Radial analysis and scaling of housing prices in French urban areas

Urban scaling laws summarize how attributes evolve with city size. However, one limitation concerns the aggregate view of this approach, which leads to neglecting the internal structure of cities. This is an important issue regarding housing prices, given their significant variations across space. Based on a dataset compiling millions of real estate transactions over the period 2017-2021, we investigate the regularities of the radial (center-periphery) profiles of housing prices across cities, with respect to their size. Results are threefold. First, they corroborate prior findings in the urban scaling literature stating that largest cities agglomerate higher housing prices. Second, we find that housing price radial profiles scale in three dimensions with the power 1/5 of city population. After rescaling, great regularities between radial profiles can be observed, although some locational amenities have a significant impact on prices. Third, it appears that our approach with rescaled profiles fails to explain housing price variations in the city center across cities. In fact, prices near the city center rise much faster with city size than in the periphery. This has strong implications for low-income households seeking homeownership because prohibitive prices in the center may contribute to pushing them out into peripheral locations, especially in large cities.