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Local Projections and VARs Estimate the Same Impulse Responses

Mikkel Plagborg‐Møller and Christian Wolf
Authors registered in the RePEc Author Service: Mikkel Plagborg-Moller

Econometrica, 2021, vol. 89, issue 2, 955-980

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.

Date: 2021
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