Sharp Identification Regions in Models With Convex Moment Predictions

• 成果类型: Article
• 署名作者: Beresteanu, Arie; Molchanov, Ilya; Molinari, Francesca
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; University of Bern; Cornell University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA8680
• 发表日期: 2011
• 页码: 1785-1821
• 关键词: discrete response; inference; entry; sets; distributions; equilibria; parameters; volume

摘要

We provide a tractable characterization of the sharp identification region of the parameter vector ? in a broad class of incomplete econometric models. Models in this class have set-valued predictions that yield a convex set of conditional or unconditional moments for the observable model variables. In short, we call these models with convex moment predictions. Examples include static, simultaneous-move finite games of complete and incomplete information in the presence of multiple equilibria; best linear predictors with interval outcome and covariate data; and random utility models of multinomial choice in the presence of interval regressors data. Given a candidate value for ?, we establish that the convex set of moments yielded by the model predictions can be represented as the Aumann expectation of a properly defined random set. The sharp identification region of ?, denoted TI, can then be obtained as the set of minimizers of the distance from a properly specified vector of moments of random variables to this Aumann expectation. Algorithms in convex programming can be exploited to efficiently verify whether a candidate ? is in TI. We use examples analyzed in the literature to illustrate the gains in identification and computational tractability afforded by our method.