Scaling and Hierarchy in Urban Economies

TL;DR

This paper critically re-examines claims of super-linear and sub-linear scaling in urban economies, showing that previous evidence is confounded by data representation and that city size's influence is mainly due to industry concentration.

Contribution

It demonstrates that scaling laws in urban metrics are artifacts of data aggregation and highlights the role of industry concentration in economic productivity differences.

Findings

Scaling in urban data is largely an artifact of using total quantities.

Per-capita measures do not strongly depend on city size.

Concentration of high-value industries explains productivity variations.

Abstract

In several recent publications, Bettencourt, West and collaborators claim that properties of cities such as gross economic production, personal income, numbers of patents filed, number of crimes committed, etc., show super-linear power-scaling with total population, while measures of resource use show sub-linear power-law scaling. Re-analysis of the gross economic production and personal income for cities in the United States, however, shows that the data cannot distinguish between power laws and other functional forms, including logarithmic growth, and that size predicts relatively little of the variation between cities. The striking appearance of scaling in previous work is largely artifact of using extensive quantities (city-wide totals) rather than intensive ones (per-capita rates). The remaining dependence of productivity on city size is explained by concentration of specialist service industries, with high value-added per worker, in larger cities, in accordance with the long-standing economic notion of the "hierarchy of central places".