Scaling and universality in urban economic diversification
HyejinYoun, Luís M. A.Bettencourt, JoséLobo, DeborahStrumsky, HoracioSamaniego, Geoffrey B.West
Published 20 January 2016.DOI: 10.1098/rsif.2015.0937
Institute for New Economic Thinking, University of Oxford, Oxford OX2 6ED, UKMathematical Institute, University of Oxford, Oxford OX2 6GG, UKSanta Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
Institute for New Economic Thinking, University of Oxford, Oxford OX2 6ED, UKSanta Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USAMathematics Department, Imperial College, London SW7 2AZ, UK
(a) The total number of establishments Nf scales linearly with city size: Nf ∼ Nα, where α = 0.98 ± 0.02 with R2 = 0.97. (b) The number of distinct business types D(N) normalized by its maximum value Dmax at various levels of classification, r, based on the NAICS scheme, from the lowest resolution (three-digit) to the highest (six-digit) denoted by green circles, blue triangles, red diamonds and black squares, respectively (corresponding values of Dmax are 317, 722 and 1160). All values are scaled by the corresponding size of the classification scheme at that resolution, Dmax, such that all values fall in between 0 and 1. The black solid line and orange dashes are the predictions from equation (2.5), with and without ϕ.
Rank-abundance of establishment types. (a) The number of establishments at rank x ranging from 1 to 90 in descending order of their frequencies (from common to rare) for New York City, Chicago, Phoenix and San Jose. Establishment types are colour coded by their classification at the two-digit level. (b) Universal rank-abundance shape of the establishment type by dividing Nx by the population size of city in semi-log for all ranges. All 366 metropolitan statistical areas are denoted by grey circles. Seven selected cities are denoted by various colours and shapes; New York city, Chicago, Phoenix, Detroit, San Jose, Champaign-Urbana and Danville are, respectively, marked by red squares, pink diamonds, orange triangles, yellow left triangles, green right triangles, sky blue pluses and blue crosses. The black dash line and the black solid line are fits to equation (2.3) without and with ϕ, respectively. The inset shows the first 200 types on a log–log plot showing an approximate Zipf-like power law behaviour.
Multidimensional allometric scaling of industry types. (a) The number of lawyers' offices scales super-linearly with population size, Nlo ∼ N1.17±0.04 with R2 = 0.92. (b) The rank of lawyers' offices goes up with population size, expressing an increase in their relative abundance: xlo ∼ N−0.4±0.06 with R2 = 0.32. (c) Histogram of scaling exponents γ for all establishment types at the two-digit level. While primary sectors disappear, managerial, professional, technical and scientific establishments increase in relative abundance, helping to explain the increased productivity of larger cities despite the slow addition of new business types. Each scaling analysis is shown in the electronic supplementary material.