Randomized saturation designs are two-stage experiments: they first randomly assign treatment probabilities over the clusters and then randomly assign the treatment to the units within the clusters. The existing literature on randomized saturation designs focuses on estimating within-cluster spillover effects by assuming away between-cluster spillover effects. However, the units may interact across clusters in many practical randomized saturation designs. A leading example is that some units are geographically close to each other, so spillover effects arise across clusters. Based on the potential outcomes framework, we formulate the causal inference problem of estimating within-cluster and between-cluster spillover effects in randomized saturation designs. We clarify the causal estimands and establish the statistical theory for estimation and inference. We also apply our method to analyze a recent randomized saturation design of cash transfer on household expenditure in Kenya.

翻译：随机化饱和度设计是一种两阶段实验：首先随机分配各簇的处理概率，然后在簇内随机分配单元的处理状态。现有关于随机化饱和度设计的文献通过假设不存在簇间溢出效应对簇内溢出效应进行估计。然而，在实际的许多随机化饱和度设计中，单元之间可能跨簇交互。一个典型例子是某些单元在地理上相互邻近，因此溢出效应会跨簇产生。基于潜在结果框架，我们构建了随机化饱和度设计中估计簇内和簇间溢出效应的因果推断问题。我们阐明了因果估计量，并建立了估计与推断的统计理论。此外，我们将该方法应用于分析肯尼亚现金转移对家庭支出的一项近期随机化饱和度设计。