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Main Authors: Lu, Sizhu, Shi, Lei, Ding, Peng
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.19573
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author Lu, Sizhu
Shi, Lei
Ding, Peng
author_facet Lu, Sizhu
Shi, Lei
Ding, Peng
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_19573
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Estimating within-cluster and between-cluster spillover effects in randomized saturation designs
Lu, Sizhu
Shi, Lei
Ding, Peng
Methodology
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.
title Estimating within-cluster and between-cluster spillover effects in randomized saturation designs
topic Methodology
url https://arxiv.org/abs/2603.19573