Causal Inference Under Approximate Neighborhood Interference

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 estimator based 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.