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

Author

Listed:
  • Ivan A. Canay

    (Institute for Fiscal Studies and Northwestern University)

  • Vishal Kamat

    (Institute for Fiscal Studies and Northwestern University)

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

    as
    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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    Citations

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    Cited by:

    1. 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.
    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. repec:eee:jbfina:v:99:y:2019:i:c:p:192-201 is not listed on IDEAS
    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.

    More about this item

    Keywords

    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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