We extend the continuity-based framework to Regression Discontinuity Designs (RDDs) to identify and estimate causal effects in the presence of interference when units are connected through a network. In this setting, assignment to an "effective treatment," which comprises the individual treatment and a summary of the treatment of interfering units (e.g., friends, classmates), is determined by the unit's score and the scores of other interfering units, leading to a multiscore RDD with potentially complex, multidimensional boundaries. We characterize these boundaries and derive generalized continuity assumptions to identify the proposed causal estimands, i.e., point and boundary causal effects. Additionally, we develop a distance-based nonparametric estimator, derive its asymptotic properties under restrictions on the network degree distribution, and introduce a novel variance estimator that accounts for network correlation. Finally, we apply our methodology to the PROGRESA/Oportunidades dataset to estimate the direct and indirect effects of receiving cash transfers on children's school attendance.

翻译：本文将连续性框架扩展至断点回归设计（RDD），以在单元通过网络相互连接的干扰存在情况下识别和估计因果效应。在此设定中，“有效处理”的分配——包括个体处理及干扰单元（如朋友、同学）处理的汇总——由单元自身分数及其他干扰单元的分数共同决定，从而形成一个具有潜在复杂多维边界的多分数断点回归设计。我们刻画了这些边界特征，并推导出广义连续性假设以识别所提出的因果估计量，即点因果效应与边界因果效应。此外，我们开发了一种基于距离的非参数估计量，在网络度分布的限制条件下推导了其渐近性质，并引入了一种考虑网络相关性的新型方差估计量。最后，我们将该方法应用于PROGRESA/Oportunidades数据集，以估计接受现金转移对儿童入学率的直接与间接效应。