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 three common estimation approaches for linear equations — the “instrumental variables,” “fitted value,” and “control function” approaches — may or may not be applicable to nonparametric generalizations of the linear model and to their semiparametric variants. The discussion then turns to 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 function” approach. This estimator is then applied to an empirical problem of the relation of labor force participation to nonlabor income, viewed as an endogenous regressor. ∗University College London, Department of Economics, Gower Street, London, WC1E 6BT and Institute for Fiscal Studies. [email protected] †Econometrics Laboratory, Department of Economics, University of California at Berkeley, Berkeley, CA 94720-3880.