Local Projections and VARs Estimate the Same Impulse Responses

Mikkel Plagborg‐Møller · Christian K. Wolf

738 citations0/0 files storedEconometrica

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Monetary Policy and Economic Impact Forecasting Techniques and Applications Diverse Scientific and Economic Studies

Abstract

We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures; instead, they are simply two dimension reduction techniques with common estimand but different finite‐sample properties. (ii) VAR‐based structural identification—including short‐run, long‐run, or sign restrictions—can equivalently be performed using LPs, and vice versa. (iii) Structural estimation with an instrument (proxy) can be carried out by ordering the instrument first in a recursive VAR, even under noninvertibility. (iv) Linear VARs are as robust to nonlinearities as linear LPs.

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References

1980Macroeconomics and Reality 2005Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy 2005Estimation and Inference of Impulse Responses by Local Projections 2007Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach 2005What are the effects of monetary policy on output? Results from an agnostic identification procedure 2011Identifying Government Spending Shocks: It's all in the Timing*2004A New Measure of Monetary Shocks: Derivation and Implications 1986Alternative Explanations of the Money-Income Correlation

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