Non-parametric Identication and Testable Implications of the Roy Model

This paper studies non-parametric identi…cation and the testable implications of the Roy Model. Results in the literature are generalized in three directions. First, my model allows fully general functions that characterize the income of di¤erent occupations. Second, identi…cation is obtained using strictly weaker exclusion restrictions. For example, the model with additive heterogeneity is non-parametrically identi…ed without any exclusion restriction. Third, testable implications of a general occupational choice model are derived. The analysis draws on results on the existence and uniqueness of solutions to systems of partial di¤erential equations. I thank Fernando Alvarez, Pierre-Andre Chiappori, Ivar Ekeland, Xavier Gine, James Heckman, Rosa Matzkin, Hugo Sonnenschein, Chris Taber, Elie Tamer, Robert Townsend and Ivan Werning for valuable comments and suggestions. I have also bene…ted from the comments of participants at seminars at the University of Chicago, Universidad Torcuato Di Tella and Northwestern University.