Double Robustness of Local Projections and Some Unpleasant VARithmetic

TL;DR

This paper demonstrates that local projection confidence intervals maintain correct coverage under model misspecification due to a double robustness property, unlike conventional VAR intervals which can undercover unless very large lag lengths are used.

Contribution

It introduces the concept of double robustness in impulse response inference, showing LP intervals are reliable under misspecification while VAR intervals require large lag lengths for robustness.

Findings

LP confidence intervals have correct coverage even under large misspecification

VAR confidence intervals can undercover with small to moderate lag lengths

Robust VAR coverage requires very large lag lengths, making intervals as wide as LP intervals

Abstract

We consider impulse response inference in a locally misspecified vector autoregression (VAR) model. The conventional local projection (LP) confidence interval has correct coverage even when the misspecification is so large that it can be detected with probability approaching 1. This result follows from a "double robustness" property analogous to that of popular partially linear regression estimators. By contrast, the conventional VAR confidence interval with short-to-moderate lag length can severely undercover for misspecification that is small, difficult to detect statistically, and cannot be ruled out based on economic theory. The VAR confidence interval has robust coverage if, and only if, the lag length is so large that the interval is as wide as the LP interval.