Numerous studies use regression discontinuity design (RDD) for panel data by assuming that the treatment effects are homogeneous across all individuals/groups and pooling the data together. It is unclear how to test for the significance of treatment effects when the treatments vary across individuals/groups and the error terms may exhibit complicated dependence structures. This paper examines the estimation and inference of multiple treatment effects when the errors are not independent and identically distributed, and the treatment effects vary across individuals/groups. We derive a simple analytical expression for approximating the variance-covariance structure of the treatment effect estimators under general dependence conditions and propose two test statistics, one is to test for the overall significance of the treatment effect and the other for the homogeneity of the treatment effects. We find that in the Gaussian approximations to the test statistics, the dependence structures in the data can be safely ignored due to the localized nature of the statistics. This has the important implication that the simulated critical values can be easily obtained. Simulations demonstrate our tests have superb size control and reasonable power performance in finite samples regardless of the presence of strong cross-section dependence or/and weak serial dependence in the data. We apply our tests to two datasets and find significant overall treatment effects in each case.

翻译：大量研究通过假设处理效应在个体/群体间具有同质性并合并数据，采用断点回归设计（RDD）分析面板数据。当处理效应因个体/群体而异且误差项可能呈现复杂依赖性结构时，如何检验处理效应的显著性尚不明确。本文考察了误差项非独立同分布且处理效应在个体/群体间存在异质性情况下的多重处理效应估计与推断问题。我们在一般依赖条件下推导了处理效应估计量方差-协方差结构的简单解析近似表达式，并提出了两种检验统计量：一种用于检验处理效应的整体显著性，另一种用于检验处理效应的同质性。研究发现，在检验统计量的高斯逼近中，由于统计量的局部化特性，数据中的依赖结构可被安全忽略，这一重要性质使得模拟临界值易于获取。仿真结果表明，无论数据中是否存在强截面依赖或弱序列依赖，本文提出的检验在有限样本中均具有优异的尺寸控制能力和合理的势性能。我们将所提检验应用于两个数据集，发现每种情形下均存在显著的整体处理效应。