centre for microdata methods and practice

ESRC centre

cemmap is an ESRC research centre

ESRC

Keep in touch

Subscribe to cemmap news

Robust Bayesian inference for set-identified models

Authors: Raffaella Giacomini and Toru Kitagawa
Date: 07 November 2018
Type: cemmap Working Paper, CWP61/18

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.

Download full version
Previous version:
Raffaella Giacomini and Toru Kitagawa November 2014, Inference about Non-Identiļ¬ed SVARs, cemmap Working Paper, CWP45/14, cemmap

Search cemmap

Search by title, topic or name.

Contact cemmap

Centre for Microdata Methods and Practice

How to find us

Tel: +44 (0)20 7291 4800

E-mail us