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Distributional Tests for Regression Discontinuity: Theory and Empirical Examples


  • Shu Shen

    (University of California, Davis)

  • Xiaohan Zhang

    (California State University, Los Angeles)


This paper proposes consistent testing methods for examining the effect of a policy treatment on the whole distribution of a response outcome within the setting of a regression discontinuity design. These methods are particularly useful when a policy is expected to produce treatment effects that are heterogeneous along some unobserved characteristics. The test statistics are Kolmogorov-Smirnov-type and are asymptotically distribution free when the data are i.i.d. The proposed tests are applied to three seminal RD studies (Pop-Eleches & Urquiola, 2013; Abdulkadiroglu, Angrist, & Pathak, 2014; and Battistin et al., 2009).

Suggested Citation

  • Shu Shen & Xiaohan Zhang, 2016. "Distributional Tests for Regression Discontinuity: Theory and Empirical Examples," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 685-700, October.
  • Handle: RePEc:tpr:restat:v:98:y:2016:i:4:p:685-700

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    Cited by:

    1. Ivan A Canay & Vishal Kamat, 2018. "Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design," Review of Economic Studies, Oxford University Press, vol. 85(3), pages 1577-1608.
    2. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    3. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    4. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    5. Federico A. Bugni & Ivan A. Canay, 2018. "Testing Continuity of a Density via g-order statistics in the Regression Discontinuity Design," Papers 1803.07951,, revised Feb 2020.
    6. Caro, Juan Carlos, 2020. "Parental investments, socioemotional development and nutritional health in Chile," MPRA Paper 98867, University Library of Munich, Germany.
    7. Caro, Juan Carlos, 2020. "Child development and obesity prevention: evidence from the Chilean School Meals Program," MPRA Paper 98865, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models


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