Local Projections and VARs Estimate the Same Impulse Responses
Mikkel Plagborg-Møller, Christian K. Wolf
Econometrica · 2021 · Volume 89 · Issue 2
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.
Keywords
External instrument, impulse response function, local projection, proxy variable, structural vector autoregression
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