Diffusive Nature of Housing Prices

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, some fitted on impulse response data. Our analysis reveals that price shocks are persistent in time and their amplitude is strongly heterogeneous in space. Our study quantifies the diffusive nature of housing prices that was anticipated in the 1990s, albeit on much restricted local datasets.