Correct Specification and Identification of Nonparametric Transformation Models

December 2008
Pierre-André Chiappori, Ivana Komunjer

This paper derives necessary and sufficient conditions for nonparametric transformation models to be (i) correctly specified, and (ii) identified. Our correct specification conditions come in a form of partial differential equations; when satisfied by the true distribution, they ensure that the observables are indeed generated from a nonparametric transformation model. Our nonparametric identification result is global; we derive it under conditions that are substantially weaker than full independence. In particular, we show that a completeness assumption combined with independence with respect to one of the regressors suffices for the model to be identified.