Radial analysis and scaling of housing prices in French urban areas

TL;DR

This study analyzes how housing prices vary radially within French cities and how these profiles scale with city size, revealing regularities and disparities especially in city centers affecting affordability.

Contribution

It introduces a novel radial analysis of housing prices across multiple cities and demonstrates their scaling behavior with city population size.

Findings

Housing prices are higher in larger cities.

Radial profiles scale with the fifth root of city population.

Prices in city centers increase faster than in peripheries as city size grows.

Abstract

Urban scaling laws summarize how urban attributes evolve with city size. Recent criticism questions notably the aggregate view of this approach, which leads to neglecting the internal structure of cities. This is all the more relevant for housing prices due to their important 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 rescaled profiles approach 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 those 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.