Selective Randomization Inference for Interference

Abstract

Empirical researchers often use tests for interference as pretests or robustness checks. However, when the results guide the choice of models, parameters, or hypotheses, the resulting data-dependent selection can compromise the validity of subsequent inference. This paper develops a two-stage selective randomization inference framework for interference that explicitly conditions on the selection event to account for data-dependent selection. We first test the null hypothesis of no treatment spillover using a conditional randomization method. If this null is rejected, we test the null hypothesis of zero exposure contrast under a pre-specified exposure mapping that allows for spillover effects; otherwise, we test the null hypothesis of no direct effects under the assumption of no spillover. We prove that each second-stage test controls the selective Type I error rate in finite samples and evaluate the size and power of the proposed tests through Monte Carlo experiments.