Applied macroeconomists often compute confidence intervals for impulse responses using local projections, that is, direct linear regressions of future outcomes on current covariates. This paper proves that local projection inference robustly handles two issues that commonly arise in applications: highly persistent data and the estimation of impulse responses at long horizons. We consider local projections that control for lags of the variables in the regression. We show that lag‐augmented local projections with normal critical values are asymptotically valid uniformly over (i) both stationary and non‐stationary data, and also over (ii) a wide range of response horizons. Moreover, lag augmentation obviates the need to correct standard errors for serial correlation in the regression residuals. Hence, local projection inference is arguably both simpler than previously thought and more robust than standard autoregressive inference, whose validity is known to depend sensitively on the persistence of the data and on the length of the horizon.

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.