Nonparametric identification and estimation of the extended Roy model

We propose a new identification 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 in causal inference. We exploit the extended Roy model structure and the monotonicity assumption but do not require any functional form assumption nor any support assumption. The identification is achieved by matching the indifferent agents across choices, who are identified by the local instrumental variable method. Based on the identification result, we propose an easy-to-implement nonparametric simulation-based estimator and derive its convergence rate. An empirical illustration on Malawian farmers’ hybrid maize adoption is provided.