Breaking Ties: Regression Discontinuity Design Meets Market Design

Abstract

Many schools in large urban districts have more applicants than seats. Centralized school assignment algorithms ration seats at over‐subscribed schools using randomly assigned lottery numbers, non‐lottery tie‐breakers like test scores, or both. The New York City public high school match illustrates the latter, using test scores and other criteria to rank applicants at the city's screened schools, combined with lottery tie‐breaking at the rest. We show how to identify causal effects of school attendance in such settings. Our approach generalizes regression discontinuity methods to allow for multiple treatments and multiple running variables, some of which are randomly assigned. The key to this generalization is a local propensity score that quantifies the school assignment probabilities induced by lottery and non‐lottery tie‐breakers. The utility of the local propensity score is demonstrated in an assessment of the predictive value of New York City's school report cards. Schools that earn the highest report card grade indeed improve SAT math scores and increase graduation rates, though by much less than OLS estimates suggest. Selection bias in OLS estimates of grade effects is egregious for screened schools.

Study abroad programmes and student outcomes: Evidence from Erasmus

“…Our research design is close in spirit to the methodology developed in Abdulkadiroglu et al (2022) in the context of centralised school assignment. We discuss the similarities between the two approaches in Appendix A.2 and provide an additional robustness check inspired by their approach.…”

“…exploiting the discontinuity in Erasmus participation probability at the cutoff values of a student ability measure and looking at previously overlooked relevant outcomes. Furthermore, our research design is novel in that it makes use of very recent methodological advancements developed in other contexts ( Abdulkadiroglu et al, 2022 , Abdulkadiroglu et al, 2017 , Fort et al, 2022 , Fort et al, 2020 ) regarding how to generalise regression discontinuity designs to allow for multiple cutoffs and multiple running variables. To the best of our knowledge, our study is the first application of this method to the investigation of ISM impacts.…”

Effect of Secondary Education on Cognitive and Non-Cognitive Skills

“…In our data, we only observe GPA, and have no information on these other admission criteria. This also prevents us from using DA propensity score methods suggested in (Abdulkadıroglu et al, 2022). However, dropping all applicants who had ranked at least one vocational program above the least selective general program had no effects on the results.…”

Education, Gender, and Family Formation

“…This allows us to incorporate any differences in the effects on admissions probabilities as we assess the differential magnitudes for men and women. Finally, we control for applicant type by including a propensity score measuring the application rank that is binding for each student (δ x P ikg ) (Abdulkadiroglu et al, 2022). So that our estimates are as local to the cutoff as possible, we use triangular kernel weights (Hahn et al, 2001).…”