  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 common
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 a smaller, but potentially nonzero, effect
on the ego's response. We formally verify that ANI holds for well-known models
of social interactions. Under ANI, restrictions on the network topology, and
asymptotics under which the network size increases, we prove that standard
inverse-probability weighting estimators consistently estimate useful exposure
effects and are approximately normal. 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.
