  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.
