Semiparametric instrumental variable estimation of simultaneous equation sample selection models

Abstract

The identification and estimation of a semiparametric simultaneous equation model with selectivity have been considered. The identification of structural parameters from reduced form parameters in the semiparametric model requires stronger conditions than the usual rank condition in the classical simultaneous equation model or the parametric simultaneous equation sample selection model with normal disturbances. The necessary order condition for identification in the semiparametric model corresponds to the overidentification condition in the classical model. Semiparametric two-stage estimation methods which generalize the two-stage least squares method and the generalized two-stage least squares method for the parametric model are introduced. The semiparametric generalized two-stage least squares estimator is shown to be asymptotically efficient in a class of semiparametric instrumental variable estimators.