• Abstract: This paper proposes novel Bayesian procedures for partially identified models when the identified set is convex with a smooth boundary, whose support function is locally smooth with respect to the data distribution. Using the posterior of the identified set, we construct Bayesian credible sets for the identified set, the partially identified parameter and their scalar transformations. These constructions, based on the support function, benefit from several computationally attractive algorithms when the identified set is convex, and are proved to have valid large sample frequentist coverages. These results are based on a local linear expansion of the support function of the identified set. We provide primitive conditions to verify such an expansion.

• The paper: pdf

• Supplement: pdf

• Previously circulated as the 2013 working paper: Liao and Simoni (2013) ``Semi-parametric Bayesian Partially Identified Models based on Support Function"

• Slides: talk

• Matlab codes: talk

• Hansen-Jagannathan bound: A simulated example for the identified set of the stochastic discount factor derived in Hansen and Jagannathan (1991)

  

• Related literature:

  Moon, H. and Schorfheide, F. (2012).
  Bayesian and frequentist inference in partially identified models.
  Econometrica, 80 755-782.

  Liao and Jiang (2010).
  Bayesian analysis in moment inequality models
  Ann. Statist., 38 275-316.