Causal Inference when Intervention Units and Outcome Units Differ

2025-07-27

AI Summary

This paper addresses bipartite structural causal inference under interference: treatment and outcome units are distinct, their relationships are encoded by a bipartite graph, and each outcome unit may be jointly influenced by multiple treatment units. Moving beyond conventional methods that impose strong parametric assumptions—such as linearity or additivity—on exposure mappings and potential outcomes, we propose a model-free framework for defining and estimating causal effects, accommodating arbitrary heterogeneity, nonlinearity, nonadditivity, and treatment interactions. From a design-based perspective, we construct an unbiased weighted estimator that integrates the bipartite graph structure with general randomized experimental designs. We derive its exact variance and establish asymptotic consistency of outcome-unit-level estimators. Our theory identifies a nontrivial positivity condition jointly determined by network topology, experimental design, and estimator form. The method is empirically validated using data on the economic impact of high-speed rail construction.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

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.

Problem

• Causal inference with differing intervention and outcome units
• Estimating effects in bipartite interference settings
• Unbiased weighting estimators for bipartite network designs

Innovation

• Bipartite graph models intervention-outcome relationships
• Unbiased weighting estimators for causal estimands
• Design-based approach with general experimental designs