Sharp identification regions in models with convex predictions: games, individual choice, and incomplete data

Arie Beresteanu (), Ilya Molchanov () and Francesca Molinari
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Ilya Molchanov: Institute for Fiscal Studies and University of Bern, Institute of Mathematical Statistics and Actuarial Science

No CWP27/09, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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 model variables. In short, we call these models with convex predictions. Examples include static, simultaneous move finite games of complete information in the presence of multiple mixed strategy Nash equilibria; random utility models of multinomial choice in the presence of interval regressors data; and best linear predictors with interval outcome and covariate 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. We show that 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. This paper is a revised version of cemmap working paper CWP15/08

Date: 2009-10-02
New Economics Papers: this item is included in nep-ecm
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