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Robust Bayesian Inference for Set-Identified Models

Giacomini, R; Kitagawa, T; (2021) Robust Bayesian Inference for Set-Identified Models. Econometrica , 89 (4) pp. 1519-1556. 10.3982/ECTA16773. Green open access

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Abstract

This paper reconciles the asymptotic disagreement between Bayesian and frequentist inference in set‐identified models by adopting a multiple‐prior (robust) Bayesian approach. We propose new tools for Bayesian inference in set‐identified models and show that they have a well‐defined posterior interpretation in finite samples and are asymptotically valid from the frequentist perspective. The main idea is to construct a prior class that removes the source of the disagreement: the need to specify an unrevisable prior for the structural parameter given the reduced‐form parameter. The corresponding class of posteriors can be summarized by reporting the ‘posterior lower and upper probabilities’ of a given event and/or the ‘set of posterior means’ and the associated ‘robust credible region’. We show that the set of posterior means is a consistent estimator of the true identified set and the robust credible region has the correct frequentist asymptotic coverage for the true identified set if it is convex. Otherwise, the method provides posterior inference about the convex hull of the identified set. For impulse‐response analysis in set‐identified Structural Vector Autoregressions, the new tools can be used to overcome or quantify the sensitivity of standard Bayesian inference to the choice of an unrevisable prior.

Type: Article
Title: Robust Bayesian Inference for Set-Identified Models
Open access status: An open access version is available from UCL Discovery
DOI: 10.3982/ECTA16773
Publisher version: https://doi.org/10.3982/ECTA16773
Language: English
Additional information: © 2021 The Authors. Econometrica published by John Wiley & Sons Ltd on behalf of The Econometric Society. Raffaella Giacomini is the corresponding author on this paper. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Keywords: Multiple priors, identified set, credible region, consistency, asymptotic coverage, identifying restrictions, impulse-response analysis.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/10110203
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