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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

This paper proposes an asymptotically valid permutation test for a testable implication of the identi?cation assumption in the regression discontinuity design (RDD). Here, by testable implication, we mean the requirement that the distribution of observed baseline covariates should not change discontinuously at the threshold of the so-called running variable. This contrasts to the common practice of testing the weaker implication of continuity of the means of the covariates at the threshold. When testing our null hypothesis using observations that are “close” to the threshold, the standard requirement for the ?nite sample validity of a permutation does not necessarily hold. We therefore propose an asymptotic framework where there is a ?xed number of closest observations to the threshold with the sample size going to in?nity, and propose a permutation test based on the so-called induced order statistics that controls the limiting rejection probability under the null hypothesis. In a simulation study, we ?nd that the new test controls size remarkably well in most designs. Finally, we 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, 2015. "Approximate permutation tests and induced order statistics in the regression discontinuity design," CeMMAP working papers CWP27/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:27/15
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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.
    2. Miguel Urquiola & Eric Verhoogen, 2009. "Class-Size Caps, Sorting, and the Regression-Discontinuity Design," American Economic Review, American Economic Association, vol. 99(1), pages 179-215, March.
    3. David S. Lee & Thomas Lemieux, 2010. "Regression Discontinuity Designs in Economics," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 281-355, June.
    4. Federico A. Bugni & Ivan A. Canay & Azeem M. Shaikh, 2015. "Inference under covariate-adaptive randomization," CeMMAP working papers CWP45/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    10. Gerard, Francois & Rokkanen, Miikka & Rothe, Christoph, 2016. "Bounds on Treatment Effects in Regression Discontinuity Designs under Manipulation of the Running Variable, with an Application to Unemployment Insurance in Brazil," CEPR Discussion Papers 11668, C.E.P.R. Discussion Papers.
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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

    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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