  We conduct a simulation study of Local Projection (LP) and Vector
Autoregression (VAR) estimators of structural impulse responses across
thousands of data generating processes (DGPs), designed to mimic the properties
of the universe of U.S. macroeconomic data. Our analysis considers various
structural identification schemes and several variants of LP and VAR
estimators, and we pay particular attention to the role of the researcher's
loss function. A clear bias-variance trade-off emerges: Because our DGPs are
not exactly finite-order VAR models, LPs have lower bias than VAR estimators;
however, the variance of LPs is substantially higher than that of VARs at
intermediate or long horizons. Unless researchers are overwhelmingly concerned
with bias, shrinkage via Bayesian VARs or penalized LPs is attractive.
