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Breaking Ties: Regression Discontinuity Design Meets Market Design

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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 e"ects 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 quanti"es 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.

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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 2170R Publication Status:, Cowles Foundation for Research in Economics, Yale University, revised Dec 2020.
  • Handle: RePEc:cwl:cwldpp:2170r
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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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