A simple measure of beta-convergence revisited

Abstract

Convergence among regions to long-run, non-zero income differentials is predicted by mainstream and alternative spatial theories. A variety of convergence, considered by Sala-i-Martin, focuses on the rank order over time. As some must be growing faster than others, intra-distributional mobility implies convergence of regions. A measure of this from Boyle and McCarthy is the trend in rank concordance. As it is a measure of similarity between a given distribution and other sample periods, we propose that Kendall’s criterion ranking coefficient, combined with concordance, provides better insight into intra-distributional mobility and convergence. Agreement with a distribution can be traced over a series to highlight the mobility over time. This has the advantage of revealing whether mobility entails converging from, reverting to or converging to an order. Although there are phases of sigma-convergence and divergence, what is found in an analysis of regional house prices is that the rank-order is little affected by cycle phase. In trend, the UK price distribution appears to converge to a hierarchy, corresponding better with a very large monocentric urban model or Zipf-type, than a core–periphery-type distribution of prices. The broadening of price spreads is likely to be facilitated by the liberalisation of finance seen elsewhere, and by an appetite for greater mortgage debt.