Estimating within-cluster and between-cluster spillover effects in randomized saturation designs

2026-03-19

AI Summary

This study addresses a critical limitation in existing randomized saturation designs, which typically ignore inter-cluster spillover effects and thus fail to capture the cross-cluster interference commonly observed in real-world settings. Building upon the potential outcomes framework, this work proposes the first systematic approach to simultaneously model both intra- and inter-cluster spillovers within a randomized saturation design, deriving corresponding causal estimands and establishing rigorous statistical inference theory. By moving beyond the conventional focus on within-cluster effects alone, the method substantially enhances the realism and accuracy of causal inference. Applied to data from a cash transfer experiment in Kenya, the approach successfully identifies and quantifies dual spillover effects on household expenditures, demonstrating its practical relevance and improved inferential performance.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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.

Problem

• spillover effects
• randomized saturation designs
• within-cluster
• between-cluster
• causal inference

Innovation

• randomized saturation design
• spillover effects
• between-cluster interference
• causal inference
• potential outcomes framework