Title

Local Projections and VARs Estimate the Same Impulse Responses

Author(s)

Mikkel Plagborg-Møller Mikkel Plagborg-Møller (Princeton University)

Christian K. Wolf Christian Wolf (Princeton University)

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 non-invertibility. (iv) Linear VARs are as robust to non-linearities as linear LPs.

Creation Date

2020-10

Section URL ID

Paper Number

2020-16

URL

https://scholar.princeton.edu/sites/default/files/mikkelpm/files/lp_var.pdf

File Function

Jel

C32, C36

Keyword(s)

external instrument, impulse response function, local projection, proxy variable, structural vector autoregression

Suppress

false

Series

13