Average Direct and Indirect Causal Effects under Interference

TL;DR

This paper introduces a new definition for the average indirect causal effect in models with interference, enabling analysis without multiple experiments and maintaining interpretability across parametric models.

Contribution

It defines the average indirect effect in the potential outcomes framework and proves its decomposition property, extending causal inference under interference.

Findings

The indirect effect can be estimated without cross-experiment comparisons.

The sum of direct and indirect effects equals the effect of an infinitesimal policy change.

The non-parametric indirect effect remains meaningful across various interference models.

Abstract

We propose a definition for the average indirect effect of a binary treatment in the potential outcomes model for causal inference under cross-unit interference. Our definition is analogous to the standard definition of the average direct effect, and can be expressed without needing to compare outcomes across multiple randomized experiments. We show that the proposed indirect effect satisfies a decomposition theorem whereby, in a Bernoulli trial, the sum of the average direct and indirect effects always corresponds to the effect of a policy intervention that infinitesimally increases treatment probabilities. We also consider a number of parametric models for interference, and find that our non-parametric indirect effect remains a natural estimand when re-expressed in the context of these models.