Design and Analysis of Bipartite Experiments under a Linear Exposure-Response Model

In a bipartite experiment, units that are assigned treatments differ from the units for which we measure outcomes. The two groups of units are connected by a bipartite graph, governing how the treated units can affect the outcome units. Often motivated by experiments in marketplaces, the bipartite experimental framework has been used for example to investigate the causal effects of supply-side changes on demand-side behavior. In this paper, we consider the problem of estimating the average total treatment effect in the bipartite experimental framework under a linear exposure-response model. We introduce the Exposure Reweighted Linear (ERL) Estimator, an unbiased linear estimator of the average treatment effect in this setting. We show that the estimator is consistent and asymptotically normal, provided that the bipartite graph is sufficiently sparse. We derive a variance estimator which facilitates confidence intervals based on a normal approximation. In addition, we introduce Exposure-Design, a cluster-based design which aims to increase the precision of the ERL estimator by realizing desirable exposure distributions. Finally, we demonstrate the effectiveness of the described estimator and design with an application using a publicly available Amazon user-item review graph.