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Testing Continuity of a Density via g-order statistics in the Regression Discontinuity Design

Author

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  • Federico A. Bugni
  • Ivan A. Canay
Abstract
In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing the continuity of the density of the running variable at the cut-off, e.g., McCrary (2008). In this paper we propose an approximate sign test for continuity of a density at a point based on the so-called g-order statistics, and study its properties under two complementary asymptotic frameworks. In the first asymptotic framework, the number q of observations local to the cut-off is fixed as the sample size n diverges to infinity, while in the second framework q diverges to infinity slowly as n diverges to infinity. Under both of these frameworks, we show that the test we propose is asymptotically valid in the sense that it has limiting rejection probability under the null hypothesis not exceeding the nominal level. More importantly, the test is easy to implement, asymptotically valid under weaker conditions than those used by competing methods, and exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity. In a simulation study, we find that the approximate sign test provides good control of the rejection probability under the null hypothesis while remaining competitive under the alternative hypothesis. We finally apply our test to the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.

Suggested Citation

  • Federico A. Bugni & Ivan A. Canay, 2018. "Testing Continuity of a Density via g-order statistics in the Regression Discontinuity Design," Papers 1803.07951, arXiv.org, revised Feb 2020.
    • Handle: RePEc:arx:papers:1803.07951
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    References listed on IDEAS

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    2. Takuya Ishihara & Masayuki Sawada, 2020. "Manipulation-Robust Regression Discontinuity Designs," Papers 2009.07551, arXiv.org, revised Sep 2024.
    3. Yoichi Arai & Yu‐Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2022. "Testing identifying assumptions in fuzzy regression discontinuity designs," Quantitative Economics, Econometric Society, vol. 13(1), pages 1-28, January.
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    7. Leopoldo Fergusson & Arturo Harker & Carlos Molina & Juan Camilo Yamín, 2023. "Political incentives and corruption evidence from ghost students," Documentos CEDE 20732, Universidad de los Andes, Facultad de Economía, CEDE.
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    9. Koki Fusejima & Takuya Ishihara & Masayuki Sawada, 2022. "A unified diagnostic test for regression discontinuity designs," Papers 2205.04345, arXiv.org, revised Jul 2024.
    10. 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).
    11. Hsu, Yu-Chin & Shiu, Ji-Liang & Wan, Yuanyuan, 2024. "Testing identification conditions of LATE in fuzzy regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 241(1).
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    13. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
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    16. Somdeep Chatterjee & Pushkar Maitra & Manhar Manchanda, 2024. "The Relevant Third: Threat of Coalition and Economic Development," Monash Economics Working Papers 2024-13, Monash University, Department of Economics.
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    19. Federico Crippa, 2024. "Manipulation Test for Multidimensional RDD," Papers 2402.10836, arXiv.org, revised Jun 2024.

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    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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