Estimating a nonparametric triangular model with binary endogenous regressors

We consider identification and estimation in a nonparametric triangular system with a binary endogenous regressor and nonseparable errors. For identification we take a control function approach utilizing the Dynkin system idea developed in Jun, Pinkse, and Xu (2010b, JPX10). We show our method to be an alternative (but potentially more general) approach to the use of local instruments, as in e.g. Carneiro and Lee (2009), Heckman and Vytlacil (1999). We propose a nonparametric estimator of the structural function evaluated at particular values. Our estimator uses nonparametric kernel regression techniques and its statistical properties are derived using the functional delta method. We establish that it is n2=7–convergent and has a limiting normal distribution. We apply the method to estimate the returns to a college education.