Regional inequality dynamics, stochastic dominance, and spatial dependence


Stochastic dominance tests are used to measure whether distributions are directionally-distinct. Using stochastic dominance measures, an income distribution can be measured to be more favorable for its members at all income levels than another distribution. This contrasts with conventional σ and β-convergence approaches that compare distributions at a set of predetermined income levels. Given this comprehensiveness, stochastic dominance measures can yield novel insight into the relationship between income distributions, and thus to the relative economic welfare of inhabitants of different societies. However, stochastic dominance measures used in the analysis of regional income convergence have ignored the complications of geography. In this paper we examine the properties of common tests for stochastic dominance using various descriptive models of geographically-realistic income growth processes. We find that the false positive rate of stochastic dominance tests increases significantly when comparing spatially-informed income distributions growing over time. Further, this over-eager rejection rate requires only that one distribution be spatially-dependent, unlike some other bivariate statistics. We demonstrate that both the parametric and non-parametric spatial filtering procedures are effective at resolving these issues in restricted circumstances for higher-order dominance tests. Overall, while providing a novel and useful perspective on income distribution dynamics, stochastic dominance measures are demonstrated to have undesirable properties when used in geographically-realistic scenarios and they resist one common method to address these issues. Solutions to the concerns expressed here remain open.

Papers in Regional Science