Estimating causal effects under non-individualistic treatments due to network entanglement

Summary In many observational studies, the treatment assignment mechanism is not individualistic, as it allows the probability of treatment of a unit to depend on quantities beyond the unit’s covariates. In such settings, unit treatments may be entangled in complex ways. In this article, we consider a particular instance of this problem where the treatments are entangled by a social network among units. For instance, when studying the effects of peer interaction on a social media platform, the treatment on a unit depends on the change of the interactions network over time. A similar situation is encountered in many economic studies, such as those examining the effects of bilateral trade partnerships on countries’ economic growth. The challenge in these settings is that individual treatments depend on a global network that may change in a way that is endogenous and cannot be manipulated experimentally. In this paper, we show that classical propensity score methods that ignore entanglement may lead to large bias and wrong inference of causal effects. We then propose a solution that involves calculating propensity scores by marginalizing over the network change. Under an appropriate ignorability assumption, this leads to unbiased estimates of the treatment effect of interest. We also develop a randomization-based inference procedure that takes entanglement into account. Under general conditions on network change, this procedure can deliver valid inference without explicitly modelling the network. We establish theoretical results for the proposed methods and illustrate their behaviour via simulation studies based on real-world network data. We also revisit a large-scale observational dataset on contagion of online user behaviour, showing that ignoring entanglement may inflate estimates of peer influence.