This study introduces a doubly robust (DR) estimator for regression discontinuity (RD) designs. In RD designs, treatment effects are estimated in a quasi-experimental setting where treatment assignment depends on whether a running variable surpasses a predefined cutoff. A common approach in RD estimation is to apply nonparametric regression methods, such as local linear regression. In such an approach, the validity relies heavily on the consistency of nonparametric estimators and is limited by the nonparametric convergence rate, thereby preventing $\sqrt{n}$-consistency. To address these issues, we propose the DR-RD estimator, which combines two distinct estimators for the conditional expected outcomes. If either of these estimators is consistent, the treatment effect estimator remains consistent. Furthermore, due to the debiasing effect, our proposed estimator achieves $\sqrt{n}$-consistency if both regression estimators satisfy certain mild conditions, which also simplifies statistical inference.

翻译：本研究提出了一种用于回归断点设计的双重稳健估计量。在回归断点设计中，处理效应是在一种准实验设定下进行估计的，其中处理分配取决于一个运行变量是否超过预定义的断点。回归断点估计中一种常见的方法是应用非参数回归方法，例如局部线性回归。在此类方法中，估计的有效性严重依赖于非参数估计量的一致性，并受到非参数收敛速度的限制，从而无法实现$\sqrt{n}$-一致性。为了解决这些问题，我们提出了DR-RD估计量，它结合了两种不同的条件期望结果估计量。只要这两种估计量中的任意一种是一致的，处理效应估计量就保持一致性。此外，由于去偏效应，如果两个回归估计量都满足某些温和条件，我们提出的估计量就能达到$\sqrt{n}$-一致性，这也简化了统计推断。