Local Projections and VARs Estimate the Same Impulse Responses

2021/01/01 by Mikkel Plagborg‐Møller, Christian K. Wolf · 16 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #Control Systems and Identification #Monetary Policy and Economic Impact #Statistical Methods and Inference

paper · pdf · doi:10.3982/ecta17813

openalex publication_date 2021/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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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• Impulse Response Estimation by Smooth Local Projections

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