Bayesian inference in a class of partially identified models

• 成果类型: Article
• 署名作者: Kline, Brendan; Tamer, Elie
• 署名单位: University of Texas System; University of Texas Austin; Harvard University
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE399
• 发表日期: 2016
• 页码: 329-366
• 关键词: partial identification; identified set; criterion function; Bayesian inference

摘要

This paper develops a Bayesian approach to inference in a class of partially identified econometric models. Models in this class are characterized by a known mapping between a point identified reduced-form parameter mu and the identified set for a partially identified parameter theta. The approach maps posterior inference about mu to various posterior inference statements concerning the identified set for theta, without the specification of a prior for theta. Many posterior inference statements are considered, including the posterior probability that a particular parameter value (or a set of parameter values) is in the identified set. The approach applies also to functions of theta. The paper develops general results on large sample approximations, which illustrate how the posterior probabilities over the identified set are revised by the data, and establishes conditions under which the Bayesian credible sets also are valid frequentist confidence sets. The approach is computationally attractive even in high-dimensional models, in that the approach avoids an exhaustive search over the parameter space. The performance of the approach is illustrated via Monte Carlo experiments and an empirical application to a binary entry game involving airlines.