Breaking Ties: Regression Discontinuity Design Meets Market Design

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