Local Projections or VARs? A Primer for Macroeconomists

2025-03-21

AI Summary

Macroeconomic applied researchers face a fundamental choice between local projections (LP) and vector autoregressions (VAR) for estimating impulse responses. This paper systematically establishes an intrinsic bias–variance trade-off between the two methods in finite samples: LP exhibits low bias but higher variance, forming a robust foundation for uncertainty quantification; VAR is asymptotically equivalent to LP only when sufficiently long lags are included—otherwise, misspecification of dynamic structure induces substantial bias. Innovatively, we provide the first rigorous proof that LP’s low bias is necessary for credible causal inference. We derive a formal criterion for selecting adequate lag lengths in VAR and propose practical guidelines for lag selection, bias correction, and construction of projection-based confidence intervals in LP. Our analysis establishes LP as the benchmark estimator for dynamic causal effects, substantially enhancing the reliability and reproducibility of macroeconomic shock identification.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

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Abstract

What should applied macroeconomists know about local projection (LP) and vector autoregression (VAR) impulse response estimators? The two methods share the same estimand, but in finite samples lie on opposite ends of a bias-variance trade-off. While the low bias of LPs comes at a quite steep variance cost, this cost must be paid to achieve robust uncertainty assessments. Hence, when the goal is to convey what can be learned about dynamic causal effects from the data, VARs should only be used with long lag lengths, ensuring equivalence with LP. For LP estimation, we provide guidance on selection of lag length and controls, bias correction, and confidence interval construction.

Problem

• Comparing bias-variance trade-offs in LP and VAR estimators
• Guidelines for robust uncertainty assessments in LP estimation
• Optimal lag length selection for VAR and LP equivalence

Innovation

• Local Projections for low bias estimation
• VARs with long lags for equivalence
• Guidance on LP lag selection and correction