Design-based causal inference in bipartite experiments

Abstract: Bipartite experiments arise in various fields, in which the treatments are randomized over one set of units, while the outcomes are measured over another separate set of units. However, existing methods often rely on strong model assumptions about the data-generating process. Under the potential outcomes formulation, we explore design-based causal inference in bipartite experiments under weak assumptions by leveraging the sparsity structure of the bipartite graph that connects the treatment units and outcome units. We make several contributions. First, we formulate the causal inference problem under the design-based framework that can account for the bipartite interference. Second, we propose a consistent point estimator for the total treatment effect, a policy-relevant parameter that measures the difference in the outcome means if all treatment units receive the treatment or control. Third, we establish a central limit theorem for the estimator and propose a conservative variance estimator for statistical inference. Fourth, we discuss a covariate adjustment strategy to enhance estimation efficiency.