Nonparametric Identification and Estimation of Random Coefficients in Nonlinear Economic Models

We show how to nonparametrically identify and estimate the distribution of random coefficients that characterizes the heterogeneity among agents in a general class of economic choice models. We introduce an axiom that we term separability and prove that separability of a structural model ensures identification. Identification naturally gives rise to a nonparametric minimum distance estimator. We prove identification of distributions of utility functions in multinomial choice, distributions of labor supply responses to tax changes, and distributions of wage functions in the Roy selection model. We also reconsider the problem of endogeneity in economic choice models, leading to new results on the two-stage least squares model. ∗Thanks to Stephane Bonhomme, Steven Durlauf, James Heckman, Salvador Navarro, Philip Reny, Susanne Schennach, Azeem Shaikh, Christopher Taber, Harald Uhlig and Edward Vytlacil for helpful comments. Also thanks to seminar participants at Boston University, Brown, the Brown / UCL Demand Conference, Caltech, CREST, Chicago, Cowles, EC2 Rome, Georgetown, Indiana, LSE, Michigan, Michigan State, Minnesota, Northwestern, Penn State, Pittsburgh, Rochester, the SED, Stanford, Toulouse, UCL, USC, Washington University in St. Louis, Wisconsin and Yale. Fox thanks the National Science Foundation, the Olin Foundation, and the Stigler Center for financial support. Thanks to Chenchuan Li for research assistance. Our email addresses our [email protected] and [email protected].