The role of the prior in estimating VAR models with sign restrictions

  • Several recent studies have expressed concern that the Haar prior typically imposed in estimating sign-identi.ed VAR models may be unintentionally informative about the implied prior for the structural impulse responses. This question is indeed important, but we show that the tools that have been used in the literature to illustrate this potential problem are invalid. Speci.cally, we show that it does not make sense from a Bayesian point of view to characterize the impulse response prior based on the distribution of the impulse responses conditional on the maximum likelihood estimator of the reduced-form parameters, since the the prior does not, in general, depend on the data. We illustrate that this approach tends to produce highly misleading estimates of the impulse response priors. We formally derive the correct impulse response prior distribution and show that there is no evidence that typical sign-identi.ed VAR models estimated using conventional priors tend to imply unintentionally informative priors for the impulse response vector or that the corre- sponding posterior is dominated by the prior. Our evidence suggests that concerns about the Haar prior for the rotation matrix have been greatly overstated and that alternative estimation methods are not required in typical applications. Finally, we demonstrate that the alternative Bayesian approach to estimating sign-identi.ed VAR models proposed by Baumeister and Hamilton (2015) su¤ers from exactly the same conceptual shortcoming as the conventional approach. We illustrate that this alternative approach may imply highly economically implausible impulse response priors.

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Author:Atsushi Inoue, Lutz KilianGND
Parent Title (English):Center for Financial Studies (Frankfurt am Main): CFS working paper series ; No. 660
Series (Serial Number):CFS working paper series (660)
Publisher:Center for Financial Studies
Place of publication:Frankfurt, M.
Document Type:Working Paper
Year of Completion:2021
Year of first Publication:2021
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2021/11/16
Tag:Prior; absolute loss; impulse response; joint inference; loss function; median; posterior
Issue:This version: December 9, 2020
Page Number:56
Institutes:Wirtschaftswissenschaften / Wirtschaftswissenschaften
Wissenschaftliche Zentren und koordinierte Programme / Center for Financial Studies (CFS)
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
JEL-Classification:C Mathematical and Quantitative Methods / C2 Single Equation Models; Single Variables / C22 Time-Series Models; Dynamic Quantile Regressions (Updated!)
C Mathematical and Quantitative Methods / C3 Multiple or Simultaneous Equation Models / C32 Time-Series Models; Dynamic Quantile Regressions (Updated!)
C Mathematical and Quantitative Methods / C5 Econometric Modeling / C52 Model Evaluation and Selection
Licence (German):License LogoDeutsches Urheberrecht