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Approximate permutation tests and induced order statistics in the regression discontinuity design


  • Ivan A. Canay

    (Institute for Fiscal Studies and Northwestern University)

  • Vishal Kamat

    (Institute for Fiscal Studies and Toulouse School of Economics)


In the regression discontinuity design, it is common practice to asses the credibility of the design by testing whether the means of baseline covariates do not change at the cuto ff (or threshold) of the running variable. This practice is partly motivated by the stronger implication derived by Lee (2008), who showed that under certain conditions the distribution of baseline covariates in the RDD must be continuous at the cuto ff. We propose a permutation test based on the so-called induced ordered statistics for the null hypothesis of continuity of the distribution of baseline covariates at the cutoff ; and introduce a novel asymptotic framework to analyze its properties. The asymptotic framework is intended to approximate a small sample phenomenon: even though the total number n of observations may be large, the number of eff ective observations local to the cuto ff is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cuto ff as n ? 8 , our framework keeps the number q of observations local to the cutoff fixed as n ? 8. The new test is easy to implement, asymptotically valid under weak conditions, exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity, and has favorable power properties relative to tests based on means. In a simulation study, we fi nd that the new test controls size remarkably well across designs. We then use our test to evaluate the validity of the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.

Suggested Citation

  • Ivan A. Canay & Vishal Kamat, 2016. "Approximate permutation tests and induced order statistics in the regression discontinuity design," CeMMAP working papers CWP33/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:33/16

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    References listed on IDEAS

    1. Frandsen, Brigham R. & Frölich, Markus & Melly, Blaise, 2012. "Quantile treatment effects in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 168(2), pages 382-395.
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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. Yoichi Arai & Yu-Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2018. "Testing identifying assumptions in fuzzy regression discontinuity designs," CeMMAP working papers CWP50/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Yingying DONG & Ying-Ying LEE & Michael GOU, 2019. "Regression Discontinuity Designs with a Continuous Treatment," Discussion papers 19058, Research Institute of Economy, Trade and Industry (RIETI).
    4. Chen, Heng & Huynh, Kim P. & Shy, Oz, 2019. "Cash versus card: Payment discontinuities and the burden of holding coins," Journal of Banking & Finance, Elsevier, vol. 99(C), pages 192-201.
    5. Zhang, Yali & Li, Wenqi & Wu, Feng, 2020. "Does energy transition improve air quality? Evidence derived from China’s Winter Clean Heating Pilot (WCHP) project," Energy, Elsevier, vol. 206(C).
    6. 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.
    7. Fernando Aragón & Ricardo Pique, 2020. "Better the devil you know? Reelected politicians and policy outcomes under no term limits," Public Choice, Springer, vol. 182(1), pages 1-16, January.
    8. Adam C. Sales & Ben B. Hansen, 2020. "Limitless Regression Discontinuity," Journal of Educational and Behavioral Statistics, , vol. 45(2), pages 143-174, April.
    9. Chen, Heng & Fan, Yanqin, 2019. "Identification and wavelet estimation of weighted ATE under discontinuous and kink incentive assignment mechanisms," Journal of Econometrics, Elsevier, vol. 212(2), pages 476-502.
    10. Makarin, Alexey & Piqué, Ricardo & Aragón, Fernando, 2020. "National or sub-national parties: Does party geographic scope matter?," Journal of Development Economics, Elsevier, vol. 146(C).
    11. Giuntella, Osea & Mazzonna, Fabrizio, 2019. "Sunset time and the economic effects of social jetlag: evidence from US time zone borders," Journal of Health Economics, Elsevier, vol. 65(C), pages 210-226.
    12. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    13. Bonilla-Mejía, Leonardo & Higuera-Mendieta, Iván, 2019. "Protected Areas under Weak Institutions: Evidence from Colombia," World Development, Elsevier, vol. 122(C), pages 585-596.

    More about this item


    Regression discontinuity design; permutation tests; randomization tests; induced ordered statistics; rank tests.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General


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