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.
Original language | English (US) |
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Pages (from-to) | 955-980 |
Number of pages | 26 |
Journal | Econometrica |
Volume | 89 |
Issue number | 2 |
DOIs | |
State | Published - Mar 2021 |
All Science Journal Classification (ASJC) codes
- Economics and Econometrics
Keywords
- External instrument
- impulse response function
- local projection
- proxy variable
- structural vector autoregression