Estimation in Semiparametric Partially Linear Models with Parametric and/or Nonparametric Endogeneity

Abstract

Semiparametric partially linear models are advantageous to use in empirical studies of various economic problems due to a special feature such that both the parametric and nonparametric components can simultaneously exist in the model. However, a systematic estimation procedure and method have not yet been satisfactorily developed to deal effectively with a well-known endogeneity problem which may be present in some empirical applications. In the current paper, we aim to comprehensively address endogeneity, 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 due to the fact that a critical part known as the control-regressor is not observable in practice and hence must be nonparametrically estimated. We show theoretically, i.e. through the derivation of some important asymptotic properties, and experimentally, i.e. through the use of some simulation exercises, that our newly introduced method can help overcoming the above - mentioned endogeneity problem. For the sake of completion, we also discuss an adaptive data - driven method of bandwidth selection and show its asymptotic optimality.

Keywords: semiparametric models with endogeneity

JEL Classification: C12, C14, C22