-focused) reduction, so the quantitative results may not generalize to settings where trade partners differ substantially.

Q10. What alternative explanations for the inventory rise does the paper consider or rule out?

The paper acknowledges three alternative forces that could contribute to the post-2005 inventory rise but are not modeled: (1) increasing demand volatility (e.g., from Amazon’s market penetration or rising trade-policy uncertainty), which would raise the value of inventories through the demand-risk channel; (2) improvements in inventory storage technology, which lower the cost of holding inventories; and (3) the low-interest-rate environment post-2008, which reduces the opportunity cost of holding inventories. The paper argues these are not the focus and that the delivery-time channel alone can explain 81% of the rise, leaving a residual 19% for which these other factors could account. The demand variance is held constant in the benchmark, so any time-varying demand risk that coincided with the post-2005 period is absorbed into the unexplained residual. The model is described as flexible enough to accommodate and quantify these forces if desired.

Q11. What is the model’s treatment of the technology channel and how is it calibrated?

Technology improvements are modeled as a steady reduction in the mean and variance of the domestic delivery-time distribution, proxying for advances in transportation infrastructure (high-speed rail, road investment, air freight) and information technology (just-in-time management, ERP systems). The mean of domestic delivery times is calibrated to ISM monthly data on average commitment lead times for production materials and maintenance/operation supplies, adjusted for the growing foreign input share (subtracting the fraction of ISM-reported lead times attributable to Chinese ocean transit), then smoothed with an HP filter. The mean starts at 35 days in 1992 and declines thereafter, with a mild uptick after 2003–2004. The variance is treated as a fixed proportion of the mean, so it co-moves with the mean. In the model this declining domestic delivery time reduces the value of holding domestic inventories, generating the observed decline in the domestic component of the inventory ratio (−0.5% per year over the full period). When only this channel is simulated (holding foreign input shares fixed at 1992 levels), inventories initially decline but then stagnate or rise only slightly—the trade channel is required to produce the full post-2005 acceleration.

Key Concepts

Delivery time (λ): In the model, the fraction of an input order that arrives within the current period and is available for production, where 1−λ arrives at the start of the following period. Calibrated as λ = max(0, 1 − delivery_days/T) where T = 90 days per quarter. A lower λ means longer delivery times and greater exposure to demand shocks.

Global sourcing: The practice of firms sourcing production inputs from distant foreign locations to exploit cost advantages, specifically the substitution of domestic inputs for cheaper inputs from countries such as China. In this paper it is the primary driver of rising inventories after 2005, because foreign inputs carry longer and more volatile delivery times than domestic alternatives.

Delivery-time risk: The volatility component of the delivery-time shock: because λ is drawn from a distribution with positive variance, firms face uncertainty about what fraction of an order will arrive in the current period. Distinct from demand risk (uncertainty about the quantity demanded). Delivery-time risk accounts primarily for the growth of inventories over time as reliance on volatile-delivery foreign inputs increases, rather than for the level of inventories.

Inventory-intensive inputs: Inputs—primarily foreign inputs in this paper’s framework—that by virtue of their long and/or volatile delivery times require firms to hold a disproportionately large stock of inventories per unit of input used. Foreign inputs from China are inventory-intensive because ocean transit averages 25–35 days and is subject to frequent delays.

Stock-out: An event in which a firm’s available input inventory (on-hand stock plus the fraction of the current order that arrives in time) is insufficient to satisfy its realized demand. When a stock-out occurs, the firm raises its price until the consumer is willing to demand only what the firm can supply. Longer delivery times increase stock-out frequency: the share of constrained firms rises from 8% to 12% as the economy moves from 1992 to 2018 import shares.

Efficiency-volatility tradeoff: The aggregate implication of globalization in the model: a higher share of cheaper foreign inputs lowers average prices and raises average output (the efficiency gain), but simultaneously raises the volatility of prices and output because longer delivery times amplify demand shocks and increase stock-out frequency. Inventories partially but incompletely offset this volatility increase.

Technology channel vs. trade channel: Two opposing forces shaping the delivery-time distribution over 1992–2018. The technology channel (improvements in transportation and information technology) reduces the mean and variance of domestic delivery times, lowering inventory incentives. The trade channel (China’s WTO accession and rising productivity driving down foreign input prices) shifts the input mix toward foreign inputs with longer and more volatile delivery times, raising inventory incentives. Both channels are necessary to reproduce the observed U-shaped inventory trend.

Information and the Formation of Inflation Expectations by Firms: Evidence from a Survey of Israeli Firms

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

Layer 1: Overview

Research question and motivation. How do firms form and update inflation expectations during a monetary-policy regime change and a transition from high/volatile inflation to a low, stable, inflation-targeting environment? This matters because tracking and managing expectations is central to modern monetary policy (especially under forward guidance), yet high-quality firm-level expectations data—particularly across regime changes—are scarce (Bernanke 2007). A central tension in the literature is that firms and households in long-stable advanced economies are largely inattentive to inflation and monetary policy, plausibly because successful stabilization removes the incentive to monitor them. Israel offers a natural experiment: its recent history of high inflation and dollarization, followed by disinflation, de-dollarization, and the anchoring of expectations at the ~2% target midpoint around 2003.

Data and design. The authors use the Bank of Israel Firms’ Survey, a quarterly survey (quantitative inflation-expectation questions added in 1997), covering six industries (post-2009 shares: manufacturing 36%, services 36%, commerce 14%, transportation/communications 5%, hotels 5%, construction 4%). The main analysis sample is 2001Q3–2018Q3. The survey is voluntary, unbalanced, not nationally representative; late-sample participation fell to ~250–300 firms with a response rate around 30%. Identification exploits within-quarter variation in response timing: because Israel’s CPI is published monthly on the 15th and policy-rate decisions are scheduled, firms responding after a release (“treatment”) had information that firms responding earlier (“control”) did not. Surprises are defined relative to professional forecasters’ mean expectations: an inflation (CPI) surprise and a monetary (policy-rate) surprise. Identification assumes response timing is random; the authors show firm characteristics generally do not predict either response period (Table 4) or the cross-section of expectations (Table 3). Estimation uses two-way (firm and quarter) fixed-effects panel regressions interacting treatment dummies with surprise size, plus a lagged dependent variable; local projections (Jordà 2005) first show output/employment respond to the shocks, motivating that beliefs should too.

Main quantitative findings (Table 9, full sample 2001Q3–2018Q3). A positive inflation surprise of one percentage point raises 1-year inflation expectations by about 0.5 pp from the second-monthly-CPI surprise (coefficient 0.467) and about 0.7 pp from the third-monthly-CPI surprise (0.700). The effect on 1-quarter expectations is weaker (≈0.12 and ≈0.29). Because the annual response exceeds the quarterly response, firms on average treat CPI surprises as persistent, not transitory. A surprise one-percentage-point hike in the policy rate lowers 1-year inflation expectations by about 0.3 pp (coefficient 0.343, negative sign) and 1-quarter expectations by roughly 0.15 pp. The mean second-month-CPI treatment dummy itself is small (-0.07 pp), so the interaction terms carry the economic content.

Mechanisms and scope conditions. The inflation-surprise result is robust across sub-periods, before/after 2010, firm sizes, and industries. The monetary-surprise result is NOT robust: dropping the large 2001–2002 policy shocks (sample 2002Q3–2018Q3) renders it insignificant and sign-flipped, consistent with policy shocks having little effect on beliefs in stable environments (Coibion et al. 2020; Ilek 2021 for Israeli forecasters). Implication: even after de-dollarization and prolonged low/stable inflation, Israeli firms keep monitoring macro news; (re)anchoring expectations—making them insensitive to news—may take a long time, an insight relevant for countries now facing high inflation.

In depth

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

The strategy exploits variation in survey response timing within each quarter. Because Israel publishes CPI on the 15th of each month and policy-rate decisions are on scheduled dates, firms that respond after a release (treatment) have seen information that firms responding earlier (control) have not. Responses are grouped into Periods 1, 2, 3 (and Period 0 for missing/late dates), generating two CPI surprises (second- and third-monthly index) and one interest-rate surprise per quarter. The key identifying assumption is that response timing is as-good-as random. The main threat is selection—if attentive or expectation-distinctive firms systematically respond later, treatment status would be endogenous. The authors address this by regressing exposure-period indicators on observable firm characteristics (Table 4) and finding characteristics generally do not predict response period; they also confirm firm characteristics do not explain cross-sectional expectation levels (Table 3). A placebo test replacing the dependent variable with the prior quarter’s expectation (t-1) finds no effect (Appendix Table B5), supporting the timing identification. A residual threat is unobservable correlates of timing not captured by observables.

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

Two mechanisms: (1) firms update inflation expectations to new CPI information, and (2) firms update to monetary-policy information. They are distinguished by using separate, independently timed surprises (CPI releases vs. policy-rate decisions) and separate interaction terms. Persistence vs. transitory perception is inferred from the horizon pattern: because the 1-year response to a CPI surprise (~0.5–0.7 pp) exceeds the 1-quarter response (~0.12–0.29 pp), firms must expect the price increase to continue over subsequent quarters, i.e., they perceive CPI shocks as persistent. For monetary policy, the smaller 1-quarter than 1-year effect is read as consistent with monetary policy operating with a lag. The output/employment local projections (Table 8) show a non-monotonic response to rate surprises (rises in quarters 0–1, declines in quarters 2–3), which the authors note could mix conventional contractionary effects with an information effect (a higher rate signaling a stronger economy).

Q3. What heterogeneity is documented?

By firm size (Table 11): all three size groups (small, medium, large) respond to CPI surprises on 1-year expectations and the differences across groups are generally not statistically significant; the interest-rate-surprise effect resembles the pooled estimate for medium and large firms but is not statistically significant for small firms. By industry (Table 12): the CPI-surprise effect on 1-year expectations is positive and statistically significant in nearly every industry, whereas the interest-rate-surprise effect on 1-year expectations (full sample) is negative and significant only in manufacturing. Over time (Table 10): the 1-year CPI-surprise effect is almost identical before and after 2010 (the year the monetary committee was established), and the 1-quarter effect is similar or if anything stronger in the later period. Cross-sectionally, firm size, industry, and region are mostly statistically and economically insignificant predictors of expectation levels (Table 3).

Q4. What robustness checks are run?

(1) Shorter sample 2002Q3–2018Q3 excluding the large 2001–2002 policy shocks—CPI-surprise results essentially unchanged, monetary-surprise results become insignificant and change sign. (2) Split before/after 2010 allowing time-varying effects (Table 10). (3) Heterogeneity by size (Table 11) and industry (Table 12) as consistency checks. (4) A placebo test regressing the previous quarter’s (t-1) expectation on current-quarter news, finding no effect (Appendix Table B5). (5) Checks that firm characteristics predict neither response timing (Table 4) nor expectation levels (Table 3), supporting the random-timing assumption. (6) Local projections on output and employment (Table 8) establishing that firms’ real-side behavior responds to the shocks, motivating belief responses. Standard errors are White and clustered at the firm level throughout.

It builds on the firm-expectations literature (Coibion, Gorodnichenko, Kumar 2018; Candia, Coibion, Gorodnichenko 2023) showing firms’ expectations lie between professional forecasters’ and households’—confirmed here by intermediate disagreement among firms. It connects to expectation-formation work (D’Acunto et al. 2021 on shopping experience; Coibion-Gorodnichenko 2015 on exchange-rate sensitivity in Ukraine; Kumar et al. 2015 on New Zealand managers) and to studies of news effects on expectations (Beechey, Johannsen, Levin 2011). It is closest in spirit to Lamla and Vinogradov (2019), who compare household expectations before/after monetary announcements; the contribution is to study firms in an economy with a recent history of high inflation and dollarization undergoing disinflation. It also relates to regime-change classics (Sargent 1982 on ending hyperinflations; Mankiw, Reis, Wolfers 2003 on Volcker disinflation), filling the gap that little is known about firms’ expectations across a policy-regime change. Its Israeli monetary-surprise null in the stable period echoes Coibion et al. (2020) and Ilek (2021).

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

Central implication: even after successful de-dollarization and a prolonged low-and-stable inflation environment, Israeli firms continued to monitor and react to inflation news—so de-dollarization (firms’ renewed trust in local currency) does not necessarily translate into inattention, and (re)anchoring expectations in the sense of making them insensitive to news may take a long time. For countries currently experiencing high inflation, the Israeli experience suggests firm expectations can remain news-sensitive for an extended period. Scope conditions: the firm sample is not nationally representative; results are specific to Israel’s institutional setting (monthly CPI on the 15th, scheduled rate decisions); the monetary-policy result is fragile—it is driven mainly by the unusually large 2001–2002 shocks and disappears in calmer periods, so the conclusion that monetary surprises move firm expectations holds chiefly when shocks are large.

Q7. Are there other significant findings or caveats?

Descriptive facts: firms’ average annual inflation expectations (2001Q3–2018Q3) averaged 2.34% (vs. 1.81% for professional forecasters, 1.57% for the capital market); in the 2011Q1–2018Q3 panel households averaged 3.02% while firms averaged 1.83%, banks 1.07%. Firms’ expectations are about one percentage point below households’ but 0.5–1 pp above other (forecaster/market) sources, and disagreement among firms lies between that of households and professional forecasters—consistent with prior literature. Expectations co-move strongly across sources and across industries. Raw cross-period descriptive evidence (Table 5) shows average and median expectations decline as more information becomes available (Period 1 mean 2.52 → Period 3 mean 2.26), and disagreement weakly declines. The largest interest-rate surprises (1.5–2 pp) occurred at the sample start: in December 2001 the Bank cut the rate by 2 pp to 3.8%, triggering capital outflow, depreciation, and price increases, then reversed to 9.1%. A caveat is that the survey was discontinued at end-2020 (replaced by a CBS survey), and the unbalanced, voluntary panel limits representativeness.

Key Concepts

Monetary Policy without Commitment

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

Layer 1: Overview

Research question and motivation: Post-pandemic inflation across advanced economies rose to levels not seen since the early 1980s, reviving interest in central bank credibility. The standard quantitative macro models used to interpret this episode assume exogenous central bank reaction functions and inflation targets, which limits their usefulness. This paper instead makes monetary policy endogenous: a welfare-maximizing central bank that lacks the ability to commit re-optimizes every period. The goal is to characterize how lack of commitment shapes long-run inflation and transition dynamics, questions that prior credibility work (Barro-Gordon 1983; Rogoff 1985) could not address because it used static or log-linearized settings.

Model setup: The authors embed central bank lack of commitment into a standard fully non-linear New Keynesian model (not log-linearized around zero-inflation steady state). Monopolistically competitive firms set prices under Calvo rigidity: a random fraction 1-theta resets prices each period, the rest keep last period’s price. Wages are flexible; households choose consumption, labor, savings. The environment is deterministic with permanent unanticipated shocks. An exogenous proportional labor wedge tau (payroll tax capturing taxes, regulation, unionization) is assumed large enough (Assumption 1: tau > -1/sigma) that monopoly distortions persist. Two distortions operate: monopoly power (underproduction) and price dispersion from sticky prices (labor misallocation). The solution concept is Markov Perfect Competitive Equilibrium. Crucially, firms set prices BEFORE the central bank sets the interest rate, so the central bank takes the price distribution (hence dispersion D_t) as predetermined and optimally sets static welfare-maximizing policy: it eliminates monopoly distortions by setting the labor share to 1 (Y_t = D_t^{-1}). Equilibrium reduces to two difference equations: a forward-looking non-linear Phillips curve and a backward-looking price-dispersion law of motion, yielding a unique steady state. The analysis is conducted in a continuous-time limit for transition dynamics.

Main findings (with magnitudes and scope): (1) Long-run inflation is determined by the interaction of lack of commitment and the environment; steady-state inflation and price dispersion are strictly increasing in the labor wedge tau and strictly decreasing in the elasticity of substitution sigma (the dispersion comparative static in sigma holds for tau below a threshold tau-bar(sigma); the inflation comparative static is unambiguous). (2) Transitions to a higher-inflation steady state feature inflation OVERSHOOTING: inflation jumps on impact then gradually declines, because the central bank’s incentive to stimulate is largest early when dispersion/misallocation are low. (3) Quantitative magnitudes are large. Calibration (monthly): beta=(1.02)^{-1/12}, theta=0.86 (7-month price duration, Nakamura-Steinsson 2008), sigma=7 (Coibion et al. 2012), psi=2.5 (Chetty et al. 2011), tau=-0.1427 to target 2% annual inflation. A permanent 0.5% increase in the labor wedge raises steady-state inflation from 2% to 8.76%, with inflation overshooting to 10.11% on impact; it takes 12 months to decline within 25 basis points of the new steady state. A 0.5% decrease in sigma yields similarly large effects.

Implications: Welfare under inflation targeting strictly exceeds that under no-commitment in both shock scenarios; the welfare gain is about 6% in consumption-equivalent terms (targeting 0.981 vs no-commitment 0.922/0.921). The large magnitudes stem from a nearly vertical long-run Phillips curve (the labor share is insensitive to inflation when beta is near 1). Post-pandemic shocks (lower immigration raising the labor wedge; reduced globalization/supply-chain disruption lowering sigma) do not raise inflation on their own but do so through their interaction with central bank lack of commitment, and may make returning inflation to historic norms unlikely absent strict commitment to inflation targeting.

In depth

Q1. What is the identification/solution strategy, and what makes the model tractable?

This is a theory paper, so ‘identification’ is the equilibrium characterization rather than econometric identification. The authors solve for Markov Perfect Competitive Equilibria of a fully non-linear (not log-linearized) New Keynesian model. Tractability comes from the timing assumption: flexible-price firms set prices BEFORE the central bank chooses the interest rate. Because the equilibrium is Markov, the central bank at date t takes the price distribution (and hence future dispersion D_{t+1} and continuation value V(D_{t+1})) as predetermined; it cannot change future welfare off the equilibrium path. So it optimally maximizes STATIC welfare conditional on current dispersion, yielding the simple first-order condition Y_t = D_t^{-1} (labor share = 1). Equilibrium then reduces to two difference equations in inflation (forward-looking Phillips curve) and dispersion (backward-looking), giving a unique steady state. A key technical innovation is an auxiliary variable delta_t (the inverse of a discounted sum of future relative prices) capturing the passthrough of real wages to current inflation holding future inflation fixed, which itself has a recursive representation and is related to the slope of the Phillips curve.

Q2. What is the core economic mechanism generating higher long-run inflation under lack of commitment?

Starting from a steady state, a permanent rise in tau (or fall in sigma) increases monopoly distortions and would, under commitment, lower the labor share while keeping inflation fixed. But a no-commitment central bank wants to undo the rise in monopoly distortions by cutting interest rates and stimulating output to push the labor share back to 1. Flexible-price firms rationally anticipate this future stimulus, higher future labor demand, and higher future real wages, so they raise prices today to offset expected future costs. Sequential price increases raise price dispersion. The economy converges to a new steady state once rising dispersion reduces aggregate productivity (labor misallocation) enough that the central bank’s marginal benefit from cutting rates vanishes. Hence both long-run dispersion and inflation are permanently higher.

Q3. Why does inflation overshoot in the transition rather than monotonically rise?

Overshooting arises from the evolution of central bank incentives as dispersion rises along the transition. Early in the transition, dispersion and labor misallocation are low, so stimulating output to boost consumption is relatively beneficial; later, once dispersion/misallocation are high, the productivity cost of stimulation is high and the benefit falls. Flexible-price firms anticipate that monetary stimulus is front-loaded, so they front-load their price increases. The result is high inflation early that declines toward the new (lower but still elevated) steady-state level. In the phase diagram (dispersion-inflation plane, holding delta fixed), the dispersion-zero locus is upward sloping and the inflation-zero locus is downward sloping; the saddle path has negative slope, so along it inflation and dispersion move in opposite directions. A labor-wedge shock shifts the inflation-zero locus up (leaving the dispersion locus unchanged); inflation jumps to the new saddle path then declines as dispersion rises.

Q4. Why are the quantitative magnitudes so large?

The steady-state labor share is relatively insensitive to inflation because the positive effect of inflation on the labor share (via overhiring sticky-price firms) is largely offset by the negative effect via forward-looking flexible-price firms that raise prices to protect against future overhiring. Standard New Keynesian calibrations use high beta and low theta, so there is a large fraction (1-theta) of flexible-price firms that raise prices substantially, putting downward pressure on the labor share. Formally, the long-run Phillips curve linking labor share mu and inflation Pi (equation 33) becomes almost vertical when beta is near 1. A nearly vertical long-run Phillips curve means small changes in tau or sigma require large changes in inflation to keep mu unchanged. Implication: any change that flattens the long-run Phillips curve would shrink the magnitudes, lower the value of commitment, and imply meaningful benefits from positive long-run inflation.

Q5. What is the central bank’s reaction function and how does it compare to a Taylor rule?

Substituting the FOC Y_t = D_t^{-1} into the Euler equation gives 1 + i_t = (1/beta) * Pi_{t+1} * Y_{t+1} * D_t. This endogenously-derived rule resembles exogenous Taylor rules: the interest rate is increasing in expected future inflation and expected future output, and it also reacts to current price dispersion. Higher dispersion reduces labor productivity via misallocation, lowering the benefit of stimulating the economy, so the central bank raises rates. Like Atkeson, Chari, and Kehoe (2010), the central bank responds to off-equilibrium increases in inflation/dispersion by raising rates enough that an individual flexible-price firm would actually want lower price increases off the equilibrium path.

Q6. How does the comparative static differ between the labor-wedge shock and the elasticity-of-substitution shock?

Both raise long-run inflation and (generally) dispersion and produce overshooting. For inflation the comparative static is unambiguous in both cases. For dispersion, the tau result is clean (Dss strictly increasing in tau), but the sigma result requires a bound: Dss is strictly decreasing in sigma only for tau < tau-bar(sigma) (where tau-bar(sigma)=infinity if sigma<=2, else 1/(sigma^2-2sigma)), because sigma also enters the dispersion law of motion and could in principle make dispersion increase with sigma when tau is large. A second difference appears in the comparison with inflation targeting: under a tau shock, an inflation-targeting central bank keeps rates fixed, output falls permanently, and dispersion is unchanged. Under a sigma shock, sigma directly affects the dispersion-inflation relationship, so even under inflation targeting steady-state dispersion would decline (greater differentiation makes relative price differences a less important source of misallocation) and rates would adjust to facilitate the transition.

Q7. What is the welfare comparison and how is welfare measured?

Welfare is expressed in consumption-equivalent terms relative to an otherwise-identical flexible-price economy: how much consumption a household would require, right after the shock, to be indifferent between the sticky-price economy (under targeting or no-commitment) and a flexible-price economy with constant consumption and implied labor. For the labor-wedge shock: welfare under targeting 0.981 vs no-commitment 0.922 (difference 0.059). For the elasticity shock: targeting 0.981 vs no-commitment 0.921 (difference 0.060). In both cases targeting strictly dominates, with gains of about 6% consumption-equivalent. The intuition: targeting reduces the misallocation cost of long-run price dispersion, while no-commitment reduces the cost of rising monopoly distortions; the dispersion costs dominate, especially because high beta makes long-run costs weigh heavily.

Q8. How does this paper relate to and differ from prior work on credibility and non-linear monetary policy?

It extends the Barro-Gordon (1983) and Rogoff (1985) credibility tradition, which used static or linearized settings that cannot speak to long-run inflation or transition dynamics. It differs from Markovian linearized approaches (e.g., Halac and Yared 2022) which feature no transition dynamics and significantly OVERESTIMATE the effect of permanent shocks on long-run inflation (because linearization underestimates the welfare cost of rising dispersion). It departs from fiscal-commitment models (Alvarez-Kehoe-Neumeyer 2004; Aguiar et al. 2015) and from Davila-Schaab (2023, which uses quadratic adjustment costs and thus has no price dispersion) by emphasizing the Calvo dispersion cost and its dynamic feedback on the inflation-output tradeoff. Relative to the discretionary-multiplicity literature (Albanesi-Chari-Christiano 2003; King-Wolman 2004; Zandweghe-Wolman 2019), this model obtains a UNIQUE equilibrium and provides an analytical (not numerical) characterization of the steady state and transition. It also contributes a novel recursive representation of the non-linear Phillips curve via the auxiliary variable delta_t.

Q9. What are the transition dynamics of the macro variables in the calibrated exercise?

Following the permanent labor-wedge increase: inflation jumps up from 2% and gradually declines toward its higher steady state (overshooting). The nominal interest rate jumps up and continues rising throughout the transition (the higher steady-state nominal rate reflects the Fisherian effect present in the non-linear model). The real interest rate jumps DOWN initially (the central bank stimulates to weather the shock) then gradually returns to its original level. Output falls gradually as price dispersion and labor misallocation increase. Nominal wage inflation jumps up with price inflation but stays below it, converging from below; this gap underpins a permanent long-run decline in the real wage.

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

Permanent changes in the global economy (e.g., lower immigration shifting labor toward more regulated/higher-wedge sources; slower globalization or supply-chain disruptions raising domestic firms’ market power, i.e., lower sigma) can raise long-run inflation, but only through their interaction with central bank lack of commitment, not on their own. The post-pandemic inflation spike, and its overshooting, can be partly understood as the private sector rationally anticipating accommodative policy. Scope condition: this holds as long as the central bank operates with FULL DISCRETION; a strict commitment to inflation targeting would prevent it. There can therefore be significant benefits to institutions that enhance commitment. A caveat from the model’s own logic: if structural changes flatten the long-run Phillips curve, magnitudes shrink, the value of commitment falls, and there are real benefits to positive long-run inflation (so targeting too low an inflation rate would be costly).

Q11. What are the main caveats and directions for future research the authors flag?

The model is deterministic with permanent shocks and abstracts from monetary-fiscal interactions by assuming lump-sum taxes and Ricardian equivalence (debt is payoff-irrelevant, set to zero). It focuses on the stable steady state, setting aside equilibrium implementation and off-equilibrium inflation stability. The discretionary policy (labor share = 1) is invariant to the price-setting model, so the approach extends to menu-cost or rational-inattention models. Future work: relax Ricardian equivalence to study interactions between central bank and fiscal lack of commitment (facilitated by the framework not assuming a long-run debt level since it is not linearized), and examine off-equilibrium inflation stability.

Key Concepts

Nonlinear Monetary Policy Tradeoffs

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

Layer 1: Overview

This paper measures how the inflation-unemployment tradeoff associated with monetary policy varies with both the sign of the monetary intervention (easing versus tightening) and the state of the business cycle (booms versus recessions) for the US economy over 1973:M1 to 2019:M6. The motivation is that standard linear Phillips-curve estimates implicitly impose a constant tradeoff, yet a flat Phillips curve would simultaneously predict that (i) stimulating activity during a recession costs nothing in terms of inflation and (ii) reducing inflation costs very large amounts of unemployment — both empirically extreme predictions that have very different policy implications. The paper challenges both extremes.

The empirical strategy extends the Proxy-SVAR approach of Mertens-Ravn (2013) and Stock-Watson (2018) to a nonlinear setting. The economy is described by a Vector Moving Average augmented with nonlinear functions of the monetary policy shock — specifically its absolute value (capturing sign dependence) and its interaction with a recession indicator (capturing state dependence). Under a finite-order VARX representation assumption and a linear monetary policy rule assumption, the paper proves (Proposition 1) that even though the underlying VARX is nonlinear, the monetary shock can be recovered as the projection of an external instrument onto residuals of a misspecified linear VAR. Once the shock is recovered, it and its nonlinear functions are used as regressors in a VARX to estimate nonlinear impulse responses. The instrument is the Degasperi-Ricco (2022) extension of Miranda-Agrippino and Ricco (2021), with a baseline span of 1991:M1-2015:M12 extrapolated to the full sample. The VAR contains five variables: the 1-year Treasury bond rate, industrial production growth, the Gilchrist-Zakrajsek excess bond premium, the unemployment rate, and CPI inflation, estimated with 7 lags. The recession indicator equals 1 when average GDP growth over the previous 12 months is negative.

The monetary policy tradeoff is defined analogously to the fiscal multiplier: the ratio of the cumulative average impulse response of inflation (unemployment) to the cumulative average impulse response of unemployment (inflation) over horizons H. In a nonlinear setting the easing tradeoff and tightening tradeoff are no longer inverses of one another and must be treated separately.

The main quantitative findings are as follows. For monetary easing during recessions, the inflation cost of reducing unemployment is small and statistically insignificant: point estimates of T+ range from -0.03 to -0.17 (in absolute value) across horizons H = 12 to H = 48 months, with 68% confidence intervals spanning from approximately -5.3 to +2.8 at H = 12 and -3.4 to +2.7 at H = 48. For monetary tightening during booms, the unemployment cost of reducing inflation is moderate and statistically significant: T- estimates range from -0.51 to -0.61 across H = 12 to H = 48, with 68% confidence intervals entirely below zero (e.g., -1.10 to -0.26 at H = 12 and -1.23 to -0.24 at H = 48). In other words, reducing inflation by 1 percentage point during a boom requires raising unemployment by roughly 0.5 to 0.6 percentage points. These results are qualitatively robust to excluding the post-2008 zero-lower-bound period (pre-2009 subsample) and to alternative specifications. By contrast, monetary tightening during recessions implies a very large and unfavorable tradeoff. Easing during booms is extremely inflationary with virtually no real effect.

A Likelihood Ratio test for the null hypothesis that all nonlinear terms are zero is rejected at the 1% level, confirming the statistical importance of nonlinearities. The null hypothesis of shock invertibility (Assumption A4) is not rejected at the 5% level across all combinations of VAR lags and residual leads tested.

A simple model with downward nominal wage rigidities — in which the wage floor introduces a kink in the aggregate supply curve — provides a theoretical rationale for the sign- and state-dependent tradeoff: an expansionary shock in a full-employment economy raises inflation with no output effect (the economy sits on the vertical AS segment), while a contractionary shock makes the wage rigidity binding and reduces output with no price effect (the horizontal AS segment). Monte Carlo validation using artificial data generated by the calibrated DSGE model shows that the proposed empirical procedure recovers the theoretical nonlinear impulse responses very accurately.

In depth

Q1. What is the identification strategy and what are the main assumptions required?

Identification proceeds in two steps. First, the monetary shock is recovered by projecting an external instrument (Degasperi-Ricco 2022) onto the residuals of a standard linear VAR — this is justified by Proposition 1, which shows that even though the VAR is misspecified (it omits the nonlinear terms), the shock can still be recovered as a linear combination of VAR residuals under four assumptions: (A0) a structural VMA representation in which the shock is orthogonal to past observables and to the remaining structural shocks at all leads and lags; (A1) a finite-order VARX representation; (A2) invertibility of the Wold representation; (A3) a valid instrument (relevance and exogeneity); and (A4) informational sufficiency, meaning the monetary shock can be expressed as a linear combination of current and past observables — a condition implied by a linear monetary policy rule. Second, once the estimated shock and its nonlinear functions (absolute value and interaction with the state dummy) are in hand, they are used as exogenous regressors in a VARX to estimate nonlinear impulse response functions.

Q2. What are the main threats to identification?

Three main threats are acknowledged. (1) Instrument validity: if the instrument (Degasperi-Ricco 2022) is weak or contaminated by information shocks, the first-stage projection may recover a mislabeled shock. The authors note the first-stage F-statistic is adequate per Miranda-Agrippino and Ricco (2021) but acknowledge that the weak-instrument problem in the nonlinear context is non-trivial and left for future research. (2) Assumption A4 (informational sufficiency): if the central bank follows a nonlinear rule or the VAR variables are not sufficient to recover the shock, identification fails. The authors test this using the Forni-Gambetti-Ricco (2023) invertibility test — regressing the instrument on current and future VAR residuals and checking whether future residuals matter — and fail to reject invertibility at 5% across all lag/lead combinations. (3) Model misspecification in the nonlinear VARX: the VARX approximation may not capture all relevant nonlinearities generated by the true DSGE. The Monte Carlo validation on artificial DSGE data provides reassurance that the approach recovers the true nonlinear responses accurately.

Q3. How does the paper distinguish sign dependence from state dependence?

The paper includes two nonlinear terms as regressors in the VARX: the absolute value of the shock |u_t^r|, which captures sign-dependent effects (i.e., whether a tightening and an easing of equal magnitude have asymmetric effects), and the product s_{t-1} * u_t^r, which captures state-dependent effects (i.e., whether the same-sign shock has different effects depending on whether the economy was in a recession before the shock arrived). The two components are estimated simultaneously, allowing their separate contributions to be read off impulse responses in Figure 3. Robustness checks in the Online Appendix report models estimated with only sign dependence and only state dependence in isolation, with results described as qualitatively similar to Barnichon-Matthes (2018) and Tenreyro-Thwaites (2016), respectively.

Q4. What are the key quantitative results on impulse responses?

In the full nonlinear model, monetary tightening generates large and significant effects on real variables (unemployment, industrial production) regardless of the state, while monetary easing has more muted real effects. For prices, sign and state components operate in opposite directions: the largest inflation responses are associated with tightening during expansions. Numerically, the tradeoff estimates from Table 2 show: (a) easing during recessions — T+ point estimates of -0.03 at H=12, -0.12 at H=24, -0.17 at H=36, -0.17 at H=48 months (all statistically insignificant at 68%); (b) tightening during booms — T- point estimates of -0.51 at H=12, -0.61 at H=24, -0.59 at H=36, -0.53 at H=48 months (all statistically significant at 68%). For the pre-2009 subsample (excluding the ZLB period), tightening-in-booms estimates are somewhat larger in absolute value (-0.63 to -0.70) but confidence intervals widen to include zero at longer horizons.

Q5. What is the key implication for ‘pushing on a string’ results in the prior literature?

Tenreyro-Thwaites (2016) and Barnichon-Matthes (2018) document that monetary easing is less effective at stimulating real activity, especially during recessions — an apparent ‘pushing on a string’ result. The current paper accepts that the real effect of easing in recessions is muted, but adds a crucial dimension: price responses are also muted in the same circumstances, so the inflation-unemployment tradeoff is actually favorable even when the absolute size of real effects is small. The policy implication is that central banks can still usefully deploy monetary easing during recessions as long as interventions are sufficiently aggressive to achieve the desired stimulus, since the inflationary cost of doing so is low.

Q6. How does this paper measure the tradeoff differently from Phillips-curve regressions?

The tradeoff is defined as the ratio of the cumulative average impulse response of inflation to the cumulative average impulse response of unemployment (or vice versa) in response to an identified monetary shock, analogous to a fiscal multiplier. This approach avoids three problems that plague standard Phillips-curve estimates: (i) it does not require specifying a structural Phillips-curve equation, reducing misspecification risk; (ii) it does not require data on inflation expectations or the natural rate of unemployment, which are unobserved and introduce measurement error; (iii) identification comes from exogenous monetary shocks rather than OLS variation in unemployment, so the endogeneity problem is avoided.

Q7. What theoretical mechanism rationalizes the nonlinear tradeoffs?

A simple New-Keynesian-style model with downward nominal wage rigidities (Wt >= theta * W_{t-1}) generates a kink in the aggregate supply curve. When the economy operates at full employment and inflation is non-negative, an expansionary monetary shock stimulates demand but the wage rigidity is non-binding, so the economy sits on the vertical segment of the AS curve: output cannot exceed its natural level, and the only effect is higher inflation. By contrast, a contractionary shock makes the wage rigidity binding, pushing the economy onto the flat segment of the AS curve: firms cut employment rather than nominal wages, so output falls but prices are unaffected. More generally, averaging over periods of full employment and periods of involuntary unemployment, tightening has larger real effects and weaker price effects than easing — matching the empirical pattern — because a contractionary shock keeps the economy below full employment for a longer time.

Q8. What robustness checks are conducted?

Three main robustness checks are reported in the main text, each presented with impulse-response figures (Figures 6, 7, 8): (1) replacing the authors’ state dummy (based on 12-month average GDP growth) with NBER recession dates; (2) replacing the 1-year Treasury bond rate with the Federal Funds rate and with the 6-month Treasury Bill rate; (3) replacing the baseline Degasperi-Ricco instrument with the Jarocinski-Karadi (2020) instrument both raw and cleaned (regressed on six lags of VAR variables). In all cases, the qualitative result — tightening in booms produces larger real effects than easing in recessions, while price responses are more muted in recessions — is preserved, and the tradeoff pattern remains favourable for easing in recessions and tightening in booms. The Online Appendix additionally reports results using: the unemployment rate as the state variable (instead of industrial production); the VAR extended with the 10-year Treasury Bill rate and M2 monetary aggregate; models with only sign dependence; models with only state dependence; and an alternative estimation using the instrument directly in place of the estimated shock (which yields implausible results, validating the two-stage procedure).

Q9. What does the Monte Carlo validation using the DSGE model establish?

The paper generates 1000 artificial realizations from a calibrated downward-nominal-wage-rigidity DSGE model (beta=0.99, sigma=1, theta=1, phi_pi=1.5, rho_m=0.5, sigma_r=0.25%, sigma_a=0.45%, solved by nonlinear global projection using Chebyshev polynomials). It then applies the nonlinear Proxy-SVAR procedure to each artificial dataset and compares average estimated impulse responses with average true (model-generated) generalized impulse responses. The two are described as ‘very similar’ (Figure 10), demonstrating that the empirical nonlinear VARX representation accurately approximates the nonlinearities of the DSGE even though the VARX is in principle misspecified relative to the true model. This validates both the econometric procedure and the interpretive link between the empirical findings and the theoretical mechanism.

Q10. Why does the paper estimate the shock from a misspecified linear VAR rather than the VARX directly?

The monetary shock is latent. Proposition 1 shows that, under the stated assumptions, the monetary shock equals (up to a scaling constant) the projection of the external instrument onto the VAR residuals of the linear VAR, even though the VAR omits the nonlinear terms. This is because the linear monetary policy rule implies the shock is a linear combination of current observables, and the VAR residuals span the same space. Using the instrument directly in the VARX instead of going through steps I and II introduces a non-proportional bias in the nonlinear case (unlike the linear case where the attenuation bias from measurement error in the instrument is proportional across units and corrects under normalization). The Online Appendix shows that bypassing the two-stage shock-estimation procedure yields implausible impulse response estimates.

Q11. What is the scope of the empirical findings and what caveats apply?

Three scope conditions are explicitly stated. (1) State uncertainty: the tradeoff varies significantly with the state of the economy, so if the central bank is uncertain about current economic conditions, interventions carry considerable risk — a disinflation during what turns out to be a weaker-than-anticipated economy could incur very large unemployment costs. (2) Historical average: estimates reflect the effects of average monetary interventions over 1973-2019 and may not generalize to unusually large, persistent, or unconventional policy actions. (3) Accompanying fiscal policy: the tradeoff could be influenced by fiscal policy measures that accompanied monetary interventions during the sample period. The sample also excludes the post-2019 inflation surge, so inference about that episode is not direct. The identification requires a valid external instrument, whose strength in the nonlinear context is an open question.

Q12. How does this paper relate to Barnichon-Mesters (2020, 2021) and Gali-Gambetti (2020)?

Barnichon-Mesters (2020, 2021) and Gali-Gambetti (2020) also exploit identified monetary shocks to estimate the conditional inflation-unemployment relationship (the ‘Phillips multiplier’) and to investigate whether the Phillips curve slope has changed over time. The main additional contribution of the present paper is to show that the relationship is not only time-varying but specifically sign- and state-dependent, driven by the direction of monetary intervention and the current phase of the business cycle. The sign- and state-dependent tradeoff framework provides a richer characterization that can explain why a flat aggregate Phillips curve is compatible with moderate costs of disinflation and low inflationary costs of stimulus — something a time-varying-slope model alone does not deliver.

Q13. What does the paper say about the implications for disinflation episodes like 2022-23?

The paper does not directly analyze the 2022-23 episode (the sample ends at 2019:M6 and the paper was written with November 2025 dating for the online appendix). However, the results imply that if the economy is in a boom when disinflation begins — as was broadly the case in 2022 — the unemployment cost of reducing inflation is moderate (roughly 0.5-0.6 percentage points of unemployment per percentage point of inflation at a 24-36 month horizon), substantially less than would be implied by a flat Phillips curve. The authors explicitly note that their results suggest central banks can pursue disinflation without necessarily incurring very large unemployment costs, subject to the caveats about state uncertainty and scale of the intervention.

Key Concepts

Monetary policy tradeoff: In this paper’s usage: the ratio of the cumulative average impulse response of inflation to the cumulative average impulse response of unemployment (for easing) or vice versa (for tightening), in response to an identified monetary shock, averaged over a horizon H. In a linear model easing and tightening tradeoffs are inverses; in the nonlinear model they must be estimated separately. The concept is deliberately defined without assuming a Phillips curve and without requiring inflation expectations or the natural rate.

Sign dependence: The property that a monetary easing and a monetary tightening of equal magnitude have asymmetric effects on inflation and unemployment, not just opposite-signed effects of the same absolute magnitude. Captured in the VARX by including the absolute value of the monetary shock as an exogenous regressor.

State dependence: The property that the effects of a monetary shock of given sign and magnitude differ depending on whether the economy was in a recession or a boom in the period before the shock arrived. Captured in the VARX by including the product of the recession indicator (s_{t-1}) and the monetary shock as an exogenous regressor.

Nonlinear Proxy-SVAR: The paper’s proposed econometric framework: a Vector Moving Average augmented with nonlinear functions of the monetary shock, which admits a VARX representation. Identification extends the standard Proxy-SVAR by showing — via Proposition 1 — that the latent monetary shock can be recovered from the residuals of a misspecified linear VAR, using an external instrument, under a linear monetary policy rule. The estimated shock and its nonlinear functions are then used as exogenous regressors to recover nonlinear impulse response functions.

Downward nominal wage rigidity: A labor market friction, modeled as the constraint W_t >= theta * W_{t-1}, that creates a kink in the aggregate supply curve. When the constraint binds (during downturns), firms respond to contractionary shocks by cutting employment rather than nominal wages, generating unemployment without deflation. When the constraint is non-binding (during expansions), expansionary shocks raise nominal wages and prices without affecting employment beyond full-employment output. In this paper the rigidity is the key mechanism generating a sign- and state-dependent monetary tradeoff.

Informational sufficiency (Assumption A4): The identifying assumption that the monetary policy shock can be expressed as a linear combination of current and past observable variables — equivalently, that the central bank follows a linear monetary policy rule. This allows the shock to be recovered from the residuals of a standard linear VAR even when the true model is nonlinear. Tested empirically via the Forni-Gambetti-Ricco (2023) invertibility test (checking whether the instrument Granger-causes future VAR residuals); not rejected at the 5% level in the authors’ data.

Generalized Impulse Response Function (GIRF): In this nonlinear context, defined as E(x_{t+h} | u_t^r = u-bar) - E(x_{t+h} | u_t^r = 0) for h = 0, 1, …, where u-bar is a given shock size. Unlike linear IRFs, GIRFs depend on the sign and magnitude of the shock and on the state of the economy, and are computed by summing the linear response alpha(L)*u-bar and the nonlinear response Phi(L)*g(u_t^r, …).

Oil Prices, Monetary Policy and Inflation Surges

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

Layer 1: Overview

Gagliardone and Gertler ask why the US inflation surge that began in mid-2021 was both sudden and persistent, and whether a simple structural model can account for it without targeting inflation in estimation. The paper’s central claim is that the surge was driven primarily by the combination of large oil price shocks and accommodative (“easy”) monetary policy by the Federal Reserve, with oil complementarities and real wage rigidity as the key amplification mechanisms. Secondary factors — demand shocks and labor-market tightening — matter but do not drive the surge on their own.\n\nThe model is a New Keynesian framework with three non-standard features relative to the Blanchard-Gali (2007) benchmark: (1) oil enters both household utility and firm production as a complement rather than a substitute (elasticities of substitution estimated at ψ = 0.02 for households and ε = 0.37 for firms, both well below unity); (2) a Mortensen-Pissarides search-and-matching labor market that makes unemployment endogenous and allows shocks to matching efficiency; and (3) real wage rigidity parameterized by γ, estimated at 0.697, meaning actual wages adjust only about one-third as much as Nash bargaining wages would.\n\nEstimation uses simulated method of moments, matching model impulse responses to two sets of SVAR impulse responses identified via high-frequency external instruments: oil-price surprises around OPEC announcement dates (following Känzig 2021) and monetary-policy surprises around FOMC dates (following Gertler-Karadi 2015, extended by Bauer-Swanson 2022). The SVAR sample runs 1973:01–2019:12, with 2020–2022 reserved as an out-of-sample validation window. The model is then taken to the 2010–2022 period for a historical shock decomposition, targeting unemployment, real oil price inflation, the Federal Funds rate, and labor-market tightness; headline and core PCE inflation are left entirely untargeted and used as the key test of model fit.\n\nMain quantitative findings: the estimated elasticity of substitution between oil and labor in production is ε = 0.37 (s.e. 0.16) and between oil and consumption goods for households ψ = 0.02 (s.e. 0.34), both significantly below unity and confirming strong complementarity. Real wage rigidity γ = 0.697 (s.e. 0.145): actual wages move roughly one-third as far as Nash wages. The Calvo price parameter λ = 0.945 implies an average price duration of approximately six quarters at monthly frequency, and habit persistence h = 0.914.\n\nIn the structural VAR, a monetary tightening of 15 basis points reduces GDP by about 10 basis points (peak after ~10 months) and raises unemployment by roughly 0.5 percentage points; a 6 percent increase in the real oil price reduces GDP 20–30 basis points and raises the core PCE price level about 20 basis points. Complementarities matter quantitatively: at the estimated parameters, the peak GDP drop following an oil shock is 0.13 percent versus only 0.04 percent under Cobb-Douglas (no complementarity), and the core PCE inflation response is more than double in the benchmark. The decline in the marginal product of labor accounts for more than half the increase in marginal cost during the 2021 surge.\n\nIn the historical decomposition (2010–2022), oil shocks and easy monetary policy shocks jointly account for the bulk of the 2021–22 inflation surge; labor-market matching shocks contribute little to either unemployment variation or inflation; demand shocks dominate unemployment variation but are not the primary inflation driver in the surge. The model also explains the 2014–2019 low-inflation/low-unemployment puzzle: declining oil prices and tight money shocks kept inflation down despite a tight labor market, the mirror image of 2021–22. Baseline forecasts (as of spring 2023) under a Taylor rule with coefficient 2 project headline and core PCE declining to roughly 3 percent in about one year then converging slowly to 2 percent, with unemployment rising to approximately 5 percent (its steady state) and overshooting by about half a percentage point. A more aggressive tightening (funds rate held at 4.6 percent through September 2023) reduces inflation by about half a percentage point faster but raises unemployment by an additional persistent 1 percentage point.

In depth

Q1. What is the identification strategy for the oil and monetary policy shocks, and what are the main threats?

Both shocks are identified as external instruments in an SVAR. The oil shock uses daily surprises in oil futures prices on days of OPEC meetings (Känzig 2021): the surprise is the change in the log oil futures price between the day before the meeting and the close on the announcement day. The money shock uses surprises in the first principal component of the first four quarterly Eurodollar futures in a 30-minute window around FOMC announcements and non-FOMC Fed communication dates (Gertler-Karadi 2015, extended by Bauer-Swanson 2022). The key identifying assumption is relevance and exogeneity: each surprise must be correlated with the structural shock of interest but uncorrelated with the other structural shocks. The primary threat addressed is endogeneity between oil prices and monetary policy: oil price movements prior to FOMC meetings predict the monetary policy surprise (coefficient 0.073, s.e. 0.038), plausibly because the Fed responds systematically to energy prices. The authors regress money surprises on the monthly log change in oil spot prices and use residuals as the cleaned monetary instrument. Without this purging, the SVAR counterfactually predicts a surprise tightening raises oil prices. The authors also drop the Lehman Brothers date from the sample because confounds from the financial collapse would distort the monetary impulse response. A secondary threat is the use of a daily (rather than intraday) window for oil surprises, justified by evidence that oil markets react more slowly to OPEC announcements than financial markets react to FOMC meetings.

Q2. How does strong complementarity between oil and labor amplify the inflation response, and how is this mechanism isolated empirically?

With a CES production function where ε < 1, firms cannot easily substitute away from oil when its price rises. The marginal product of labor declines sharply because each worker needs roughly the same amount of oil to be productive, raising marginal cost of output for any given wage. The Phillips curve then transmits this cost-push increase to inflation. The authors show analytically that the sensitivity of the marginal product of labor to the ratio of oil to labor is proportional to 1/ε: as ε falls, the oil shock’s impact on marginal cost and hence inflation rises sharply. This is isolated by comparing the benchmark model against a Cobb-Douglas version (ε = 1, ψ = 1): peak GDP decline is 0.13 percent with complementarities versus 0.04 percent without; the unemployment response is large and persistent only with complementarities; and the core PCE inflation response is more than double in the benchmark. The historical decomposition further shows that the decline in the marginal product of labor accounts for more than half the increase in marginal cost during the 2021 surge.

Q3. What role does real wage rigidity play, and what is the resulting inflation-unemployment trade-off?

Real wage rigidity introduces a cost-push term into the Phillips curve. Without rigidity (γ = 0), the Nash bargaining wage absorbs the oil shock, and the central bank can achieve both price stability and efficient employment simultaneously. With γ = 0.697, actual wages fall by only about one-third as much as Nash wages after an oil shock. The gap between Nash and actual wages enters the Phillips curve as a cost-push term Δt. If the central bank tries to stabilize prices, it must contract demand enough to push the efficient component of marginal cost negative, forcing output and unemployment well below the flexible-price equilibrium — in the model, pursuing price stability after an oil shock causes output and unemployment to deviate from the flexible-price benchmark by more than double over the first 8–10 months. This trade-off rationalizes partial monetary accommodation and is quantitatively important for matching the historical behavior of inflation in 2021–22.

Q4. How does the historical shock decomposition work, and what are its key identifying assumptions?

The authors use the estimated DSGE model with the Kalman smoother to perform a historical shock decomposition over 2010–2022. They estimate persistence and standard deviations of four shocks (demand εbt, monetary policy εrt, oil εst, and matching efficiency εΦt) using Bayesian methods, targeting four observable series: unemployment, real oil price inflation, the Federal Funds rate, and labor-market tightness from JOLTS. Nominal variables — headline PCE, core PCE, nominal wage growth, real product wage growth — are entirely untargeted and serve as out-of-sample validation. One important wrinkle is that the spot oil price contains high-frequency speculative volatility that does not pass through to the prices households and firms face. The authors filter this by assuming nominal oil price inflation equals PCE energy inflation plus an i.i.d. speculation shock, so that only the persistent component enters real allocations. The posterior mean of the speculation shock standard deviation (σm = 0.239) is substantially larger than that of the persistent oil shock (σo = 0.042), confirming the filter’s importance.

Q5. What sub-sample variation is documented, and what explains it?

The model resolves three sub-sample puzzles. First, the 2014–2019 period had low unemployment but persistently low inflation — the model attributes this to declining oil prices and tight monetary policy shocks that offset demand pressures and kept marginal cost subdued. Second, the 2010–2012 period had rising oil prices but also low inflation — attributable to a large negative demand shock from the Great Recession lingering, which depressed marginal cost sufficiently to offset the oil price effect. Third, the high labor-market tightness of 2022 is shown to be largely an endogenous response to easy monetary policy and oil shocks rather than an autonomous labor supply shock. The matching shock does not materially contribute to either unemployment variation or inflation over the sample.

Q6. What robustness checks are reported?

(1) Taylor rule coefficient: calibrating ϕπ to 1.5 instead of 2 adds roughly 0.5 percentage points to PCE inflation at the peak of the 2022 surge due to money shocks but does not change qualitative conclusions. (2) Matching shock persistence: results are robust to calibrating persistence to 0.9 or 0.95 instead of the estimated 0.548, confirming that the matching shock’s minimal contribution to inflation is not an artifact of low persistence. (3) Unemployment demeaning: using 6 percent instead of 5 percent does not change results. (4) Oil price speculation filter: removing the filter has only minor quantitative effect because anomalous spike-and-reversal days are few. (5) Monetary policy shock orthogonalization: without purging oil-price predictability from the money surprise, the SVAR counterfactually predicts tightening raises oil prices, confirming the necessity of the adjustment.

Q7. How does this paper relate to and differ from Blanchard and Gali (2007)?

The paper descends most directly from Blanchard-Gali (2007), which also features oil in a New Keynesian model with real wage rigidity. Key differences: (i) Gagliardone-Gertler make oil a complement rather than a substitute or Cobb-Douglas input in both utility and production, which they argue is necessary to match quantitatively the observed impact of oil shocks on inflation; (ii) they incorporate a Mortensen-Pissarides search-and-matching labor market with endogenous unemployment, enabling labor-market tightness to function as a separate inflation driver; (iii) they estimate the model formally by matching SVAR impulse responses to externally identified shocks rather than calibrating; and (iv) they apply the model specifically to explaining the 2021–22 inflation surge. The real wage rigidity mechanism is retained from Blanchard-Gali as a central feature.

Q8. How does this paper relate to the broader literature on the 2021–22 inflation surge?

The paper explicitly positions itself against work emphasizing supply chain disruptions and goods-sector reallocation (Guerrieri et al. 2021, Di Giovanni et al. 2022, Ferrante et al. 2023) as the main drivers of 2021 inflation. The authors accept that supply chains mattered in 2021 but argue they moderated by end of 2021 while inflation persisted through 2022, so their framework targets the more durable sources. Papers closer in spirit emphasize monetary policy (Ball et al. 2022, Amiti et al. 2022, Benigno-Eggertsson 2023, Pflueger 2023), but Gagliardone-Gertler differ by using a structural DSGE model estimated to identified shocks and by giving oil shocks a prominent co-equal role alongside monetary accommodation. Lorenzoni and Werning (2023) share the emphasis on production complementarities and wage rigidity.

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

The primary policy implication is that the 2021–22 inflation surge was jointly caused by oil shocks and monetary accommodation, and unwinding it involves a short-run cost in real activity due to the inflation-unemployment trade-off generated by real wage rigidity. The baseline forecast is slow convergence to 2 percent inflation with a quasi soft landing: headline and core PCE reaching roughly 3 percent in about one year then declining slowly, and unemployment rising to 5 percent steady state and overshooting by about half a percentage point. A more aggressive tightening (funds rate at 4.6 percent through September 2023) brings inflation to 2 percent faster by about half a percentage point by June 2023 but at the cost of an additional persistent unemployment increase of about 1 percentage point. Scope conditions: (i) results depend critically on long-run inflation expectations remaining anchored at 2 percent — if expectations drift to 3 percent, the disinflation task becomes harder; (ii) the model abstracts from supply chain disruptions, downward nominal wage rigidity, and open-economy channels; (iii) the quantitative conclusions rest on estimated complementarities that carry large standard errors, especially for household oil complementarity ψ.

Q10. What is the role of labor-market tightness as an inflation driver in this framework?

Labor-market tightness (θt = vt/ut) raises marginal cost through two channels: it increases net hiring costs (a tighter market requires more vacancies to fill a given number of positions, raising the per-hire cost) and it raises the Nash bargaining wage (because unemployment becomes less painful, improving workers’ outside option). In the historical decomposition, however, the matching efficiency shock — the exogenous source of tightness variation — contributes negligibly to both unemployment variation and inflation over the 2010–2022 sample. The high tightness of 2022 is shown to be largely an endogenous response to easy monetary policy and oil shocks rather than an autonomous labor-supply disruption. This finding challenges the narrative that autonomous labor-market tightening was a primary independent cause of the inflation surge.

Key Concepts

Oil complementarity (ε, ψ): In the paper’s CES framework, oil is a complement when the elasticity of substitution with labor in production (ε) or with consumption goods for households (ψ) is below unity. A value below unity means that when oil becomes scarce, the marginal productivity of labor (or marginal utility of other consumption) falls more than proportionally, amplifying the macroeconomic impact of oil price shocks. Estimated values of ε = 0.37 and ψ = 0.02 imply strong complementarity in both sectors.

Real wage rigidity (γ): A parameter ∈ [0,1] measuring how sticky the actual real wage is relative to the Nash bargaining wage. With γ = 0.697, the actual wage moves only about one-third as far as the Nash wage in response to a shock (wqt = (w°qt)^{1−γ}(wq)^γ). This is adopted as a reduced-form mechanism — not derived from deeper frictions — that generates realistic unemployment volatility and introduces a short-run inflation-unemployment trade-off absent from fully flexible-wage models.

Cost-push term (Δt): The component of inflation in the Phillips curve that arises purely from the gap between actual wages and Nash bargaining wages when real wage rigidity is present. Equals −κγ times the deviation of the Nash wage from steady state. It is the mechanism through which oil supply shocks create an inflation-unemployment trade-off: even if the central bank stabilizes the efficient component of marginal cost, the cost-push term generates inflation, and offsetting it requires contracting demand below the efficient level.

Impulse-response matching estimation: The paper’s estimation procedure: simulated method of moments minimizes the weighted squared distance between model-implied impulse responses and SVAR-estimated impulse responses to externally identified oil and monetary shocks. Precision weights from the SVAR IRF confidence bands determine which moments receive more weight. Confidence intervals for structural parameters are obtained via the delta method. This approach ensures the model can simultaneously explain the dynamics following both supply (oil) and demand (monetary) disturbances.

Easy monetary policy shock: A negative realization of the monetary policy shock εrt in the Taylor rule, representing the actual Federal Funds rate falling below what the estimated Taylor rule coefficient on inflation would prescribe. In the historical decomposition, such shocks from roughly mid-2020 onward are attributed substantial responsibility for low unemployment and upward pressure on inflation in 2021–22, distinct from endogenous policy responses to demand or oil shocks.

Speculation shock (εmt): An i.i.d. component of nominal oil price changes that is not reflected in the PCE energy price index and therefore does not pass through to real allocations in the model. Introduced to prevent high-frequency gyrations in spot oil prices (attributed to financial-market speculation) from generating counterfactually large macroeconomic swings. Its estimated standard deviation (posterior mean 0.239) is substantially larger than that of the persistent structural oil shock (0.042).

Historical shock decomposition (untargeted nominal variables): The primary empirical test of the model: after estimating shocks from four targeted real/financial series (unemployment, real oil price inflation, Federal Funds rate, labor-market tightness), the model constructs predicted paths and shock contributions for headline PCE inflation, core PCE inflation, nominal wage growth, and real product wage growth — none of which were targeted in identification. Agreement between model predictions and data for these untargeted nominal variables is the main evidence that the model correctly identifies the sources of the inflation surge.

Optimal Taxation of Inflation

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

This paper analyzes the effectiveness of a tax on inflation policy (TIP)—a fiscal instrument that would require firms to pay a tax proportional to the increase in their prices—as a complement to conventional monetary policy in a New Keynesian framework with multiple sources of inflation. The central result is that combining TIP with conventional monetary policy can implement the first-best allocation in which inflation is zero and the output gap is closed at all times under any path of shocks. Policy instruments should completely specialize: monetary policy should track the neutral rate of interest (addressing demand and productivity shocks by keeping output at its efficient level), while TIP should rise with markup and inflation expectation shocks. Unlike the 1970s view that saw TIP as a substitute for monetary policy, TIP is shown to be a complement. TIP corrects an externality in firms’ pricing decisions without exacerbating relative price distortions. Calibrated simulations suggest a reasonably calibrated TIP could lower the variance of inflation by 45% and of output by 44% relative to a Taylor-rule-only regime.

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 TIP and what externality does it correct?

TIP (tax on inflation policy) is a fiscal instrument that requires firms to pay a tax proportional to the increase in their prices, and it corrects an externality in firms’ pricing decisions created by markup and inflation expectation shocks that cause private and social returns to price increases to diverge. When shocks to markups or inflation expectations create strategic price-setting incentives, firms’ individually optimal price increases exceed the socially optimal level; TIP re-aligns private with social valuations by making price increases costly. The proposal originated with Wallich and Weintraub (1971) and was widely discussed in the 1970s, but was absent from recent policy discourse until this paper revived it in a microfounded framework.

Q2. What is the complete-specialization result?

Monetary policy and TIP should completely specialize: monetary policy should track the neutral rate of interest—varying with aggregate demand and productivity shocks to keep output at its efficient level—while TIP should respond to markup and inflation expectation shocks, addressing the externalities those shocks create in firms’ pricing. This sharp division of labor arises because each instrument is best suited to a different source of inflation: monetary policy’s power lies in aggregate demand management, while TIP directly corrects the pricing externality. Under complete specialization, the first-best allocation with zero inflation and zero output gap can be implemented under any shock path.

Q3. Does TIP exacerbate relative price distortions?

In contrast with price controls, TIP is found not to exacerbate distortions in relative prices, because TIP is linear in price increases and symmetric across firms, so it does not prevent efficient relative price adjustments across sectors. In an extension with sector-specific TFP shocks requiring relative price adjustments, the paper shows analytically (under some conditions) and numerically (more generally) that TIP has no effect on relative prices across sectors. Firms that face negative productivity shocks moderate their price increases, while firms that otherwise would not change prices are incentivized to decrease them to earn a subsidy, keeping the relative price structure broadly intact.

Q4. How large are the stabilization gains from TIP?

Calibrated simulations show that the stabilization gains from using TIP alongside a Taylor rule are substantial: a reasonably calibrated TIP could lower the variance of inflation by 45% and of output by 44%, with gains especially large for markup and inflation expectation shocks. Welfare gains from TIP are smaller for TFP and demand shocks because the reduction in inflation volatility is partially offset by higher output gap volatility. These quantitative results are based on a calibrated New Keynesian model and are presented as illustrative magnitudes rather than precise empirical estimates.

Q5. What equivalent instruments does the paper consider?

The paper shows a formal equivalence between TIP, production/payroll subsidies (the more traditional tools for markup distortions), a feebate (combining a tax on price increases with a rebate to all firms), and a market for inflation permits. Subsidies can also implement the first best but entail large and persistent fiscal costs; the feebate provides incentives without increasing the average tax burden; the market for inflation permits (proposed by Lerner, 1978) minimizes fiscal authority involvement. TIP is distinguished from these alternatives by its directness and its non-distortionary effect on relative prices.

Key concepts

tax on inflation policy (TIP) : a fiscal instrument requiring firms to pay a tax proportional to the increase in their prices, designed to internalize the externality that individual firms’ price increases impose on aggregate inflation; first proposed by Wallich and Weintraub (1971). inflation externality : the divergence between private and social returns to a firm’s price increase created by markup or inflation expectation shocks; private returns include the markup gain, while social costs include the contribution to aggregate inflation, which TIP is designed to correct. complete specialization : the optimal policy regime in which monetary policy exclusively addresses demand and productivity shocks (by tracking the neutral rate) while TIP exclusively addresses markup and inflation expectation shocks; enables the first-best allocation. feebate : an instrument equivalent to TIP that combines a tax on price increases with a rebate distributed to all firms, providing anti-inflation incentives without increasing the average firm tax burden.

Price Setting and Volatility: Evidence from Oil Price Volatility Shocks

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

Layer 1: Overview

This paper asks whether increases in aggregate volatility reduce the effectiveness of monetary policy by making aggregate prices more flexible. The motivation is concrete: policymakers worry that during episodes of high volatility, prices may become more synchronized in their adjustment, reducing monetary non-neutrality and limiting the ability of nominal stimulus to raise real output.

The empirical strategy exploits variation in oil price volatility as a plausibly exogenous source of aggregate cost volatility. Oil price volatility is measured using a stochastic volatility model estimated on monthly WTI spot prices from 1986 to 2014 (Bayesian MCMC with particle filter). The key identification device is a Bartik-style interaction: an industry’s pre-determined oil input share (from the 1997 Input-Output Use Table, expressed as oil spending relative to value added) is interacted with the time-varying aggregate oil price volatility. Industries more dependent on oil should respond more strongly to oil price volatility shocks, while the time fixed effects absorb any aggregate confounders. The micro-price data are confidential item-level Producer Price Index records from the BLS covering 81 four-digit NAICS manufacturing industries from January 1998 to December 2014, with roughly 100,000 prices collected monthly from about 25,000 reporters.

Two price-setting moments are the main outcomes: price change frequency (fraction of items with non-zero price change within an industry-month) and price change dispersion (standard deviation of non-zero price changes within an industry-month).

The main empirical findings, from Table 6 (industry-specific oil demand variable regressions with both industry and time fixed effects):

A one standard deviation increase in oil price volatility raises price change dispersion by approximately 2 percent relative to the mean for a 90th-percentile oil-share industry relative to a 10th-percentile oil-share industry (coefficient of 4.511, significant at 1 percent). This finding is robust to alternative oil price series (WTI, Brent, RAC), alternative volatility measures (stochastic volatility, GARCH, realized volatility), exclusion of the 2008 crisis period, and alternative dispersion measures (interquartile range).
The same cross-industry comparison shows that a one standard deviation increase in oil price volatility reduces price change frequency by approximately 1 percent relative to the mean for high-oil versus low-oil industries (coefficient of -2.486, significant at 5 percent in Table 6 column 1). This negative frequency result holds inside and outside the financial crisis period.
The time-series correlation between price change dispersion and oil price volatility for the top-10-percent oil-share industries is 0.45, versus only 0.08 for the bottom-10-percent industries, previewing the cross-sectional identification.

These findings contrast sharply with what the literature documents for idiosyncratic volatility (Vavra 2014), where both frequency and dispersion rise together. For aggregate (oil) volatility, dispersion rises but frequency does not, implying a different mechanism.

To interpret these facts, the paper constructs and calibrates a general equilibrium state-dependent pricing model. Firms produce using labor and oil (Cobb-Douglas), face menu costs, and receive idiosyncratic productivity shocks with leptokurtic draws. The key modeling choice is random menu costs (drawn each period from a non-degenerate distribution, following Dotsey, King, and Wolman 1999 and Luo and Villar 2020) rather than fixed menu costs. With random menu costs, the selection of which prices adjust is attenuated relative to the common shock: many firms will not adjust because they drew a high menu cost regardless of the oil shock, keeping the mix of adjusting prices more disperse. A fixed-menu-cost model (Appendix A.3) produces a counterfactual negative relationship between oil price volatility and price change dispersion, because the strong selection effect causes prices to bunch in the direction of the cost shock.

The calibrated one-sector random menu cost model matches the positive empirical link between oil price volatility and dispersion, with a muted frequency response. The multisector model (eight sectors calibrated to oil-share octiles of PPI industries) is fed the actual observed oil price and volatility series from 1998 to 2014, and the regression run on model-generated data matches the empirical coefficient on dispersion within one standard error of the data estimate (model: 3.876 versus data: 4.511). The model cannot replicate the empirical negative frequency response.

The key quantitative implication for monetary policy: in the multisector model, a permanent increase in log nominal output of 0.002 (doubling one month’s growth rate) translates 59.1 percent into real output at baseline oil price volatility, and 58.8 percent after a one standard deviation increase in oil price volatility. The ability of nominal stimulus to raise consumption on impact falls by only 0.5 percent. The average decline across the full historical distribution of oil price volatility (1998-2014) is 1 percent lower at peak volatility (e.g. 2009) than at trough volatility (e.g. 2013). Supporting aggregate evidence using state-dependent local projections with Romer-Romer monetary shocks (1974-2007) confirms that the price level response to identified monetary shocks is not significantly different across high and low oil price volatility states.

The policy implication is direct: the output-inflation tradeoff is nearly time-invariant with respect to aggregate volatility. Policymakers who respond to periods of high aggregate volatility by increasing nominal stimulus under the belief that policy effectiveness has declined would be overreacting and would generate unnecessary inflation. The source of volatility — aggregate versus idiosyncratic — matters critically for the price-setting implications and thus for the correct policy response.

In depth

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

The strategy is a Bartik-style interaction: each industry’s pre-determined oil input share (oil spending as a share of value added, from the 1997 Input-Output tables, before the sample period) is interacted with aggregate time-varying oil price volatility. Industry fixed effects absorb time-invariant heterogeneity; time fixed effects absorb all aggregate shocks common to all industries in a given month. Identification of the oil price volatility effect is thus from within-industry variation over time, scaling by the pre-existing oil dependence. The main threats are: (1) the interaction term could be correlated with unobserved shocks that are industry-specific and vary with oil price volatility; (2) oil prices could respond to aggregate U.S. economic conditions, threatening exogeneity. The paper defends against (2) by arguing that large oil price movements over the sample can be traced to external events (Middle East conflicts, Venezuelan oil strike, Asian demand expansion, Libyan uprising) rather than U.S. conditions, and that individual industries are price takers in the global oil market. For (1), the paper adds controls for industrial production growth, industry inflation, excess bond premium, and realized stock volatility within industries, and shows results are unchanged.

Two effects operate. The real options effect: higher volatility increases the option value of waiting, so firms expand the inaction band, decreasing frequency. The volatility effect: larger common shocks push more firms outside the band, but because it is a common shock, the resulting price changes are synchronized in the direction of the cost shock, which compresses dispersion. For idiosyncratic volatility, the volatility effect pushes price changes in both directions symmetrically, so both frequency and dispersion rise. This asymmetry is why aggregate and idiosyncratic volatility have different implications for monetary non-neutrality.

A fixed menu cost model (as in Golosov and Lucas 2007) features too strong a selection effect. When oil price volatility rises, more firms are pushed outside the action bands and they all move in the direction of the common cost shock, compressing price change dispersion (model predicts a 2.7 percent decline in dispersion per one standard deviation volatility increase) while frequency rises by 8.1 percent. This is the opposite of the empirical finding. Random menu costs break the tight link between the common shock and which firms adjust, because each firm draws a random menu cost each period. A substantial fraction of firms draw very large menu costs and never adjust regardless of the oil shock, while firms that do adjust include those reacting to idiosyncratic shocks (low menu cost draws), keeping the mix of price changes disperse even when aggregate volatility is high.

Q4. What heterogeneity is documented across industries?

The main documented heterogeneity is in oil input intensity. The 10th percentile oil share is approximately 0.001 (oil spending equals 0.1 percent of value added) and the 90th percentile is 0.022 (2.2 percent of value added), with the average at 0.8 percent. The top-10-percent oil-share industries (e.g. Basic Chemical Manufacturing at 16.1 percent, Railroad Rolling Stock Manufacturing at 5.1 percent) show substantially stronger responses to oil price volatility shocks than low-oil industries. In terms of price setting statistics, across the eight octile sectors used in the multisector calibration, price change frequency ranges from 0.10 to 0.27, average size from 0.17 to 0.28, and standard deviation from 0.10 to 0.15 — heterogeneity that the multisector model replicates closely. There is no documented differential effect of oil price volatility between durable and non-durable goods industries.

Q5. What are the pass-through estimates from oil prices to producer prices, and why do they matter for the main analysis?

The paper first establishes that oil prices actually pass through to producer prices, validating the cost-channel story. The short-run pass-through (impact month) is 1.0 percent (significant at 1 percent), meaning a 1 percent change in real oil prices raises producer price inflation by 1 percent in the same month. The 12-month cumulative pass-through is 8.6 percent (significant at 1 percent). These estimates are obtained from an industry-level panel regression with industry fixed effects and 12 lags of real oil price changes. The large pass-through relative to the average oil share of 0.8 percent is attributed to indirect transmission through input-output linkages. Pass-through establishes that oil is a relevant cost shifter for manufacturing producers, supporting the premise that oil price volatility would affect price-setting decisions.

Q6. What robustness checks are run on the main empirical findings?

The paper conducts extensive robustness checks: (1) Alternative oil price series: WTI, Brent Crude, and Composite Refined Acquisition Cost — all give qualitatively and often quantitatively similar results. (2) Alternative volatility measures: stochastic volatility, GARCH(1,1), and realized volatility (within-month standard deviation of daily log price changes) — all produce consistent findings. (3) Crisis period: splitting the sample into 2008 crisis and non-crisis periods shows the dispersion result holds equally inside and outside the crisis. (4) Alternative dispersion measure: interquartile range of price changes in place of standard deviation — results unchanged. (5) Long-run oil usage: averaging the oil share across 1997, 2002, and 2007 IO tables rather than using only 1997 — dispersion results remain significant. (6) Trimming sensitivity: including all observations regardless of few price changes per industry-month does not change results. (7) Industry-level idiosyncratic volatility control: adding median realized stock volatility within the industry does not alter coefficients on oil price volatility.

Q7. How does this paper relate to and differ from Vavra (2014)?

Vavra (2014) studies idiosyncratic volatility and finds that both price change frequency and dispersion are countercyclical using CPI data. He matches these facts with a standard menu cost model with second-moment idiosyncratic productivity shocks. Klepacz differs by studying aggregate (oil price) volatility rather than idiosyncratic volatility, using PPI data, and finding that dispersion rises but frequency does not. These are the opposite implications from the mechanism standpoint: Vavra’s model would predict decreased dispersion when common volatility rises (because more prices synchronize), which is why Klepacz needs to modify the model with random menu costs. Klepacz then confirms that his random menu cost model can also reproduce Vavra’s idiosyncratic volatility facts when augmented with time-varying idiosyncratic volatility, with price change dispersion rising 1.2 percent and frequency rising 0.5 percent per one standard deviation idiosyncratic volatility shock. This shows the models are complementary, not contradictory.

Q8. What does the model imply for the magnitude of the change in monetary policy effectiveness across the full empirical distribution of oil price volatility?

Beyond the 0.5 percent decline per one standard deviation oil price volatility increase, the paper simulates the full 1998-2014 oil price and volatility series through the model. At each point, it computes the on-impact output response to a 0.002 permanent log nominal output shock. The average monetary policy efficacy is 1 percent lower on impact during periods of the highest observed oil price volatility (such as 2009) relative to periods of the lowest oil price volatility (such as 2013). The cumulative consumption response is reduced by less than 1 percent throughout the first year following the monetary shock. These magnitudes are small enough that the paper concludes changes in aggregate volatility do not substantially alter the output-inflation tradeoff.

Q9. What is the aggregate time-series evidence on monetary policy effectiveness across oil price volatility states?

Section VI uses state-dependent local projections (Auerbach and Gorodnichenko 2013) with Romer-Romer (2004) monetary policy shocks over 1974-2007. The transition function equals one when the three-month moving average of oil price volatility exceeds the sample median. Controls include two lags of the monetary shock, current and two lags of the federal funds rate, log industrial production index, unemployment rate, log PPI, and log real oil price. Results show that the impulse response of the PPI price level to an expansionary monetary shock is not significantly different between high and low oil price volatility states. The high-volatility state estimates are less precise but are consistent with the linear model response, supporting the model’s implication that monetary policy effectiveness is not a function of oil price volatility.

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

The paper implies that policymakers should not systematically increase nominal stimulus in response to high aggregate volatility on the grounds that policy is less effective. The output-inflation tradeoff is nearly time-invariant. If policymakers over-stimulate believing effectiveness has declined, the result is unnecessary inflation. However, this conclusion is specific to aggregate (common) volatility shocks, not idiosyncratic volatility — the source of volatility matters for the direction of price-setting response and hence for the policy implications. The paper explicitly states that the analysis applies to oil price volatility but extends conceptually to policy uncertainty, exchange rate volatility, and global demand volatility. One scope condition: the model abstracts from a monetary policy reaction function that responds directly to oil prices (as in Kilian and Lewis 2011 or Bodenstein et al. 2012), so the quantitative results apply to the partial equilibrium price-setting channel rather than to the full general equilibrium policy transmission.

Q11. What are the business cycle properties of price change moments in the PPI, and how do they compare to CPI findings?

Table 1 shows that the standard deviation of PPI price changes is countercyclical: the recession dummy adds 0.008 to the mean dispersion of 0.127 (significant at 5 percent). Price change frequency rises during recessions by 0.017 but the coefficient is not statistically significant. These patterns are qualitatively consistent with Vavra (2014) and Bachmann et al. (2019). Comparing PPI and CPI (Table 2): both have frequency around 15 percent and average absolute size around 7-8 percent. The main difference is that the PPI has a higher fraction of small price changes (22 percent vs. 12 percent in the CPI), reflecting a higher frequency of very small adjustments. Price change dispersion is higher in the PPI (standard deviation 0.13) than the CPI (0.08). Monthly inflation correlation between the two series is 0.80 over 1998-2014.

Q12. What caveats or limitations does the paper acknowledge?

The main caveats are: (1) The model does not feature a monetary policy reaction function for oil prices, abstracting from the general equilibrium feedback between oil shocks and interest rate policy. (2) The multisector model replicates the positive relationship between oil price volatility and price change dispersion but cannot match the empirically negative frequency response — the model predicts higher relative frequency for high-oil sectors during volatility episodes, while the data show lower relative frequency. (3) The time-varying idiosyncratic volatility extension uses a simplifying assumption that idiosyncratic volatility is perfectly negatively correlated with oil prices, primarily for computational tractability. (4) The model focuses on manufacturer producer prices (the PPI) and on oil as a non-produced input, abstracting from oil in the household consumption function.

Key Concepts

Price change dispersion: The within-industry standard deviation of non-zero price changes in a given month, measuring how spread out the price changes are in the cross-section of items. A more disperse distribution means price changes are scattered across a wide range of sizes and directions, so a monetary shock shifts fewer prices past the adjustment threshold and has larger real effects. The paper measures it as the square root of the mean squared deviation of item-level price changes from the industry mean, computed only over non-zero changes.

Real options effect: One of two mechanisms through which higher volatility affects price-setting in a menu cost model. Higher volatility increases the value of waiting before paying the menu cost to adjust, because the expected loss from being at a suboptimal price for one more period is smaller relative to the cost of adjusting when future shocks are large and uncertain. This pushes the action and inaction bands outward, reducing the frequency of price adjustment.

Volatility effect: The second mechanism through which higher volatility affects price-setting. For idiosyncratic volatility, larger idiosyncratic shocks push prices outside the inaction bands in both directions, increasing both frequency and dispersion. For common (aggregate) volatility, larger common shocks push prices outside the bands mostly in one direction, increasing frequency but decreasing dispersion (in a fixed-menu-cost model). In a random menu cost model, this synchronization is attenuated, allowing dispersion to rise.

Random menu costs: A modeling device where each firm draws an i.i.d. menu cost each period from a non-degenerate distribution (specifically, a transformation of an exponential distribution as in Luo and Villar 2020) rather than paying a single fixed cost. The distribution has fat tails, giving substantial probability of very low or very high cost draws. This randomness breaks the tight selection effect of fixed-menu-cost models: which firms adjust depends not only on how far their price is from optimal but also on their menu cost draw, so many firms do not adjust even when their price gap is large. This attenuates the synchronization of price changes in response to a common shock.

Industry-specific oil demand variable: A Bartik-style instrument constructed by multiplying an industry’s pre-determined oil input share (oil spending as a fraction of value added from the 1997 IO tables) by aggregate oil price volatility or oil price inflation. The pre-determined share measures the industry’s structural sensitivity to oil, while the aggregate oil volatility provides exogenous time variation. The interaction captures the differential exposure of high-oil industries to aggregate oil price volatility shocks, enabling identification via cross-industry variation after controlling for time and industry fixed effects.

Stochastic volatility of oil prices: A latent volatility process estimated from real WTI oil prices using an AR(1) model for the log oil price level and a mean-reverting AR(1) process for the log standard deviation of oil price innovations. Estimated via Bayesian MCMC with a particle filter (Sequential Importance Resampling) to handle the nonlinearity, using data from 1986-2014. Produces a smoothed series of time-varying oil price uncertainty. Key estimated parameters: oil price persistence ρ_o = 0.999, volatility persistence ρ_σ = 0.887, unconditional mean log-volatility σ = -2.607 (implying standard deviation of oil price shock ≈ 7.4 percent), and volatility shock size φ = 0.127.

Selection effect: In state-dependent pricing models, the mechanism by which the prices that actually change are not a random subset but are selected based on how far they are from their optimal level. A strong selection effect (as in Golosov and Lucas 2007) means that only prices far from optimal change, so average price change size is large and price change frequency is low. Under a common volatility shock with a strong selection effect, more prices are pushed far from optimal in the same direction, causing them all to adjust together — compressing dispersion and increasing frequency. Random menu costs weaken the selection effect.

Monetary non-neutrality: The degree to which a change in the money supply (or nominal spending) affects real output rather than just the price level. In menu cost models, non-neutrality arises because not all prices can adjust instantaneously: a monetary shock shifts the desired price change distribution, but only firms near the adjustment threshold respond, leaving real prices for the others unchanged. After conditioning on price change frequency, higher price change dispersion implies fewer prices are near the threshold, so a given monetary shock affects fewer prices in one direction and has larger real effects (greater non-neutrality). This is the key channel linking the paper’s empirical findings to monetary policy effectiveness.

Pricing-to-market in business cycle models

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

Layer 1: Overview

This paper evaluates five microfounded pricing-to-market (PTM) mechanisms and one reduced-form aggregator in a two-country DSGE model with volatile exchange rates driven by financial shocks (following Gabaix and Maggiori 2015) and real productivity shocks. The central question is whether existing open-economy theories can jointly achieve three empirically mandated targets — low exchange-rate pass-through to import prices, muted expenditure switching (low short-run trade elasticity), and plausible producer markups — when exchange rates are volatile and act as a major independent source of fluctuations. The paper’s main contribution is to show analytically and quantitatively that no existing microfounded PTM model fully escapes a structural tension among these three targets, which the authors call the parameterization trilemma.

The models evaluated are: (i) the Kimball Aggregator (KA; reduced-form, Itskhoki-Mukhin application); (ii) the Distribution Cost model (CD; Corsetti-Dedola 2005); (iii) the Price Dispersion model (PD; Alessandria 2009); (iv) the Nested CES/Cournot model (NCES; Atkeson-Burstein 2008); (v) the Deep Habits model (DH; Ravn-Schmitt-Grohe-Uribe 2007); and (vi) the Customer Capital model (CC; Drozd-Nosal 2012). The encompassing framework uses the Backus-Kehoe-Kydland (1995) two-country structure augmented with a financial sector that generates UIP deviations via a capacity-constrained arbitrageur segment and exogenous noise-trader positions. The model is estimated/calibrated to quarterly U.S. data (1981Q1–2009Q4 for prices, 1980Q1–2004Q1 for quantities), HP-filtered with lambda = 1,600.

The baseline markup target is 50%, consistent with BEA input-output tables for U.S. tradable sectors (ranging 45–50% across 2007, 2012, 2017); listed-firm SEC data imply higher values around 73–75%, which the authors treat as an upper bound. The empirical pass-through target is 0.4 (midpoint of a 0.2–0.6 range estimated by Campa-Goldberg 2005 and others; Gopinath-Itskhoki 2022 estimate 0.2–0.3). The short-run trade elasticity target is 0.7, measured using the volatility ratio of quantities to prices, which yields an upper-bound estimate. Real exchange rate volatility is targeted at 3.97 (standard deviations relative to GDP). Imports-to-GDP ratio is targeted at 12%.

The central analytic finding — the parameterization trilemma — is characterized precisely for each model. For the KA model, the demand elasticity parameter gamma(1) simultaneously pins down both the markup and the trade elasticity, so matching 50% markups implies trade elasticity of approximately 1.5 (above the desired range of less than 1) and any value below TE = 1 is simply unattainable. For the CD model, pass-through of 0.4 requires a distribution cost markup wedge of 150% above the producer’s markup, which is inconsistent with the 50% markup target. For the PD model, the structural formula links PT and markups but less severely, so the trilemma is partially mitigated. For the NCES model, the trade elasticity equals the firm-level elasticity theta, which is also the main driver of pass-through, recreating a binding version of the KA trilemma on the quantity side. For the CC model, the market-expansion friction (captured by adjustment-cost parameter psi) provides an additional degree of freedom that allows trade elasticity to be set independently of pass-through and markups; at symmetric bargaining power eta = 0.5 and 50% markups, the model delivers PT = 0.33 analytically, close to the data target.

Quantitative results confirm the analytic predictions. The KA model fails on quantity statistics because it implies trade elasticity far above target, generating counterfactually negative international comovement of consumption, investment, and employment. The CD model delivers only moderately incomplete pass-through (substantially above the 0.4 target), underperforming on price statistics, and implies a counterfactual correlation of net exports with the terms of trade. The PD model delivers pass-through of approximately 0.70 — better than CD but still above target — and performs well on quantities. The NCES model achieves pass-through of 0.63 (close to but above the 0.4 target) but at the cost of large, negative international comovement in general equilibrium, including a counterfactual positive correlation of net exports with output. The DH model generates more-than-complete pass-through in the presence of persistent exchange rates, failing on prices. The CC model delivers PT = 0.36, closest to the empirical target, achieves correct signs for international quantity comovement, and generates a positive terms-of-trade/net-exports correlation — but requires assumed productivity shock correlation of 0.75 to match measured TFP correlation of 0.3 due to endogenous marketing investment affecting measured TFP, and fails to deliver a positive correlation between terms of trade and the exchange rate.

The paper concludes that further research is needed into frictions that simultaneously dampen the price and quantity responses to volatile exchange rates without violating markup discipline. The reduced-form KA model neither nests nor outperforms the microfounded alternatives. The CC and PD search-based models perform best overall but introduce frictions that are harder to identify and measure directly.

In depth

Q1. What is the parameterization trilemma and how is it characterized analytically?

The trilemma is the structural impossibility of jointly satisfying three empirically necessary targets: (a) plausible steady-state producer markups (calibrated at 50%), (b) low short-run trade elasticity (targeted at 0.7 or below), and (c) low exchange-rate pass-through to import prices (targeted at 0.4). The authors derive closed-form expressions for pass-through (PT), trade elasticity (TE), and markups (mu) for each model and show that satisfying any two targets forces a violation of the third. For the KA model, the key parameter gamma(1) satisfies TE = gamma(1) and mu = (gamma(1) - 1)^{-1}, so targeting 50% markups forces TE = 3 and targeting TE = 1.5 forces markups of 200%. For the CD model, PT = 0.4 requires the distribution-cost wedge xi/(theta-1) = 1.5, implying markups more than 150% above the friction-free level, incompatible with a 50% target. For the PD model the formula is PT = 1 - mu/(1+mu), which is less restrictive. For the NCES model, TE = theta (the firm-level elasticity) and theta also drives pass-through, recreating the KA-type trilemma on the quantity side. For the CC model, the friction parameter psi in marketing capital accumulation independently controls TE, providing an extra degree of freedom that lets the model partially escape the trilemma.

Q2. What is the identification strategy for pass-through and trade elasticity, and what are its main assumptions?

The theoretical pass-through coefficient (PT) is defined as the partial equilibrium, on-impact elasticity of the import price with respect to the exchange rate, computed at the steady state while holding constant marginal costs (v, v*), the stochastic discount factor, and the domestic price of the home good. This mimics what regression-based pass-through estimates do (controlling for local costs). Trade elasticity (TE) is defined analogously as the PT-scaled elasticity of the import/domestic quantity ratio with respect to the exchange rate, under a one-time shock that reverts to the steady state next period (except for the DH model, where a permanent shock is considered). A key assumption is that importers take aggregate price indices as consistent with all importers behaving the same way (a rational-expectations fixed point). General-equilibrium co-movements between exchange rates and marginal costs are abstracted from in the analytic section, consistent with the goal of isolating each model’s intrinsic PTM mechanism.

Q3. Why does the KA model fail on quantity statistics despite being able to match any degree of pass-through?

The KA model can match pass-through of 0.4 by freely choosing the curvature of the demand aggregator g’’(1) (independently of gamma(1)). However, the steady-state demand elasticity gamma(1) simultaneously determines both the markup (mu = (gamma(1)-1)^{-1}) and the trade elasticity (TE = gamma(1)). Matching 50% markups forces gamma(1) = 3 and therefore TE = 3, far above the target of 0.7. This excessive trade elasticity generates counterfactually large expenditure switching in response to exchange-rate shocks, leading to counterfactual negative international comovement of consumption, investment, and employment. A modified Kimball aggregator with a convex adjustment cost (equation 62) does not resolve the problem because the convex cost parameter also enters the steady-state markup formula, so targeting 50% markups still forces high effective trade elasticity.

Q4. Why does the Deep Habits model generate more-than-complete pass-through when exchange rates are persistent?

In the DH model, producers internalize the law of motion for habits: by lowering prices today they accumulate more customer habits, which allows them to raise prices later. When the exchange rate appreciates persistently (from the foreign exporter’s perspective), exporters expect their foreign sales and thus foreign habit stocks to fall over time. This reduces the shadow value of habit (Delta_f), so producers let prices fall by more than the exchange rate movement, generating pass-through greater than one. The authors derive analytically that, for a permanent shock, PT > 1 because dlog(gh)/dlog(x) < 0 (habit falls upon appreciation), and this dominates the direct pricing effect. For a purely transitory shock, the sign reverses (PT < 1), but since exchange rates are highly persistent in the data, the first property dominates. The quantitative section confirms this: the DH model generates PT > 1, marked as 1.00 in Table 4, disqualifying it on prices.

Q5. How does the Customer Capital (CC) model partially escape the trilemma?

The CC model introduces two key elements absent from other frameworks: (1) Nash bargaining over prices within bilateral matches, which directly ties pass-through to the sharing of exchange-rate-driven surplus rather than to demand elasticity; and (2) a convex adjustment friction on marketing capital (psi) that controls the pace of trade-share adjustment, independently setting the short-run trade elasticity. Because prices are determined by bargaining (equation 53: pf = eta*P_d + (1-eta)*v), they depend on the retail marginal value of the foreign good (P_d) and the foreign marginal cost (v), but not on quantity within the match. This decouples PT from TE. Analytically, at static steady state, PT = (1-eta)(1 + mu - (TE/gamma)(eta+mu)*omega)^{-1}; for eta = 0.5 and 50% markups and TE/gamma approaching zero, PT approaches (1-eta)/(1+mu) = 1/3. The psi parameter then tunes TE separately from markups and PT. However, a high long-run elasticity gamma (= 7.9) is required to generate sufficient retail-price responsiveness.

Q6. What does the NCES model achieve on prices and why does it fail on quantities?

The NCES (Nested CES with Cournot competition) model generates incomplete pass-through of 0.63, the second-best performance on prices after the CC model. The mechanism is that non-atomistic (Cournot) firms internalize the impact of their pricing on the sectoral price index; when the exchange rate moves, foreign exporters’ market share changes, altering the endogenous demand elasticity they face and dampening their pass-through. To calibrate the model with only one exporting firm (NX=1 out of N=5), the authors maximize the Cournot effect. However, this calibration implies TE = theta (the firm-level elasticity, set at 7.9 in calibration), far exceeding the target of 0.7. A quantity adjustment cost cannot remedy this because it would simultaneously constrain import-share movements, which are the source of the endogenous demand elasticity variation that generates incomplete pass-through. Consequently, the model implies large negative international comovement of output, consumption, employment, and investment — a worse quantity performance than most other models.

Q7. How does the paper measure markups and what data sources does it use?

The paper equates markups with gross margins under the maintained assumptions of Cobb-Douglas production and static cost minimization (Hall 1988; De Loecker et al. 2020). Under Cobb-Douglas, marginal cost v = wl/y, so markup mu = Py/(wl) - 1 = sales/(cost of goods sold) - 1. Three data sources are used, all for U.S. data 2007-2017: (1) BEA 402 Industry Input-Output Use Tables, which give gross margins of approximately 39-41% for all sectors and 45-50% for traded sectors (import share > 3%). (2) S&P 500 Compustat with BEA sector value-added adjustment, yielding approximately 73-74% for all non-FIRE/GOV/NGO firms. (3) Unadjusted Compustat, yielding 43-49%. The paper adopts 50% as the baseline calibration target, treating it as conservative given the data range, and noting that the BEA I-O measure is the broadest and likely most accurate. The paper explicitly holds that models must respect profit and margin accounting within their own structure.

Q8. How does the paper’s conclusion differ from Itskhoki and Mukhin (2021) regarding the Kimball Aggregator?

Itskhoki and Mukhin (2021) use indirect inference and treat producer margins/markups as a free parameter, implicitly allowing for a much higher markup value — substantially above 50%. Under their calibration approach, the KA model can reconcile low pass-through with better quantity performance. Drozd, Kolasa, and Nosal instead impose a markup discipline: models must match empirically observed gross margins of 50% (for tradable sectors from BEA I-O tables) in their steady state. Under this discipline, the KA model’s trilemma becomes binding, and the model fails on quantity statistics. The authors argue that higher markup assumptions change the effective structure of the model and should be treated as a separate research agenda rather than a free calibration choice.

Q9. What is the role of financial shocks in the model and how are they implemented?

Financial shocks generate exchange-rate volatility that is largely decoupled from real fundamentals — mimicking the observed ’exchange rate disconnect’ from output and consumption. They are modeled following Gabaix and Maggiori (2015): a global financial sector with short-lived arbitrageurs and noise traders. Arbitrageurs face a capacity constraint (parameterized by Gamma) that prevents them from fully exploiting UIP violations, resulting in a distorted UIP condition where the interest rate differential includes a term proportional to the arbitrageur’s position. Noise traders take exogenous positions n(t) that follow an AR(1) process (persistence rho_n = 0.97 in calibration) with standard deviations ranging from 21.2 (CC model) to 114.9 (NCES model) across calibrations. These shocks generate real exchange rate volatility of 3.97% (standard deviations relative to GDP), matching the data target. The paper notes that the precise implementation (Gabaix-Maggiori vs. Itskhoki-Mukhin) has little impact on exchange-rate properties in a linearized setting.

Q10. What robustness checks and extensions does the paper consider?

The paper considers a modified Kimball aggregator with a convex adjustment cost on the ratio of imported to domestic quantities (equation 62) as a potential fix for the KA model’s high trade elasticity. This is shown not to resolve the trilemma because the convex cost parameter also enters the steady-state markup formula, keeping the binding constraint in place. Results for this modified model are reported in the Online Appendix. The paper also notes that the DH model’s pass-through is analyzed under both permanent and transitory shocks, with the sign reversal for purely transitory shocks documented analytically. The paper abstracts from nominal rigidities throughout, justifying this by citing Gopinath-Itskhoki (2011) evidence that conditioning pass-through on price adjustments versus non-adjustments makes little difference in observed pass-through patterns, suggesting limited pass-through is largely a real phenomenon.

Q11. What are the paper’s main implications for the DSGE modeling of open economies?

The paper implies that the standard toolkit for generating incomplete exchange-rate pass-through and muted expenditure switching is inadequate when exchange rates are volatile and act as a major shock. All models face tension among the three targets; the best performers (CC and PD) do so by introducing search frictions that are intrinsically difficult to identify and measure directly. The paper does not claim to provide a solution; rather, it performs a clean diagnostic showing that more research is needed into real frictions that simultaneously insulate import prices and trade quantities from exchange-rate volatility. The finding that the Kimball reduced-form aggregator neither nests nor outperforms microfounded alternatives has implications for monetary-policy DSGE models that frequently use the KA for tractability, suggesting that researchers should be aware of the high implicit markup that is required for the KA to work well in open-economy settings with volatile exchange rates.

Q12. What moments from the data are targeted in calibration and what is the quantitative approach?

The model is calibrated quarterly and HP-filtered (lambda = 1,600). Common targets include: imports/GDP = 12%; 50% producer markups; 30% work hours relative to time endowment; investment volatility relative to GDP = 2.79; short-run trade elasticity (volatility ratio) = 0.7; cross-country TFP correlation = 0.3; TFP volatility = 0.8% and autocorrelation = 0.72; real exchange rate volatility = 3.97%. The pass-through target of 0.4 is used only as an additional degree of freedom for the KA model; for all others, pass-through is an outcome of the structural parameterization. The financial shock persistence is set arbitrarily at rho_n = 0.97 for lack of a target. When a model cannot satisfy all targets (as with KA and NCES on trade elasticity), that target is dropped in favor of best performance on prices. Pass-through is measured in the quantitative section by running regressions analogous to Campa-Goldberg (2005) on model-generated data, rather than using the analytic partial-equilibrium formula.

Q13. What is the sign of the terms-of-trade and exchange-rate correlation, and what does it imply for model evaluation?

In model-generated data (without noise), the correlation of terms of trade (tot = pf/px) with the exchange rate (x) is either -1 (when PT < 0.5) or +1 (when PT > 0.5). The empirical target from U.S. data is approximately -1. This means matching PT < 0.5 and a negative tot-x correlation are equivalent predictions. In the quantitative results, only the KA and CC models achieve PT < 0.5 and thus generate the correct negative correlation; all other models (CD, PD, NCES, DH) generate PT > 0.5 and thus positive tot-x correlation. The authors note that the strict 0.4 target may be too aggressive for aggregate data — PT slightly above 0.5 would be consistent with a positive (near zero) correlation — pointing to Gopinath et al. (2020) who find small, statistically insignificant tot-x coefficients ranging from positive to negative.

Key Concepts

Parameterization Trilemma: The structural impossibility of jointly achieving three empirically necessary targets in standard PTM models: (1) plausible producer gross margins (~50%), (2) low short-run trade elasticity (~0.7 or below), and (3) low exchange-rate pass-through to import prices (~0.4). Each PTM model can satisfy at most two of the three targets simultaneously under quantitative discipline; the third is either infeasible or inconsistent given the model’s internal constraints.

Pricing-to-Market (PTM): The practice by which internationally active firms set different prices in home and foreign markets as a function of the bilateral exchange rate, rather than uniformly passing exchange-rate changes through to import prices. In this paper, PTM is measured by the degree of incomplete pass-through (PT < 1) and is generated by specific microfounded frictions (distribution costs, search, habits, market power, customer capital) rather than by nominal rigidities.

Exchange-Rate Pass-Through (PT): The elasticity of the import price (in the importing country’s currency) with respect to the bilateral real exchange rate, computed in partial equilibrium at the steady state, controlling for local costs. Values used in calibration: empirical short-run range 0.2–0.6; paper target 0.4. Models in which PT = 1 satisfy the law of one price; models with PT < 1 exhibit pricing-to-market.

Short-Run Trade Elasticity (TE): The elasticity of import quantities relative to domestic quantities with respect to the exchange rate (equivalently, the expenditure-switching response to import price changes), measured at business-cycle frequencies. The paper measures this using the volatility ratio of trade-flow quantities to prices (an upper-bound estimate abstracting from correlations), targeting a value of 0.7. Long-run elasticity estimates based on trade liberalization episodes are much higher (typically 6 and above) and are used as the long-run elasticity parameter gamma in search-based models.

Customer Capital (CC) Model: A PTM model (Drozd-Nosal 2012) in which firms build market-specific customer relationships through costly, time-consuming investment in marketing capital, and within-match prices are set by Nash bargaining. The combination of a capacity constraint on quantities traded within each match and bargaining-determined prices decouples the short-run trade elasticity from pass-through, allowing the model to partially escape the parameterization trilemma via the adjustment-cost parameter psi.

Kimball Aggregator (KA): A reduced-form, implicitly defined demand aggregator (Kimball 1995) that generates variable demand elasticity through the curvature of the function g(·) around the steady state. In the open-economy application of Itskhoki-Mukhin (2021), two curvature parameters (g’(1) and g’’(1)) can independently control markup and pass-through — but not trade elasticity simultaneously, which is bound to the steady-state demand elasticity gamma(1) and hence to the markup. The paper shows this model neither nests nor outperforms microfounded alternatives under markup discipline.

Financial Shock: An exogenous disturbance to the position of noise traders in the international bond market (following Gabaix-Maggiori 2015), which drives deviations from Uncovered Interest Parity via the capacity constraint on arbitrageurs. These shocks generate exchange-rate volatility that is largely disconnected from real fundamentals (productivity), calibrated with persistence rho_n = 0.97 to match U.S. real exchange rate volatility of 3.97% relative to GDP.

Gross Margin / Producer Markup: In this paper, defined as (price - marginal cost) / marginal cost = (sales - cost of goods sold) / cost of goods sold, where under Cobb-Douglas production and static cost minimization, the markup equals the gross margin. The paper targets 50% for U.S. tradable-sector firms based on BEA 402 Industry I-O Use Tables (which yield 45–50% for tradable sectors across 2007–2017), treating this as a hard empirical constraint that models must satisfy in the steady state.

TFPR: Dispersion and Cyclicality

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

Layer 1: Overview

This paper investigates what drives the countercyclical dispersion of TFPR — total factor productivity measured in revenue terms — a pattern that is well documented empirically but poorly understood theoretically. The central motivation is a gap between data measurement and model theory: empirical studies (Kehrig 2011; Bloom, Floetotto, Jaimovich, Eksten, and Terry 2018) document countercyclical dispersion of TFPR, yet the models that seek to explain it routinely conflate TFPR with TFPQ (quantity-based TFP) and treat the two as interchangeable. Cooper and Ozturk argue this conflation is misleading because the distribution of TFPR is endogenous — it depends both on the exogenous distribution of TFPQ and on the endogenous price-setting decisions of firms.

The paper builds an overlapping generations (OG) model with monopolistic competition and state-dependent pricing (menu costs). Young agents set prices ex ante, observe idiosyncratic productivity shocks, menu cost draws, and aggregate shocks, then decide whether to adjust prices ex post at a fixed cost. Old agents consume a CES bundle of goods produced by the young. The aggregate state includes shocks to the money supply, to the mean (µQ) and dispersion (dispQ) of TFPQ, and to the dispersion of idiosyncratic demand (dispD). The model is solved as a stationary rational expectations equilibrium (SREE) without linear approximations, allowing the nonlinear hazard of price adjustment to propagate to the aggregate.

The calibration matches three moments: the standard deviation of TFPR (dispR = 0.102 in data, 0.103 in model), the ratio of dispersion in TFPQ to TFPR (1.181 in both), and the monthly frequency of price adjustment (0.110 in data, 0.127 in model), using parameters from Vavra (2014) and Foster, Haltiwanger, and Syverson (2008). The model period is one month. A key structural feature is a U-shaped hazard of price adjustment: firms with very large or very small gaps between actual and desired prices are most and least likely to adjust, respectively.

The central empirical target is three jointly countercyclical moments: (i) dispersion of TFPR, (ii) dispersion of price changes, (iii) frequency of price adjustment. The paper’s first set of findings is negative. Taken individually, no single shock source reproduces all three patterns. Specifically, shocks to dispQ alone produce procyclical TFPR dispersion — output expands when dispersion rises because high-productivity firms can produce more, but TFPR dispersion rises with dispQ (and hence with output), contradicting the data. Money shocks produce procyclical TFPR dispersion and an inverse U-shaped relationship between dispR and the money shock: at extreme shock values, more firms adjust to the common nominal shock, compressing TFPR dispersion; at moderate values, idiosyncratic heterogeneity dominates and dispR is higher. Shocks to µQ alone leave TFPR dispersion nearly flat. Shocks to dispD produce slight countercyclical TFPR dispersion but counterfactually procyclical price adjustment moments.

Two combinations succeed. First, a joint shock to dispQ and µQ with perfect negative correlation (corr = -1, as in Vavra 2014) generates all three countercyclical moments: as dispQ rises, µQ falls, and output contracts while TFPR dispersion increases; from Table 5, dispR is 0.126 in contraction versus 0.020 in expansion, disp∆p is 0.208 in contraction versus 0.082 in expansion, and freq∆p is 0.328 in contraction versus 0.164 in expansion. Second, a monetary feedback rule where the central bank leans against the wind (ζ = -0.05) — tightening money when dispQ is above average — also replicates all three countercyclical moments (Table 5, leaning-against-the-wind rows).

Two additional findings emerge. The model generates state-dependent monetary policy effectiveness: the response of output to a monetary shock is larger in expansions (coefficient 0.644) than in contractions (0.578) when business cycle state is measured by output growth, consistent with Tenreyro and Thwaites (2016) only for the growth-based measure. The paper also finds no role for uncertainty distinct from realized dispersion: when Markov-switching uncertainty over TFPQ dispersion is introduced, the ex ante price is essentially unchanged, consistent with Berger, Dew-Becker, and Giglio (2020).

The theoretical contribution is a TFPR decomposition: Var(tfpr) = Var(tfpq) + Var(ln p) + 2·Cov(ln p, tfpq). In the FHS data, Var(tfpr) = 0.0484, Var(tfpq) = 0.0676, Var(ln p) = 0.0324, Cov(ln p, tfpq) = -0.0258. In recessions, Var(tfpr) rises to 0.0618, driven by an increase in Var(ln p) to 0.0506 while Var(tfpq) stays at 0.0676. This means countercyclical TFPR dispersion can be generated through endogenous price adjustment even holding TFPQ dispersion fixed — a mechanism entirely absent from models that equate TFPR with TFPQ.

In depth

Q1. What is the fundamental measurement-theory gap the paper identifies?

Existing business cycle models (Bloom et al. 2018, Vavra 2014) are calibrated to observed countercyclical dispersion of TFPR but then build theoretical mechanisms around countercyclical dispersion of TFPQ, treating the two as equivalent. Cooper and Ozturk show this is incorrect: TFPR = TFPQ × (p/P), so the TFPR distribution is endogenous, shaped by both the exogenous TFPQ distribution and the endogenous price-setting decisions of firms. Changes in the distribution of prices — through extensive and intensive margins of price adjustment — can move TFPR dispersion independently of TFPQ dispersion.

Q2. Why does the OG framework give the model tractability advantages?

In the OG model, young sellers make price decisions within a single period, so the ex post price is independent of the ex ante price. This means the state space is simplified (no lagged own-price), individual choice problems are tractable, the ex post pricing problem is static, and the full SREE can be characterized without log-linear approximations. Crucially, this allows the nonlinear U-shaped price adjustment hazard to propagate to aggregate outcomes exactly, without the approximation errors that would arise in linearized dynamic models.

Q3. What are the main shocks in the model and how are they parameterized?

There are four aggregate shocks: (i) money supply shocks x, (ii) shocks to the mean of TFPQ (µQ), (iii) shocks to the dispersion of TFPQ (dispQ, implemented as a mean-preserving spread in z), and (iv) shocks to the dispersion of idiosyncratic demand (dispD). At the individual level, sellers face idiosyncratic productivity shocks z with standard deviation σz = 0.0378 and idiosyncratic demand shocks with σd = 0.0069. Menu costs follow the Dotsey and Wolman (2019) distribution with a fraction ψ = 0.053 of firms having zero adjustment costs.

Q4. Why does a dispQ shock alone produce procyclical, not countercyclical, TFPR dispersion?

An increase in dispQ expands the tails of the productivity distribution. High-productivity firms can produce more and expand output (reallocating labor to them raises aggregate output), so output rises with dispQ. Simultaneously, higher dispQ directly raises TFPR dispersion because TFPR = (p/P)×TFPQ and the increased heterogeneity in z carries through to TFPR. Since dispR rises when output rises, the cyclicality is procyclical — directly contradicting the empirical pattern. The pricing response (more adjustment for extreme z draws) magnifies rather than offsets this pattern.

Q5. How do monetary shocks affect TFPR dispersion, and why is the relationship non-monotone?

Money shocks cause a rightward shift in the price gap distribution rather than a spread. For moderate money shocks (near average), few firms adjust, so non-adjusters retain their ex ante prices and face heterogeneous gaps — TFPR dispersion is high. For extreme money shocks (very high or very low), many firms adjust to align their prices with the common nominal shock, compressing idiosyncratic price dispersion. Combined with U-shaped adjustment frequency, this creates an inverse U-shaped relationship between dispR and the money shock: TFPR dispersion is highest at moderate shocks and lowest at extreme shocks. Consequently, money shocks alone produce procyclical TFPR dispersion on average, but the model can produce countercyclical dispersion for extreme realizations.

Q6. How does the joint (dispQ, µQ) shock with perfect negative correlation work to match the data?

Following Vavra (2014), the paper assumes corr(dispQ, µQ) = -1: the highest dispQ state is paired with the lowest µQ state and so on. When dispQ rises, µQ falls. The mean productivity drop dominates in determining output (output contracts), while the dispersion increase drives up TFPR dispersion. This creates countercyclical dispR. From Table 5, in contractions: dispR = 0.126, disp∆p = 0.208, freq∆p = 0.328; in expansions: dispR = 0.020, disp∆p = 0.082, freq∆p = 0.164. All three moments are countercyclical, matching the data. The key mechanism is that the two shocks drive a wedge between the movements in mean output (dominated by µQ) and the movements in dispersion (dominated by dispQ).

Q7. How does the monetary ’leaning against the wind’ feedback rule generate countercyclical TFPR dispersion?

The central bank sets money growth as Mt+1 = Mt[Φ(st+1) + x̃t+1] where Φ(dispQ) = ζ × (dispQ − µdispQ) with ζ < 0 (specifically ζ = -0.05 in the main experiment). When dispQ is above average, the central bank contracts money supply. Since without this rule increased dispQ raises output (procyclical), the monetary contraction more than offsets this, turning the dispQ shock into a net recessionary force. Meanwhile TFPR dispersion still tracks dispQ and rises. Result: both dispR and recession coincide. Table 5 shows that with leaning against the wind on dispQ shocks, dispR = 0.093 in contraction versus 0.082 in expansion, and all three moments remain countercyclical. A second case (feedback to µQ shocks) also produces countercyclical dispR but fails to match the pricing-frequency moment (which becomes procyclical due to asymmetry in the U-shaped hazard).

Q8. What are the nonlinearities in the model and why does the paper avoid using correlations as summary statistics?

The U-shaped price adjustment hazard creates nonlinear aggregate responses: variables can be positively correlated with output in expansions and negatively correlated in contractions, or vice versa. For example, under money shocks the correlation of frequency of price adjustment with output is -0.648 in contractions and +0.977 in expansions (Table 7). The dispersion of TFPR under money shocks also switches sign across states. Standard unconditional correlations average over these sign switches and can give misleading or zero correlations, masking the underlying structure. The SREE is solved exactly without linearization so these nonlinearities are not averaged away in the solution.

Q9. What is the finding on the state-dependence of monetary policy effectiveness?

Table 8 reports regressions of log output on the log money shock separately in contractions and expansions. When recessions are defined by output below trend, the coefficient is 0.578 in contractions and 0.644 in expansions — monetary policy is less effective in recessions. When recessions are defined by three consecutive periods of negative output growth (as in Tenreyro and Thwaites 2016), coefficients are 0.589 in contractions and 0.611 in expansions — the same qualitative finding. However, this contrasts with Tenreyro and Thwaites (2016) in that the paper finds the asymmetry holds regardless of whether the cycle state is measured in levels or growth rates, whereas Tenreyro and Thwaites find the effect only for growth-based definitions. The mechanism is that recessions (high dispQ, low µQ) are associated with more frequent price adjustment, which attenuates the real effect of money shocks.

Q10. What is found regarding the effects of uncertainty versus realized dispersion?

The paper introduces Markov-switching uncertainty where firms do not know in advance which dispersion regime they are in (high or low dispQ). For the ex ante price setting problem, this amounts to taking an expectation over the future dispersion distribution. The quantitative finding is that the ex ante price is essentially unchanged when uncertainty over the dispersion regime is added versus the baseline without such uncertainty. This confirms that the effects on price adjustment and TFPR dispersion in the model come from the realized dispersion, not from ex ante uncertainty about which regime will prevail — consistent with Berger, Dew-Becker, and Giglio (2020) who find that uncertainty shocks have negligible real effects.

Q11. How does the variance decomposition of TFPR characterize the empirical patterns?

The paper uses the identity Var(tfpr) = Var(tfpq) + Var(ln p) + 2·Cov(ln p, tfpq). In the FHS data: Var(tfpr) = 0.0484, Var(tfpq) = 0.0676, Var(ln p) = 0.0324, Cov(ln p, tfpq) = -0.0258. The covariance is negative (prices are lower for high-productivity firms, consistent with markup compression), which is why Var(tfpr) < Var(tfpq). In recessions: Var(tfpr) rises to 0.0618, Var(tfpq) is held fixed at 0.0676 (by assumption in the thought experiment), Var(ln p) rises to 0.0506 (from Vavra 2014), and Cov(ln p, tfpq) becomes more negative at -0.0282. This decomposition shows that countercyclical TFPR dispersion can be generated by endogenous price changes — through both higher price variance and a larger (absolute) covariance between prices and productivity — even if TFPQ dispersion is fixed.

Q12. What is the role of the U-shaped adjustment hazard in the model?

The U-shaped hazard (probability of price adjustment as a function of the price gap or idiosyncratic shock z) is a key structural feature inherited from state-dependent pricing. Adjustment probability is near zero for small gaps (moderate z) and rises steeply for large gaps (extreme z). This creates nonlinear responses: a mean-preserving spread in z (dispQ shock) pushes more mass into the tails, sharply increasing adjustment frequency; a mean shift in z (µQ shock) shifts the gap distribution rightward, also raising adjustment but asymmetrically; a money shock shifts all gaps in one direction (rightward for a positive shock). The interaction between the shock type and the hazard shape determines whether the covariance of prices and productivity rises or falls, which in turn determines whether TFPR dispersion moves countercyclically.

Q13. How does price stickiness create a non-degenerate TFPR distribution without needing other frictions?

In the flexible-price monopolistic competition benchmark (used for comparison), if production is linear in labor (α=1), TFPR = ω/(1-η) and is independent of z — the TFPR distribution is degenerate. In the sticky-price model, non-adjusters set prices ex ante proportional to the money supply, while adjusters set prices that depend on both z and the money shock. The resulting cross-sectional distribution of prices is non-degenerate and generates a non-degenerate TFPR distribution. The coexistence of adjusters and non-adjusters — with prices reflecting both idiosyncratic productivity and aggregate conditions to different degrees — is sufficient to generate TFPR heterogeneity without additional distortions or wedges.

Q14. What are the robustness checks and how do they affect the main findings?

Table 6 reports robustness under money shocks alone across three parameter changes: (1) Higher elasticity of substitution ε = 4 (versus baseline 2.37): higher adjustment frequency, lower price change dispersion, but still procyclical TFPR dispersion. (2) Lower labor supply convexity φ = 1.5 (versus baseline 2): moments become nearly acyclical; TFPR dispersion is much higher than baseline. (3) Equal demand and productivity shock dispersion σd = σz: frequency of price adjustment is nearly four times the baseline, but the monetary shock model still fails to generate countercyclical TFPR dispersion. None of these alternatives bring the money-shock-only model into line with the data, confirming that the main positive results (joint dispQ-µQ shock, or monetary feedback) are not artifacts of baseline parameterization. The paper also notes its calibrated ε is lower than Vavra (2014) and Golosov-Lucas (2007), which use higher elasticities and linear labor disutility.

Q15. How does this paper relate to and differ from Vavra (2014) and Bloom et al. (2018)?

Vavra (2014) documents countercyclical dispersion of price changes and frequency, and argues this follows from countercyclical TFPQ dispersion driving volatility of firm-level productivity shocks. He calibrates to TFPR moments but treats TFPQ and TFPR as equivalent. Bloom et al. (2018) combine uncertainty and dispersion shocks to TFPQ to generate aggregate fluctuations, requiring both a rise in dispQ and a fall in mean TFPQ to avoid counterfactual negative correlation between consumption and investment. Cooper and Ozturk differ in three respects: (i) they explicitly model the TFPQ-to-TFPR mapping through state-dependent pricing; (ii) they show that dispQ shocks alone produce procyclical (not countercyclical) TFPR dispersion in their model; (iii) while they confirm that the joint (dispQ, µQ) combination matches data, they attribute the mechanism to the pricing wedge rather than uncertainty — uncertainty per se has no effect in their framework.

Q16. What are the limitations and directions for future work noted by the authors?

The OG model’s one-period price-setting horizon misses forward-looking dynamics in price adjustment — specifically, the distinction between permanent and temporary adjustment opportunities that matters in infinite-horizon models. However, the authors show the OG model’s policy functions and hazard shape closely replicate those from infinite-horizon state-dependent pricing models, so this limitation is argued to be minor. On the data side, the authors note the ideal structural estimation would use high-frequency joint data on prices and quantities at the firm level, which is not yet available. They suggest future work extending the model to incorporate real-options-style wait-and-see behavior (as in Bloom 2009) combined with state-dependent pricing, and point to the value of non-linear empirical methods (analogous to Tenreyro and Thwaites 2016) for studying price adjustment dynamics.

Q17. What is the relationship between idiosyncratic demand shocks and TFPR dispersion?

Idiosyncratic demand shocks (αi) directly affect a seller’s revenue without changing physical productivity z. Under flexible prices they would affect TFPR directly; under sticky prices the adjustment decision interacts with both the demand and productivity shocks. From Table 5, dispD shocks generate slightly countercyclical TFPR dispersion, but the pricing moments (dispersion of price changes and adjustment frequency) are procyclical — inconsistent with the data. Additionally, the dispersion of demand shocks (σd = 0.0069) is calibrated to be about 18% of productivity shock dispersion (σz = 0.0378), so demand shocks play a smaller quantitative role in the baseline. When σd = σz (equal dispersions), adjustment frequency is nearly four times the baseline but the model still fails to match all three target moments.

Key Concepts

TFPR (Revenue Total Factor Productivity): In this paper, TFPR = (p/P) × TFPQ, where p is a firm’s price and P is the aggregate price index. It is the revenue-based measure of productivity that is directly observed in plant-level data. Its distribution is endogenous because prices are set by sellers; unlike TFPQ, it is not a primitive of the model.

TFPQ (Quantity Total Factor Productivity): The physical or quantity-based measure of productivity, denoted z in the model. It is exogenous to the individual seller and drawn from a distribution that can shift in mean (µQ) or dispersion (dispQ). TFPQ is the primitive shock; TFPR is derived from TFPQ through the pricing decisions of sellers.

State-Dependent Pricing (SDP): A pricing framework in which firms adjust prices only when the gain from adjustment exceeds a menu cost. In this paper, sellers set prices ex ante and then decide ex post whether to pay a stochastic cost to reset. Price adjustment depends on the realized state (idiosyncratic z, money shock x), creating both extensive margin (who adjusts) and intensive margin (what price to set) decisions.

Stationary Rational Expectations Equilibrium (SREE): The equilibrium concept used in the paper. It is a set of ex ante prices, ex post prices, critical adjustment costs, and aggregate price levels that are mutually consistent across all aggregate and idiosyncratic states. The SREE is solved exactly without log-linear approximations, allowing the model’s nonlinearities to be preserved.

U-Shaped Adjustment Hazard: The probability of price adjustment as a function of the gap (difference between desired and actual log price) is U-shaped: near-zero for small gaps and sharply increasing for large gaps in either direction. This creates nonlinear aggregate responses to shocks — aggregate variables can comove differently in expansions versus contractions — and is a central driver of the model’s results on TFPR cyclicality.

Leaning Against the Wind (Monetary Feedback Rule): A monetary policy rule in the paper where the central bank contracts the money supply when the dispersion of TFPQ (dispQ) rises above its average (ζ < 0 in the feedback rule). By doing so, the authority converts what would otherwise be a procyclical dispQ shock into a recessionary one, generating countercyclical TFPR dispersion as a byproduct.

dispQ Shock: An aggregate mean-preserving spread in the distribution of idiosyncratic productivity z. It widens the cross-sectional distribution of TFPQ without changing its mean. Taken alone, it produces procyclical TFPR dispersion; combined with a negative shock to µQ (or with monetary tightening), it can produce countercyclical TFPR dispersion.

Price Gap: The difference between the log of the price a seller would optimally set if adjustment were free and the log of the seller’s current ex ante price. The gap is the sufficient statistic for the price adjustment decision: sellers with larger gaps (in absolute value) have larger gains to adjustment and hence higher adjustment probability. The distribution of gaps across sellers responds to aggregate shocks and shapes aggregate price dynamics.

Wage Adjustment in Efficient Long-Term Employment Relationships

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

Layer 1: Overview

This paper develops a tractable theoretical model of wage dynamics in long-term employment relationships, situated between two polar extremes in the existing literature: continual Nash renegotiation (Mortensen and Pissarides 1994) and wage adjustment only when participation constraints bind (MacLeod and Malcomson 1993). The central motivation is that neither polar extreme matches well-documented empirical facts about wage adjustment — wages are adjusted neither continuously nor as rarely as participation constraints alone would imply.

The model’s key ingredients are: (1) match-specific productivity that evolves as a geometric Brownian motion, generating persistent idiosyncratic shocks; (2) on-the-job search, whereby employed workers receive outside job offers at rate s*lambda; and (3) renegotiation costs modeled as breakdown probabilities (Delta_W for workers, Delta_F for firms) that apply whenever a party unilaterally initiates a renegotiation. These breakdown risks create a wedge between what each party can guarantee by threatening to renegotiate and the full Nash share, thereby generating inaction regions within which the wage remains unchanged. When either party’s surplus falls to the boundary of this inaction region, wage adjustment occurs by mutual consent at zero cost, keeping separations bilaterally efficient. The result is a “drunken walk” for wages: constant most of the time, adjusting minimally when productivity shocks or outside job offers drive the system to the boundary.

An analytical general solution for firm and worker surpluses is derived — a methodological innovation, since prior work with persistent idiosyncratic shocks has required numerical methods.

The model is calibrated at monthly frequency to: a 5% annual real interest rate; a 1% per month exogenous separation rate (from Farber 1999); a 6% steady-state unemployment rate; a 2.5% per month employer-to-employer (E-to-E) transition rate (from Fujita, Moscarini, and Postel-Vinay 2021); a standard deviation of annual log base wage changes among job stayers of 0.053; and an incidence of total compensation (base plus bonus) freezes of 17% (both from Grigsby et al. 2021). Worker bargaining power is set to beta=0.2, which delivers a wage pass-through elasticity of 0.22 (in range of Lamadon et al. 2022 and Kline et al. 2019), hiring costs of 1.4 months of wages (consistent with Oi 1962 and subsequent work), and a base pay share of compensation of 97% at the median (matching Grigsby et al. 2021). The breakdown probability calibrates to Delta=0.33 for both workers and firms.

Key quantitative findings:

First, the calibrated model generates a hump-shaped separation hazard peaking at just over 0.08 at around 3 to 5 months of tenure and declining thereafter, closely matching Farber (1999) — a nontargeted moment. Cumulative wage growth after 10 years of tenure is approximately 15%, lying between Topel’s (1991) estimate of over 25% and Altonji and Williams’ (2005) estimate of 11%.

Second, the model-implied distribution of annual base wage changes among job stayers features over 30% with zero change, substantially more wage increases than cuts, and limited downward flexibility — all key features documented in microdata (Altonji and Devereux 2000; Grigsby et al. 2021). The distribution of total compensation (base plus bonus) is far more symmetric and has lower incidence of freezes (targeted at 17%), consistent with Grigsby et al.’s finding that bonus pay drives most compensation flexibility. The sequential auctions special case (without renegotiation costs) greatly overstates pay freezes, underscoring that renegotiation costs are the mechanism generating empirically realistic intermediate wage adjustment.

Third, the model delivers a near-memorylessness property for hiring wages: because idiosyncratic shocks and outside job offers necessitate ex post wage adjustments that preserve bilateral efficiency, subsequent wages become independent of the initial hiring wage once the first adjustment occurs. Quantitatively, this largely negates Hall’s (2005) result that rigid hiring wages can generate substantial unemployment fluctuations: in the calibrated model with empirically realistic adjustment, the allocative effect of entry wage flexibility on labor market tightness is much smaller than in Hall’s special case.

Fourth, the model provides a novel theory of recruitment and retention bonuses. Because persistent productivity shocks are best met with adjustments to the flow wage, while transitory outside offers are best met partly with lump-sum bonuses (flow wage increases are credibly capped by the firm’s inaction boundary), the model predicts non-base pay as an equilibrium outcome. Counterfactual experiments show that eliminating firms’ ability to pay retention bonuses reduces total match surplus at the date of new matches by approximately 15.1% and raises the employment-to-unemployment separation rate by approximately 9.5%; eliminating both retention and recruitment bonuses raises these figures to 16.0% and 10.3%, respectively.

The paper also extends the baseline model to accommodate positive inflation (nominal wages held fixed absent renegotiation), using a perturbation method due to Fleming (1971), generating a spike at zero nominal wage change that decays with inflation — consistent with the large empirical literature on nominal wage adjustment.

The implication for macroeconomics is that efficient long-term relationships with realistic sporadic wage adjustment cannot be the source of cyclical unemployment volatility, pointing toward either violations of bilateral efficiency (asymmetric information, wage-cut costs) or volatile labor demand as the necessary ingredient.

In depth

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

The paper is primarily theoretical and quantitative, not empirical, so it does not employ a conventional identification strategy. The model is calibrated to match a set of moments from existing microdata (Farber 1999; Fujita et al. 2021; Grigsby et al. 2021) and then evaluated on nontargeted moments such as the shape of the separation hazard by tenure. Threats to the model’s quantitative conclusions include: (a) the calibration sets beta=0.2 somewhat informally (targeted to four informal moments rather than formally estimated); (b) the baseline restricts mu=sigma^2/2 so that log match productivity is driftless, and Delta_W=Delta_F (symmetric breakdown risk) — the paper checks in the appendix that relaxing mu gives essentially unchanged main results; (c) the model abstracts from risk aversion, general human capital accumulation, and permanent firm heterogeneity, any of which could alter wage dynamics or calibrated parameter values; (d) the Grigsby et al. (2021) moments used for calibration pertain to a period of very low inflation, which the paper treats as approximately a zero-inflation environment.

Q2. What is the drunken walk and why is it called that?

The ‘drunken walk’ is the wage path that emerges from the model. The wage remains constant whenever both parties’ surpluses lie strictly within their respective inaction regions (neither party can credibly threaten to renegotiate). When idiosyncratic productivity hits the upper or lower boundary of the inaction set, the wage adjusts minimally upward (to restore the worker’s surplus to the threshold) or minimally downward (to restore the firm’s surplus to the threshold). The path therefore wanders irregularly, making small adjustments only when forced to by the boundaries, analogously to a drunken walk — a term echoing the dynamic contracting literature (Thomas and Worrall 1988), where the same path arises from insurance motives rather than renegotiation costs.

Q3. How does the paper characterize the surplus analytically and why is this novel?

The key innovation is that bilateral efficiency decouples the total match surplus (determined as an optimal stopping problem) from the division of that surplus between firm and worker. Total surplus S(x) is characterized analytically as a function of match productivity x alone, solving an ODE with boundary conditions (value-matching and smooth-pasting at the separation threshold). Given S(x), the firm surplus J(w,x) and worker surplus V(w,x) satisfy ordinary differential equations (not PDEs) for any fixed wage w, because wages change only at boundaries. This reduces the wage determination problem to one of iterating over constants rather than functions, allowing analytical general solutions (Propositions 2, 3, 4) that prior work with persistent idiosyncratic shocks could not obtain, requiring numerical methods instead (Yamaguchi 2010; Lise et al. 2016).

Q4. What are the two special cases studied and what do they reveal?

The costly renegotiation case (s=0, no on-the-job search) isolates adjustment driven purely by idiosyncratic productivity shocks and breakdown risk. In this case, the wage adjustment boundaries simplify to an upper bound from the worker’s threat and a lower bound from the firm’s threat; there is a fundamental asymmetry in that workers cannot credibly threaten a wage increase in the face of complete breakdown risk (Delta_W=1), since they receive no outside offers. The sequential auctions case (beta=0, Delta_F=1, on-the-job search only) recovers and extends Postel-Vinay and Robin (2002) to persistent productivity shocks with analytical solutions. In this case, wage adjustment is one-sided in a surprising direction: wage increases are triggered by reductions in match productivity, because lower productivity reduces the recruitment compensation that a worker could extract if an outside offer arrived, lowering her match value and necessitating a raise. This case greatly overstates pay freezes relative to data, confirming that renegotiation costs are essential to match empirical wage adjustment frequency.

Q5. What is the memorylessness property and what are its implications for Hall (2005)?

The memorylessness property states that, conditional on the occurrence of a wage adjustment, the subsequent path of wages is independent of the initial hiring wage. Once the wage is adjusted, the history is ‘forgotten.’ This arises because ex post wage adjustments are determined solely by contemporaneous productivity and the bilateral efficiency requirement, not by the history of wages up to that point. The implication for Hall (2005) is that the allocative effect of hiring wage rigidity on unemployment fluctuations — which rests on the hiring wage having an indefinite legacy (no adjustment ever needed in Hall’s special case of zero idiosyncratic shocks, zero on-the-job search, and full breakdown risk) — is largely negated once realistic wage adjustment is introduced. The decomposition in equation (27) shows that the entry wage effect on firm surplus and labor market tightness is much smaller in the baseline calibration than in Hall’s special case, and that general equilibrium effects (firms anticipating future wage adjustments in booms) further moderate volatility. This dovetails with the empirical literature initiated by Beaudry and DiNardo (1991) finding that economic conditions at the start of a job have little explanatory power for current wages once one controls for the history of conditions since job start.

Q6. What is the model’s theory of recruitment and retention bonuses and why does it matter?

Bonuses arise from the asymmetry between the type of shocks and the type of compensation instrument best suited to absorb them. When match productivity changes persistently, adjusting the flow wage is efficient; but when an outside offer arrives temporarily, the value delivered to retain a worker cannot always be committed credibly via flow wages — the firm can only raise the base wage up to the threshold at which the firm would immediately trigger another renegotiation to cut it back. Any remaining value above that threshold must be delivered as a lump-sum retention bonus. Analogously, when recruiting a worker from another firm, the new employer has an upper bound on the flow wage it can credibly offer; remaining value goes to a recruitment bonus. This provides an endogenous theory of non-base pay. The allocative stakes are large: eliminating retention bonuses reduces match surplus at new matches by 15.1% and raises the E-to-U separation rate by 9.5%; eliminating both retention and recruitment bonuses raises these figures to 16.0% and 10.3%. Even though bonuses are transitory and account for only a small share of overall compensation (the base pay share is 97% at the median in the calibration), they are allocatively important — the paper calls this an instance of the general principle that marginal variation can be allocatively consequential.

Q7. What heterogeneity is documented or analyzed?

The main model is deliberately parsimonious and abstracts from worker and firm heterogeneity. However, the paper notes that the model can accommodate permanent worker type differences in efficiency units: if x, b, and vacancy costs all scale with efficiency units, the log wage change distribution is identical across worker types while the initial wage scales proportionally. The paper also analyzes two sources of heterogeneity in wage outcomes that emerge endogenously: variation in wage change incidence with match tenure (separation hazard that is hump-shaped in tenure) and variation in base-wage versus total-compensation changes (base wages change less frequently and are more asymmetric than total compensation). The appendix contains an extended model allowing general drift mu, encompassing specific human capital accumulation, with results described as essentially unchanged.

Q8. What robustness checks are performed?

Key robustness exercises include: (1) The appendix provides the extended model with general mu (not restricted to mu=sigma^2/2), encompassing specific human capital accumulation; main results are stated to be essentially unchanged. (2) Recalibrated versions of the two special cases (s=0 for costly renegotiation; Delta_F=1 and beta=0 for sequential auctions) are examined separately to understand which mechanism drives empirical fit. (3) An alternative special case with Delta_W=Delta_F=1 and beta>0 is confirmed to generate a similarly counterfactual share of pay freezes (~75%), reinforcing that wage-adjustment-only-at-participation-constraints is empirically rejected. (4) The inflation extension in Section 3 uses an approximate analytical solution (Taylor expansion to first order in pi) following Fleming (1971) to show the model generates sensible nominal wage change distributions and a decaying zero-spike with inflation. (5) Proposition 2 result (ii) establishing the expected duration of wage spells provides an internal consistency check linking the allocative effects of wages to their duration.

MacLeod and Malcomson (1993) is the closest theoretical predecessor: it studies renegotiation by mutual consent with efficient long-term relationships and generates a drunken walk. This paper extends it by adding idiosyncratic productivity shocks and on-the-job search and making the model quantitative with analytically tractable solutions, moving beyond MacLeod-Malcomson’s polar case (Delta=1). Postel-Vinay and Turon (2010) study a similar environment to the sequential auctions special case but with i.i.d. productivity shocks, requiring numerical methods; this paper obtains analytical solutions even with persistent shocks. Postel-Vinay and Robin (2002) and Cahuc et al. (2006) are nested as special cases. Hall (2005) is nested and shown to be quantitatively non-generic: its result on hiring wages and unemployment fluctuations relies on special-case assumptions that are empirically rejected. Gertler and Trigari (2009) achieve large unemployment fluctuations via time-dependent staggered wage adjustment; this paper studies state-dependent adjustment and finds the opposite result. Grigsby et al. (2021) provide the key calibration moments on the incidence of pay changes; the paper replicates their finding that total compensation is more flexible than base pay and provides a theoretical interpretation. Balke and Lamadon (2022) study long-term contracts with directed search but without wage inaction, which is a central object here. Dupraz et al. (2022) model wage rigidities that generate inefficient separations; this paper instead maintains bilateral efficiency and generates wage rigidity endogenously.

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

The central policy-relevant conclusion is that, within a model of efficient long-term relationships with realistic sporadic wage adjustment, hiring wage flexibility (or rigidity) is much less consequential for unemployment fluctuations than Hall (2005) suggested. This implies that policies aimed at wage flexibility at the point of hiring are unlikely to substantially moderate unemployment fluctuations if the broader employment relationship is bilaterally efficient. The model instead points to wage-cut costs, asymmetric information, or impediments to matching outside offers as the necessary ingredients for hiring-wage stickiness to matter for unemployment. The allocative importance of non-base pay (retention and recruitment bonuses) suggests that regulations or institutional arrangements that restrict bonus pay could meaningfully retard match formation and raise separations, even when bonuses appear small as a share of total compensation. The scope conditions are bilateral efficiency, risk neutrality, and the absence of aggregate shocks (the paper focuses on idiosyncratic shocks in a stationary equilibrium, with only a perturbation analysis for aggregate shocks in the allocation-of-entry-wages section).

Q11. What does the user cost of labor framework reveal?

Section 1.6 extends the user cost of labor concept of Kudlyak (2014) — the shadow flow price of labor in long-term relationships — to this environment. The user cost in this model contains components absent from simple Diamond-Mortensen-Pissarides: turnover costs due to on-the-job search (proportional to the firm surplus of a new match, contributing sλ*J(w0,x0)), and the value of future productivity drift and variance (which act as a source of moderation of user cost). The key message is that idiosyncratic shocks and on-the-job search diminish the importance of the initial wage in the firm’s effective flow cost of labor, because future wage adjustments are anticipated. This provides a flow-based interpretation of the memorylessness property and complements the work of Doniger (2021) and Bils et al. (2023) on quality-adjusted labor costs.

Q12. How does inflation affect wage adjustment in the extended model?

In the extension (Section 3), the nominal wage is held fixed absent renegotiation, so the real wage drifts downward at the inflation rate pi. This creates an additional source of value to the firm (and loss to the worker), valued at -piwJ_w. Because J_w<0 (higher wages reduce firm surplus), inflation raises firm value and consequently shifts the adjustment boundaries inward: for a given productivity, firms are less likely to demand nominal wage cuts and workers are more likely to demand nominal wage increases. The zero-change spike in the distribution of nominal wage changes decays as inflation rises, a well-established empirical feature. The analytical solution uses a first-order Taylor expansion in pi (following Fleming 1971), which the authors note may also be extendable to approximate solutions for aggregate shocks.

Key Concepts

Drunken walk (wage dynamics): The equilibrium wage path in the model: wages remain constant for extended periods and adjust minimally — only enough to prevent a unilateral renegotiation — when idiosyncratic productivity shocks or outside job offers drive firm or worker surplus to the boundary of their respective inaction sets. The name reflects the irregular, boundary-regulated wandering of wages over time.

Renegotiation costs (breakdown risk): The cost of unilaterally initiating a wage renegotiation, modeled as a probability Delta_W (Delta_F) that the match breaks down if the worker (firm) forces a renegotiation. These costs generate inaction regions in which neither party can credibly threaten a unilateral renegotiation, so the wage remains unchanged. They are the key parameter governing the frequency of equilibrium wage adjustment, nesting both continual bargaining (Delta=0) and adjustment only at participation constraints (Delta=1) as polar cases.

Inaction set: For any current wage w, the set of match productivities x within which neither the firm nor the worker can credibly issue a unilateral threat to renegotiate. The wage remains constant when productivity lies in the interior of both parties’ inaction sets. The boundaries of these sets are the thresholds x_W(w) and x_F(w) at which wage adjustments are triggered by mutual consent.

Memorylessness (of hiring wages): The property that, once a wage adjustment occurs, the subsequent path of wages is independent of the initial hiring wage. This arises because ex post adjustments are determined solely by contemporaneous productivity and the bilateral efficiency requirement. As a result, the legacy of any hiring wage is truncated to the duration of the first wage spell, negating the allocative importance of hiring wage rigidity for unemployment fluctuations in Hall’s (2005) sense.

Recruitment and retention bonuses: Lump-sum payments made by the current or prospective employer when an employed worker receives an outside job offer, in situations where the value to be delivered to retain or recruit the worker exceeds what can credibly be committed via increases to the flow base wage (which face a ceiling imposed by the firm’s inaction boundary). The model predicts these bonuses as an equilibrium outcome of bilateral efficiency, arising from the asymmetry between persistent productivity shocks (best absorbed by flow wage changes) and transitory outside offers (partially absorbed by lump-sum bonuses).

Bilateral efficiency (in long-term employment relationships): The property that firm and worker jointly maximize total match surplus, so that separations occur if and only if total surplus is exhausted, and wages are set to preserve this condition. In this paper, bilateral efficiency is preserved on the equilibrium path because costless mutual-consent wage adjustments preempt costly unilateral renegotiations. The term is used specifically for bilateral efficiency of individual relationships (not equilibrium efficiency of aggregate allocations).

User cost of labor: The shadow flow price of labor in a long-term employment relationship, extending Kudlyak (2014) and the Jorgenson (1963) capital user cost concept to this environment. It equals flow output at a new match and consists of the flow wage plus flow-equivalent discounting and separation costs, minus the capital gains from anticipated future wage adjustments induced by productivity drift, variance, and on-the-job search. Idiosyncratic shocks and on-the-job search reduce the importance of the initial wage in this user cost, providing a flow-based expression of the memorylessness property.

Wage pass-through elasticity: The elasticity of the equilibrium wage with respect to a change in match-specific productivity — the log change in wages induced by a one log-point rise in match productivity. In the calibrated model this equals 0.22, reflecting that efficient renegotiation shares only part of idiosyncratic productivity gains with the worker (bounded by the worker’s bargaining power beta=0.2 and the renegotiation cost structure). This is the model’s analogue to empirical rent-sharing elasticities in Lamadon et al. (2022) and Kline et al. (2019).

What Drives the Recent Surge in Inflation? The Historical Decomposition Roller Coaster

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

Layer 1: Overview

The paper addresses what drove the post-COVID inflation surge in the United States and internationally. Before answering the substantive question, the authors identify and diagnose a methodological obstacle: the standard tool used for such analysis — the historical shock decomposition in a structural VAR — can produce wildly inconsistent narratives depending on small, likelihood-inconsequential changes in the model’s parameters.

The mathematical core is the VAR decomposition of observed data into a deterministic component (DC, the model’s period-zero forecast in the absence of any realized shocks) and a stochastic component (SC, the discounted cumulative sum of shock contributions). Because DC and SC sum to data, imprecision in DC is mechanically transmitted to SC, making inferences about shock contributions unreliable. The authors establish that conditional likelihood-based estimation leaves the VAR constant C poorly identified: parameter perturbations that move the likelihood only negligibly can shift DC dramatically. This “excess volatility” in DC is distinct from the better-known overfitting problem: excess volatility is about cross-draw uncertainty in DC, not its average level, and can be severe even when overfitting is mild.

The illustrative case is a bivariate SVAR of US real GDP and the GDP deflator (log first differences, 1983:Q1–2022:Q4, four lags, sign restrictions, Jeffreys diffuse prior). The three draws closest to the point-wise median impulse response — draws whose impulse responses are virtually indistinguishable — produce entirely contradictory post-pandemic narratives: the first assigns more than two-thirds of the inflation rise to supply shocks, the second assigns more than two-thirds to demand shocks, and the third assigns roughly equal shares. The US GDP deflator peaked at 7.7 percent in 2022:Q2; euro area inflation peaked around 10 percent on an annual basis, with some European countries exceeding 15 percent in 2022.

The excess volatility problem is shown to be pervasive: it arises regardless of identification scheme (sign restrictions, Blanchard-Quah long-run restrictions, Cholesky zero-impact restrictions), persists with standard priors (Normal-Inverse Wishart and Minnesota) that shrink AR coefficients but leave the constant diffuse, worsens with longer or more heterogeneous samples (the 1949:Q1–2022:Q4 sample produces substantially larger dispersion than the baseline), and survives in larger VAR systems (the problem is if anything more severe in a 5-variable BVAR).

The preferred solution is the single-unit-root prior (Sims 1993), implemented as a dummy initial observation that constrains the VAR’s unconditional mean to the sample average. As the tightness hyperparameter δ → 0, DC converges across all posterior draws to a common value. The modal posterior value of δ, estimated data-adaptively using the approach of Giannone et al. (2015) with a Gamma prior of mode 1, is 0.0001 for US data — indicating the data strongly favor tight shrinkage. In simulations, after roughly 20 periods, all 1,000 draws of DC converge to virtually identical values regardless of data persistence or sample size.

With the single-unit-root prior, the US results are unambiguous: supply shocks were important in the initial phase of the inflation surge, but demand factors became the main driver from 2021 onward, accounting for 56 percent of inflation fluctuations in 2021 and 77 percent in 2022. Two pragmatic alternatives for frequentists — demeaning the data prior to estimation, and computing point-wise median historical decompositions — both corroborate demand dominance.

International evidence is estimated using the same bivariate SVAR and identification restrictions. For the euro area (industrial production and HICP inflation, 2001:M1–2023:M3), demand factors account for more than 50 percent of inflation fluctuations in 2022, but supply shocks remain significant through at least mid-2023, reflecting the region’s greater exposure to the Ukraine-war commodity supply shock. For four small open economies (Norway, Sweden, Canada, Australia; quarterly GDP growth and year-on-year CPI inflation, 1993:Q1–2023:Q2), the pattern closely resembles the US: supply shocks dominate in 2020, but demand forces become prevalent already in 2021 and are nearly dominant in some cases thereafter. The finding that demand factors were the primary driver of the inflation surge thus holds robustly across six economies with heterogeneous policy responses, supply-chain exposures, and Ukraine-war commodity price effects. The policy implication is that the aggressive monetary tightening implemented by central banks was appropriate given the demand-driven nature of the surge — though the paper is careful to note that its “demand shock” aggregates monetary, fiscal, and other demand-side disturbances, limiting precise policy prescriptions.

In depth

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

The baseline uses sign restrictions: a demand shock moves real GDP and the GDP deflator in the same direction on impact; a supply shock moves them in opposite directions. Restrictions are imposed only on impact, following Canova and De Nicolo (2002). The authors acknowledge that the demand shock bundles monetary, fiscal, and other demand-side disturbances, while the supply shock aggregates productivity, commodity, markup, and other supply-side factors. Blanchard-Quah (long-run zero restrictions) and Cholesky (impact zero restrictions) are used as alternative schemes to show the excess-volatility problem is identification-independent. The main threat to credible decompositions is not misidentification of shocks per se but rather imprecision in the VAR’s deterministic component, which contaminates all inferences about shock contributions regardless of the identification scheme.

Q2. What exactly is the excess volatility problem and why does it arise?

The VAR’s deterministic component DC_t depends on the companion matrix A and the constant vector C. Conditional likelihood-based estimation identifies A well — impulse responses are relatively precisely estimated — but leaves C poorly pinned down, because many combinations of (A, C) produce nearly identical likelihood values while implying very different unconditional means and thus very different DC paths. Even parameter perturbations negligible relative to the likelihood surface can shift DC dramatically. Because the stochastic component SC_t = Data - DC_t, imprecision in DC is mechanically transmitted to SC_t and to estimated shock contributions. The problem is a property of the reduced-form model and arises before any structural identification is imposed.

Q3. How is excess volatility distinguished from the overfitting problem?

Overfitting (Sims 1996, 2000; Giannone et al. 2019) refers to the deterministic component attributing an implausibly large share of low-frequency data variation to itself — the DC level tracks the data in-sample but implies poor out-of-sample forecasts. Excess volatility refers to the uncertainty across posterior draws in DC, not the average level of DC. A model can exhibit mild overfitting (as in the baseline bivariate model, whose DC paths stabilize after only two or three years) while having extreme excess volatility across draws. Solving the overfitting problem — for example by using the prior for the long run (Giannone et al. 2019) — does not solve the excess volatility problem. The single-unit-root prior addresses both, but for distinct reasons.

Q4. How does the single-unit-root prior solve the excess volatility problem technically?

The prior adds a dummy observation that imposes the stochastic constraint [I − A]Ȳ₀ − C = δu₀, where Ȳ₀ is set to the sample average and δ governs tightness. Substituting into the DC formula shows that, for a stationary ergodic system, A^t(Y₀ − Ȳ₀) → 0 as t grows, so DC_t converges across all posterior draws to Ȳ₀. The hyperparameter δ is estimated from the data using a Gamma prior with mode 1, following Giannone et al. (2015). The modal posterior value is 0.0001 with negligible posterior dispersion, indicating strong data support for near-exact shrinkage. The prior does not eliminate uncertainty in the stochastic component — draws of A and F still produce variation in shock contributions — but that remaining uncertainty is the same type as in impulse response estimation, making the two statistics mutually consistent.

Q5. Why do standard priors (Normal-Inverse Wishart, Minnesota) fail to solve the problem?

Standard priors shrink the AR coefficient matrices and the residual covariance matrix but leave the prior on the VAR constant C diffuse. Because the excess volatility arises specifically from poorly identified values of C, these priors leave the deterministic component as uncertain as with a diffuse prior. The paper demonstrates this directly by plotting deterministic component draws under Normal-Inverse Wishart and Minnesota priors (Figure 3, rows 2) — the dispersion remains large and whimsical historical decompositions persist.

Q6. What heterogeneity is documented across countries?

The euro area shows a more balanced demand-supply split than the US: demand and supply factors contribute roughly equally overall, with demand becoming prevalent in 2022 (exceeding 50 percent of inflation fluctuations) but supply shocks remaining significant through mid-2023. The authors attribute this persistence of supply shocks in the euro area to the region’s greater exposure to the Russia-Ukraine energy supply disruption. The four small open economies (Norway, Sweden, Canada, Australia) have outcomes surprisingly similar to the US: supply shocks drive inflation in 2020, demand becomes prevalent in 2021 and is nearly dominant in some cases in 2022. Overall, despite heterogeneity in fiscal stimulus, supply-chain exposure, and commodity price effects, demand factors are the primary driver across all six economies examined.

Q7. What robustness checks are run?

The paper runs five main robustness exercises. (1) Three identification schemes — sign restrictions, Blanchard-Quah, and Cholesky — all exhibit the same excess-volatility problem under diffuse priors and produce similar demand-dominance results with the single-unit-root prior. (2) Four prior specifications — diffuse, Normal-Inverse Wishart, Minnesota, single-unit-root — are compared using a proposed dispersion measure (max-minus-min across top 100 draws, averaged over time); the single-unit-root prior uniformly produces the smallest dispersion across all identification schemes. (3) Two sample periods for the US: the baseline 1983:Q1–2022:Q4 and an extended 1949:Q1–2022:Q4 sample; excess volatility is substantially larger with the longer, heterogeneous sample. (4) A 5-variable VAR (real GDP, GDP deflator, real private investment, federal funds rate, real wages), baseline sample and diffuse prior — the excess-volatility problem remains and is more severe for variables like inflation and the federal funds rate. (5) Two alternative approaches for frequentists (demeaning the data; computing point-wise median historical decompositions) both reproduce the demand-dominance finding.

Q8. What are the two pragmatic alternatives offered for researchers reluctant to use priors?

First, demeaning all variables before estimation and estimating the VAR without a constant. This eliminates the first term of DC (which depends on C) and forces DC to follow A^t·Y₀, which approaches zero for stationary systems. It is a partial solution — draws with different A matrices still produce different DC paths, so dispersion is reduced but not eliminated; dispersion is smaller than under a diffuse prior but larger than under the single-unit-root prior. Second, computing the point-wise median historical decomposition: across all posterior draws, take the median contribution of each shock at each date. The resulting summary is non-additive (a residual deterministic component absorbs the gap between data and the two median stochastic components) but robust to outliers and reflective of parameter uncertainty. Bergholt et al. (2023) use this approach in prior work. The paper shows that median decompositions under all four prior specifications deliver demand-dominance conclusions similar to those from the single-unit-root prior.

Q9. What dispersion measure do the authors propose, and what do the numbers show?

The authors define D_{i,j,t} as the max-minus-min spread of shock j’s contribution to variable i at time t across the 100 draws closest to the point-wise median impulse response. M_{i,j} is the time-average of D_{i,j,t}. Applied to the contribution of demand shocks to US inflation over 2020:Q2–2022:Q4, the values are: diffuse prior — 1.07 (sign), 0.88 (Blanchard-Quah), 2.33 (Cholesky); Normal-Inverse Wishart — 1.53, 1.20, 0.91; Minnesota — 0.87, 0.71, 0.61; single-unit-root — 0.68, 0.48, 0.54. The single-unit-root prior produces the smallest dispersion uniformly across all identification schemes.

Bernanke and Blanchard (2024) use a simple wage-price dynamic model and find most of the surge resulted from shocks to prices given wages. Rubbo (2023) uses disaggregated price data and finds roughly three-quarters of the CPI rise since 2021 is demand-driven. Eickmeier and Hofmann (2022) use a large factor model and find demand predominant. Ascari et al. (2023) use a Bayesian SVAR on euro area data and find demand factors crucial from fall 2020. The present paper’s demand-dominance conclusion is broadly consistent with this literature. Its distinctive contribution is not the substantive finding but the methodological diagnosis: it shows that standard VAR-based historical decompositions are whimsical under diffuse priors, explains why, and provides credible solutions. It also contributes international evidence spanning six economies with comparable methodology.

Q11. What are the policy implications and their scope conditions?

The finding that demand factors were the primary driver of the post-COVID inflation surge supports the appropriateness of the aggressive monetary tightening implemented by the Federal Reserve and other central banks. A demand-driven inflation surge calls for a different policy response than a supply-driven one; the paper’s results vindicate the central bank interpretation that monetary tightening was warranted. However, scope conditions are important: the identified ‘demand shock’ aggregates monetary, fiscal, and other demand-side disturbances; the paper cannot decompose the demand category further into, for example, fiscal stimulus versus pent-up household demand. Additionally, the bivariate model omits many potentially relevant variables. The policy implication applies to the broad nature of the shock (demand vs. supply) and does not prescribe specific instruments or magnitudes of policy response.

Q12. What future research directions are identified?

The authors note that the excess volatility problem is even more acute when separating permanent from transitory components of data, because imprecision in DC translates directly into imprecision in the level of the permanent component. In small samples, long-run shock contributions are also imprecisely estimated, compounding the problem. These issues make estimates of trend inflation poor and inflation regimes difficult to characterize. The authors flag this as a planned area of future research.

Key Concepts

Deterministic component (DC_t): The period-zero forecast of the endogenous variables in the absence of any unforecastable shock realizations — the counterfactual trajectory the VAR assigns based on its parameters and initial conditions alone. Not a statistical trend, but the baseline path the model says would have prevailed had no shocks occurred.

Stochastic component (SC_t): The discounted cumulative sum of all structural shock realizations from period 1 through period t. Together with the deterministic component, it sums to the observed data; it is the part of the observed series attributable to identified economic shocks.

Historical shock decomposition: The retrospective attribution of observed data fluctuations at each point in time to the contributions of individual identified structural shocks. Distinct from the impulse response function (which characterizes prospective shock propagation): the historical decomposition integrates shock realizations and is thus a function of the stochastic component’s draw-specific paths.

Excess volatility (of the deterministic component): The phenomenon whereby posterior draws of VAR parameters that produce nearly identical impulse response functions nevertheless imply radically different paths for the deterministic component. Caused by the likelihood surface being nearly flat with respect to the VAR constant C. Distinct from overfitting: excess volatility is cross-draw uncertainty in DC, not the average level of DC.

Single-unit-root prior (dummy initial observations prior): A prior on VAR parameters implemented by adding one artificial observation, where both current and lagged values equal (1/δ)·Ȳ₀ and the intercept equals 1/δ. As tightness parameter δ → 0, the prior constrains the VAR’s unconditional mean to equal Ȳ₀ across all posterior draws, eliminating excess volatility in DC while leaving structural shock uncertainty intact.

Dispersion measure (M_{i,j}): The authors’ proposed metric for quantifying how whimsical a historical decomposition is: the time-average of the max-minus-min spread of shock j’s contribution to variable i across the 100 draws closest to the point-wise median impulse response. Smaller values indicate more robust, less draw-dependent decompositions.

Whimsical historical decomposition: The paper’s term for a shock decomposition whose narrative about the relative importance of structural drivers changes substantially across draws that are otherwise observationally equivalent in terms of impulse responses. Caused by excess volatility in the deterministic component forcing shocks to compensate for different DC paths.

A Model of Post-2008 Monetary Policy

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

Layer 1: Overview

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

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

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

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

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

In depth

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Q9. What robustness checks support the determinacy result?

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

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

Q11. What are notable caveats the authors themselves raise?

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

Key Concepts

Does the Phillips Curve Lie Down as We Age?

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

Layer 1: Overview

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

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

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

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

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

In depth

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

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

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

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

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

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

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

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

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

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

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

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

Q7. What heterogeneity is documented beyond the age gradient?

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

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

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

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

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

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

Key Concepts

Inflationary Household Uncertainty Shocks

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

Layer 1: Overview

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

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

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

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

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

In depth

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

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

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

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

Q3. What heterogeneity is documented?

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

Q4. What robustness checks are run?

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

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

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

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

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

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

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

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

Key Concepts

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

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

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

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

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

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

Monetary Policy When Preferences Are Quasi-Hyperbolic

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

Layer 1: Overview

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

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

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

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

In depth

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Q9. What robustness/extensions are considered?

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

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

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

Key Concepts

Nonresponse Bias in Household Inflation Expectations Surveys

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

Layer 1: Overview

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

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

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

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

In depth

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

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

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

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

Q3. What heterogeneity is documented?

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

Q4. What robustness checks are run?

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

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

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

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

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

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

Q8. What does the comparison with professional forecasters show?

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

Key Concepts

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

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

Layer 1: Overview

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

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

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

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

In depth

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

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

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

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

Q3. What heterogeneity is documented?

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

Q4. What robustness checks are run?

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

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

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

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

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

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

Key Concepts

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

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

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

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

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

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

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

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

Layer 1: Overview

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

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

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

In depth

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

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

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

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

Q3. What heterogeneity is documented?

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

Q4. What role did unconventional fiscal policy play?

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

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

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

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

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

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

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

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

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

Q9. What are the main caveats and robustness considerations?

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

Key Concepts

Monetary Cooperation during Global Inflation Surges

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

In a multicountry model with nominal wage rigidities, two sectors (tradable with convex supply, nontradable with flat supply), and free capital mobility, the paper studies optimal monetary policy during a global demand reallocation shock — a shift in preferences toward tradables (ω₀ > ω). Under cooperation (Proposition 1), the optimal response allows inflation to rise: higher tradable goods prices reduce real wages (restoring labor demand), generate expenditure switching back toward nontradables, and boost nontradable employment through an income effect. Cooperation achieves full employment as long as the inflation cost is below the full-employment threshold; otherwise it strikes the optimal inflation-unemployment balance. Under noncooperation (Proposition 3), each national central bank perceives it can attract capital inflows by raising its policy rate — inflows sustain nontradable demand and reduce the domestic sacrifice ratio of disinflation. But in a symmetric Nash equilibrium, synchronized rate hikes cancel each other through global credit market clearing; only the global monetary contraction remains. The result is lower inflation than under cooperation but higher unemployment — a competitive appreciation trap that mirrors the competitive depreciation failures of the Great Depression and the 2008 crisis, but in the opposite direction (global scarcity rather than deficiency of tradables). In a numerical example calibrated to α = 0.64 (convex tradable supply, implying 0.57 price-output elasticity, from Boehm and Pandalai-Nayar 2022) and ω = 0.3 (US pre-COVID tradables share), a 3 percentage point demand reallocation (matching the US COVID episode) requires approximately 1.5 percentage points of inflation to maintain full employment under cooperation; without any inflation, unemployment rises by approximately 8 percentage points. At ω₀ = 0.35, the uncooperative equilibrium reduces inflation by approximately 1 percentage point relative to cooperation but pushes unemployment to approximately 7 percent. For the COVID-19 episode, the authors conclude gains from cooperation were likely small (full employment maintained globally); for the 1980s synchronized tightening — when central banks explicitly sacrificed employment to fight inflation — the model implies substantially positive gains, consistent with the heated cooperation debates and the 1985 Plaza Accord.

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

In depth

Q1. How does a demand reallocation shock generate an inflation-unemployment tradeoff?

A shift in preferences toward tradable goods (ω₀ > ω) reduces demand for nontradable goods, causing nontradable firms to fire workers; since nominal wages are rigid, the only way to sustain full employment is through a rise in the price of tradables (P^T), which operates through three distinct channels. First, higher P^T raises tradable sector firms’ real revenue per worker (nominal wages fixed), inducing them to hire more workers and expand output — the direct labor demand channel. Second, higher P^T generates income effects: as tradable output and income rise, households increase consumption of both tradable and nontradable goods, boosting nontradable employment through the income channel. Third, higher P^T generates expenditure switching away from tradables and toward nontradables (since nontradable goods become relatively cheaper), which also sustains nontradable employment. All three channels require letting P^T rise, which means tolerating inflation. In this sense, the demand reallocation shock acts as a cost-push shock — it shifts the Phillips curve upward, so that higher inflation is required to achieve any given level of employment. If the inflation cost is sufficiently low, the optimal response allows full employment; otherwise an interior solution trades off inflation against economic slack.

Q2. What is the optimal cooperative monetary policy, and how large are the quantitative tradeoffs?

Proposition 1: under international cooperation, the optimal response to ω₀ > ω entails a rise in inflation; if the full-employment inflation level P^fe satisfies χ’(P^fe) ≤ (1/ω₀)(α/(1−α) + 1 − ω₀), the cooperative optimum achieves full employment; otherwise the interior optimum sets χ’(P̄) equal to that expression, balancing marginal inflation cost against marginal employment benefit. The cooperative optimum is strictly superior to strict inflation targeting (P = 1) because the latter allows large unemployment without achieving any structural rebalancing. The global central bank internalizes the income effect from tradable expansion: as Y^T rises, households immediately spend the income on consumption of both goods, further boosting nontradable employment — an amplification mechanism that self-oriented national banks will not fully internalize. In the calibrated numerical example (α = 0.64, ω = 0.3, χ(P) = χ̄(P−1)²/2 with χ̄ = 299.25), a reallocation shock matching the US COVID-19 episode (ω₀ − ω ≈ 0.03) requires approximately 1.5 percentage points of inflation to maintain full employment; under strict inflation targeting (P = 1), unemployment rises by approximately 8 percentage points. These magnitudes are consistent with the observation that during the pandemic inflation cycle, central banks were willing to allow inflation rather than trigger a labor market collapse.

Q3. How does capital mobility change the inflation-unemployment tradeoff faced by individual countries?

Capital mobility reduces the domestic sacrifice ratio — the employment cost of disinflation — through two channels: trade deficits directly sustain nontradable demand (offsetting the fall in tradable sector employment), and they buffer tradable consumption from drops in domestic tradable output. When a single country contracts its monetary policy and P^T falls, domestic tradable output falls; but households react by borrowing internationally, so domestic consumption of tradables falls by less than one-for-one with output (formally: ∂C^T/∂Y^T = ω_{i,0}(1−β)/(ω_{i,0}(1−β)+β) < 1). Capital inflows thus sustain nontradable demand and nontradable employment, partially offsetting the contractionary effect on employment. From each country’s perspective, containing inflation “exports” part of the output loss abroad, making disinflation individually less costly than in a closed economy. This is precisely what creates the coordination failure in the global case: each country perceives a lower sacrifice ratio for disinflation because it does not internalize that this lower sacrifice ratio exists only if the rest of the world continues to produce and lend tradable goods.

Q4. How does the coordination failure arise in a global reallocation shock, and what is the precise mechanism of competitive appreciations?

Proposition 3: in a Nash equilibrium with a global symmetric shock, the full-employment inflation level P^fe coincides with the cooperative benchmark (since C^T_i = Y^T_i in symmetric equilibrium and capital flows net to zero), but if the inflation cost is high enough, self-oriented central banks impose a lower inflation ceiling (MP^u < MP^c) — resulting in lower inflation and higher unemployment than cooperation. Each national central bank individually seeks to reduce domestic inflation by hiking its policy rate to attract capital inflows (which ease the nontradable sector employment constraint through the open economy Phillips curve). But the individual strategy of hiking to attract inflows — which amounts to trying to appreciate the exchange rate (S_i = P^T_{i,t}/P^T_t) — is frustrated in a symmetric Nash equilibrium: when all countries hike simultaneously, capital flows net to zero globally, exchange rates remain unchanged, and only the synchronized monetary contraction remains. This is the mechanism of competitive appreciations: countries try to fight domestic inflation by appreciating their currencies, but appreciate against each other, leaving only a global slump. In the numerical example at ω₀ = 0.35, the uncooperative equilibrium reduces inflation by approximately 1 percentage point relative to cooperation but pushes unemployment to approximately 7 percent (vs. full employment under cooperation at that shock size).

Q5. How do competitive appreciations differ from competitive depreciations, and what are the scope conditions?

Competitive appreciations are the mirror image of competitive depreciations (which characterized the Great Depression and the aftermath of the 2008 GFC): in both cases each country uses its monetary policy to shift costs abroad, but the direction differs — depreciations arise during periods of weak global demand when countries try to steal demand from neighbors; appreciations arise during periods of global tradable goods scarcity and high inflation when countries try to export inflation. The structural difference is the initial state: competitive depreciations occur when global aggregate demand is deficient and the zero lower bound binds — each country wants to depreciate to boost exports; competitive appreciations occur when global demand for tradables is strong relative to supply (ω₀ > ω) and inflation is high — each country wants to appreciate to attract capital inflows that buffer domestic employment from disinflation. The key asymmetry is the direction of the international spillover: in the depreciation case, countries export demand; in the appreciation case, countries export inflation costs. The gains from cooperation in both cases arise for the same reason — the Nash equilibrium involves globally excessive monetary tightening or loosening relative to the cooperative benchmark — but the policy recommendation is opposite in sign.

Q6. What do the model’s predictions imply for the COVID-19 episode and the 1980s disinflation, and when do gains from cooperation materialize?

Gains from monetary cooperation arise only when condition (28) is violated — when central banks are willing to sacrifice full employment to fight inflation; for the COVID-19 episode, gains were likely small (labor markets remained strong throughout); for the 1980s synchronized tightening, the model implies positive gains that would have been achievable through international cooperation. For the COVID-19 episode: throughout the 2021–2023 inflation cycle, unemployment rates in advanced economies remained low and fiscal support maintained aggregate demand, suggesting monetary policy did not sacrifice employment — the model implies condition (28) did not bind and the cooperative optimum was approximately achieved. The world “escaped competitive appreciations this time.” For the 1980s disinflation: the synchronized monetary tightening under Volcker (US), Bundesbank (Germany), and others was accompanied by a deep global recession and explicitly prioritized inflation reduction over employment — precisely the conditions under which condition (28) binds and competitive appreciations generate a suboptimal outcome. These dynamics motivated the heated international cooperation debates of the period, culminating in the Plaza Accord of 1985 (Sachs 1985; Frankel 2015). The model also applies to negative tradable supply shocks (supply chain disruptions, tariffs) in Supplemental Appendix E, so its predictions about cooperation gains extend to protectionist-driven scarcity.

Key concepts

demand reallocation shock : a shift in the preference weight on tradable goods (ω₀ > ω) that reduces nontradable demand relative to tradable demand; in the model it corresponds to a structural demand shift toward durables and goods (as observed during the COVID-19 recovery), creating simultaneous inflationary pressure in tradables and deflationary pressure in nontradables, and generating an inflation-unemployment tradeoff absent in standard cost-push formulations.

convex tradable supply : the feature of the tradable sector (parameterized by α > 0) whereby supply is upward-sloping due to capacity constraints — a 1% rise in the tradable goods price P^T raises tradable output by (1−α)/α percent; calibrated to α = 0.64 (implying a 0.57 price-output elasticity) following Boehm and Pandalai-Nayar (2022) for sectors at high capacity utilization; without this feature, tradable supply would be perfectly elastic and the inflation-unemployment tradeoff would disappear.

competitive appreciations : the Nash equilibrium coordination failure in which each national central bank hikes its policy rate to attract capital inflows (reducing domestic disinflation costs), generating nominal exchange rate appreciation; since all countries do this simultaneously, appreciations cancel out in equilibrium, leaving only a globally excessive monetary contraction with lower-than-cooperative inflation and higher-than-cooperative unemployment; mirror image of competitive depreciations but arising from global scarcity (not deficiency) of tradables.

sacrifice ratio : the employment cost per unit of disinflation; reduced in open economies relative to closed economies because capital inflows buffer domestic tradable consumption from drops in domestic tradable output, and sustain nontradable demand; self-oriented central banks perceive a lower sacrifice ratio than a global central bank, which is the source of the competitive appreciation externality.

nominal wage rigidity : the short-run friction that makes demand reallocation shocks costly: with flexible wages, reallocation from nontradable to tradable employment would occur through real wage adjustment alone; with rigid nominal wages, real wages fall only if tradable goods prices rise (inflation), so monetary accommodation is required for structural reallocation without unemployment.

Monetary policy trade-offs amid global supply chain disruptions

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

This paper employs a proxy structural VAR model to examine the effects of global supply chain (GSC) shocks on U.S. macroeconomic variables and the Federal Reserve’s historical response, and evaluates two counterfactual monetary policy rules using the COVID-19 episode. Large fiscal stimulus amplifies inflation while cushioning the output downturn from GSC shocks. Historically, the Fed adopted a loose stance, looking through price surges from supply chain disruptions. The first counterfactual—which stabilizes inflation—entails less accommodation and yields a more favorable inflation-output trade-off, reflecting greater price flexibility and limited output losses. The second counterfactual—which minimizes a dual-mandate loss function—calls for greater initial easing; under inflation targeting (IT) this involves moderate accommodation, while under average inflation targeting (AIT) the looser initial policy generates more persistent inflation and ultimately requires a contractionary response, worsening the trade-off.

Summary based on a working paper version, AI-assisted and human-reviewed. See the linked published article for the authoritative version.

In depth

Q1. What is the empirical strategy?

The paper estimates a proxy structural VAR model that identifies GSC shocks using the news-based Supply Bottleneck Index (SBI) of Burriel et al. (2024) as a proxy, then evaluates the Fed’s historical response to those shocks and two counterfactual policy rules that substitute for the historical stance. The proxy SVAR approach identifies the GSC shock’s impulse response function and then traces the macroeconomic dynamics that would have obtained under alternative policy rules, holding the non-policy shocks at their historical values. The SBI captures sudden decreases in supply chain functioning from natural disasters, geopolitical events, strikes, and pandemics.

Q2. What is the role of fiscal stimulus in amplifying GSC shock effects?

Large fiscal stimulus—such as the U.S. transfers and spending during COVID-19—amplifies the inflationary impact of GSC shocks while cushioning the output downturn; the interaction between supply disruptions and fiscal expansion is thus an important determinant of the inflation-output dynamics. Without the large fiscal stimulus, GSC shocks would generate the standard supply-shock trade-off with less amplified inflation. With stimulus, the combination of higher aggregate demand (from fiscal transfers) and reduced aggregate supply (from GSC disruptions) creates a strongly inflationary environment.

Q3. What does the first counterfactual (inflation-stabilizing policy) show?

The counterfactual that stabilizes inflation requires less monetary accommodation than the historical stance and yields a more favorable inflation-output trade-off, suggesting that the Fed’s historical ’look-through’ approach was suboptimal given the interaction with fiscal stimulus. The intuition is that earlier and firmer monetary tightening in response to GSC-driven inflation would have reduced inflation expectations pass-through and prevented a larger buildup of price pressures, while the output cost of that tighter stance was limited by the greater price flexibility the model identifies in this environment.

Q4. What is the comparison between IT and AIT in the second counterfactual?

The second counterfactual calls for greater initial easing than the historical stance; under inflation targeting (IT) this involves moderate accommodation, while average inflation targeting (AIT) implies an even looser initial policy that generates more persistent inflation and ultimately requires a contractionary response, worsening the inflation-output trade-off relative to IT. The AIT result reflects the design of that framework: making up for periods of below-target inflation with above-target periods creates a commitment to easy policy even when supply-side inflationary pressures are elevated, producing a worse outcome when supply shocks drive inflation above target.

Key concepts

proxy structural VAR : a structural VAR identified using an external instrument (the proxy variable) that is correlated with the structural shock of interest but uncorrelated with other shocks; used here to identify GSC shocks using the Supply Bottleneck Index. global supply chain (GSC) shock : a sudden decrease in the supply provision or functioning of supply chains stemming from adverse events (natural disasters, pandemics, geopolitical events); identified in this paper as acting like supply shocks, lowering output and raising prices. average inflation targeting (AIT) : a monetary policy framework in which the central bank targets the average rate of inflation over time, implying accommodation of below-target periods with above-target periods; shown here to imply looser initial policy and more persistent inflation in response to supply shocks, worsening the trade-off relative to standard IT.