Sharp Identification Regions in Models With Convex Moment Predictions
Arie Beresteanu, Ilya Molchanov, Francesca Molinari
Econometrica · 2011 · Volume 79 · Issue 6
Abstract
We provide a tractable characterization of the sharp identification region of the parameter vectorθin 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 thesemodels 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 forθ, 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 ofθ, denotedΘI, 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 candidateθis inΘI. We use examples analyzed in the literature to illustrate the gains in identification and computational tractability afforded by our method.
Keywords
Partial identification, random sets, Aumann expectation, support function, finite static games, multiple equilibria, random utility models, interval data, best linear prediction
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