On the Distribution of Spatial Polarization Indices

ABSTRACT This paper develops a statistical framework for inference on recently developed spatial polarization indices and clarifies their relationship to spatial inequality and dependence. The framework builds on a graph‐theoretic decomposition of polarization into global, meso, and local components and accommodates an asymmetry common in regional economic data: low‐income areas often form cohesive clusters, whereas high‐income areas are more spatially fragmented. The principal contributions are a graph‐preserving randomization procedure and asymptotic results for the spatial polarization index. These methods permit assessment of the significance and robustness of observed polarization patterns while connecting spatial statistics, inequality decomposition, and graph theory. A series of Monte Carlo experiments examines the properties of the inferential methods. Two case studies focusing on polarization in Mexico and the United States provide empirical illustrations.