Endogeneity in nonparametric and semiparametric regression models
Richard Blundell () and
James L. Powell ()
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James L. Powell: Institute for Fiscal Studies and University of California, Berkeley
No CWP09/01, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies
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 function" 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 function" approach. This estimator is applied to estimating the relation of labor force participation to nonlabor income, viewed as an endogenous regressor.
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