Travelling Wave Dynamics in Housing Markets

Abstract We analyse England and Wales transactional house price data to describe a robust, empirical regularity across two cycles: a systematic progression of ranked annual returns. We demonstrate that whilst a geographical analysis by Local Authority appears intuitive, an analysis by quantile provides a superior description of information propagation through housing markets. This travelling wave pattern, independent of the underlying house price growth, is both a data-driven version of Ricardo’s Law of Rent and a leading indicator of house market crashes. We propose a simple model where the log-logistic distribution of house prices is subject to drift and diffusion. In addition, a constant-speed travelling wave ensures that over time the fastest-growing quantile travels from the highest to the lowest in order. When the travelling wave reaches the lowest quantile or margin, there is a crash in house prices. The trough is reached when the land value at the margin is again worth zero; subsequently, the cycle restarts. The benefits of a land value tax are briefly discussed. The analysis makes testable statements not only about the future but also about other countries’ national housing datasets.