Estimation and inference in regression discontinuity designs with asymmetric kernels

We study the behaviour of the Wald estimator of causal effects in regression discontinuity design when local linear regression (LLR) methods are combined with an asymmetric gamma kernel. We show that the resulting statistic is no more complex to implement than existing methods, remains consistent at the usual non-parametric rate, and maintains an asymptotic normal distribution but, crucially, has bias and variance that do not depend on kernel-related constants. As a result, the new estimator is more efficient and yields more reliable inference. A limited Monte Carlo experiment is used to illustrate the efficiency gains. As a by product of the main discussion, we extend previous published work by establishing the asymptotic normality of the LLR estimator with a gamma kernel. Finally, the new method is used in a substantive application.

本研究探讨了回归断点设计（Regression Discontinuity Design）中，当局部线性回归（Local Linear Regression, LLR）与不对称伽马核（asymmetric gamma kernel）结合时，因果效应的Wald估计量（Wald estimator）的表现。研究表明，由此得到的统计量的实现复杂度不高于现有方法，仍能以常规非参数速率保持一致性，且渐近服从正态分布；尤为关键的是，其偏差与方差不依赖于与核函数相关的常数。因此，该新型估计量效率更高，可生成更可靠的统计推断。本研究通过有限蒙特卡洛（Monte Carlo）实验验证了该方法的效率提升效果。作为核心讨论的附带成果，本研究拓展了既往已发表的研究工作，证明了采用伽马核的局部线性回归估计量的渐近正态性。最后，本研究将该新型方法应用于一项实际实证案例中。