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

2025-12-13

AI Summary

In interference settings—such as those involving social or physical interactions—individual outcomes depend on others’ treatment assignments, rendering standard causal inference methods invalid. This paper develops a unified framework that expresses various spillover effects (average and conditional) as weighted averages of unit-level spillovers. It introduces, for the first time, a nonparametric weighted least squares (WLS) estimator grounded in experimental design; under dyadic, sender-, and receiver-centric perspectives, this estimator is equivalent to the Hájek estimator. Theoretical contributions include: (i) proving the exact equivalence of three distinct average spillover estimators; (ii) establishing sufficient conditions for consistency of conditional spillover estimates; and (iii) deriving asymptotic normality and a computable conservative variance estimator that remains valid when both the number of clusters and cluster sizes grow jointly.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Security and Privacy: Large-scale security measurements

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.

Problem

• Estimating spillover effects in interference environments with weighted regression.
• Developing design-based estimators for average and conditional spillover effects.
• Analyzing asymptotic properties and variance estimation for spillover estimators.

Innovation

• Weighted least squares estimators for spillover effects
• Nonparametric estimators under dyadic, sender, receiver perspectives
• Asymptotic theory with concentration inequalities and variance estimators