Local Projections or VARs? A Primer for Macroeconomists

Abstract

What should applied macroeconomists know about local projection (LP) and vector autoregression (VAR) impulse response estimators? The two methods share the same estimand, but in finite samples lie on opposite ends of a bias-variance trade-off. While the low bias of LPs comes at a quite steep variance cost, this cost must be paid to achieve robust uncertainty assessments. Hence, when the goal is to convey what can be learned about dynamic causal effects from the data, VARs should only be used with long lag lengths, ensuring equivalence with LP. For LP estimation, we provide guidance on selection of lag length and controls, bias correction, and confidence interval construction.