Local projections vs. VARs for structural parameter estimation

Abstract

This paper conducts a Monte Carlo study to examine the small sample performance of impulse response (IRF) matching and Indirect Inference estimators that target IRFs that have been estimated with Local Projections (LP) or Vector Autoregressions (VAR). The analysis considers various identification schemes for the shocks and several variants of LP and VAR estimators. Results show that the lower bias from LP responses is a big advantage when it comes to IRF matching, while the lower variance from VAR is desirable for Indirect Inference applications as it is robust to the higher bias of VAR-IRFs. Overall, I recommend the use of Indirect Inference over IRF matching when estimating Dynamic Stochastic General Equilibrium (DSGE) models as the former is robust to potential misspecification coming from invalid identification assumptions, small sample issues or incorrect lag selection.