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. The authors use data from a social experiment on a job training program combined with rich data from a nonexperimental comparison group to test the identifying assumptions of three widely-used classes of estimators: matching, classical econometric selection models, and difference-in-differences. They find that matching and its extensions are not effective in reducing selection bias, while the index-sufficient selection bias model and the conditional semiparametric version of the difference-in-differences estimator are supported by the data. The paper also highlights the importance of defining selection bias on a common support of the probability of participation and demonstrates how to extend the analysis to estimate the impact of treatment on the treated using ordinary observational 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. The authors use data from a social experiment on a job training program combined with rich data from a nonexperimental comparison group to test the identifying assumptions of three widely-used classes of estimators: matching, classical econometric selection models, and difference-in-differences. They find that matching and its extensions are not effective in reducing selection bias, while the index-sufficient selection bias model and the conditional semiparametric version of the difference-in-differences estimator are supported by the data. The paper also highlights the importance of defining selection bias on a common support of the probability of participation and demonstrates how to extend the analysis to estimate the impact of treatment on the treated using ordinary observational data.