# Local Projections and VARs Estimate the Same Impulse Responses

### Citation:

Plagborg-Møller, Mikkel, and Christian K. Wolf. Forthcoming. “Local Projections and VARs Estimate the Same Impulse Responses.” Econometrica.

### 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.

Last updated on 12/07/2020