Local Projections vs. VARs: Lessons From Thousands of DGPs

TL;DR

This study compares Local Projection and VAR estimators for structural impulse responses using extensive simulations, revealing bias-variance trade-offs and guiding method choice based on researcher priorities.

Contribution

It provides a comprehensive simulation-based comparison of LP and VAR estimators across diverse data generating processes, highlighting their bias-variance trade-offs and practical recommendations.

Findings

Bias-corrected LP reduces bias but increases variance.

VAR methods offer better precision at various horizons.

Bayesian VARs outperform least-squares VARs at certain horizons.

Abstract

We conduct a simulation study of Local Projection (LP) and Vector Autoregression (VAR) estimators of structural impulse responses across thousands of data generating processes, designed to mimic the properties of the universe of U.S. macroeconomic data. Our analysis considers various identification schemes and several variants of LP and VAR estimators, employing bias correction, shrinkage, or model averaging. A clear bias-variance trade-off emerges: LP estimators have lower bias than VAR estimators, but they also have substantially higher variance at intermediate and long horizons. Bias-corrected LP is the preferred method if and only if the researcher overwhelmingly prioritizes bias. For researchers who also care about precision, VAR methods are the most attractive -- Bayesian VARs at short and long horizons, and least-squares VARs at intermediate and long horizons.