A simple measure of beta-convergence revisited

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.