Endogeneity in Nonparametric and Semiparametric Regression Models

This paper considers the nonparametric and semiparametric methods for estimating regression models with continuous endogenous regressors. We list a number of different generalizations of the linear structural equation model, and discuss how two common estimation approaches for linear equations-the instrumental variables and control approaches-may be extended to nonparametric generalizations of the linear model and to their semiparametric variants. We consider the identification and estimation of the Average Structural Function and argue that this is a parameter of central interest in the analysis of semiparametric and nonparametric models with endogenous regressors. We consider a particular semiparametric model, the binary response model with linear index function and nonparametric error distribution, and describes in detail how estimation of the parameters of interest can be constructed using the control approach. This estimator is applied to estimating the relation of labor force participation to nonlabor income, viewed as an endogenous regressor.