Scaling behavior of public procurement activity

Public procurement refers to the purchase by public sector entities—such as government departments or local authorities—of Services, Goods, or Works. It accounts for a significant share of OECD countries’ expenditures. However, while governments are expected to execute them as efficiently as possible, there is a lack of methodologies for an adequate comparison of procurement activity between institutions at different scales, which represents a challenge for policymakers and academics. Here, we propose using methods borrowed from urban scaling laws literature to study public procurement activity among 278 Portuguese municipalities between 2011 and 2018. We find that public procurement expenditure scales sublinearly with population size, indicating an economy of scale for public spending as cities increase their population size. Moreover, when looking at the municipal Scale-Adjusted Indicators (the deviations from the scaling law) by contract categories—Works, Goods, and Services—we are able to identify a richer local characterisation of municipalities based on the similarity of procurement activity. These results make up a framework for quantitatively studying local public expenditure by enabling policymakers a more appropriate foundation for comparative analysis.

Do house price-earnings ratios in England and Wales follow a power law? An application of Lavalette’s law to district data

This paper considers Lavalette’s function and its applicability to district house price-earnings ratios. Drawing on work in the urban scaling literature and Zipf’s law, in conjunction with finance theories of pricing and affordability, the paper considers how stable the distribution of ratios is over time, how robust the ranking order of ratios is in the face of variations in affordability over 2004–2019, and proffers an explanation for the shape and movement of the distribution. It draws on issues found in the economic growth literature where sigma-convergence is applied to spatial variables, and a narrowing of the distribution is said to indicate convergence. It proposes that, when plotted over time, the Lavalette exponent and Spearman’s correlation coefficient point to divergence and rank-order stability.

Commuting network effect on urban wealth scaling

Urban scaling theory explains the increasing returns to scale of urban wealth indicators by the per capita increase of human interactions within cities. This explanation implicitly assumes urban areas as isolated entities and ignores their interactions. Here we investigate the effects of commuting networks on the gross domestic product (GDP) of urban areas in the US and Brazil. We describe the urban GDP as the output of a production process where population, incoming commuters, and interactions between these quantities are the input variables. This approach significantly refines the description of urban GDP and shows that incoming commuters contribute to wealth creation in urban areas. Our research indicates that changes in urban GDP related to proportionate changes in population and incoming commuters depend on the initial values of these quantities, such that increasing returns to scale are only possible when the product between population and incoming commuters exceeds a well-defined threshold.

Urban scaling of opioid analgesic sales in the United States

Opioid misuse is a public health crisis in the United States. The origin of this crisis is associated with a sharp increase in opioid analgesic prescribing. We used the urban scaling framework to analyze opioid prescribing patterns in US commuting zones (CZs), i.e., groups of counties based on commuting patterns. The urban scaling framework postulates that a set of scaling relations can be used to predict health outcomes and behaviors in cities. We used data from the Drug Enforcement Administration’s Automated Reports and Consolidated Ordering System (ARCOS) to calculate counts of oxycodone/hydrocodone pills distributed to 607 CZs in the continental US from 2006 to 2014. We estimated the scaling coefficient of opioid pill counts by regressing log(pills) on log(population) using a piecewise linear spline with a single knot at 82,363. Our results show that CZs with populations below the knot scaled superlinearly (β = 1.36), i.e., larger CZs had disproportionally larger pill counts compared to smaller CZs. On the other hand, CZs with populations above the knot scaled sublinearly (β = 0.92), i.e., larger CZs had disproportionally smaller pill counts compared to smaller CZs. This dual scaling pattern was consistent across US census regions. For CZs with population below the knot, the superlinear scaling of pills is consistent with the explanation that an increased number of successful matches between prescribers and users will lead to higher prescribing rates. The non-linear scaling behavior observed could be the result of a combination of factors, including stronger health care systems and prescribing regulation in largely populated commuting zones, as well as high availability of other opioids such as heroin in these commuting zones. Future research should explore potential mechanisms for the non-linearity of prescription opioid pills.

Estimating the drivers of urban economic complexity and their connection to economic performance

Estimating the capabilities, or inputs of production, that drive and constrain the economic development of urban areas has remained a challenging goal. We posit that capabilities are instantiated in the complexity and sophistication of urban activities, the know-how of individual workers, and the city-wide collective know-how. We derive a model that indicates how the value of these three quantities can be inferred from the probability that an individual in a city is employed in a given urban activity. We illustrate how to estimate empirically these variables using data on employment across industries and metropolitan statistical areas in the USA. We then show how the functional form of the probability function derived from our theory is statistically superior when compared with competing alternative models, and that it explains well-known results in the urban scaling and economic complexity literature. Finally, we show how the quantities are associated with metrics of economic performance, suggesting our theory can provide testable implications for why some cities are more prosperous than others.

Urban population size and road traffic collisions in Europe

Millions of road traffic collisions take place every year, leading to significant knock-on effects. Many of these traffic collisions take place in urban areas, where traffic levels can be elevated. Yet, little is known about the extent to which urban population size impacts road traffic collision rates. Here, we use urban scaling models to analyse geographic and road traffic collision data from over 300 European urban areas in order to study this issue. Our results show that there is no significant change in the number of road traffic collisions per person for urban areas of different sizes. However, we find individual urban locations with traffic collision rates which are remarkably high. These findings have the potential to inform policies for the allocation of resources to prevent road traffic collisions across the different cities.

Scaling of urban income inequality in the USA

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.

Multiscale accessibility and urban performance

Accessibility is fundamentally thought to be related to functional, economic, and social performances of cities and geographical systems and, therefore, constitutes an essential aspect for spatial planning. Previous studies focused on cities or metropolitan scales, often disregarding their position within regional and national systems, which can greatly affect their performance. Although accessibility at various spatial scales has been examined, the studies focused on accessibility patterns at different scales, with no reference to the level of accessibility of cities over local, regional, and national scales simultaneously, i.e. multiscale accessibility. This study aims to elucidate the multiscale accessibility level of individual cities and examine its relationship to urban performance in the urban system of Israel. Spatial accessibility was analyzed using the space syntax methodology for the entire national road network across multiple geographic scales—from the local to the national scale. Based on three distinct spatial accessibility systems identified, a unique multiscale accessibility profile was created for individual cities in Israel. Subsequently, each city’s multiscale accessibility profiles were examined against urban performance indicators determined from urban scaling theory. We found that the superiority of cities characterized by high accessibility level plays a role not only for a specific scale but also over scales and spatial systems. Moreover, most urban performance indicators related to the multiscale accessibility profiles of cities, while some multiscale accessibility profiles can be related to over- or under-performance of cities. The findings suggest that pervasive accessibility across spatial scales is inherently connected to urban performance and may indicate on the implementation and interpretation of accessibility. These findings may assist in various aspects of spatial planning at various scales.

Urban scaling in rapidly urbanising China

Understanding the scaling characteristics in China is critical for perceiving the development process of rapidly urbanising countries. This paper conducts a comprehensive scaling analysis with quantitative assessment of a large number of diverse urban indicators of 275 Chinese cities. Our findings confirm that urban scaling laws can also be applied to rapidly urbanising China but demonstrate some unique features echoing its distinct urbanisation. Chinese urban population agglomeration results in more effective economic production but the economies of scale for infrastructure are less obvious. Some urban indicators associated with infrastructure and living facilities surprisingly scale super-linearly with urban population size, contrary to expected sublinear scaling behaviours. In developing countries, different-sized cities have diverse agglomeration, industrial and resource allocation advantages, which can be reflected by scaling exponents. We characterise these unique features in detail, exploring the spatial disparities and temporal evolution of scaling exponents ( β). Strong regional variations and differences are particularly pronounced in Northeast China and the Beijing-Tianjin-Hebei Urban Agglomeration. Scaling exponent variations over time reflect the temporal evolution of the urban system and measure the coordination and balance of urbanisation. Economic output was most efficient in 2009 and β of GDP was slightly greater than 1.15 in recent years. Urban land expansion has been accelerating since 2000 with β remaining around 0.85–0.90. The study of urban scaling in China is enlightening in elaborating the uniqueness and coordination of urban development in rapidly urbanising countries and provides support in formulating differentiated urban planning for different-sized cities to promote coordinated development.