Robust Inference for the Direct Average Treatment Effect with Treatment Assignment Interference

TL;DR

This paper introduces a robust inference framework for causal effects in networked settings with interference, utilizing an Ising model to account for complex dependencies and providing valid inference across various interference regimes.

Contribution

It develops a novel robust inference method for the direct average treatment effect under network interference, incorporating an Ising model and a new resampling technique.

Findings

Established a Berry-Esseen-type approximation for the distribution of the estimator.

Developed a uniform distributional approximation valid across interference regimes.

Validated the proposed inference method through Monte Carlo simulations.

Abstract

This paper develops methods for uncertainty quantification in causal inference settings with random network interference. We study the large-sample distributional properties of the classical difference-in-means Hajek treatment effect estimator, and propose a robust inference procedure for the (conditional) direct average treatment effect. Our framework allows for cross-unit interference in both the outcome equation and the treatment assignment mechanism. Drawing from statistical physics, we introduce a novel Ising model to capture complex dependencies in treatment assignment, and derive three results. First, we establish a Berry-Esseen-type distributional approximation that holds pointwise in the degree of interference induced by the Ising model. This approximation recovers existing results in the absence of treatment interference, and highlights the fragility of inference procedures that do not account for the presence of interference in treatment assignment. Second, we establish a uniform distributional approximation for the Hajek estimator and use it to develop robust inference procedures that remain valid uniformly over all interference regimes allowed by the model. Third, we propose a novel resampling method to implement the robust inference procedure and validate its performance through Monte Carlo simulations. A key technical innovation is the introduction of a conditional i.i.d. Gaussianization that may have broader applications. We also discuss extensions and generalizations of our results.