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.
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.
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