This paper studies causal inference in randomized experiments under network interference. Most existing models of interference posit that treatments assigned to alters only affect the ego 's response through a low-dimensional exposure mapping, which only depends on units within some known network radius around the ego. We propose a substantially weaker  "approximate neighborhood interference" (ANI) assumption, which allows treatments assigned to alters far from the ego to have a small , but potentially nonzero, impact on the ego's response. Unlike the exposure mapping model, we can show that ANI is satisfied in well-known models of social interactions. Despite its generality, inference in a single-network setting is still possible under ANI, as we prove that standard inverse-probability weighting estimators can consistently estimate treatment and spillover effects and are asymptotically normal . For practical inference, we propose a new conservative variance estimatorbased on a network bootstrap and suggest a data-dependent bandwidth using the network diameter. Finally, we illustrate our results in a simulation study and empirical application .
This paper studies causal inference in randomized experiments under network interference. Most of the literature assumes a model of interference under which treatments assigned to alters beyond a certain network distance from the ego have no effect on the ego 's response . However, many models of social interactions do not satisfy this assumption. This paper proposes 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, impact on the ego's response. We show that ANI is satisfied in well-known models of social interactions. We also prove that, under ANI, standard inverse-probability weighting estimators can 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 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 .
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