Semiparametric Estimation of Selectivity Models.

Abstract

This paper provides a comprehensive summary of the most promising estimation methods for the (dichotomous) selectivity models. Selectivity models, often referred to as sample selection models, are frequently used in structural analysis and evaluation studies, wherever individuals select among different alternatives. Selectivity models strive to estimate structural outcome equations under explicit consideration of the fact that individuals are heterogeneous and that the selection into or out of different alternatives (e.g. treatment/non-treatment) is not random and based on observed and unobserved characteristics. Hence individuals that are selected into one group are likely to be inherently different from individuals that selected into any other group. Neglecting this non-random selection leads to selection bias, either on the basis of observed characteristics or on unobservables, which is the focus of this work. The core idea of all approaches modelling this selection problem is to forecast counterfactual outcomes, that are the hypothetical outcomes a certain individual would have acquired if it selected into an other alternative. At first structural models contaminated by selectivity and the nature of the selection problem are defined rigorously. Different identifying assumptions such as exclusion restrictions, an index assumption, or identification at infinity are illuminated. An extensive discussion of parametric and semiparametric procedures for the 2-categories selectivity model exposes how the different estimators cope with the selection problem. In contrast to the parametric ones, like the Heckman two-step, the semiparametric estimators do not impose tight restrictions on the error terms. The estimators of Gallant/Nychka, Klein/Spady, Powell, Newey, Ahn/Powell, Robinson, Chen and Andrews/Schafgans are presented. Finally, the properties of these estimators, an illustrating example estimating the effect of unionism on wages, and recommen