Causal Inference under Interference: Regression Adjustment and Optimality

TL;DR

This paper extends regression adjustment methods to network interference settings, establishing their asymptotic properties, proposing new estimators, and demonstrating their efficiency through simulations and real data.

Contribution

It introduces a central limit theorem for linear regression-adjusted estimators under interference and develops a nonparametric estimator with proven asymptotic optimality.

Findings

Linear regression adjustment achieves optimal asymptotic variance.

The proposed estimators outperform existing methods in simulations.

Kernel and trimming techniques improve efficiency in nonlinear adjustments.

Abstract

In randomized controlled trials without interference, regression adjustment is widely used to enhance the efficiency of treatment effect estimation. This paper extends this efficiency principle to settings with network interference, where a unit's response may depend on the treatments assigned to its neighbors in a network. We make three key contributions: (1) we establish a central limit theorem for a linear regression-adjusted estimator and prove its optimality in achieving the smallest asymptotic variance within a class of linear adjustments; (2) we develop a novel, consistent estimator for the asymptotic variance of this linear estimator; and (3) we propose a nonparametric estimator that integrates kernel smoothing and trimming techniques, demonstrating its asymptotic normality and its optimality in minimizing asymptotic variance within a broader class of nonlinear adjustments. Extensive simulations validate the superior performance of our estimators, and a real-world data application illustrates their practical utility. Our findings underscore the power of regression-based methods and reveal the potential of kernel-and-trimming-based approaches for further enhancing efficiency under network interference.