Open Access
Translator Disclaimer
February 2010 Bayesian analysis in moment inequality models
Yuan Liao, Wenxin Jiang
Ann. Statist. 38(1): 275-316 (February 2010). DOI: 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 δ-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.


Download Citation

Yuan Liao. Wenxin Jiang. "Bayesian analysis in moment inequality models." Ann. Statist. 38 (1) 275 - 316, February 2010.


Published: February 2010
First available in Project Euclid: 31 December 2009

zbMATH: 1181.62025
MathSciNet: MR2589323
Digital Object Identifier: 10.1214/09-AOS714

Primary: 62F15 , 62N01
Secondary: 62F99

Keywords: consistent set estimation , Identified region , limited information likelihood , maximum posterior , model and moment selection

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 1 • February 2010
Back to Top