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Double Robustness of Local Projections and Some Unpleasant VARithmetic

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  • Jos'e Luis Montiel Olea
  • Mikkel Plagborg-M{o}ller
  • Eric Qian
  • Christian K. Wolf

Abstract

We consider impulse response inference in a locally misspecified vector autoregression (VAR) model. The conventional local projection (LP) confidence interval has correct coverage even when the misspecification is so large that it can be detected with probability approaching 1. This result follows from a "double robustness" property analogous to that of popular partially linear regression estimators. In contrast, the conventional VAR confidence interval with short-to-moderate lag length can severely undercover, even for misspecification that is small, economically plausible, and difficult to detect statistically. There is no free lunch: the VAR confidence interval has robust coverage only if the lag length is so large that the interval is as wide as the LP interval.

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  • Jos'e Luis Montiel Olea & Mikkel Plagborg-M{o}ller & Eric Qian & Christian K. Wolf, 2024. "Double Robustness of Local Projections and Some Unpleasant VARithmetic," Papers 2405.09509, arXiv.org, revised Aug 2024.
  • Handle: RePEc:arx:papers:2405.09509
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    References listed on IDEAS

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    1. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    2. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
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    Cited by:

    1. Oriol Gonzalez-Casasus & Frank Schorfheide, 2025. "Misspecification-Robust Shrinkage and Selection for VAR Forecasts and IRFs," PIER Working Paper Archive 25-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    2. Checherita-Westphal, Cristina & Pesso, Tom, 2024. "Fiscal policy and inflation: accounting for non-linearities in government debt," Working Paper Series 2996, European Central Bank.
    3. Simon Freyaldenhoven & Christian Hansen, 2025. "(Visualizing) Plausible Treatment Effect Paths," Papers 2505.12014, arXiv.org.
    4. Oriol Gonz'alez-Casas'us & Frank Schorfheide, 2025. "Misspecification-Robust Shrinkage and Selection for VAR Forecasts and IRFs," Papers 2502.03693, arXiv.org.
    5. Òscar Jordà & Alan M. Taylor, 2024. "Local Projections," Working Paper Series 2024-24, Federal Reserve Bank of San Francisco.
    6. Ordoñez Lucas Sebastián, 2024. "The transmission of Supply Shocks to inflation: The case of Argentina (2004-2023)," Asociación Argentina de Economía Política: Working Papers 4750, Asociación Argentina de Economía Política.
    7. Nabil Daher, 2025. "Is growth at risk from natural disasters ? Evidence from quantile local projections," EconomiX Working Papers 2025-9, University of Paris Nanterre, EconomiX.
    8. Lucas Ordóñez, 2025. "The Transmission of Supply Shocks to Inflation: the Case of Argentina (2004-2022)," Working Papers 351, Red Nacional de Investigadores en Economía (RedNIE).

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