Local Projections and VARs Estimate the Same Impulse Responses

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.

Asymmetric effects of sectoral shifts under low and high uncertainty

“…One advantage of this local projections approach is that it is less prone to misspecification, as documented by Jordà (2005) and Plagborg‐Møller and Wolf (2020). The local projections are a sequence of regressions estimated separately for horizons h = 0, …, 12 and also separately during periods of low and high uncertainty.…”

Local Projection Inference Is Simpler and More Robust Than You Think

“…Several extensions of the results in this paper could be pursued by adopting techniques from the VAR literature. First, the results of Plagborg‐Møller and Wolf (2021) suggest straightforward ways to generalize our results on reduced‐form impulse response inference to structural inference. Second, our assumption of no deterministic dynamics in the VAR model could presumably be relaxed using standard arguments.…”

“…Despite its popularity, there exist no theoretical results justifying the use of local projection inference over autoregressive procedures. From an identification and estimation standpoint, Kilian and Lütkepohl (2017) and Plagborg‐Møller and Wolf (2021) argued that neither local projections nor vector autoregressions (VARs) dominate the other in terms of mean squared error in finite samples, and in population the two methods are equivalent. However, from an inference perspective, the only available guidance on the relative performance of local projections comes in the form of a small number of simulation studies, which by necessity cannot cover the entire range of empirically relevant data generating processes.…”

Monetary Policy, Redistribution, and Risk Premia

“…22 Between the SVAR-IV and LP-IV is the approach of including the IV (and its lags) in the VAR and ordering it first as part of a recursive identification strategy. Plagborg-Moller and Wolf (2019) prove that this strategy is robust to non-invertibility, while estimation using a VAR still means that we can implement (26). While the impulse responses using this approach are noisier than our baseline using the SVAR-IV, the point estimates imply that 69% of the increase in the stock market following a monetary shock is due to news about lower future excess returns.…”