The size-growth relationship: Exploring the rank order of city populations in mainland Britain

Abstract

This paper considers the relationship between city-size and growth in a UK context. This has a number of elements. Using population data from 62 cities with an extended Turok and Mykhnenko (2007) classification of time paths, aligned ranks of population shares reveals that persistent advantageous or disadvantageous trends are in the majority. These persistent paths are at odds with the proposition that Zipf's law for cities is perpetuated by shocks being randomly distributed across the size spectrum.Three contributions in the field of convergence that can be applied here are: intra-distributional mobility; convergence, where there are persistent trends, implies eventual leapfrogging and divergence; which is explored by Boyle and McCarthy's (1997) concordance-based tests for beta-convergence.As population growth is found to be inversely related to city-prominence, there is evidence for convergence, but only in part. There is a U-shape in the size-growth relationship that is obscured by a decline in prominence among the very large cities whilst the primate city, London, is pulling away from the rest of UK urban system. It is argued that ‘path-dependency’ that reflects the inheritance of deindustrialisation is more appropriate than a Gibrat-type stochastic model of growth for the north and west.