Comparing the homogeneity of income distributions using Polarization Indices

In the context of polarized societies, income homogeneity is linked to the frequency and the intensity of social unrest. Most homogenous countries exhibit a lower frequency of intense social conflicts and less homogeneous countries show a higher frequency of moderate social conflicts. This paper develops a methodology to compare the degree of homogeneity of two income distributions. We use for that purpose an index of polarization that does not account for alienation. This index is the identification component of polarization that measures the degree to which individuals feel alike in an income distribution. This development leads to identification dominance curves and derives first-order and higher-order stochastic dominance conditions. First-order stochastic dominance is performed trough identification dominance curves drawn on a support of identification thresholds. These curves are used to determine whether identification, homogeneity, or similarity of individuals is greater in one distribution than in another for general classes of polarization indices and ranges of possible identification thresholds. We also derive the asymptotic sampling distribution of identification dominance curves and test dominance between two distributions using Intersection Union tests and bootstrapped p-values. Our methodology is illustrated by comparing pairs of distributions of eleven countries drawn from the Luxembourg Income Study database.