Network Experiments with Edge Treatments and Node Outcomes

Abstract

We present a methodology for analyzing node-level outcomes while experimenting with edge-level treatments in a population connected by an undirected graph. Under our design, nodes are randomly assigned to test or control, and each edge inherits the treatment of its endpoints, with conflicts resolved by randomization. We use each node's assigned status as an instrument for its treatment exposure. We show that the Wald estimator is consistent for the global average treatment effect (GATE), even when the edge weights used to construct the exposure are misspecified. We formalize the assumptions needed both in terms of the linearity of potential outcomes and the sparsity of the graph, and prove the asymptotic normality of the Wald estimator. The estimator is straightforward to implement, requiring no assignment simulations over the graph. Our Monte Carlo study demonstrates the strong performance of our approach in the context of a social platform.