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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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Analyzing urban scaling laws in the United States over 115 years
The scaling relations between city attributes and population are emergent and ubiquitous aspects of urban growth. Quantifying these relations and understanding their theoretical foundation, however, is difficult due to the challenge of defining city boundaries and a lack of historical data to study city dynamics over time and space. To address this issue, we analyze scaling between city infrastructure and population across 857 metropolitan areas in the conterminous United States over an unprecedented 115 years (1900–2015) using dasymetrically refined historical population estimates, historical urban road network models, and multi-temporal settlement data to define dynamic city boundaries. We demonstrate that urban scaling exponents closely match theoretical models over a century. Despite some close quantitative agreement with theory, the empirical scaling relations unexpectedly vary across regions. Our analysis of scaling coefficients, meanwhile, reveals that contemporary cities use more developed land and kilometers of road than cities of similar population in 1900, which has serious implications for urban development and impacts on the local environment. Overall, our results provide a new way to study urban systems based on novel, geohistorical data.
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- Award ID(s):
- 2121976
- PAR ID:
- 10499845
- Publisher / Repository:
- SAGE Publications
- Date Published:
- Journal Name:
- Environment and Planning B: Urban Analytics and City Science
- Volume:
- 51
- Issue:
- 9
- ISSN:
- 2399-8083
- Format(s):
- Medium: X Size: p. 2249-2263
- Size(s):
- p. 2249-2263
- Sponsoring Org:
- National Science Foundation
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