Superlinear scaling in the urban system of England of Wales. A comparison with US cities

Abstract: According to the theory of urban scaling, urban indicators scale with city size in a predictable fashion. In particular, indicators of social and economic productivity are expected to have a superlinear relation. This behavior was verified for many urban systems, but recent findings suggest that this pattern may not be valid for England and Wales (E&W), where income has a linear relation with city size. This finding raises the question of whether the cities of E&W exhibit any superlinear relation with respect to quantities such as the level of education and occupational groups. In this paper, we evaluate the scaling of educational and occupational groups of E&W to see if we can detect superlinear relations in the number of educated and better-paid persons. As E&W may be unique in its linear scaling of income, we complement our analysis by comparing it to the urban system of the United States (US), a country for which superlinear scaling of income has already been demonstrated. To make the two urban systems comparable, we define the urban systems of both countries using the same method and test the sensitivity of our results to changes in the boundaries of cities. We find that cities of E&W exhibit patterns of superlinear scaling with respect to education and certain categories of better-paid occupations. However, the tendency of such groups to have superlinear scaling seems to be more consistent in the US. We show that while the educational and occupational distributions of US cities can partly explain the superlinear scaling of earnings, the distribution leads to a linear scaling of earnings in E&W.