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Semiparametric Inference for Regression-Discontinuity Designs

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  • Weiwei Jiang
  • Rong J. B. Zhu

Abstract

Treatment effects in regression discontinuity designs (RDDs) are often estimated using local regression methods. \cite{Hahn:01} demonstrated that the identification of the average treatment effect at the cutoff in RDDs relies on the unconfoundedness assumption and that, without this assumption, only the local average treatment effect at the cutoff can be identified. In this paper, we propose a semiparametric framework tailored for identifying the average treatment effect in RDDs, eliminating the need for the unconfoundedness assumption. Our approach globally conceptualizes the identification as a partially linear modeling problem, with the coefficient of a specified polynomial function of propensity score in the linear component capturing the average treatment effect. This identification result underpins our semiparametric inference for RDDs, employing the $P$-spline method to approximate the nonparametric function and establishing a procedure for conducting inference within this framework. Through theoretical analysis, we demonstrate that our global approach achieves a faster convergence rate compared to the local method. Monte Carlo simulations further confirm that the proposed method consistently outperforms alternatives across various scenarios. Furthermore, applications to real-world datasets illustrate that our global approach can provide more reliable inference for practical problems.

Suggested Citation

  • Weiwei Jiang & Rong J. B. Zhu, 2024. "Semiparametric Inference for Regression-Discontinuity Designs," Papers 2403.05803, arXiv.org, revised Dec 2024.
  • Handle: RePEc:arx:papers:2403.05803
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    References listed on IDEAS

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    1. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
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    3. Matias D. Cattaneo & Nicolas Idrobo & Rocio Titiunik, 2019. "A Practical Introduction to Regression Discontinuity Designs: Foundations," Papers 1911.09511, arXiv.org.
    4. 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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