Evaluating Education Programs That Have Lotteried Admission and Selective Attrition

The purpose of this paper is to provide a new framework for evaluating education programs that ration excess demand by admission lotteries when selective attrition cannot be ignored. Differential attrition arises in these models because students that lose the lottery are more likely to pursue educational options outside the school district. When students leave the district, important outcome variables are often not observed. We provide conditions that allow us to identify the proportions of latent student types and, thereby, the extent of differential attrition. We provide estimators of the proportions of the these latent types and their characteristics. We apply our methods to study the effectiveness of magnet programs in a mid-sized urban school district. We show that the students that cause the differential attrition have very different observed characteristics than the other students. Selective attrition implies that treatment effects are not point identified. We discuss how to construct informative bounds when point identification is not feasible. Our findings show that magnet programs help the district to attract and retain students. The bound estimates also demonstrate that magnet programs offered by the district improve behavioral outcomes such as offenses, timeliness, and attendance.