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A unified diagnostic test for regression discontinuity designs

Author

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  • Koki Fusejima
  • Takuya Ishihara
  • Masayuki Sawada

Abstract

Diagnostic tests for regression discontinuity design face a size-control problem. We document a massive over-rejection of the identifying restriction among empirical studies in the top five economics journals. At least one diagnostic test was rejected for 21 out of 60 studies, whereas less than 5% of the collected 799 tests rejected the null hypotheses. In other words, more than one-third of the studies rejected at least one of their diagnostic tests, whereas their underlying identifying restrictions appear valid. Multiple testing causes this problem because the median number of tests per study was as high as 12. Therefore, we offer unified tests to overcome the size-control problem. Our procedure is based on the new joint asymptotic normality of local polynomial mean and density estimates. In simulation studies, our unified tests outperformed the Bonferroni correction. We implement the procedure as an R package rdtest with two empirical examples in its vignettes.

Suggested Citation

  • Koki Fusejima & Takuya Ishihara & Masayuki Sawada, 2022. "A unified diagnostic test for regression discontinuity designs," Papers 2205.04345, arXiv.org, revised Jul 2024.
    • 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.
    2. Ivan A Canay & Vishal Kamat, 2018. "Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1577-1608.
    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. Matias D. Cattaneo & Michael Jansson & Xinwei Ma, 2020. "Simple Local Polynomial Density Estimators," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1449-1455, July.
    5. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    6. Takuya Ishihara & Masayuki Sawada, 2020. "Manipulation-Robust Regression Discontinuity Designs," Papers 2009.07551, arXiv.org, revised Sep 2024.
    7. 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.
    8. Taisuke Otsu & Ke-Li Xu & Yukitoshi Matsushita, 2013. "Estimation and Inference of Discontinuity in Density," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 507-524, October.
    9. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
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    Cited by:

    1. Rodríguez Arenas, Jorge Leonardo, 2024. "¿Ampliando oportunidades o desigualdades? Efectos de un crédito-beca en estudiantes de bajo desempeño académico," Documentos CEDE 21189, Universidad de los Andes, Facultad de Economía, CEDE.

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