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Distributional Tests for Regression Discontinuity: Theory and Empirical Examples

Author

Listed:
  • Shu Shen

    (University of California, Davis)

  • Xiaohan Zhang

    (California State University, Los Angeles)

Abstract

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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    Citations

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    Cited by:

    1. Silvia H. Barcellos & Leandro S. Carvalho & Patrick Turley, 2019. "Distributional Effects of Education on Health," NBER Working Papers 25898, National Bureau of Economic Research, Inc.
    2. Bugni, Federico A. & Canay, Ivan A., 2021. "Testing continuity of a density via g-order statistics in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 221(1), pages 138-159.
    3. Ivan A Canay & Vishal Kamat, 2018. "Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1577-1608.
    4. 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.
    5. Kemper, Johanna & Renold, Ursula, 2024. "Evaluating the impact of general versus vocational education on labor market outcomes in Egypt by means of a regression discontinuity design," Journal of Development Economics, Elsevier, vol. 166(C).
    6. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    7. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    8. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    9. Federico A. Bugni & Ivan A. Canay & Deborah Kim, 2025. "Testing Conditional Stochastic Dominance at Target Points," Papers 2503.14747, arXiv.org, revised Apr 2025.
    10. Maike Hohberg & Peter Pütz & Thomas Kneib, 2020. "Treatment effects beyond the mean using distributional regression: Methods and guidance," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-29, February.
    11. Yixiao Sun & Haitian Xie & Yuhang Zhang, 2025. "Difference-in-Differences Meets Synthetic Control: Doubly Robust Identification and Estimation," Papers 2503.11375, arXiv.org.
    12. Caro, Juan Carlos, 2020. "Parental investments, socioemotional development and nutritional health in Chile," MPRA Paper 98867, University Library of Munich, Germany.
    13. Li, Yanan & Sunder, Naveen, 2024. "Distributional effects of education on mental health," Labour Economics, Elsevier, vol. 88(C).
    14. Caro, Juan Carlos, 2020. "Child development and obesity prevention: evidence from the Chilean School Meals Program," MPRA Paper 98865, University Library of Munich, Germany.
    15. Xie, Haitian, 2024. "Nonlinear and nonseparable structural functions in regression discontinuity designs with a continuous treatment," Journal of Econometrics, Elsevier, vol. 242(1).
    16. Yu‐Chin Hsu & Shu Shen, 2021. "Testing monotonicity of conditional treatment effects under regression discontinuity designs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(3), pages 346-366, April.

    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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