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Joint diagnostic test of regression discontinuity designs: multiple testing problem

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  • Koki Fusejima
  • Takuya Ishihara
  • Masayuki Sawada

Abstract

Current diagnostic tests for regression discontinuity (RD) design face a multiple testing problem. We find a massive over-rejection of the identifying restriction among empirical RD studies published in top-five economics journals. Each test achieves a nominal size of 5%; however, the median number of tests per study is 12. Consequently, more than one-third of studies reject at least one of these tests and their diagnostic procedures are invalid for justifying the identifying assumption. We offer a joint testing procedure to resolve the multiple testing problem. Our procedure is based on a new joint asymptotic normality of local linear estimates and local polynomial density estimates. In simulation studies, our joint testing procedures outperform the Bonferroni correction. We implement the procedure as an R package, rdtest, with two empirical examples in its vignettes.

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  • Koki Fusejima & Takuya Ishihara & Masayuki Sawada, 2022. "Joint diagnostic test of regression discontinuity designs: multiple testing problem," Papers 2205.04345, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2205.04345
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    References listed on IDEAS

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    1. 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.
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    6. McCrary, Justin, 2008. "Manipulation of the running variable in the regression discontinuity design: A density test," Journal of Econometrics, Elsevier, vol. 142(2), pages 698-714, February.
    7. Cattaneo, Matias D & Jansson, Michael & Ma, Xinwei, 2020. "Simple Local Polynomial Density Estimators," University of California at San Diego, Economics Working Paper Series qt9vt997qn, Department of Economics, UC San Diego.
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