Smooth coefficient models with endogenous environmental variables

We develop a three-step, oracle-efficient estimator for a structural semiparametric smooth coefficient model with endogenous variables in the nonparametric part of the model. We use a control function approach, combined with both series and kernel estimators to obtain consistent and asymptotically normal estimators of the functions and their partial derivatives. We develop a residual-based test statistic for testing endogeneity, and demonstrate the finite sample performance of our estimators, as well as our test, via Monte Carlo simulations. Finally, we develop an application of our estimator to the relationship between public benefits and private savings.