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Simultaneous selection of optimal bandwidths for the sharp regression discontinuity estimator

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  • Yoichi Arai
  • Hidehiko Ichimura

Abstract

A new bandwidth selection rule that uses different bandwidths for the local linear regression estimators on the left and the right of the cut-off point is proposed for the sharp regression discontinuity estimator of the mean program impact at the cut-off point. The asymptotic mean squared error of the estimator using the proposed bandwidth selection rule is shown to be smaller than other bandwidth selection rules proposed in the literature. An extensive simulation study shows that the proposed method's performances for the samples sizes 500, 2000, and 5000 closely match the theoretical predictions.Supplementary material for this paper is available here.

Suggested Citation

  • Yoichi Arai & Hidehiko Ichimura, 2015. "Simultaneous selection of optimal bandwidths for the sharp regression discontinuity estimator," CeMMAP working papers 42/15, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:42/15
    DOI: 10.1920/wp.cem.2015.4215
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    5. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell & Rocío Titiunik, 2019. "Regression Discontinuity Designs Using Covariates," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 442-451, July.
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    8. YANAGI, Takahide & 柳, 貴英, 2015. "Regression Discontinuity Designs with Nonclassical Measurement Error," Discussion Papers 2015-09, Graduate School of Economics, Hitotsubashi University.
    9. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell & Filippo Palomba & Rocio Titiunik, 2025. "rdhte: Conditional Average Treatment Effects in RD Designs," Papers 2507.01128, arXiv.org.
    10. Arai, Yoichi & Ichimura, Hidehiko, 2016. "Optimal bandwidth selection for the fuzzy regression discontinuity estimator," Economics Letters, Elsevier, vol. 141(C), pages 103-106.
    11. Gary Cornwall & Beau Sauley, 2021. "Indirect effects and causal inference: reconsidering regression discontinuity," Journal of Spatial Econometrics, Springer, vol. 2(1), pages 1-28, December.
    12. Masayuki Sawada & Takuya Ishihara & Daisuke Kurisu & Yasumasa Matsuda, 2024. "Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs," Papers 2402.08941, arXiv.org, revised Jan 2026.
    13. Jun Ma & Zhengfei Yu, 2020. "Empirical Likelihood Covariate Adjustment for Regression Discontinuity Designs," Papers 2008.09263, arXiv.org, revised May 2024.
    14. Takahide Yanagi, 2014. "The Effect of Measurement Error in the Sharp Regression Discontinuity Design," KIER Working Papers 910, Kyoto University, Institute of Economic Research.
    15. Shi, Xunpeng & Tian, Binbin & Yang, Longjian & Yu, Jian & Zhou, Siyang, 2023. "How do regulatory environmental policies perform? A case study of China's Top-10,000 enterprises energy-saving program," Renewable and Sustainable Energy Reviews, Elsevier, vol. 187(C).
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    17. Yuta Okamoto & Yuuki Ozaki, 2024. "On Extrapolation of Treatment Effects in Multiple-Cutoff Regression Discontinuity Designs," Papers 2412.04265, arXiv.org, revised Sep 2025.
    18. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    19. Yoici Arai & Taisuke Otsu & Myung Hwan Seo, 2019. "Causal inference on regression discontinuity designs by high-dimensional methods," STICERD - Econometrics Paper Series 601, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    20. Mauricio Villamizar‐Villegas & Freddy A. Pinzon‐Puerto & Maria Alejandra Ruiz‐Sanchez, 2022. "A comprehensive history of regression discontinuity designs: An empirical survey of the last 60 years," Journal of Economic Surveys, Wiley Blackwell, vol. 36(4), pages 1130-1178, September.
    21. Yang Lixiong, 2019. "Regression discontinuity designs with unknown state-dependent discontinuity points: estimation and testing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(2), pages 1-18, April.

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