Unconditional Randomization Tests for Interference

Abstract: When conducting causal inference or designing policy, researchers are often concerned with the existence and extent of interference between units, which may be influenced by factors such as distance, proximity, and connection strength. However, complex correlations across units pose significant challenges for inference. This paper introduces partial null randomization tests (PNRTs), a novel framework for testing interference in experimental settings. PNRTs adopt a design-based approach, combining unconditional randomization testing with pairwise comparisons to enable straightforward implementation and ensure finite-sample validity under minimal assumptions about network structure. To illustrate the method's broad applicability, this paper applies it to a large-scale experiment by Blattman et al. (2021) in Bogota, Colombia, which evaluates the impact of hotspot policing on crime using street segments as units of analysis. The findings indicate that increasing police patrolling time in hotspots has a significant displacement effect on violent crime but not on property crime. A simulation study calibrated to this dataset further demonstrates the strong power properties of PNRTs and their suitability for general interference scenarios.