Scaling of urban income inequality in the USA

Abstract

Urban scaling analysis, the study of how aggregated urban features vary with the population of an urban area, provides a promising framework for discovering commonalities across cities and uncovering dynamics shared by cities across time and space. Here, we use the urban scaling framework to study an important, but under-explored feature in this community—income inequality. We propose a new method to study the scaling of income distributions by analysing total income scaling in population percentiles. We show that income in the least wealthy decile (10%) scales close to linearly with city population, while income in the most wealthy decile scale with a significantly superlinear exponent. In contrast to the superlinear scaling of total income with city population, this decile scaling illustrates that the benefits of larger cities are increasingly unequally distributed. For the poorest income deciles, cities have no positive effect over the null expectation of a linear increase. We repeat our analysis after adjusting income by housing cost, and find similar results. We then further analyse the shapes of income distributions. First, we find that mean, variance, skewness and kurtosis of income distributions all increase with city size. Second, the Kullback–Leibler divergence between a city’s income distribution and that of the largest city decreases with city population, suggesting the overall shape of income distribution shifts with city population. As most urban scaling theories consider densifying interactions within cities as the fundamental process leading to the superlinear increase of many features, our results suggest this effect is only seen in the upper deciles of the cities. Our finding encourages future work to consider heterogeneous models of interactions to form a more coherent understanding of urban scaling.

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“…Inequality spans between urban and rural areas and within and between urban areas ( 17 – 19 ) and emerges across multiple dimensions: economic, infrastructural (environmental), institutional, socio-cultural, technological, and others ( Fig. 1 A ).…”

Urban scaling laws arise from within-city inequalities

“…Recent research has taken important steps along the lines argued for here. First, empirical methodology has been developed to capture within-city variation in scaling [23][24][25] and to ensure the robust estimation of scaling exponents in the light of heavy-tailed urban indicators 57 . Second, a recently proposed theoretical framework 17 has acknowledged heterogeneity and inequality in urbanization processes.…”

“…Power laws are common in nature and society, present not only as scaling laws between cities but also as extremely skewed distributions within agglomerations 22 . Consequently, sums and means are poor and potentially misleading indicators of the relevant quantities of cities [23][24][25] .…”

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