  The network interference model for causal inference places all experimental
units at the vertices of an undirected exposure graph, such that treatment
assigned to one unit may affect the outcome of another unit if and only if
these two units are connected by an edge. This model has recently gained
popularity as means of incorporating interference effects into the
Neyman--Rubin potential outcomes framework; and several authors have considered
estimation of various causal targets, including the direct and indirect effects
of treatment. In this paper, we consider large-sample asymptotics for treatment
effect estimation under network interference in a setting where the exposure
graph is a random draw from a graphon. When targeting the direct effect, we
show that -- in our setting -- popular estimators are considerably more
accurate than existing results suggest, and provide a central limit theorem in
terms of moments of the graphon. Meanwhile, when targeting the indirect effect,
we leverage our generative assumptions to propose a consistent estimator in a
setting where no other consistent estimators are currently available. We also
show how our results can be used to conduct a practical assessment of the
sensitivity of randomized study inference to potential interference effects.
Overall, our results highlight the promise of random graph asymptotics in
understanding the practicality and limits of causal inference under network
interference.
