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.

翻译：断点回归设计（RDDs）中的处理效应通常采用局部回归方法进行估计。\cite{Hahn:01} 的研究表明，RDDs中在断点处平均处理效应的识别依赖于无混淆假设；若无此假设，则仅能识别断点处的局部平均处理效应。本文提出一个专为识别RDDs中平均处理效应而设计的半参数框架，无需依赖无混淆假设。我们的方法将识别问题全局地概念化为一个部分线性建模问题，其中线性部分中倾向得分特定多项式函数的系数捕捉了平均处理效应。这一识别结果为我们的RDDs半参数推断提供了基础，我们采用$P$-样条方法逼近非参数函数，并在此框架内建立了进行推断的流程。通过理论分析，我们证明相较于局部方法，我们的全局方法能达到更快的收敛速度。蒙特卡洛模拟进一步证实，所提出的方法在多种情境下均持续优于其他替代方法。此外，在实际数据集上的应用表明，我们的全局方法能为现实问题提供更可靠的推断。