Rate-Optimal Cluster-Randomized Designs for Spatial Interference

TL;DR

This paper develops rate-optimal cluster-randomized experimental designs for spatial interference, providing estimators with near-optimal convergence rates and practical clustering methods for implementation.

Contribution

It introduces a class of spatially-aware cluster-randomized designs with theoretical guarantees for estimating the global average treatment effect under interference.

Findings

Estimator achieves near-optimal convergence rates.

Estimates are asymptotically normal.

Practical clustering algorithms facilitate implementation.

Abstract

We consider a potential outcomes model in which interference may be present between any two units but the extent of interference diminishes with spatial distance. The causal estimand is the global average treatment effect, which compares outcomes under the counterfactuals that all or no units are treated. We study a class of designs in which space is partitioned into clusters that are randomized into treatment and control. For each design, we estimate the treatment effect using a Horvitz-Thompson estimator that compares the average outcomes of units with all or no neighbors treated, where the neighborhood radius is of the same order as the cluster size dictated by the design. We derive the estimator's rate of convergence as a function of the design and degree of interference and use this to obtain estimator-design pairs that achieve near-optimal rates of convergence under relatively minimal assumptions on interference. We prove that the estimators are asymptotically normal and provide a variance estimator. For practical implementation of the designs, we suggest partitioning space using clustering algorithms.