Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/64691
Authors: 
Beresteanu, Arie
Molchanov, Ilya
Molinari, Francesca
Year of Publication: 
2009
Series/Report no.: 
cemmap working paper CWP27/09
Abstract: 
We provide a tractable characterization of the sharp identification region of the parameters θ 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 θ, 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 θ, denoted ΘI, 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 θ is in ΘI. We use examples analyzed in the literature to illustrate the gains in identification and computational tractability afforded by our method.
Subjects: 
Partial Identification
Random Sets
Aumann Expectation
Support Function
Normal Form Games
Multiple Equilibria
Random Utility Models
Interval Data
Best Linear Prediction
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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