Inference in Incomplete Models
49 Pages Posted: 28 Feb 2006
Date Written: May 26, 2006
We provide a test for the specification of a structural model without identifying assumptions. We show the equivalence of several natural formulations of correct specification, which we take as our null hypothesis. From a natural empirical version of the latter, we derive a Kolmogorov-Smirnov statistic for Choquet capacity functionals, which we use to construct our test. We derive the limiting distribution of our test statistic under the null, and show that our test is consistent against certain classes of alternatives. When the model is given in parametric form, the test can be inverted to yield confidence regions for the identified parameter set. The approach can be applied to the estimation of models with sample selection, censored observables and to games with multiple equilibria.
Keywords: partial identification, specification test, random correspondences, selections, plausibility constraint, Monge-Kantorovich mass transportation problem, Kolmogorov-Smirnov test for capacities
JEL Classification: C10, C12, C13, C14, C52, C61
Suggested Citation: Suggested Citation