Rank-based Markov chains for regional income distribution dynamics

Markov chains have become a mainstay in the literature on regional income distribution dynamics and convergence. Despite its growing popularity, the Markov framework has some restrictive characteristics associated with the underlying discretization income distributions. This paper introduces several new approaches designed to mitigate some of the issues arising from discretization. Based on the examination of rank distributions, two new Markov-based chains are developed. The first explores the movement of individual economies through the income rank distribution over time. The second provides insight on the movements of ranks over geographical space and time. These also serve as the foundation for two new tests of spatial dynamics or the extent to which movements in the rank distribution are spatially clustered. An illustration of these new methods is included using income data for the lower 48 US states for the years 1929-2009.