  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.
