We consider impulse response inference in a locally misspecified stationary 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 follows from a “double robustness” property analogous to that of modern estimators for partially linear regressions. In contrast, VAR confidence intervals dramatically undercover even for misspecification so small that it is difficult to detect statistically and cannot be ruled out based on economic theory. This is because of a “no free lunch” result for VARs: the worst-case bias and coverage distortion are small if, and only if, the variance is close to that of LP. While VAR coverage can be restored by using a bias-aware critical value or a large lag length, the resulting confidence interval tends to be at least as wide as the LP interval.
Authors
José Luis Montiel Olea, Mikkel Plagborg-Møller, Eric Qian, Christian K. Wolf
- Acknowledgements & Disclosure
- We received helpful comments from Michal Kolesár, Ulrich Müller, and seminar participants at Columbia, Princeton, and the Federal Reserve Banks of Cleveland and Philadelphia. Plagborg-Møller acknowledges that this material is based upon work supported by the NSF under Grant #2238049, and Wolf does the same for Grant #2314736. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF or the National Bureau of Economic Research.
- DOI
- https://doi.org/10.3386/w32495
- Published in
- United States of America
Table of Contents
- Introduction 3
- Overview of results 6
- Robust local projections, fragile VARs 12
- Model and assumptions 13
- Estimators 15
- Asymptotic coverage 16
- Some unpleasant VARithmetic 19
- Worst-case bias 20
- Worst-case mean squared error 21
- Worst-case coverage 22
- Bias-aware inference 25
- Simulations 27
- Deriving the VARMA representation 27
- Illustrative univariate model 28
- Misspecification in Smets and Wouters (2007) 30
- Conclusion 34
- Further theoretical results 36
- Least favorable misspecification 36
- More efficient bias-aware confidence interval 36
- Proofs of propositions 39
- Proof of Proposition 3.1 39
- Proof of Proposition 3.2 40
- Proof of Proposition 3.3 41
- Proof of Proposition 4.1 42
- Proofs of corollaries 43
- Proof of Corollary 3.1 43
- Proof of Corollary 3.2 46
- Proof of Corollary 3.3 47
- Proof of Corollary 4.1 48
- Proof of Corollary 4.2 48
- Proof of Corollary 4.4 49
- References 50
