Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/189807 
Year of Publication: 
2018
Series/Report no.: 
cemmap working paper No. CWP61/18
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
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. We show that these tools 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. 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 can be interpreted as providing 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.
Subjects: 
multiple priors
identified set
credible region
consistency
asymptotic coverage
identifying restrictions
impulse-response analysis
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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