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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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    File URL: http://www.mitpressjournals.org/doi/pdf/10.1162/REST_a_00595
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    4. 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.
    5. Ivan A. Canay & Vishal Kamat, 2017. "Approximate permutation tests and induced order statistics in the regression discontinuity design," CeMMAP working papers 21/17, Institute for Fiscal Studies.
    6. 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.
    7. 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.
    8. Caro, Juan Carlos, 2020. "Parental investments, socioemotional development and nutritional health in Chile," MPRA Paper 98867, University Library of Munich, Germany.
    9. Caro, Juan Carlos, 2020. "Child development and obesity prevention: evidence from the Chilean School Meals Program," MPRA Paper 98865, University Library of Munich, Germany.
    10. 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.
    11. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    12. Ivan A. Canay & Vishal Kamat, 2016. "Approximate permutation tests and induced order statistics in the regression discontinuity design," CeMMAP working papers 33/16, Institute for Fiscal Studies.
    13. 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.
    14. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.

    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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