The Role of the Prior in Estimating VAR Models with Sign Restrictions

Center for Financial Studies Working Paper No. 660, 2021

56 Pages Posted:

See all articles by Atsushi Inoue

Atsushi Inoue

Vanderbilt University - College of Arts and Science - Department of Economics

Lutz Kilian

Federal Reserve Banks - Federal Reserve Bank of Dallas; Centre for Economic Policy Research (CEPR)

Date Written: December 9, 2020

Abstract

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.

Keywords: C22, C32, C52, E31, Q43

JEL Classification: Prior, posterior, impulse response, loss function, joint inference, absolute loss, median.

Suggested Citation

Inoue, Atsushi and Kilian, Lutz, The Role of the Prior in Estimating VAR Models with Sign Restrictions (December 9, 2020). Center for Financial Studies Working Paper No. 660, 2021, Available at SSRN: https://ssrn.com/abstract=

Atsushi Inoue

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

Lutz Kilian (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of Dallas ( email )

2200 North Pearl Street
PO Box 655906
Dallas, TX 75265-5906
United States

Centre for Economic Policy Research (CEPR)

London
United Kingdom

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