Local Projection Inference is Simpler and More Robust Than You Think

TL;DR

This paper demonstrates that local projection inference in macroeconomics is simpler and more robust than traditionally believed, effectively handling persistent data and long-horizon impulse responses without complex corrections.

Contribution

It proves that lag-augmented local projections with normal critical values are asymptotically valid across various data persistence levels and response horizons, simplifying inference procedures.

Findings

Lag-augmented local projections are valid for both stationary and non-stationary data.

Standard errors do not need correction for serial correlation when using lag augmentation.

Local projection inference outperforms traditional autoregressive methods in robustness.

Abstract

Applied macroeconomists often compute confidence intervals for impulse responses using local projections, i.e., 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.