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: (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, the authors reject the assumptions justifying matching and their extensions 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-differences. They find that matching participants to comparison group members in the same labor market, giving them the same questionnaire, and making sure they have comparable characteristics substantially improves the performance of any econometric program evaluation estimator. The authors also show how to extend their analysis to estimate the impact of treatment on the treated using ordinary observational data. The paper highlights the importance of nonparametric methods in econometrics and the value of good data in constructing comparison groups that have outcomes close to those of an experimental control group. The authors also discuss how to extend and apply the methods analyzed in this paper to analyze the effect of treatment on the treated in the more common situation where analysts do not have access to experimental data.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: (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, the authors reject the assumptions justifying matching and their extensions 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-differences. They find that matching participants to comparison group members in the same labor market, giving them the same questionnaire, and making sure they have comparable characteristics substantially improves the performance of any econometric program evaluation estimator. The authors also show how to extend their analysis to estimate the impact of treatment on the treated using ordinary observational data. The paper highlights the importance of nonparametric methods in econometrics and the value of good data in constructing comparison groups that have outcomes close to those of an experimental control group. The authors also discuss how to extend and apply the methods analyzed in this paper to analyze the effect of treatment on the treated in the more common situation where analysts do not have access to experimental data.