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Breaking Ties: Regression Discontinuity Design Meets Market Design

Author

Listed:
  • Atila Abdulkadiroglu

    (Duke University)

  • Joshua Angrist

    (Massachusetts Institute of Technology)

  • Yusuke Narita

    (Massachusetts Institute of Technology)

  • Parag Pathak

    (Massachusetts Institute of Technology)

Abstract

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.

Suggested Citation

  • Atila Abdulkadiroglu & Joshua Angrist & Yusuke Narita & Parag Pathak, 2019. "Breaking Ties: Regression Discontinuity Design Meets Market Design," Working Papers 2019-024, Human Capital and Economic Opportunity Working Group.
  • Handle: RePEc:hka:wpaper:2019-024
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    Cited by:

    1. Elias Bouacida & Renaud Foucart, 2020. "The acceptability of lotteries in allocation problems," Working Papers 301646245, Lancaster University Management School, Economics Department.
    2. 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.
    3. Kirill Borusyak & Peter Hull, 2020. "Non-Random Exposure to Exogenous Shocks: Theory and Applications," NBER Working Papers 27845, National Bureau of Economic Research, Inc.
    4. 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).
    5. 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.
    6. Elias Bouacida & Renaud Foucart, 2022. "Rituals of Reason," Working Papers 344119591, Lancaster University Management School, Economics Department.
    7. Yusuke Narita, 2020. "A Theory of Quasi-Experimental Evaluation of School Quality," Working Papers 2020-085, Human Capital and Economic Opportunity Working Group.
    8. Atila Abdulkadiroglu & Tommy Andersson, 2022. "School Choice," NBER Working Papers 29822, National Bureau of Economic Research, Inc.
    9. 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, March.
    10. 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.
    11. Ollikainen, Jani-Petteri & Pekkarinen (decd), 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).
    12. Marin Drlje, 2020. "Identification of School Admission Effects Using Propensity Scores Based on a Matching Market Structure," CERGE-EI Working Papers wp658, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    13. Joshua D. Angrist & Parag A. Pathak & Román Andrés Zárate, 2019. "Choice and Consequence: Assessing Mismatch at Chicago Exam Schools," NBER Working Papers 26137, National Bureau of Economic Research, Inc.
    14. 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).

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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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