Treatment effect estimation under convergent network interference

TL;DR

This paper develops a central limit theorem for treatment effect estimation in dense, non-random network interference models, extending graph limit theory to causal inference and showing that treatment randomness primarily drives uncertainty.

Contribution

It extends the graph limit framework to analyze treatment effects in dense, non-random networks, filling a key gap in network interference theory.

Findings

Asymptotic normality of treatment effect estimators in dense networks.

Random treatment assignment dominates uncertainty in effect estimation.

Results apply to non-random, dense exposure graphs, broadening applicability.

Abstract

Under network interference, the treatment given to one unit may also affect the outcomes of its neighboring units in an exposure graph. Existing large-sample theory has focused on settings where either the exposure graph is sparse, or the exposure graph is randomly generated using a random graph model. The question of how to analyze treatment effect estimation in network interference models with dense, non-random exposure graphs has remained open to date. Here, we address this gap and prove a central limit theorem for possibly dense, non-random models by extending the graph limit framework pioneered by Lov\'{a}sz and Szegedy to the setting of causal inference under network interference. Our result implies that the uncertainty for average direct effect estimation is to first-order driven by random treatment assignment, and so asymptotic results derived under the random graph model correctly predict statistical behavior in non-random network interference designs.