Design-Based Weighted Regression Estimators for Average and Conditional Spillover Effects

TL;DR

This paper introduces a unified framework and new estimators for analyzing spillover effects in social and physical interactions, accommodating complex interference structures with theoretical guarantees.

Contribution

It develops a comprehensive design-based weighted regression approach for both average and conditional spillover effects, including novel nonparametric estimators from different perspectives.

Findings

All three estimators for average effects are equivalent to the Hajek estimator.

Conditions are provided for the consistency of conditional spillover estimators.

Theoretical results include concentration inequalities, a CLT, and variance estimators in large-sample regimes.

Abstract

When individuals engage in social or physical interactions, a unit's outcome may depend on the treatments received by others. In such interference environments, we provide a unified framework characterizing a broad class of spillover estimands as weighted averages of unit-to-unit spillover effects, with estimand-specific weights. We then develop design-based weighted least squares (WLS) estimators for both average and conditional spillover effects. We introduce three nonparametric estimators under the dyadic, sender, and receiver perspectives, which distribute the estimand weights differently across the outcome vector, design matrix, and weight matrix. For the average-type estimands, we show that all three estimators are equivalent to the Hajek estimator. For conditional spillover effects, we establish conditions under which the estimands are consistent for the target conditional spillover effects. We further derive concentration inequalities, a central limit theorem, and conservative variance estimators in an asymptotic regime where both the number of clusters and cluster sizes grow.