Nonparametric Instrumental Variable Estimation of Binary Response Models

We present an instrumental variable approach to the nonparametric estimation of binary response models with endogenous independent variables. We achieve nonparametric identification up to a scale via the reduced form model constructed from the decomposition of the unobserved dependent variable into the space of the instruments and we suppose the disturbances in this model to be stochastically independent of the instrumental variables. For estimation purposes, we approximate the fully nonparametric model by a sequence of locally weighted parametric ones. This approach simplifies the estimation procedure and it is robust to local model misspecification. We prove consistency of this estimator and run a simulation study to corroborate its small sample properties. We also show how to construct interesting policy parameters. We conclude the paper with an empirical illustration of female labor force participation in the US, where we showcase the implementation of our approach and we compare it with existing semiparametric estimators.