Do house price-earnings ratios in England and Wales follow a power law? An application of Lavalette's law to district data

This paper considers Lavalette's function and its applicability to district house price-earnings ratios. Drawing on work in the urban scaling literature and Zipf's law, in conjunction with finance theories of pricing and affordability, the paper considers how stable the distribution of ratios is over time, how robust the ranking order of ratios is in the face of variations in affordability over 2004-2019, and proffers an explanation for the shape and movement of the distribution. It draws on issues found in the economic growth literature where sigma-convergence is applied to spatial variables, and a narrowing of the distribution is said to indicate convergence. It proposes that, when plotted over time, the Lavalette exponent and Spearman's correlation coefficient point to divergence and rank-order stability.