Bayesian analysis in moment inequality models

Yuan Liao*, Wenxin Jiang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)275-316
Number of pages42
JournalAnnals of Statistics
Issue number1
StatePublished - Feb 2010


  • Consistent set estimation
  • Identified region
  • Limited information likelihood
  • Maximum posterior
  • Model and moment selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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