Local Projection Based Inference under General Conditions

This paper provides the uniform asymptotic theory for local projection (LP) regression when the true lag order of the model is unknown, possibly in?nity. The theory allows for various persistence levels of the data, growing response horizons, and general conditionally heteroskedastic shocks. Based on the theory, we make two contributions. First, we show that LPs are semiparametrically efficient under classical assumptions on data and horizons if the controlled lag order diverges. Thus the commonly perceived efficiency loss of running LPs is asymptotically negligible with many controls. Second, we propose LP-based inferences for (individual and cumulated) impulse responses with robustness properties not shared by other existing methods. Inference methods using two different standard errors are considered, and neither involves HAR-type correction. The uniform validity for the first method depends on a zero fourth moment condition on shocks, while the validity for the second holds more generally for martingale-difference heteroskedastic shocks.