Inference in Incomplete Models

49 Pages Posted: 28 Feb 2006

See all articles by Alfred Galichon

Alfred Galichon

NYU, Department of Economics and Courant Institute

Marc Henry

Pennsylvania State University

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

Galichon, Alfred and Henry, Marc, Inference in Incomplete Models (May 26, 2006). Available at SSRN: or

Alfred Galichon

NYU, Department of Economics and Courant Institute ( email )

269 Mercer Street, 7th Floor
New York, NY 10011
United States

Marc Henry (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States