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

TL;DR

This paper develops methods to estimate both within-cluster and between-cluster spillover effects in randomized saturation designs, addressing cross-cluster interactions often overlooked in prior studies.

Contribution

It formulates the causal inference problem for spillover effects in these designs and provides new estimation and inference techniques considering cross-cluster interactions.

Findings

Method successfully applied to Kenyan cash transfer data.

Estimates reveal significant between-cluster spillover effects.

Theoretical framework clarifies causal estimands for complex designs.

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.