A popular method for conducting inference on impulse responses in applied macroeconomics is to compute confidence intervals by 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 data. 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 impulse response horizons. Moreover, and contrary to conventional wisdom, we show that lag augmentation obviates the need to correct the standard errors for serial correlation in the regression residuals. Hence, local projection inference is arguably both simpler than previously thought and more robust than autoregressive impulse response inference, whose validity is known to depend sensitively on the persistence of the data and on the length of the horizon.
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