Joint Bayesian inference about impulse responses in VAR models

Atsushi Inoue and Lutz Kilian

Journal of Econometrics, 2022, vol. 231, issue 2, 457-476

Abstract: We derive the Bayes estimator of vectors of structural VAR impulse responses under a range of alternative loss functions. We also discuss the construction of joint credible regions for vectors of impulse responses as the lowest posterior risk region under the same loss functions. We show that conventional impulse response estimators such as the posterior median response function or the posterior mean response function are not in general the Bayes estimator of the impulse response vector obtained by stacking the impulse responses of interest. We illustrate that such pointwise estimators may imply response function shapes that are incompatible with any possible parameterization of the underlying model. Moreover, conventional pointwise quantile error bands are not a valid measure of the estimation uncertainty about the impulse response vector because they ignore the mutual dependence of the responses. In practice, they tend to understate substantially the estimation uncertainty about the impulse response vector.

Keywords: Loss function; Joint inference; Median response function; Mean response function; Modal model; Posterior risk (search for similar items in EconPapers)
JEL-codes: C22 C32 C52 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (29)

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Related works:
Working Paper: Joint Bayesian Inference about Impulse Responses in VAR Models (2020)
Working Paper: Joint Bayesian inference about impulse responses in VAR models (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:231:y:2022:i:2:p:457-476

DOI: 10.1016/j.jeconom.2021.05.010

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