Travelling Wave Dynamics in Housing Markets

Abstract

Housing market crashes cause substantial economic harm yet are commonly modelled as exogenous shocks. Patterns documented separately suggest otherwise: a spatiotemporal ‘ripple effect’, and an 18-year land value periodicity in heterodox analysis. Inspired by Ricardo’s Law of Rent, we ask whether an ordinal structure underlies the propagation of relative growth.

Using transactional data for England and Wales, 1995–2026, covering two cycles and one crash, we document a travelling wave: relative growth leadership, independent of aggregate growth rates, begins in the highest-priced segments and propagates monotonically towards the lowest over multi-year cycles, robust across geographic and quantile representations.

We model the wave by an advection equation whose velocity follows from the log-logistic price structure. The cycle time is the informational distance in the land value gradient divided by the rate at which competitive reallocation processes it. As the wave reaches the margin, capital accumulates against the boundary; when that renders land values there unsustainable, a behavioural response triggers a correction. The wave’s position is thus a leading indicator of the cycle.

The central claims, that the cycle is endogenous and ends at the margin, are offered as falsifiable hypotheses.