Local Projections vs. VARs: Lessons from Thousands of DGPs

This 2024 Journal of Econometrics paper by Dake Li, Mikkel Plagborg-Møller, and Christian K. Wolf asks a purely practical question rather than proposing a new estimator or identification scheme: when researchers estimate structural impulse responses, does the local-projection (LP) estimator or the vector-autoregression (VAR) estimator perform better in realistic macroeconomic settings, and under what conditions does the ranking flip? Because no single real-world dataset can answer this — the true DGP is never known — the authors build an “encompassing model,” a non-stationary dynamic factor model with six latent factors estimated on the 207-series Stock and Watson (2016) quarterly U.S. dataset (1959Q1-2014Q4), and use it to generate 6,000 simulated economies (3,000 built around a monetary policy shock with the federal funds rate as instrument, 3,000 around a fiscal policy shock with government spending as instrument), each simulated for T=200 quarters with 5,000 Monte Carlo draws. Across this population of realistically calibrated DGPs, comparing least-squares, bias-corrected, and penalized LP against least-squares, bias-corrected, Bayesian, and model-averaged VARs (plus SVAR-IV for the instrumented case), the paper documents a clear and pervasive bias-variance trade-off: at short horizons (h ≤ the p=4 lag length) LP and VAR have similar bias, but at longer horizons VAR bias grows substantially larger than LP bias, while LP’s standard deviation rises steeply with horizon — by h=20 roughly double the VAR’s. Bias-corrected LP removes only about a third of LP’s bias while adding variance, so it is preferred over uncorrected LP only when a researcher places very high weight (ω ≥ 0.9 in the paper’s bias-variance loss function) on bias at intermediate horizons; otherwise VAR-type methods, especially a Bayesian VAR with a Minnesota-type prior, dominate essentially throughout. A further headline finding concerns SVAR-IV: because roughly 90% of the simulated DGPs exhibit a degree of shock invertibility below 49%, the external-instrument SVAR-IV estimator carries substantially higher bias than internal-instrument alternatives at every horizon, though it also has notably lower dispersion. The authors are explicit that these are simulation-based lessons conditional on the choice of encompassing model and DGP class (quarterly, five-variable systems, no sign or long-run restrictions), not universal theorems.

Dake Li | Macro Paper Warehouse

Local Projections vs. VARs: Lessons from Thousands of DGPs