Bipartite causal inference with interference, time series data, and a random network

In bipartite causal inference with interference there are two distinct sets of units: those that receive the treatment, termed interventional units, and those on which the outcome is measured, termed outcome units. Which interventional units' treatment can drive which outcome units' outcomes is often depicted in a bipartite network. We study bipartite causal inference with interference from observational data across time and with a changing bipartite network. Under an exposure mapping framework, we define causal effects specific to each outcome unit, representing average contrasts of potential outcomes across time. We establish unconfoundedness of the exposure received by the outcome units based on unconfoundedness assumptions on the interventional units' treatment assignment and the random graph, hence respecting the bipartite structure of the problem. By harvesting the time component of our setting, causal effects are estimable while controlling only for temporal trends and time-varying confounders. Our results hold for binary, continuous, and multivariate exposure mappings. In the case of a binary exposure, we propose three matching algorithms to estimate the causal effect based on matching exposed to unexposed time periods for the same outcome unit, and we show that the bias of the resulting estimators is bounded. We illustrate our approach with an extensive simulation study and an application on the effect of wildfire smoke on transportation by bicycle.