Becker Friedman Institute

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Breaking Ties: Regression Discontinuity Design Meets Market Design

Centralized school assignment algorithms must distinguish between applicants with the same preferences and priorities. This is done with 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, grades, and interviews to rank applicants to screened schools, combined with lottery tie-breaking at unscreened schools. We show how to identify causal effects of school attendance in such settings. Our approach generalizes regression discontinuity designs to allow for multiple treatments and multiple running variables, some of which are randomly assigned. Lotteries generate assignment risk at screened as well as unscreened schools. Centralized assignment also identifies screened school effects away from screened school cutoffs. These features of centralized assignment are used to assess the predictive value of New York City’s school report cards. Grade A schools improve SAT math scores and increase the likelihood of graduating, though by less than OLS estimates suggest. Selection bias in OLS estimates is egregious for Grade A screened schools.

Authors: 
Atila Abdulkadiroglu, Duke University
Joshua Angrist, Massachusetts Institute of Technology
Yusuke Narita, Massachusetts Institute of Technology
Parag Pathak, Massachusetts Institute of Technology
Publication Date: 
April, 2019
Publication Status: 
Document Number: 
2019-024
File Description: 
First version, March 6, 2019