Causal inference with misspecified network interference structure

TL;DR

This paper investigates the impact of network misspecification on causal inference under interference, deriving bias bounds, and proposing a robust estimator that remains unbiased if at least one network is correctly specified.

Contribution

It introduces a novel estimator that leverages multiple networks simultaneously, providing robustness to network misspecification in causal inference under interference.

Findings

Bias increases with divergence between assumed and true networks.

The proposed estimator remains unbiased if at least one network is correct.

Simulation and real data demonstrate the estimator's robustness.

Abstract

Under interference, the treatment of one unit may affect the outcomes of other units. Such interference patterns between units are typically represented by a network. Correctly specifying this network requires identifying which units can affect others -- an inherently challenging task. Nevertheless, most existing approaches assume that a known and accurate network specification is given. In this paper, we study the consequences of such misspecification. We derive bounds on the bias arising from estimating causal effects using a misspecified network, showing that the estimation bias grows with the divergence between the assumed and true networks, quantified through their induced exposure probabilities. To address this challenge, we propose a novel estimator that leverages multiple networks simultaneously and remains unbiased if at least one of the networks is correct, even when we do not know which one. Therefore, the proposed estimator provides robustness to network specification. We illustrate key properties and demonstrate the utility of our proposed estimator through simulations and analysis of a social network field experiment.