Estimation in partially linear semiparametric models with parametric and/or nonparametric endogeneity

Partially linear semiparametric models are advantageous to use in empirical studies of various economic problems due to a special feature that allows the parametric and nonparametric components to exist simultaneously in the model. However, systematic estimation procedures and methods have not yet been satisfactorily developed to deal effectively with a well-known endogeneity problem that may be present in some empirical applications. In the current paper, we aim to address endogeneity comprehensively, which may take place in either a parametric or a nonparametric component or both, and to provide guidance to an appropriate estimation procedure and method in the presence of such a problem. A significant difficulty we must overcome before such goals can be achieved is a generated regressor problem which arises because a critical part, known in the literature as the "control variables", is not observable in practice and hence must be estimated. We show theoretically (i.e. through the derivation of a set of important asymptotic properties) and experimentally (i.e. through the use of simulation exercises) that our newly introduced method can help in overcoming the above-mentioned endogeneity problem. For the sake of completeness, we also discuss an adaptive data-driven method of bandwidth selection and show its asymptotic optimality.