When Is the Use of Gaussian-inverse Wishart-Haar Priors Appropriate?

Atsushi Inoue and Lutz Kilian

No 19227, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: Several recent studies have expressed concern that the Haar prior typically employed in estimating sign-identified VAR models is driving the prior about the structural impulse responses and hence their posterior. In this paper, we provide evidence that the quantitative importance of the Haar prior for posterior inference has been overstated. How sensitive posterior inference is to the Haar prior depends on the width of the identified set of a given impulse response. We demonstrate that this width depends not only on how much the identified set is narrowed by the identifying restrictions imposed on the model, but also depends on the data through the reduced-form model parameters. Hence, the role of the Haar prior can only be assessed on a case-by-case basis. We show by example that, when the identification is sufficiently tight, posterior inference based on a Gaussian-inverse Wishart-Haar prior provides a reasonably accurate approximation.

JEL-codes: C22 C32 C52 E31 (search for similar items in EconPapers)
Date: 2024-07
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Working Paper: When Is the Use of Gaussian-inverse Wishart-Haar Priors Appropriate? (2024)
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