Nonparametric Identi cation and Estimation of the Extended Roy Model

This paper proposes a new identi cation and estimation method for the extended Roy model, in which the agents maximize their utility rather than just outcome. The identi cation results substantially relax conventional functional form restrictions. No functional form restriction is imposed on the distribution of the potential outcomes. The utility functions are allowed to be nonlinear so that it can accommodate important features of utility functions such as the concavity of the utility functions. The identi cation method exploits continuous variation in instrumental variables, and can identify some useful aspects of the parameters even when the support of the instrumental variable is not large. The key assumption of the method is the monotonicity of the selection with respect to the instrument. Based on the identi cation result, I propose a nonparametric estimation procedure that builds upon a simulation-based method proposed by Dette et al. (2006). The estimator is easy to implement in practice because it only uses a closed form formula and straightforward simulations. I show that the estimator possesses a standard nonparametric rate of convergence, and examine its e cacy in nite samples by Monte Carlo simulations. I apply the estimator to analyze farmer's decisions to adopt a new agricultural technology in Malawi. JELclassi cation C14, C35, C36, C51, C53 ∗SUNY Albany, [email protected] †This paper is a chapter of my Ph.D. dissertation at Yale University. I thank my advisors, Yuichi Kitamura, Edward Vytlacil, and Donald Andrews for their guidance and support. I also thank Tavneet Suri for suggesting the data set. Finanacial supports from Cowles foundation, Korea Foundation of Advanced Studies and University at Albany are gratefully acknowledged.