This paper investigates four topics. (1) It examines the different roles played by the propensity score (the probability of selection into treatment) in matching, instrumental variable, and control function methods. (2) It contrasts the roles of exclusion restrictions in matching and selection models. (3) It characterizes the sensitivity of matching to the choice of conditioning variables and demonstrates the greater robustness of control function methods to misspecification of the conditioning variables. (4) It demonstrates the problem of choosing the conditioning variables in matching and the failure of conventional model selection criteria when candidate conditioning variables are not exogenous in a sense defined in this paper.

This note derives simply computed closed-form expressions for the average treatment effect, the effect of treatment on the treated, the local average treatment effect, and the marginal treatment effect in a latent-variable framework for both normal and nonnormal models. Asymptotic standard errors for versions of these parameters that average over observed characteristics are also obtained. The performances of the derived estimators are also evaluated in Monte Carlo experiments under correct specification and misspecification.

This paper considers two problems that arise in determining the role of cognitive ability in explaining the level of and change in the rate of return to schooling. The first problem is that ability and schooling are so strongly dependent that it is not possible, over a wide range of variation in schooling and ability, to independently vary these two variables and estimate their separate impacts. The second problem is that the structure of panel data makes it difficult to identify main age and time effects or to isolate crucial education-ability-time interactions which are needed to assess the role of ability in explaining the rise in the return to education.

One current educational reform seeks to reward the “value added” by teachers and schools based on the average change in pupil test scores over time. In this paper, we outline the conditions under which the average change in scores is sufficient to rank schools in terms of value added. A key condition is that socioeconomic outcomes be a linear function of test scores. Absent this condition, one can still derive the optimal value-added policy if one knows the relationship between test scores and socioeconomic outcomes, and the distribution of test scores both before and after the intervention. Using the National Longitudinal Survey of Youth, we find a nonlinear relationship between test scores and one important outcome: log wages. We find no consistent pattern in the curvature of log wage returns to test scores (whether percentiles, scaled, or raw scores). This implies that, used alone, the average gain in test scores is an inadequate measure of school performance and current value-added methodology may misdirect school resources.

This paper explores issues that arise in the evaluation of social programs using experimental data in the frequently encountered case where some of the experimental treatment group members drop out of the program prior to receiving treatment. We begin with the standard estimator for this case and the identifying assumption upon which it rests. We then examine the behavior of the estimator when the dropouts receive a partial “dose” of the program treatment prior to dropping out of the program. In the case of partial treatment, the identifying assumption is typically violated, thereby making the estimator inconsistent for the conventional parameter of interest: the impact of full treatment on the fully treated. We develop a test of the identifying assumption underlying the standard estimator and consider whether exclusion restrictions produce identification of the mean impact of the program when this assumption fails to hold. Finally, we discuss alternative parameters of interest in the presence of partial treatment among the dropouts and argue that the conventional parameter is not always the economically interesting one. We apply our methods to data from a recent experimental evaluation of the Job Training Partnership Act (JTPA) program.