Average treatment effects in the presence of unknown interference

TL;DR

This paper analyzes how standard treatment effect estimators perform in randomized experiments with unknown interference, showing they remain consistent under certain conditions and discussing implications for inference accuracy.

Contribution

It extends the understanding of treatment effect estimation to settings with unknown interference, demonstrating consistency of common estimators and highlighting conditions affecting their convergence.

Findings

Estimators are consistent for a generalized effect under limited interference.

Convergence rates depend on interference growth and treatment assignment dependencies.

Standard estimators may be close to true effects even if interference is ignored.

Abstract

We investigate large-sample properties of treatment effect estimators under unknown interference in randomized experiments. The inferential target is a generalization of the average treatment effect estimand that marginalizes over potential spillover effects. We show that estimators commonly used to estimate treatment effects under no interference are consistent for the generalized estimand for several common experimental designs under limited but otherwise arbitrary and unknown interference. The rates of convergence depend on the rate at which the amount of interference grows and the degree to which it aligns with dependencies in treatment assignment. Importantly for practitioners, the results imply that if one erroneously assumes that units do not interfere in a setting with limited, or even moderate, interference, standard estimators are nevertheless likely to be close to an average treatment effect if the sample is sufficiently large. Conventional confidence statements may, however, not be accurate.