This article develops the uniform asymptotic theory for local projection (LP) regression when the true lag order of the model is unknown and potentially infinite. The theory allows for varying degrees of persistence in the data, growing response horizons, and general conditionally heteroskedastic martingale-difference shocks. Based on the theory, we make two main contributions. First, we show that LPs can achieve semiparametric efficiency at a given horizon under classical assumptions on the data, provided that the controlled lag order diverges. Thus, the commonly perceived efficiency loss of LPs can become asymptotically negligible with many controls. Second, we propose LP-based inference procedures for (level and cumulated) impulse responses that possess robustness properties not shared by existing methods. Inference methods using two distinct standard errors are considered. The uniform validity for the first method depends on a zero fourth-order cumulant condition on shocks, while that of the second holds more generally for conditionally heteroskedastic martingale-difference shocks. We propose a bootstrap procedure that improves finite-sample performance and extend the standard error construction to structural responses.

Research in finance and macroeconomics has routinely employed multiple horizons to test asset return predictability. In a simple predictive regression model, we find the popular scaled test can have zero power when the predictor is not sufficiently persistent. A new test based on implication of the short-run model is suggested and is shown to be uniformly more powerful than the scaled test. The new test can accommodate multiple predictors. Compared with various other widely used tests, simulation experiments demonstrate remarkable finite-sample performance. We reexamine the predictive ability of various popular predictors for aggregate equity premium.