• Abstract: 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.

• Paper: pdf file

• Supplementary materials
  Estimation when the identified region has no interior: pdf file.
  This is a supplementary material of Liao and Jiang (2010). We consider the case when the identified region has no interior. We show that the posterior distribution converges to zero on any δ -contraction outside the identified region exponentially fast, and is bounded below by a polynomial rate on any neighborhood of element in a dense subset, defined by both exact moment conditions and strict moment inequalities. Hence the consistent estimation of the identified region can be constructed based on the log-posterior pdf.

  Moment and Model Selection: pdf file.
  This is a chapter of my Ph.D. dissertation, which provides a more reliable setting of the selection procedure than those given in the main paper. Proofs can be found in Appendix B of my thesis:
  Bayesian Analysis in Partially Identified Parametric and Non-Parametric Models

• Slides: pdf file

• Related literature:

  Chernozhukov, Hong and Tamer (2007).
  Estimation and confidence regions for parameter sets in econometric models
  Econometrica, 75 1243-1284.

  Kim, J. (2002).
  Limited information likelihood and Bayesian analysis
  Journal of Econometrics, 107 175-193.

  Moon, H. and Schorfheide, F. (2009).
  Bayesian and frequentist inference in partially identified models.
  To appear in Econometrica.