Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and derive high-level conditions under which the standard local linear RD estimator is asymptotically normal. We verify that our high-level assumptions hold across a wide range of empirical designs, including settings of growing cluster sizes. We further show that clustered standard errors that are currently used in practice can be either inconsistent or overly conservative in finite samples. To address these issues, we propose a novel nearest-neighbor-type variance estimator and illustrate its properties in a diverse set of empirical applications.

翻译：聚类抽样在实证断点回归设计中普遍存在，但该问题在理论文献中尚未得到充分关注。本文针对此类场景提出一个通用的模型化分析框架，并推导了标准局部线性断点回归估计量渐近正态性的高阶条件。我们验证了所提出的高阶假设在包括簇规模递增情形在内的广泛实证设计中成立。进一步研究表明，当前实践中使用的聚类稳健标准误在有限样本中可能不一致或过于保守。为解决这些问题，我们提出一种新型最近邻型方差估计量，并通过多种实证应用场景阐明其性质。