Sharp identification regions in models with convex moment predictions

Abstract

We provide a tractable characterization of the sharp identi…cation 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 …nite 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 de…ned random set. The sharp identi…cation region of ; denoted I ; can then be obtained as the set of minimizers of the distance from a properly speci…ed vector of moments of random variables to this Aumann expectation. Algorithms in convex programming can be exploited to e¢ ciently verify whether a candidate is in I : We use examples analyzed in the literature to illustrate the gains in identi…cation and computational tractability a¤orded by our method.