  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.
