The Diffusive Nature of Housing Prices

TL;DR

This paper demonstrates that housing prices in France exhibit diffusive behavior with spatial and temporal correlations, revealing persistent shocks and heterogeneity, supported by a stylized diffusion model applied to extensive data.

Contribution

It introduces a diffusion-based model to analyze housing prices, extending previous local studies to a national scale with high-resolution data.

Findings

Price correlations decay logarithmically with distance

Price shocks are persistent and spatially heterogeneous

Housing prices follow a diffusive spatial-temporal pattern

Abstract

We analyze the French housing market prices in the period 1970-2022, with high-resolution data from 2018 to 2022. The spatial correlation of the observed price field exhibits logarithmic decay characteristic of the two-dimensional random diffusion equation -- local interactions may create long-range correlations. We introduce a stylized model, used in the past to model spatial regularities in voting patterns, that accounts for both spatial and temporal correlations with reasonable values of parameters. Our analysis reveals that price shocks are persistent in time and their amplitude is strongly heterogeneous in space. Our study confirms and quantifies the diffusive nature of housing prices that was anticipated long ago (Clapp et al. 1994, Pollakowski et al. 1997), albeit on much restricted, local data sets.