Abstract: I study the sorting of students to school districts using new lottery data from an inter-district school choice program in Massachusetts. I find that moving to a more preferred school district increases student math scores by 0.19 standard deviations. The program also generates positive effects on coursework quality, high-school graduation, and college attendance. Motivated by these findings, I develop a rich model of treatment effect heterogeneity and estimate it using an empirical-Bayes-type procedure that leverages non-experimental data to increase precision in quasi-experimental designs. The estimator I propose is a weighted average of experimental and non-experimental variation, with the weights chosen according to the correlation of the heterogeneous effects across samples. I use the heterogeneous effects to examine Roy selection into the choice program. Students who would be negatively impacted by the program are both less likely to apply and, conditional on taking up an offer to enroll, are more likely to subsequently return to their home district. I find that this selection drives almost all of the program evaluation treatment effect identified with the lottery. The fact that families sort students to school districts according to potential benefit suggests that research relying on school choice lotteries to learn about differences in school quality may lack a broad claim to external validity.
Link to the paper: http://www.jessebruhn.com/jesse_bruhn_jmp.pdf?attredirects=0