  The bipartite experimental framework is a recently proposed causal setting,
where a bipartite graph links two distinct types of units: units that receive
treatment and units whose outcomes are of interest to the experimenter. Often
motivated by market experiments, the bipartite experimental framework has been
used for example to investigate the causal effects of supply-side changes on
demand-side behavior. Similar to settings with interference and other
violations of the stable unit treatment value assumption (SUTVA), additional
assumptions on potential outcomes must be made for valid inference. In this
paper, we consider the problem of estimating the average treatment effect in
the bipartite experimental framework under a linear exposure-response model. We
propose the Exposure Reweighted Linear (ERL) Estimator, an unbiased linear
estimator of the average treatment effect in this setting. Furthermore, we
present 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 proposed estimator and design
on a publicly available Amazon user-item review graph.
