On the Impossibility of Specification Testing of Interference Models Based on Exposure Mappings

2026-05-10

AI Summary

This study addresses the challenge of testing the correct specification of exposure mapping interference models in randomized experiments with spillover effects. By integrating tools from causal inference, hypothesis testing, and extreme value analysis, the authors construct theoretical counterexamples and derive sharp bounds to demonstrate a strong impossibility result: any test with power against a broader class of exposure mappings necessarily incurs a worst-case sum of Type I and Type II error probabilities equal to one. This implies that existing specification tests offer no advantage over a naive random-rejection strategy. Building on this insight, the paper further proposes a novel test that achieves uniform validity under both no-interference and linear-in-means network interference assumptions.

Abstract

In order to estimate causal effects in a randomized experiment where spillovers are suspected to occur, analysts must posit a model of interference. The most popular class of interference models are those based on exposure mappings. In practice, it is rarely clear which interference model accurately captures the true nature of spillovers in the experiment. In response, researchers have developed specification tests which seek to determine whether a given interference model is correctly specified. In this context, Type I error is the rejection rate when the interference model is actually correct and Type II error is the acceptance rate when the interference model is incorrectly specified. While existing tests have been explicitly constructed to control Type I error, their Type II error remains less well understood. In this paper, we provide a strong impossibility result: any specification test for an exposure mapping model which aims to have power against a larger exposure mapping model has worst-case Type I and Type II errors that sum to one. This means that no specification test can provide uniformly better performance than the naive test which discards all data and rejects the null at random. Our negative result holds for all sample sizes, for uniformly bounded outcomes, and for alternatives which are maximally separated from the null. Informative specification tests must therefore further restrict the alternative model against which they seek to attain power. To this end, we provide a uniformly consistent test for differentiating no-interference from a network-linear-in-means model.

Problem

• interference models
• exposure mappings
• specification testing
• spillover effects
• causal inference

Innovation

• exposure mapping
• interference model
• specification test
• causal inference
• impossibility result