Physics

Inference

Computer network

Mathematics

Regression

Algorithm

Statistics

Covariate

Autoregressive model

Mathematical analysis

Econometrics

Artificial intelligence

Composite material

Materials science

Range (aeronautics)

Computer science

Quantum mechanics

Impulse response

Applied mathematics

Projection (relational algebra)

Impulse (physics)

Econometrica

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.

Local Projection Inference Is Simpler and More Robust Than You Think