Closed-form expressions for causal effects and rates of convergence for causal effect estimators under dependence
Abstract
Causal inference in connected populations is non-trivial, because the treatment assignments of units can affect the outcomes of other units via treatment and outcome spillover. Since outcome spillover induces dependence among outcomes, closed-form expressions for causal effects and convergence rates for causal effect estimators are challenging and unavailable. We make three contributions. First, we provide closed-form expressions for causal effects under treatment and outcome spillover without making assumptions about the joint probability law of treatment assignments, outcomes, and connections beyond linearity of conditional expectations of outcomes and the standard assumptions of ignorability and positivity. The main results permit complex dependence among outcomes and connections. Second, we show that ignoring dependence among outcomes due to outcome spillover can induce asymptotic bias in causal effect estimators. Third, we establish convergence rates for causal effect estimators by controlling dependence and characterizing a high-probability subset of data that addresses collinearity issues.
Cite
@article{arxiv.2504.06108,
title = {Closed-form expressions for causal effects and rates of convergence for causal effect estimators under dependence},
author = {Subhankar Bhadra and Michael Schweinberger},
journal= {arXiv preprint arXiv:2504.06108},
year = {2025}
}