Local-Projections | Macro Paper Warehouse

Estimation and Inference by the Method of Projection Minimum Distance: An Application to the New Keynesian Hybrid Phillips Curve

This 2011 International Economic Review paper by Óscar Jordà and Sharon Kozicki proposes “projection minimum distance” (PMD), a two-step semiparametric estimator for macroeconomic models whose likelihood score function is nonlinear in the structural parameters but whose mapping from reduced-form Wold impulse-response coefficients to those parameters is linear – a class that includes forward-looking Euler equations and ARMA-type representations. In the first step, PMD estimates the Wold coefficients b_h semi-parametrically using Jordà’s (2005, 2009) local-projection regressions of y_{t+h} on lagged variables, run separately for each horizon; in the second step it exploits the model-implied linear restrictions on those coefficients via minimum distance (following Ferguson 1958) to estimate the structural parameters, with an information criterion following Hall, Inoue, Nason, and Rossi (2007) selecting the truncation horizon H by trading off identification gain from extra horizons against a many-weak-instruments cost. The paper establishes formally (Propositions 1-2 for the first-stage local-projection estimator; Lemmas 3-4 for the second-stage minimum-distance estimator) that both stages are consistent and asymptotically normal under stated rate conditions, and shows that in the simple case of i.i.d. shocks PMD coincides exactly with a GMM estimator that uses the lagged dependent variable as instrument – but the two estimators diverge once shocks are serially correlated, because the lagged dependent variable is then no longer a valid GMM instrument while the different (longer-lagged) instrument set implicitly used by local projections remains valid. Monte Carlo experiments (Section 4) show that in a univariate ARMA(1,1) design PMD converges to the true parameters even at T=50 and matches MLE’s standard errors closely by T=100-400, while MLE suffers numerical convergence difficulties in the pure-AR(1) and pure-MA(1) special cases that leave PMD unaffected; in a three-equation New Keynesian (Phillips-IS-Taylor) design calibrated from Lindé (2005) across 36 DGP variants, PMD has smaller bias than GMM in the majority of cases – both perform well when shocks are i.i.d. (though GMM’s output-gap estimates are somewhat downward biased), and both deteriorate once serial correlation and additional lagged terms are introduced, with GMM deteriorating more. Applying PMD to re-estimate Fuhrer and Olivei’s (2005) hybrid New Keynesian output and inflation Euler equations on 1966:Q1-2001:Q4 U.S. quarterly data, the paper finds PMD point estimates broadly similar to GMM, MLE, and OI-GMM but generally with similar or smaller standard errors, and uses the instability of the estimated coefficients across different choices of H together with frequent rejections of the overidentifying-restrictions test to argue that the hybrid Phillips curve is dynamically misspecified in ways that the other estimators’ point estimates alone do not reveal.

Estimation and Inference of Impulse Responses by Local Projections

This 2005 American Economic Review paper by Òscar Jordà introduces “local projections” (LP) — a way to estimate impulse responses directly from a sequence of single-horizon regressions of the future value of a variable on current shocks and lags, rather than by iterating forward a fitted vector autoregression (VAR) — and shows the method delivers valid inference even when the underlying data-generating process is not correctly captured by the fitted VAR. Formally, an impulse response at horizon s is the coefficient on the shock variable in a separate OLS regression of y_{t+s} on lagged variables, run once per horizon; when the true process actually is a VAR(p), Jordà shows the local-projection estimator coincides with the VAR-implied impulse response (a VAR is a restricted special case of LP), but LP remains valid even when the process lacks a standard Wold (linear, Gaussian) representation, and Newey-West standard errors correctly account for the resulting moving-average error structure at each horizon. Monte Carlo evidence based on a monetary VAR calibrated to Evans and Marshall (1998) shows that local-projection impulse responses stay within the true confidence bands at all horizons, while a misspecified low-order VAR generates a spurious, statistically significant “price puzzle” that the local projections do not exhibit; a second Monte Carlo exercise shows a cubic (nonlinear) local-projection specification tracks a genuinely nonlinear, time-varying-volatility data-generating process much more closely than a linear time-varying-parameter VAR. In an empirical application to U.S. inflation-output dynamics (1955-2003), the linear local-projection estimate of the output-gap response to a monetary tightening is roughly twice as large as the equivalent VAR(4) estimate, and a nonlinear, threshold-based local-projection specification finds statistically significant regime-dependence — with much larger output and inflation responses, and no price puzzle, in the low-inflation regime that has prevailed since the mid-1980s.

Fear thy neighbor: Spillovers from economic policy uncertainty

Economic policy uncertainty rose sharply after 2008 – US debt-ceiling standoffs and threatened trade-agreement annulments, Brexit negotiations and European elections, China’s leadership transition and currency adjustments – and this paper asks whose uncertainty actually hurts whom. It begins with a conceptual point that shapes how its results should be read: higher policy uncertainty “is not necessarily bad news,” since a wider distribution of future shocks “includes shocks that would lead to better outcomes,” but the existing evidence is that agents dislike it and respond by re-weighting probabilities toward unfavorable events, “in essence confounding certain for good and uncertain for bad and taking a ‘wait-and-see’ approach.” Two estimators are then run in parallel on the newspaper-based Baker-Bloom-Davis index, available monthly for 19 advanced and emerging economies and aggregated to quarterly. The first is Pedroni’s (2013) heterogeneous structural panel VAR, whose distinctive feature is that it splits each shock into a common component – uncertainty originating anywhere else in the sample and spilling in – and a country-specific one. At the median, a ten-unit rise in the index is associated with a 0.1 percentage point fall in real GDP growth one quarter later, a 0.1 point fall in private consumption growth after two quarters, and a 0.3 point fall in private investment growth after two quarters, with the output response statistically significant for up to three years. The decomposition is the paper’s headline: the common shock “explains roughly two-thirds of the decline in GDP growth across all horizons,” and dominates for consumption and investment as well – so most of the damage policy uncertainty does to a country comes from abroad. The second estimator, Jorda (2005) local projections estimated separately for shocks originating in the United States, Europe and China (and excluding the originating countries from the response sample), locates and sizes those spillovers. A ten-unit rise in US policy uncertainty is associated with roughly a 0.2 percentage point decline in real GDP growth across 64 other economies three quarters later and about 0.6 points for private investment; scaled to the 53-unit jump in the US index between 2008Q2 and 2008Q3, that implies a 1.1 percentage point average decline in other economies’ GDP growth. European and Chinese shocks are similar to each other and smaller than US shocks, with effects lasting about two years. Regionally, the spillovers are significant for Asia and Pacific, Europe and the Western Hemisphere, and largest for the latter two – which the authors read as consistent with transmission between more closely integrated economies. Throughout, the language is associational rather than causal, the samples for consumption and especially investment are much smaller than for output (15 and 8 countries in the panel VAR), and the identification rests on a recursive ordering plus the exclusion of the shock’s origin country, both of which the paper tests rather than asserts.

Instrumental Variable Identification of Dynamic Variance Decompositions

This 2022 Journal of Political Economy paper by Mikkel Plagborg-Møller and Christian K. Wolf asks what an external instrument (a proxy correlated with one structural shock and uncorrelated with the others) can tell us about that shock’s dynamic variance decomposition – the share of a variable’s forecast-error variance it accounts for at each horizon – when the instrument may contain classical measurement error and the shock need not be “invertible” (recoverable from current and past values of the observed macro variables alone). Working in a structural moving-average (SVMA) model where the number of shocks need not equal the number of observables, they show that the forecast variance ratio (FVR) is generically only interval-identified: because the instrument’s relevance is governed by an unknown scale parameter (its strength net of measurement-error noise), the data pin down a sharp, generically nondegenerate identified set for the FVR rather than a point, with a lower bound coming from treating the instrument itself as if it were the shock (attenuated by measurement error) and an upper bound coming from projecting the instrument onto all observed macro leads and lags. The identified set collapses to a point only under one of two testable-or-assumable conditions: a perfect instrument (no measurement error) or “recoverability” (the shock spans all leads and lags of the observables, which is weaker than full invertibility). The paper also derives a Granger-causality pretest that can certify a shock is noninvertible but cannot certify invertibility, and shows results extend to multiple instruments, whose consistency with a rank-one cross-spectral restriction is itself testable. Applying the method to US data (January 1990-June 2012, monthly) with the Gertler-Karadi high-frequency federal-funds-futures surprise as the instrument, they find the data consistent with substantial noninvertibility of the monetary shock, and their identification-robust 90% confidence intervals rule out the shock explaining more than 31% of output growth’s forecast variance or more than 8% of inflation’s forecast variance at any horizon studied (up to 24 months); they read this as evidence that “monetary shocks are almost irrelevant for aggregate inflation” in the post-1990 sample, so that if inflation is a monetary phenomenon it is because of the systematic, rule-like part of policy rather than its unpredictable component. A companion application to an oil-supply-news instrument (Känzig 2021) finds that shock, too, is highly noninvertible, which the authors show causes conventional SVAR-IV analysis to reach spurious conclusions; a Monte Carlo study confirms the new confidence intervals achieve close-to-nominal coverage even when the true shock is noninvertible, unlike conventional SVAR-IV intervals, which undercover badly in that case.

Local Projection Inference Is Simpler and More Robust Than You Think

This 2021 Econometrica paper by José Luis Montiel Olea and Mikkel Plagborg-Møller studies what inference procedure applied researchers should use for local-projection (LP) estimates of impulse response functions, and argues that a specific variant, lag-augmented LP (LA-LP) paired with ordinary Eicker-Huber-White (EHW) heteroskedasticity-robust standard errors, is both simpler to implement than commonly assumed and uniformly valid across a much wider range of data persistence than previously understood. The key theoretical mechanism, worked out first in an AR(1) setting, is that adding a single extra lag as a control (regressing y_{t+h} on both y_t and y_{t-1} rather than on y_t alone) makes the resulting regression scores serially uncorrelated even though the LP residual itself follows an MA(h-1) process, so heteroskedasticity-robust standard errors alone suffice for correct coverage: no HAC long-run-variance estimator or bandwidth choice is needed. Extending this to a general VAR(p) system, Proposition 1 shows the LA-LP estimator’s studentized statistic converges uniformly to a standard normal distribution across the entire parameter space of stationary, near-unit-root, and unit-root processes (each variable’s persistence parameter ρ_i ranging over [-1,1]) and across every horizon h that grows no faster than the sample size (h̄_T/T → 0), so the resulting confidence intervals have correct asymptotic coverage without the researcher pretesting for unit roots or tailoring the procedure to the persistence regime. Monte Carlo evidence (T = 240, 5,000 replications, nominal 90% coverage) shows LA-LP combined with a wild recursive-VAR bootstrap achieves approximately nominal coverage across all persistence/horizon combinations examined, including the unit-root case and long horizons, whereas a delta-method confidence interval built from an estimated AR(1) badly under-covers at longer horizons when the process is persistent, and a bootstrap confidence interval built from an augmented AR model achieves coverage only by becoming extremely wide near the unit root (e.g., a reported median CI length of 23.050 for the augmented-AR bootstrap versus 0.942 for LA-LP at ρ = 0.95, h = 60 under homoscedastic innovations, with the gap growing far more extreme under ARCH innovations). The efficiency ranking between LA-LP and its competitors is not uniform, however: LA-LP is more efficient than the augmented-AR estimator for persistent processes at long horizons, and more efficient than non-augmented LP (which is biased near unit roots) for large |ρ|, but for stationary processes at short horizons the ranking is ambiguous and AR-based estimators can be tighter. On this basis the authors recommend LA-LP with EHW standard errors, or the wild bootstrap, as a default inference procedure for LP-based impulse responses, recommend choosing the lag length conservatively (more lags rather than fewer, with the theory accommodating lag order growing at rate T^{1/3} or slower), and note that the results concern pointwise, single-horizon confidence intervals rather than confidence bands that are simultaneously valid across a whole range of horizons.

Local Projections

This 2025 Journal of Economic Literature survey by Òscar Jordà (who introduced the method in a 2005 AER paper) and Alan M. Taylor takes stock of local projections (LP) as a general framework for estimating impulse responses, arguing that LPs “help bridge the divide between current best practices in applied microeconomics and standard time series methods in macroeconomics.” The baseline LP estimates the impulse response at horizon h directly as the coefficient beta_h in a single OLS regression of y_{t+h} on the intervention s_t and lagged controls x_t, requiring one separate regression per horizon rather than iterating forward a fitted VAR; the authors identify four practical advantages over VARs – no cross-equation system constraints, straightforward accommodation of nonlinearities and heterogeneity, direct estimation of cumulative multipliers, and a natural extension to panel and difference-in-differences settings – while showing LP remains asymptotically equivalent to VAR-implied impulse responses (and to VAR-based Cholesky and long-run identification) whenever the underlying process truly is a VAR of the assumed order (citing Plagborg-Møller and Wolf 2021), and retains identification via LP-IV even in “non-invertible” settings where VAR identification from the reduced-form covariance matrix breaks down. The survey then works through the full LP toolkit: levels versus long-difference specifications (long-differencing “considerably reduces” the O(T^-1) small-sample bias that is severe for persistent, near-unit-root outcomes in short samples); horizon-by-horizon smoothing via B-splines or a Gaussian basis function; inference via Newey-West HAC standard errors, lag-augmented LP (which restores ordinary White standard errors with, per Montiel Olea and Plagborg-Møller 2021, correct uniform coverage across stationary, near-unit-root, and unit-root processes), system GMM for joint hypothesis tests across horizons, sup-t simultaneous confidence bands, and Lagrange-multiplier significance bands constructed under the null; identification via selection on observables, inverse-propensity weighting, long-run restrictions, and LP-IV; projection minimum distance (PMD) for recovering structural parameters from LP-estimated auxiliary parameters; counterfactual policy-path analysis subject to a Mahalanobis-distance “modesty” test; state-dependent and nonlinear LPs; and panel LP / LP-DiD for staggered-adoption settings. Worked illustrations throughout convey magnitudes without claiming new empirical results of their own: a state-dependent local-projection estimate of the OECD fiscal-consolidation multiplier (1978-2019) finds the average four-year output response is more than twice as large in slumps (-1.78, chi-squared(5)=58.3, p=0) as in booms (-0.80, chi-squared(5)=17.2, p=0.004); a projection-minimum-distance estimate of a UK Phillips curve (1975m1-2007m12, using the Cloyne-Hürtgen 2016 monetary shock) yields coefficients of 0.838 (SE 0.593) on inflation and -1.990 (SE 0.180) on the output term; and an LP-IV estimate of the unemployment response to a Romer-Romer monetary shock (1985:1-1999:12) peaks at roughly 1.25 percentage points around 24 months before returning to zero by about 48 months.

Local Projections and VARs Estimate the Same Impulse Responses

This 2021 Econometrica paper by Mikkel Plagborg-Møller and Christian K. Wolf proves that local-projection (LP) and vector-autoregression (VAR) based impulse-response estimators are, at the population level, the same object up to a constant of proportionality, so that differences researchers observe between LP and VAR estimates in applied work reflect finite-sample and lag-truncation choices rather than the two methods identifying fundamentally different things. Working nonparametrically under covariance-stationary data with an everywhere-nonsingular spectral density and absolutely summable Wold decomposition (Assumptions 1-2), they show (Proposition 1) that the recursive-VAR impulse response theta_h at any horizon h equals the square root of E(x-tilde_t squared) times the LP coefficient beta_h, where x-tilde_t is the population residual of the impulse variable after controlling for contemporaneous and lagged covariates; the scale factor depends on neither the horizon nor the response variable, and the proof runs through the Frisch-Waugh theorem applied to the VAR(infinity) Wold representation. The equivalence extends beyond the simple recursive (Cholesky) case to nonrecursive structural rotations, to long-run restrictions (Blanchard-Quah), to sign restrictions (Uhlig; Rubio-Ramirez-Waggoner-Zha), and to instrumental-variables identification: “LP-IV” using an internal instrument recovers exactly the same relative impulse responses as an internal-instrument recursive SVAR (Corollary 1), in contrast to the popular external-instrument “SVAR-IV” approach (Stock-Watson 2012; Mertens-Ravn 2013), which is only consistent when the structural shock is invertible from current and past data and identifies absolute rather than relative responses. When lag length p is fixed rather than infinite, Proposition 2 shows the LP(p) and VAR(p) estimands agree only approximately at horizons h less than or equal to p and generally diverge at h greater than p – a divergence that vanishes when the impulse variable is a direct, serially unpredictable shock; the sample-based estimators are shown to converge to one another as p grows with the sample size T and both are asymptotically efficient at any fixed horizon under weak regularity conditions, though at finite p and T researchers still face a bias-variance trade-off at long horizons, a gap the authors explicitly flag for future research. An empirical illustration using Gertler and Karadi’s (2015) monthly monetary-policy data (January 1990-June 2012: industrial production growth, inflation, the one-year government bond rate, and the excess bond premium, with the Gertler-Karadi high-frequency futures surprise as instrument) compares LP against an internal-instrument recursive VAR at lag lengths p = 4 and p = 12: the two estimators track each other closely through horizon h = p and diverge noticeably beyond it, consistent with Proposition 2, and both recover the qualitative Gertler-Karadi finding that the excess bond premium rises initially after a contractionary monetary shock. On this basis the authors argue that four widely held claims are mistaken: that VAR estimators are generally more efficient than LP, that LP is generally more robust to misspecification than VARs, that nonrecursive non-IV identification schemes require a VAR, and that noninvertible shocks rule out simple SVAR methods. The result is explicitly a population-level equivalence for linear estimators; it does not itself resolve finite-sample estimator choice, and the paper deliberately leaves questions of inference and of multiple-instrument identification to other work.

Local Projections vs. VARs: Lessons from Thousands of DGPs

This 2024 Journal of Econometrics paper by Dake Li, Mikkel Plagborg-Møller, and Christian K. Wolf asks a purely practical question rather than proposing a new estimator or identification scheme: when researchers estimate structural impulse responses, does the local-projection (LP) estimator or the vector-autoregression (VAR) estimator perform better in realistic macroeconomic settings, and under what conditions does the ranking flip? Because no single real-world dataset can answer this — the true DGP is never known — the authors build an “encompassing model,” a non-stationary dynamic factor model with six latent factors estimated on the 207-series Stock and Watson (2016) quarterly U.S. dataset (1959Q1-2014Q4), and use it to generate 6,000 simulated economies (3,000 built around a monetary policy shock with the federal funds rate as instrument, 3,000 around a fiscal policy shock with government spending as instrument), each simulated for T=200 quarters with 5,000 Monte Carlo draws. Across this population of realistically calibrated DGPs, comparing least-squares, bias-corrected, and penalized LP against least-squares, bias-corrected, Bayesian, and model-averaged VARs (plus SVAR-IV for the instrumented case), the paper documents a clear and pervasive bias-variance trade-off: at short horizons (h ≤ the p=4 lag length) LP and VAR have similar bias, but at longer horizons VAR bias grows substantially larger than LP bias, while LP’s standard deviation rises steeply with horizon — by h=20 roughly double the VAR’s. Bias-corrected LP removes only about a third of LP’s bias while adding variance, so it is preferred over uncorrected LP only when a researcher places very high weight (ω ≥ 0.9 in the paper’s bias-variance loss function) on bias at intermediate horizons; otherwise VAR-type methods, especially a Bayesian VAR with a Minnesota-type prior, dominate essentially throughout. A further headline finding concerns SVAR-IV: because roughly 90% of the simulated DGPs exhibit a degree of shock invertibility below 49%, the external-instrument SVAR-IV estimator carries substantially higher bias than internal-instrument alternatives at every horizon, though it also has notably lower dispersion. The authors are explicit that these are simulation-based lessons conditional on the choice of encompassing model and DGP class (quarterly, five-variable systems, no sign or long-run restrictions), not universal theorems.

The Aggregate and Country-Specific Effectiveness of ECB Policy: Evidence from an External Instruments VAR Approach

This 2020 International Journal of Central Banking paper by Lucas Hafemann and Peter Tillmann studies how ECB monetary policy transmits to the euro area as a whole and, separately, across individual member countries, using monthly data from 2002:M1 to 2016:M10 – a period spanning both conventional policy and unconventional measures (the asset purchase programme, TLTROs) during which short rates sat at the effective lower bound. Because the policy stance in this period is “no longer appropriately summarized by the short-term policy rate” and Cholesky or sign-restriction schemes are hard to justify for fast-moving financial variables, the authors identify the shock with an external instrument in a proxy-SVAR framework (following Stock-Watson 2012, Mertens-Ravn 2013, and Gertler-Karadi 2015): the daily change in the German 10-year government bond yield on ECB Governing Council meeting days, augmented with three special-event days (the May 2010 and August 2011 SMP announcements and Draghi’s July 2012 “whatever it takes” speech). The instrument clears a weak-instrument check (first-stage F = 10.44, above the Stock-Wright-Yogo threshold of 10) and an event-study validation showing it moves the EURIBOR future (beta = 0.890) and corporate bond spreads (beta = 0.192) with the expected sign. In a baseline monthly four-variable VAR (log industrial production, log HICP, a corporate BBB-minus-AA bond spread proxying the external finance premium, and a Wu-Xia shadow short rate, with the oil price entered exogenously to avoid the price puzzle), an expansionary shock normalized to a 25-basis-point drop in the shadow rate significantly raises output and prices and narrows the corporate spread – evidence of a credit channel that disappears under a comparable Cholesky-identified VAR, where the spread does not react significantly. Extending the system one variable at a time shows the real exchange rate depreciates on impact, a house-price proxy (the HICP rent component) rises, and bank lending standards relax while credit demand rises, yet – a “credit puzzle” – total loan volume to nonfinancial corporations actually falls in the post-2008 sample, while unemployment and equity prices move with the expected sign but are statistically insignificant (cannot rule out zero) over the full horizon. Decomposing the instrument via a Jarocinski-Karadi (2018)-style principal-component analysis of announcement-day yield and equity changes (the first two components jointly explain 92% of the variance) into a pure policy shock and a central-bank information shock shows the baseline results are reproduced by the pure policy component, so the findings are robust to stripping out information effects. Feeding the identified aggregate shock into Jordà (2005) local projections for ten member countries (covering more than 95% of euro-area GDP) plus a synthetic euro area reveals substantial cross-country heterogeneity beneath the homogeneous aggregate response: industrial production and consumer prices respond similarly almost everywhere, but unemployment falls significantly only in core countries (Germany, France, the Netherlands) and not in the periphery (Italy, Spain, Greece), stock prices deviate negatively in several countries after about ten months, and loan volumes rise significantly only in Germany, Austria, and Greece. The authors read this as evidence that impaired transmission through bank lending and equity markets – concentrated in periphery countries with stressed banking systems – and labor-market frictions drive the uneven effectiveness of a “one-size-fits-all” ECB policy, while explicitly cautioning that their country-level results are “purely positive” and that “we should be careful not to overemphasize the normative implications.”

The long and variable lags of monetary policy: Evidence from disaggregated price indices

This 2024 Journal of Monetary Economics paper by S. Borağan Aruoba and Thomas Drechsel asks why the aggregate U.S. price level responds to monetary policy only after a long delay, and locates the answer in the cross-section of price categories rather than in uniform price stickiness. Using monthly Personal Consumption Expenditures Price Index (PCEPI) data disaggregated into as many as 136 subcomponents at five levels of aggregation (1982-2008, a sample chosen to exclude the zero lower bound and COVID episodes), the authors estimate a Jordà-style local projection for each individual price series against an external, non-market-based monetary policy shock constructed in a companion paper (Aruoba and Drechsel 2023) from natural-language processing of Federal Reserve Greenbook/Tealbook documents, following the Romer-Romer (2004) narrative approach. Because the individual-series impulse responses are estimated separately, the authors re-aggregate them into an implied aggregate PCEPI response using a weighted sum of the disaggregated coefficients, and correct the standard error of that re-aggregated response for cross-sectional correlation across price series with a seemingly-unrelated-regressions/feasible-generalized-least-squares (SUR-FGLS) procedure — showing that because price movements are mostly positively correlated across categories, naive standard errors that ignore this covariance are too small and would spuriously reject a zero response earlier than the correct SUR-corrected bands do. The headline empirical result is that, following a 100-basis-point monetary contraction, the aggregate (and core) PCEPI shows no statistically significant decline for roughly 43 months, only turning significantly negative after that point and reaching a peak reduction of roughly 4% (headline) and roughly 2.5% (core) around 54 months — consistent with Christiano, Eichenbaum, and Evans’s (1999) finding of a multi-year delay before the aggregate price level falls significantly. Critically, the paper shows this aggregate flatness does not reflect uniform stickiness: at the finest (136-series) level of disaggregation, roughly half of all price series show a significantly positive response to a monetary tightening at some horizon, and a substantial share never turn significantly negative at all, so the eventual aggregate decline emerges only once enough individual series’ responses turn negative to outweigh the persistently positive ones — a pattern the authors argue is inconsistent with standard Calvo or menu-cost stickiness models (which predict faster responses for more frequently adjusting prices, a relationship the data does not show) and better rationalized by a heterogeneous cost-channel/demand-substitution mechanism in which a monetary tightening acts as a demand shock for some sectors but raises costs (and hence prices) for financially constrained sectors in the short run. The authors also show that re-aggregating with 1959 versus 2023 expenditure shares yields similar aggregate timing and magnitude, indicating that decades of structural change in consumption patterns have not accelerated the aggregate lag — leading them to connect the finding explicitly to Friedman’s (1960, 1961) claim that monetary policy operates with “long and variable lags,” here documented in the cross-section of prices as well as in the aggregate time series.

Unconventional but Different After All? A Unified Series of Narrative Monetary Policy Shocks

Asking whether unconventional monetary policy works differently from an interest-rate cut has been hard to answer because the two kinds of policy have been measured with different tools, so any difference in the estimated effects could be a difference in the measuring rather than in the policy. This paper builds one shock series for both, running Romer and Romer’s (2004) narrative regression — policy-rate changes on the Federal Reserve’s own Greenbook/Tealbook forecasts — but substituting Wu and Xia’s (2016) shadow rate for the federal funds rate over the 2009–16 zero-lower-bound period, which yields shocks for 1969–2008 and 2009–16 built the same way. Estimating local projections on the pooled sample with a structural break at the zero lower bound, the authors cannot reject equality of the peak responses of the interest rate, industrial production, unemployment and the consumer price index across regimes (p-values from 0.09 to 0.56), which they read as unconventional policy being about as effective as rate cuts for aggregate activity. Joint Wald tests do reject equality for wealth shares and for the stock-to-house price ratio, and the sign flips: an expansionary conventional shock normalised to 25 basis points lowers the top 10% wealth share by about 0.3% at the trough, while the equivalent unconventional shock raises it by up to about 0.36% and lowers the middle 40% share by about 0.7%. The authors attribute the difference to asset prices — unconventional easing raises the stock-to-house price ratio by over 3% where conventional easing lowers it by about 3.13% — and a mechanical revaluation of Survey of Consumer Finances portfolios reproduces the pattern, with the equity-heavy top 10% capturing most of the gains and households in the bottom groups, who hold little equity and often no housing, receiving comparatively little. The distributional evidence rests on short samples — 1989–2008 for conventional and 2009–15 for unconventional shocks, at quarterly frequency — and the authors do not address the Fed-information-effect and Fed-reaction-to-news concerns directly, assessing them only indirectly by comparison with shock series that are robust to them.