Breaking Ties: Regression Discontinuity Design Meets Market Design

TL;DR

This paper extends regression discontinuity methods to settings with multiple treatments and running variables, using a local propensity score to identify causal effects in complex school assignment scenarios.

Contribution

It introduces a generalized regression discontinuity approach incorporating multiple treatments and running variables, accounting for lottery and non-lottery tie-breakers via a local propensity score.

Findings

High-rated schools improve SAT scores and graduation rates.

OLS estimates overstate effects due to selection bias.

Selection bias is severe in screened schools.

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 ``screened'' schools, combined with lottery tie-breaking at unscreened ``lottery'' schools. 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 local propensity score is applied in an empirical assessment of the predictive value of New York City's school report cards. Schools that receive a high grade indeed improve SAT math scores and increase graduation rates, though by much less than OLS estimates suggest. Selection bias in OLS estimates is egregious for screened schools.