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Breaking Ties: Regression Discontinuity Design Meets Market Design

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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.

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  • Atila Abdulkadiroglu & Joshua D. Angrist & Yusuke Narita & Parag A. Pathak, 2019. "Breaking Ties: Regression Discontinuity Design Meets Market Design," Cowles Foundation Discussion Papers 2170, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2170
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    5. Atı̇la Abdulkadı̇roğlu & Joshua D. Angrist & Yusuke Narita & Parag Pathak, 2022. "Breaking Ties: Regression Discontinuity Design Meets Market Design," Econometrica, Econometric Society, vol. 90(1), pages 117-151, January.
    6. TANAKA Mari & NARITA Yusuke & MORIGUCHI Chiaki, 2020. "Meritocracy and Its Discontent: Long-run Effects of Repeated School Admission Reforms," Discussion papers 20002, Research Institute of Economy, Trade and Industry (RIETI).
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    8. Benoit Decerf & Francois Woitrin, 2022. "Criteria to compare mechanisms that partially satisfy a property: an axiomatic study," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(4), pages 835-862, May.
    9. Elias Bouacida & Renaud Foucart, 2022. "Rituals of Reason," Working Papers 344119591, Lancaster University Management School, Economics Department.
    10. Huttunen, Kristiina & Pekkarinen, Tuomas & Uusitalo, Roope & Virtanen, Hanna, 2023. "Lost boys? Secondary education and crime," Journal of Public Economics, Elsevier, vol. 218(C).
    11. Yusuke Narita, 2020. "A Theory of Quasi-Experimental Evaluation of School Quality," Working Papers 2020-085, Human Capital and Economic Opportunity Working Group.
    12. Atila Abdulkadiroglu & Tommy Andersson, 2022. "School Choice," NBER Working Papers 29822, National Bureau of Economic Research, Inc.
    13. Florian Gunsilius & David Van Dijcke, 2023. "Free Discontinuity Regression: With an Application to the Economic Effects of Internet Shutdowns," Papers 2309.14630, arXiv.org, revised Jan 2024.
    14. Aue, Robert & Bach, Maximilian & Heigle, Julia & Klein, Thilo & Pfeiffer, Friedhelm & Zapp, Kristina, 2020. "The implication of school admission rules for segregation and educational inequality: Research report," ZEW Expertises, ZEW - Leibniz Centre for European Economic Research, number 223254.
    15. Parag A. Pathak & Tayfun Sönmez & M. Utku Ünver & M. Bumin Yenmez, 2020. "Fair Allocation of Vaccines, Ventilators and Antiviral Treatments: Leaving No Ethical Value Behind in Health Care Rationing," Boston College Working Papers in Economics 1015, Boston College Department of Economics.
    16. Marco Ovidi, 2021. "Parents know better: primary school choice and student achievement in London," Working Papers 919, Queen Mary University of London, School of Economics and Finance.
    17. Ollikainen, Jani-Petteri & Pekkarinen, Tuomas & Uusitalo, Roope & Virtanen, Hanna, 2022. "Effect of Secondary Education on Cognitive and Non-cognitive Skills," IZA Discussion Papers 15318, Institute of Labor Economics (IZA).
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    20. Marco Ovidi, 2022. "Parents Know Better: Sorting on Match Effects in Primary School," DISCE - Working Papers del Dipartimento di Economia e Finanza def121, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).
    21. Yusuke Narita, 2021. "A Theory of Quasi-Experimental Evaluation of School Quality," Management Science, INFORMS, vol. 67(8), pages 4982-5010, August.
    22. Federico Crippa, 2024. "Manipulation Test for Multidimensional RDD," Papers 2402.10836, arXiv.org.
    23. Ahmet Alkan & Sinan Sarpça & Sinan Sarpca, 2023. "Effects of High-Achieving Peers: Findings from a National High School Assignment System," CESifo Working Paper Series 10794, CESifo.

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    More about this item

    Keywords

    Causal Inference; Natural Experiment; Local Propensity Score; Instrumental Variables; Unified Enrollment; School Report Card; School Value Added;
    All these keywords.

    JEL classification:

    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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