[Paper Review] Local Projections vs. VARs: Lessons From Thousands of DGPs

Dake Li, Mikkel Plagborg‐Møller+1 more|arXiv (Cornell University)|Apr 1, 2021

Monetary Policy and Economic Impact26 citations

TL;DR

The paper conducts a large-scale simulation comparing Local Projection (LP) and VAR impulse response estimators across thousands of empirically calibrated DGPs, highlighting a bias-variance trade-off and offering guidance on when bias-corrected LP or VAR methods are preferable.

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.

Motivation & Objective

• Motivate and characterize the bias-variance trade-off between LP and VAR impulse response estimators in realistic, non-finite VAR DGPs.
• Evaluate a broad menu of LP/VAR variants (bias correction, shrinkage, model averaging, Bayesian approaches) under multiple identification schemes.
• Identify which estimator(s) perform best under different loss functions prioritizing bias, variance, or MSE across horizons.
• Provide practical guidance for researchers on default procedures in empirical macroeconometrics based on simulation results.

Proposed method

• Simulate impulse response estimation across thousands of DGPs drawn from an empirically calibrated dynamic factor model built from Stock & Watson data.
• Compare least-squares LP and VAR estimators and variants including bias correction, shrinkage, Bayesian VAR, and model averaging.
• Implement three identification schemes: observed shocks, IV/proxy, and recursive (Cholesky) identification.
• Use loss functions that weight bias and variance to evaluate performance across horizons and identify when each method excels.
• Ground the DGPs in a non-stationary DFM with latent factors and idiosyncratic components to mimic realistic macro time series dynamics.

Experimental results

Research questions

• RQ1 What is the bias-variance trade-off between LP and VAR impulse response estimators in realistic, non-finite VAR data generating processes?
• RQ2 How do bias-corrected LP, shrinkage, Bayesian VAR, and model averaging perform relative to standard LS-LP and LS-VAR across horizons and identification schemes?
• RQ3 Which estimation approach minimizes mean-squared error, and which prioritizes bias under various identifiability setups?
• RQ4 How do the results vary with horizon and the presence of persistent dynamics or cointegration in the DGPs?
• RQ5 What practical guidance can be given to researchers about default procedures for impulse response estimation in macroeconometrics?

Key findings

• LP estimators have lower bias than VAR estimators, but exhibit substantially higher variance at intermediate and long horizons.
• Bias-corrected LP is preferred only when bias is overwhelmingly prioritized over variance.
• VAR methods are more attractive under mean-squared-error loss, with Bayesian VARs performing well at short and long horizons and LS-VAR performing well at intermediate horizons.
• In IV identification, SVAR-IV is median-biased but offers reduced dispersion, justifying external IV use in some settings.
• The study emphasizes a bias-variance trade-off and suggests practical defaults: use VAR methods if precision is important; consider bias-corrected LP when bias is the primary concern.