Causal Inference Under Approximate Neighborhood Interference
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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.
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