The scaling of income distribution in Australia: Possible relationships between urban allometry, city size, and economic inequality

Abstract

Developing a scientific understanding of cities in a fast urbanizing world is essential for planning sustainable urban systems. Recently, it was shown that income and wealth creation follow increasing returns, scaling superlinearly with city size. We study scaling of per capita incomes for separate census defined income categories against population size for the whole of Australia. Across several urban area definitions, we find that lowest incomes grow just linearly or sublinearly (β = 0.94 to 1.00), whereas highest incomes grow superlinearly (β = 1.00 to 1.21), with total income just superlinear (β = 1.03 to 1.05). These findings show that as long as total or aggregate income scaling is considered, the earlier finding is supported: the bigger the city, the richer the city, although the scaling exponents for Australia are lower than those previously reported for other countries. But, we find an emergent scaling behavior with regard to variation in income distribution that sheds light on socio-economic inequality: the larger the population size and densities of a city, while lower incomes grow proportionately or less than proportionately, higher incomes grow more quickly, suggesting a disproportionate agglomeration of incomes in the highest income categories in big cities. Because there are many more people on lower incomes that scale sublinearly as compared to the highest that scale superlinearly, these findings suggest an empirical observation on inequality: the larger the population, the greater the income agglomeration in the highest income categories. The implications of these findings are qualitatively discussed for various income categories, with respect to living costs and access to opportunities and services that big cities provide.

Evidence for localization and urbanization economies in urban scaling

“…If both models are not significant, then we choose the β from the model with the least Bayesian Information Criteria (BIC) statistic [17]. The application details of the MLE based process are described in detail in [19] using the framework proposed in [17]. In general, the estimates from OLE and MLE were similar, but OLE estimates ranging from 0.98 to 1.02 were estimated as linear (i.e.…”

“…Thus, the observation that specific cities or city systems follow increasing returns to scale may well be a consequence of some of the industries, which are themselves organised around increasing returns, being disproportionately present in these cities. For the same reason, some small cities that agglomerate particular industries where increasing returns operate emerge as outliers or large heteroskedastic fluctuations in the overall scaling plot [19].…”

“…Since knowledge economy occupations tend to cluster in the largest cities, regressions against city size are also likely to show superlinear returns by city size, when in fact the superlinearity may be arising from occupational or industrial organisation and not from population size per se. For example, a smaller city with very high concentrations of high-income occupations may then emerge as an outlier (as discussed for Cambridge, for example, in[15], or for Australian mining towns in[19]). Second, when the number of workers are used as labour factor inputs to total income or GDP as output, no strong evidence for superlinear scaling of output is found, instead the evidence seems to tilt towards linear scaling and constant returns to scale.…”

Beyond Kuznets: Inequality and the size and distribution of cities

“…On the other hand, the paper is also linked to the urban economics literature. Papers in this literature study the relationship between city size and income inequality at the city level (i.e., Alperovich, ; Baum‐Snow & Pavan, ; Behrens & Robert‐Nicoud, ; Duncan & Reiss, ; Glaeser, Resseger, & Tobio, ; Haworth, Long, & Rasmussen, ; Long, Rasmussen, & Haworth, ; Ma & Tang, ; Nord, ; Richardson, ; Sarkar, Phibbs, Simpson, & Wasnik, ) . While these papers focus on size, they look at city inequality and do not consider effects on the level of economy‐wide inequality.…”

Urban form strongly mediates the allometric scaling of airshed pollution concentrations

“…where coefficient, Y j,o , and power-law exponent, α j , describe the scaling of characteristic Y j with some more commonly measured yardstick of 'scale' such as, in our case, population, P. Other yardstick measures, such as subsets of population [17,18], GDP [19], or network fractal dimension [20], can be used if more appropriate to framing a particular study; we use population because it is a fundamental unit of social organization and to be consistent with prior work [21,22]. The intention of allometric analysis is not to deduce causality, even regression-related Granger causality [23], but rather to search for simple emergent patterns in complex systems as an aid to understanding what is strictly contextual about instances of such systems and what holds more generally about them e.g.…”