Local Projections and VARs Estimate the Same Impulse Responses

Mikkel Plagborg-Møller, Christian K. Wolf

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)955-980
Number of pages26
Issue number2
StatePublished - Mar 2021

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • External instrument
  • impulse response function
  • local projection
  • proxy variable
  • structural vector autoregression


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