Sharp Identification Regions in Models with Convex Moment Predictions

• Activity Number: 276
• Type: Invited
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: JBES-Journal of Business & Economic Statistics
• Author(s): Francesca Molinari and Arie Beresteanu*+ and Ilya Molchanov
• Companies: Cornell University and University of Pittsburgh and University of Bern
• Keywords: Partial Identification ; Random Sets ; Aumann expectation

Abstract

We provide a tractable characterization of the sharp identification region of the parameters  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 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 the sharp identification region.