This paper develops the method of matching as an econometric evaluation estimator. A rigorous distribution theory for kernel-based matching is presented. The method of matching is extended to more general conditions than the ones assumed in the statistical literature on the topic. We focus on the method of propensity score matching and show that it is not necessarily better, in the sense of reducing the variance of the resulting estimator, to use the propensity score method even if propensity score is known. We extend the statistical literature on the propensity score by considering the case when it is estimated both parametrically and nonparametrically. We examine the benefits of separability and exclusion restrictions in improving the efficiency of the estimator. Our methods also apply to the econometric selection bias estimator.

This paper develops and applies semiparametric econometric methods to estimate the form of selection bias that arises from using nonexperimental comparison groups to evaluate social programs and to test the identifying assumptions that justify three widely-used classes of estimators and our extensions of them: (a) the method of matching; (b) the classical econometric selection model which represents the bias solely as a function of the probability of participation; and (c) the method of difference-in-differences. Using data from an experiment on a prototypical social program combined with unusually rich data from a nonexperimental comparison group, we reject the assumptions justifying matching and our extensions of that method but find evidence in support of the index-sufficient selection bias model and the assumptions that justify application of a conditional semiparametric version of the method of difference-in-difference. Fa comparable people and to appropriately weight participants and nonparticipants a sources of selection bias as conveniently measured. We present a rigorous defin bias and find that in our data it is a small component of conventially meausred it is still substantial when compared with experimentally-estimated program impa matching participants to comparison group members in the same labor market, givi same questionnaire, and making sure they have comparable characteristics substan the performance of any econometric program evaluation estimator. We show how t analysis to estimate the impact of treatment on the treated using ordinary obser