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

Author

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  • Ivan A. Canay

    (Institute for Fiscal Studies and Northwestern University)

  • Vishal Kamat

    (Institute for Fiscal Studies and Toulouse School of Economics)

Abstract

In the regression discontinuity design (RDD), it is common practice to asses the credibility of the design by testing whether the means of baseline covariates do not change at the cutoff (or threshold) of the running variable. This practice is partly motivated by the stronger im-plication derived by Lee (2008), who showed that under certain conditions the distribution of baseline covariates in the RDD must be continuous at the cutoff. 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 effective observations local to the cutoff is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cutoff as n ? 8, our framework keeps the number q of observations local to the cutoff ?xed as n ? 8. The new test is easy to implement, asymptotically valid under weak conditions, exhibits ?nite 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 ?nd that the new test controls size remarkably well across designs. We then use our test to evaluate the plausibility of the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.

Suggested Citation

  • Ivan A. Canay & Vishal Kamat, 2017. "Approximate permutation tests and induced order statistics in the regression discontinuity design," CeMMAP working papers CWP21/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:21/17
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    References listed on IDEAS

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    Cited by:

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    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. Matias D. Cattaneo & Rocio Titiunik & Gonzalo Vazquez-Bare, 2019. "The Regression Discontinuity Design," Papers 1906.04242, arXiv.org, revised Jun 2020.
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    13. 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).
    14. 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).
    15. 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.
    16. Yang Lixiong, 2019. "Regression discontinuity designs with unknown state-dependent discontinuity points: estimation and testing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(2), pages 1-18, April.
    17. Purevdorj Tuvaandorj, 2021. "Robust Permutation Tests in Linear Instrumental Variables Regression," Papers 2111.13774, arXiv.org.
    18. 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.
    19. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    20. Bonilla-Mejía, Leonardo & Higuera-Mendieta, Iván, 2019. "Protected Areas under Weak Institutions: Evidence from Colombia," World Development, Elsevier, vol. 122(C), pages 585-596.
    21. Yong Cai & Ivan A. Canay & Deborah Kim & Azeem M. Shaikh, 2021. "On the implementation of Approximate Randomization Tests in Linear Models with a Small Number of Clusters," Papers 2102.09058, arXiv.org, revised Mar 2022.

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    More about this item

    Keywords

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

    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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