Econometrica: Nov 2011, Volume 79, Issue 6

Sharp Identification Regions in Models With Convex Moment Predictions

https://doi.org/10.3982/ECTA8680
p. 1785-1821

Arie Beresteanu, Ilya Molchanov, Francesca Molinari

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 . 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 , 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 . We use examples analyzed in the literature to illustrate the gains in identification and computational tractability afforded by our method.

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Supplemental Material

Supplement to "Sharp Identification Regions in Models with Convex Moment Predictions"

A zip file containing Fortran and Matlab programs to replicate the simulation results appearing in the manuscript.

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Supplement to "Sharp Identification Regions in Models with Convex Moment Predictions"

This supplement includes five appendices which illustrate how to build confidence sets for the sharp identification regions, and apply the methodology provided in the manuscript to additional models with convex moment predictions.

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