Breaking Ties: Regression Discontinuity Design Meets Market Design

61 Pages Posted: 7 Mar 2019

See all articles by Atila Abdulkadiroglu

Atila Abdulkadiroglu

Duke University - Department of Economics

Joshua D. Angrist

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER); IZA Institute of Labor Economics

Yusuke Narita

Yale University - Department of Economics; Yale University - Cowles Foundation

Parag A. Pathak

Massachusetts Institute of Technology (MIT) - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: March 6, 2019

Abstract

Centralized school assignment algorithms must distinguish between applicants with the same preferences and priorities. This is done with randomly assigned lottery numbers, nonlottery 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.

Keywords: Causal Inference, Natural Experiment, Local Propensity Score, Instrumental Variables, Unified Enrollment, School Report Card, School Value Added

Suggested Citation

Abdulkadiroglu, Atila and Angrist, Joshua and Narita, Yusuke and Pathak, Parag A., Breaking Ties: Regression Discontinuity Design Meets Market Design (March 6, 2019). Cowles Foundation Discussion Paper No. 2170. Available at SSRN: https://ssrn.com/abstract=3348194 or http://dx.doi.org/10.2139/ssrn.3348194

Atila Abdulkadiroglu

Duke University - Department of Economics ( email )

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States

Joshua Angrist

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
E52-353
Cambridge, MA 02142
United States
617-253-8909 (Phone)
617-253-1330 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

Yusuke Narita (Contact Author)

Yale University - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Parag A. Pathak

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
E52-391
Cambridge, MA 02142
United States

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