Impact Evaluation in Matching Markets with General Tie-Breaking

Many centralized matching schemes incorporate a mix of random lottery and non-lottery tie-breaking. A leading example is the New York City public school district, which uses criteria like test scores and interviews to generate applicant rankings for some schools, combined with lottery tie-breaking at other schools. We develop methods that identify causal effects of assignment in such settings. Our approach generalizes the standard regression discontinuity design to allow for many running variables and treatments, some of which are randomly assigned. We show that lottery variation generates assignment risk at non-lottery programs for applicants away from non-lottery cutoffs, while non-lottery variation randomizes applicants near cutoffs regardless of lottery risk. These methods are applied to evaluate New York City's school progress assessments, which give schools letter grades as a summary measure of quality. Our estimates reveal that although Grade A schools boost achievement, these gains emerge only for students who attend lottery schools. Attendance at a coveted Grade A screened school, including some of the highest performing in the district, generates no measurable effects. Evaluation methods that fail to take advantage of both lottery and non-lottery variation miss this difference in impact