Bayesian analysis in moment inequality models

Details Bayesian analysis in moment inequality models Bayesian analysis in moment inequality models

2010-01-12

arxiv.org/abs/1001.1810v1

Annals of Statistics 2010, Vol. 38, No. 1, 275-316

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS714 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS714

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information likelihood. The posterior distribution converges to zero exponentially fast on any $\delta$-contraction outside the identified region. Inside, it is bounded below by a positive constant if the identified region is assumed to have a nonempty interior. Our simulation evidence indicates that the Bayesian approach has advantages over frequentist methods, in the sense that, with a proper choice of the prior, the posterior provides more information about the true parameter inside the identified region. We also address the problem of moment and model selection. Our optimality criterion is the maximum posterior procedure and we show that, asymptotically, it selects the true moment/model combination with the most moment inequalities and the simplest model.

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