Causal Inference Under Approximate Neighborhood Interference

This paper studies causal inference in randomized experiments under network interference. Commonly used models of interference posit that treatments assigned to alters beyond a certain network distance from the ego have no effect on the ego's response. However, this assumption is violated in many models of social interactions. We propose a substantially weaker model of "approximate neighborhood interference" (ANI) under which treatments assigned to alters further from the ego have smaller, but potentially nonzero, effects on the ego's response. For well-known models of social interactions, we can formally verify that ANI holds. We also prove that, under ANI and restrictions on the network topology, standard inverse-probability weighting estimators consistently estimate useful exposure effects and are asymptotically normal under asymptotics taking the network size large. For inference, we consider a network HAC variance estimator. Under a finite population model, we show that the estimator is biased but that the bias can be interpreted as the variance of unit-level exposure effects. This generalizes Neyman's well-known result on conservative variance estimation to settings with interference.