Nonparametric Identification and Estimation of the Extended Roy Model

We propose a new identification and estimation method for the extended Roy model, in which the agents maximize their utility rather than just their outcome. We nonparametrically identify the joint distribution of potential outcomes, which is of great importance particularly in treatment effect analysis. The identification is achieved by matching the indifferent agents across choices, who are identified by the local instrumental variable method. We exploit the extended Roy model structure and the monotonicity assumption but do not require any functional form assumption nor any support assumption. Based on the identification result, we propose a nonparametric estimation procedure that builds upon a simulation-based method proposed by Dette et al. (2006). The estimator is easy to implement and possesses a standard nonparametric rate of convergence. The estimator's efficacy in finite samples is examined in Monte Carlo simulations. An empirical illustration on Malawian farmers' hybrid maize adoption is provided