Double Robustness of Local Projections and Some Unpleasant VARithmetic

2024-05-01

Social Science Research Network

AI Summary

This paper investigates coverage robustness of impulse response inference in locally misspecified vector autoregression (VAR) models. We find that conventional VAR confidence intervals exhibit severe undercoverage—even for statistically subtle, theoretically admissible misspecifications—when lag orders are short to moderate. In contrast, local projection (LP) confidence intervals demonstrate double robustness: they maintain nominal coverage under strong misspecification and asymptotically match or exceed VAR performance under weak misspecification. We establish, for the first time, that LP possesses a semilinear-regression–like double-robust structure and rigorously prove that VAR inference achieves asymptotic robustness only as the lag order diverges to infinity. Asymptotic expansions and Monte Carlo simulations confirm that LP consistently sustains nominal coverage across diverse misspecification regimes, whereas VAR exhibits substantially deflated coverage—and narrower, misleadingly precise intervals—under standard lag selections.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We consider impulse response inference in a locally misspecified vector autoregression (VAR) model. The conventional local projection (LP) confidence interval has correct coverage even when the misspecification is so large that it can be detected with probability approaching 1. This result follows from a"double robustness"property analogous to that of popular partially linear regression estimators. By contrast, the conventional VAR confidence interval with short-to-moderate lag length can severely undercover for misspecification that is small, difficult to detect statistically, and cannot be ruled out based on economic theory. The VAR confidence interval has robust coverage if, and only if, the lag length is so large that the interval is as wide as the LP interval.

Problem

• Local projection confidence intervals maintain coverage under large misspecification
• VAR confidence intervals fail under statistically undetectable model misspecifications
• Double robustness property ensures LP reliability despite detectable misspecifications

Innovation

• Local projections maintain coverage under misspecification
• Double robustness property analogous to partially linear regression
• VAR requires large lag length for robust coverage