Causal Inference when Intervention Units and Outcome Units Differ

We study causal inference in settings characterized by interference with a bipartite structure. There are two distinct sets of units: intervention units to which an intervention can be applied and outcome units on which the outcome of interest can be measured. Outcome units may be affected by interventions on some, but not all, intervention units, as captured by a bipartite graph. Examples of this setting can be found in analyses of the impact of pollution abatement in plants on health outcomes for individuals, or the effect of transportation network expansions on regional economic activity. We introduce and discuss a variety of old and new causal estimands for these bipartite settings. We do not impose restrictions on the functional form of the exposure mapping and the potential outcomes, thus allowing for heterogeneity, non-linearity, non-additivity, and potential interactions in treatment effects. We propose unbiased weighting estimators for these estimands from a design-based perspective, based on the knowledge of the bipartite network under general experimental designs. We derive their variance and prove consistency for increasing number of outcome units. Using the Chinese high-speed rail construction study, analyzed in Borusyak and Hull [2023], we discuss non-trivial positivity violations that depend on the estimands, the adopted experimental design, and the structure of the bipartite graph.