Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 2021, Volume 89, Issue 2

Local Projections and VARs Estimate the Same Impulse Responses

https://doi.org/10.3982/ECTA17813
p. 955-980

Mikkel Plagborg‐Møller, Christian K. Wolf

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.


Log In To View Full Content

Supplemental Material

Supplement to "Local Projections and VARs Estimate the Same Impulse Responses"

This zip file contains the replication files for the manuscript.

Supplement to "Local Projections and VARs Estimate the Same Impulse Responses"

This online appendix contains supplemental material for the article “Local Projections and VARs Estimate the Same Impulse Responses”.