City Size Distribution Research Articles

Hiérarchies urbaines comparées en Méditerranée : 1960-2000

Cet article cherche a expliciter le lien entre le developpement economique et les dynamiques urbaines en Mediterranee. Il montre, plus particulierement, que les pays avec un niveau de developpement plus eleve (France, Espagne, Italie) se caracterisent par une structuration de leurs systemes urbains moins hierarchisee ou les villes moyennes occupent une place importante dans la distribution rang-taille des villes. A l’inverse, les pays emergents a revenu intermediaire (Turquie, Egypte, Maroc) connaissent des processus de concentration demographique plus marques, avec un surdimensionnement des plus grandes villes dans leur systeme urbain. Un tel constat semble confirmer l’hypothese d’une evolution en cloche des hierarchies urbaines d’un pays, avec une phase de concentration de la population dans les grandes villes durant les phases de croissance economique rapide, suivie d’une diffusion de la croissance demographique en faveur des villes moyennes, au-dela d’un certain niveau de developpement.

Modeling large Mexican urban metropolitan areas by a Vicsek Szalay approach

A modified Vicsek–Szalay model is introduced. From this, experiments are performed in order to simulate the spatial morphology of the largest metropolitan area of México: a set of clusters formed by the Valle de México metropolitan area (VMMA), Puebla metropolitan area (PMA) and Toluca metropolitan area (TMA). This case is presented in detail and here is called the Central México metropolitan area (CMMA). To verify the effectiveness of our approach we study two other cases; the set of clusters formed by the Monterrey zone (MZ, formed by the Monterrey metropolitan area and the Saltillo City metropolitan area) and the Chihuahua zone (ChZ, formed by the Chihuahua metropolitan area, Delicias City and Cuauthemoc City ), with acceptable results. Besides we compute three different fractal measures for all our areas of interest (AOI). In this paper, we focus on the global feature of these fractal measures in the description of urban geography and obtained local information which normally comes from inner city structures and small scale human decisions. Finally, we verified that the Zipf law is fulfilled by our simulated urban morphologies, so we know that our model follows it. As is normal for actual city size distributions, the CMMA case is presented in detail. We intend to pave the way in the understanding of population spatial distribution in a geographical space.

Re-examination of Zipf’s law and urban dynamic in China: a regional approach

Recent efforts have been made to interpret spatial-temporal evolution of urban system using Zipf’s law. The debates remain whether Zipf’s law holds true for large and diverse countries with long urbanization history, and how varied geographical settings with different socioeconomic conditions affect city-size distributions. This research investigates China’s urban system dynamics through expanded Zipf’s law at national and regional level. First, the paper revisits urban system dynamic theories and recent applications of Zipf’s law. The city data from 1960 to 2000 are then used to analyze rapid changes of urban systems in China through Zipf’s plots of cities over the entire nation and in six macro regions, respectively. The paper also examines top ten city rank changes nationally and regionally to examine temporal trajectories of key cities and the impacts on urban systems over space. Three types of Zipf’s law reflections are found over six China’s macro regions, based on the similarities of temporal dynamics of urban systems.

Testing the Pareto against the lognormal distributions with the uniformly most powerful unbiased test applied to the distribution of cities

Fat-tail distributions of sizes abound in natural, physical, economic, and social systems. The lognormal and the power laws have historically competed for recognition with sometimes closely related generating processes and hard-to-distinguish tail properties. This state-of-affair is illustrated with the debate between Eeckhout [Amer. Econ. Rev. 94, 1429 (2004)] and Levy [Amer. Econ. Rev. 99, 1672 (2009)] on the validity of Zipf's law for US city sizes. By using a uniformly most powerful unbiased (UMPU) test between the lognormal and the power-laws, we show that conclusive results can be achieved to end this debate. We advocate the UMPU test as a systematic tool to address similar controversies in the literature of many disciplines involving power laws, scaling, "fat" or "heavy" tails. In order to demonstrate that our procedure works for data sets other than the US city size distribution, we also briefly present the results obtained for the power-law tail of the distribution of personal identity (ID) losses, which constitute one of the major emergent risks at the interface between cyberspace and reality.

Threshold transitions in a regional urban system

In this paper we analyze the evolution of city size distributions over time in a regional urban system. This urban complex system is in constant flux with changing groups and city migration across existing and newly created groups. Using group formation as an emergent property, transition probabilities across the different groups were calculated. While short-term transition appears chaotic in the intermediate and lower rank groups, long-term transition across all rank groups reveals striking system structure over time.

Urban Accounting and Welfare

This paper proposes a simple theory of a system of cities that decomposes the determinants of the city size distribution into three main components: efficiency, amenities, and frictions. Higher efficiency and better amenities lead to larger cities, but also to greater frictions through congestion and other negative effects of agglomeration. Using data on MSAs in the United States, we parametrize the model and empirically estimate efficiency, amenities and frictions. Counterfactual exercises show that all three characteristics are important in that eliminating any of them leads to large population reallocations, though the welfare effects from these reallocations are small. Overall, we find that the gains from worker mobility across cities are modest. When allowing for externalities, we find an important city selection effect: eliminating differences in any of the city characteristics causes many cities to exit. We apply the same methodology to Chinese cities and find welfare effects that are many times larger than in the U.S.

Growth Pattern of Cities in India: Application of Statistical Models

Several probabilistic and deterministic (including economic) models have been proposed to predict the growth and pattern of distribution of cities by their population size. Among them Pareto family of distributions have shown a remarkable empirical regularity and the city size distribution in many countries is well approximated by these distributions. However, these models are useful to study the distribution of larger size cities satisfying certain regularity conditions. In the Indian context Pareto distribution fits well only to the distribution of cities with a population size of million plus. No such exercise has been made for other cities populated less than a million. In the present paper, an attempt has been made to characterize cities of all sizes through appropriate models applied to predict the growth pattern of cities in Indian context.

THE EVOLUTION OF U.S. CITY SIZE DISTRIBUTION FROM A LONG-TERM PERSPECTIVE (1900-2000)*

ABSTRACT This paper analyses the evolution of city size distribution in the United States throughout the twentieth century. It tests the validity of two empirical regularities studied in urban economics: Zipf's law (the rank-size rule), and Gibrat's law, or the law of proportionate growth. The main contribution of this work is the use of a new database with information on all the cities (understood as incorporated places), without size restrictions. Our results enable us to confirm that Gibrat's law holds (weakly), and that Zipf's law holds only if the sample is sufficiently restricted at the top, not for a larger sample.

Urban Accounting and Welfare

We use a simple theory of a system of cities to decompose the determinants of the city size distribution into three main components: efficiency, amenities, and frictions. Higher efficiency and better amenities lead to larger cities but also to greater frictions through congestion and other negative effects of agglomeration. Using data on MSAs in the United States, we estimate these city characteristics. Eliminating variation in any of them leads to large population reallocations, but modest welfare effects. We apply the same methodology to Chinese cities and find welfare effects that are many times larger than those in the US. (JEL H71, O18, P25, R11, R23, R41)

Spatial scaling of stable night lights

City size distributions, defined on the basis of population, are often described by power laws. Zipf's Law states that the exponent of the power law for rank-size distributions of cities is near −1. Verification of power law scaling for city size distributions at continental and global scales is complicated by small sample sizes, inappropriate estimation techniques, inconsistent definitions of urban extent and variations in the accuracy and spatial resolution of census administrative units. We attempt to circumvent some of these complications by using a continuous spatial proxy for anthropogenic development and treat it as a spatial complement to population distribution. We quantify the linearity and exponent of the rank-size distribution of spatially contiguous patches of stable night light over a range of brightnesses corresponding to different intensities of development. Temporally stable night lights, as measured by the Defense Meteorological Satellite Program-Operational Line Scanner (DMSP-OLS), provide a unique proxy for anthropogenic development. Brightness and spatial extent of emitted light are correlated to population density (Sutton et al., 2001), built area density (Elvidge et al., 2007c) and economic activity ( Doll et al., 2006; Henderson et al., 2009) at global scales and within specific countries. Using a variable brightness threshold to derive spatial extent of developed land area eliminates the complication of administrative definitions of urban extent and makes it possible to test Zipf's Law in the spatial dimension for a wide range of anthropogenic development. Higher brightness thresholds generally correspond to more intense development while lower thresholds extend the lighted area to include smaller settlements and less intensively developed peri-urban and agricultural areas. Using both Ordinary Least Squares (OLS) and Maximum Likelihood Estimation (MLE) to estimate power law linearity and exponent of the resulting rank-size distributions across a range of upper tail cutoffs, we consistently find statistically significant exponents in the range −0.95 to −1.11 with an abrupt transition to very large, extensively connected, spatial networks of development near the low light detection limit of the sensor. This range of exponents and transition are observed at both continental and global scales. The results suggest that Zipf's Law also holds for spatial extent of anthropogenic development across a range of intensities at both continental and global scales. The implication is that the dynamics of urban growth and development may be represented as spatial phase transitions when the spatial extent and intensity of development are treated as continuous variables rather than discrete entities.

The end of a paradigm: is Zipf’s law universal?

It is largely accepted among geographers and economists that the City Size Distribution (CSD) is well described by a power law, i.e., Zipf’s law. This opinion is shared by this community in a manner it could be treated as a paradigm. In reality, however, Zipf’s law is not always observed (even as an approximation), and we prefer to adopt a classification of the CSD into three classes. In this work, we present the characteristics of these classes and give some examples for them. We use the Israeli system of cities as an interesting case study in which the same ensemble of cities passes from one class to another. We relate this change to the urbanization process that occurred in Israel from the 1960s onwards.

Quelle est la nature de la croissance urbaine indienne ?

Résumé Les travaux sur la croissance urbaine investissent la relation entre l’activité économique et les évolutions urbaines d’un pays. Ces travaux, alimentés par l’opposition entre les théories de la croissance aléatoire et les théories de la croissance endogène furent, jusque-là, essentiellement appliqués aux systèmes extrêmement stables des pays anciennement industrialisés. Cet article propose de les transposer dans le cas d’un pays émergent. À l’aide d’un ensemble d’outils économétriques, il cherche à étudier la nature de la croissance urbaine indienne entre 1981 et 2005, une période de mutations économiques et sociales importantes dans ce pays. Classification JEL : R12, R23, N95, R15.

Unravelling the size distribution of social groups with information theory in complex networks

The minimization of Fisher’s information (MFI) approach of Frieden et al. [Phys. Rev. E 60, 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale invariant systems and classical gases [Phys. A 389, 490 (2010)]. Going beyond the ideal gas scenario is seen to be tantamount to simulating the interactions taking place, for a competitive cluster growth process, in a scale-free ideal network – a non-correlated network with a connection-degree’s distribution that mimics the scale-free ideal gas density distribution. We use a scaling rule that allows one to classify the final cluster-size distributions using only one parameter that we call the competitiveness, which can be seen as a measure of the strength of the interactions. We find that both empirical city-size distributions and electoral results can be thus reproduced and classified according to this competitiveness-parameter, that also allow us to infer the maximum number of stable social relationships that one person can maintain, known as the Dunbar number, together with its standard deviation. We discuss the importance of this number in connection with the empirical phenomenon known as “six-degrees of separation”. Finally, we show that scaled city-size distributions of large countries follow, in general, the same universal distribution.

Zipf's law for cities in the regions and the country

The salient rank-size rule known as Zipf's law is not only satisfied for Germany's national urban hierarchy, but also for the city size distributions in single German regions. To analyze this phenomenon, we build on the insights by Gabaix (1999) that Zipf's law follows from a stochastic growth process. In particular, Gabaix shows that if the follow Gibrat's law, we should observe Zipf at both the regional and the national level. This theory has never been addressed empirically. Using non-parametric techniques we find that Gibrat's law holds in each German region, irrespective of how regions are defined. In other words, Gibrat's law and therefore Zipf's law tend to hold everywhere in space. (This abstract was borrowed from another version of this item.)

Guest editorial] Networks, commuting and spatial structures: An introduction

This article introduces a special issue on networks, commuting, and spatial structures. The author focuses on the interaction between home and workplace as a central component in the travel behavior of commuting. The relation between land use (residential and employment location) and commuting is complex and is worth ongoing exploration, even though there is already a wealth of research on this issue. The author provides a brief historical overview of the literature from the 1960s to the present, covering topics including the relationship between population growth and commuting time, the size distribution of cities, commuting costs, the network concept, the relevance of dynamic data provision, and commuter preferences. The author defines the network concept as the idea that many spatial economic phenomena can be described by a network of interactions among agents, where interconnectivity and interoperability between the systems play important roles. The articles in this issue were selected with two goals in mind: to provide new analytical insights into the modeling and analysis of (complex) transportation networks, as well as into the behavioral preferences of users; and to constitute a methodological platform from which to identify novel research directions. This Special Issue originates from a Euro-NECTAR (Network for European Communication and Transport Activities Research) Conference, organized in Porto, Portugal, in May 2007. The introduction concludes with an acknowledgment of the researchers at that conference and a chart that summarizes the six papers in the special issue.

Appendix to 'Explaining Zipf's Law for US Cities'

This appendix presents evidence that the US size and growth data sets analyzed in the main body of the paper are consistent with the stylized facts of (i) Zipf's law in city size distribution tails; (ii) Lognormality of city size distribution bodies; (iii) Gibrat's law (approximately) for the growth of large cities; and (iv) Heterogeneity in city growth.

Monocentric City with Discrete Transit Stations

The monocentric model is extended by considering a discrete number of accessible mass transit stations. Households combine two modes for their daily home-to-work trip: a first mode for terminal access to stations and a second (long-haul) mode that consists of radial mass transit axes. The urban equilibrium, that is, city size and household distribution, is derived as a function of the mass transit network and the distribution of land housing capacity. At the urban equilibrium, the land rent peaks at transit stations and decreases with the travel cost from the city center, rather than with the distance to it. Accordingly, the housing lot size increases with the travel cost from the city center. These features distinguish this framework from previous monocentric models. The analysis is based on the assumptions that land owners are absent and the city is open (households’ level of utility is given and the population size is endogenous). For numerical illustration, the model is calibrated to a selected rail network in the Paris area. A sensitivity analysis of the urban structure and land use equilibrium is conducted, with key model parameters.

DOES THE RANK-SIZE RULE MATTER IN INDONESIA? DETERMINANTS OF THE SIZE DISTRIBUTION OF CITIES

In Indonesia the cities have continously grown. However they varied in size. Some cities have the population above two million citizens, while some have below than five hundred thousands. Some economic factors are hypothesized to influence such distribution. This study aims to test the rank-size rule (Zipf’s law) and to find the determinants of size distribution of cities. The panel data method is employed to satisfy the objectives of study. All district and provincial level data are used for year 1995, 2000 and 2005. The pareto exponent shows that the rank-size rule does not matter in Indonesia. Level of agglomeration economies, local government expenditure and number of administrative city increases the concentration of size of cities. The labor force participation and region’s openness affects the size of cities to be more equally distributed. Keywords: cities, rank-size rule, Zipf’s law, pareto exponent, panel data

Exploring and simulating the regularities in intra-urban population density structure

Sizes in a system of cities follow the so-called rank–size distribution or the more general Zipf's law. Previous research demonstrates that the rank–size relationship can be explained and simulated by a rather simple spatial choice model, describing individual residential behavior across cities. In studying population density within each of the 20 largest metropolitan areas in the United States, we discovered another type of regularity: population density at the tract level and the logarithm of the rank by tract density within a city exhibit a linear relationship. We call this rank–density regularity. In this article, we explore whether the simple spatial choice model originally developed to simulate city size distribution at the inter-urban scale can be used at the intra-urban scale to explain the rank–density pattern and the formation of urban density structure. We found that after adjusting the simple model for the city-edge constraint, the model can simulate the rank–density relationship reasonably well. In order to depict the spatial structure of population density more realistically, the model must include sub-centers, which increase the complexity of the model. Overall, the spatial choice model can reproduce the rank–density structure quite well. We believe the model captures the dominant forces in the formation of the population density distribution at the intra-urban scale.

The nexus of income and size distribution of Chinese cities, 1984–2003

We estimate the distribution dynamics of city income and size in China during 1984–2003 using stochastic kernel. Our results show that intra-distribution mobility are significant in both income and size and provide evidences on China experienced internal brain drain.