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

Lutz Kilian and Atsushi Inoue

No 15545, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: Several recent studies have expressed concern that the Haar prior typically imposed in estimating sign-identified 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. Specifically, 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-identified VAR models estimated using conventional priors tend to imply unintentionally informative priors for the impulse response vector or that the corresponding 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-identified VAR models proposed by Baumeister and Hamilton (2015) suffers 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: Prior; Posterior; Impulse response; Loss function; Joint inference; Absolute loss (search for similar items in EconPapers)
JEL-codes: C22 C32 C52 E31 Q43 (search for similar items in EconPapers)
Date: 2020-12
New Economics Papers: this item is included in nep-mac and nep-ore
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Citations: View citations in EconPapers (23)

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Related works:
Working Paper: The role of the prior in estimating VAR models with sign restrictions (2021)
Working Paper: The Role of the Prior in Estimating VAR Models with Sign Restrictions (2020)
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