City Size Distribution Research Articles

MetaZipf. A dynamic meta-analysis of city size distributions.

The results from urban scaling in recent years have held the promise of increased efficiency to the societies who could actively control the distribution of their cities’ size. However, little evidence exists as to the factors which influence the level of urban unevenness, as expressed by the slope of the rank-size distribution, partly because the diversity of results found in the literature follows the heterogeneity of analysis specifications. In this study, I set up a meta-analysis of Zipf’s law which accounts for technical as well as topical factors of variations of Zipf’s coefficient. I found 86 studies publishing at least one empirical estimation of this coefficient and recorded their metadata into an open database. I regressed the 1962 corresponding estimates with variables describing the study and the estimation process as well as socio-demographic variables describing the territory under enquiry. A dynamic meta-analysis was also performed to look for factors of evolution of city size unevenness. The results of the most interesting models are presented in the article, whereas all analyses can be reproduced on a dedicated online platform. The results show that on average, 40% of the variation of Zipf’s coefficients is due to the technical choices. The main other variables associated with distinct evolutions are linked to the urbanisation process rather than the process of economic development and population growth. Finally, no evidence was found to support the effectiveness of past planning actions in modifying this urban feature.

One country, two “urban” systems: focusing on bimodality in China’s city-size distribution

In this study, we demonstrate the existence of bimodality in China’s city-size distribution and develop an urban-growth forecast model that incorporates this bimodality. Main data for our analysis are $$0.{25}^{\circ }\times 0.{25}^{\circ }$$ population density grids for the past 32 years, created from China’s official census data and county-level statistics. Our results show that the mixture of two Gaussian distributions outperforms unimodal distributions in explaining China’s historic urban-growth patterns, suggesting that the conventional unitary urban-hierarchy assumption lacks ground in China’s context. We also find that the higher-density mixture component increasingly dominates the entire distribution, and this gradual transition toward a unimodal city-size distribution is partly related to increased domestic population mobility.

Global city size hierarchy: Spatial patterns, regional features, and implications for China

City size hierarchy and distribution are always at the heart of urban studies, as they have a special ability to reveal the rules of city development and urban system spatial layouts. There is however a data deficiency with regard to city size hierarchy and distribution; in particular, an absence of complete statistics and spatial differences from the global perspective. To fill this research gap, this paper investigates global city size hierarchy based on 2014 data of more than 190 countries and regions by using classic models of “rank-size” rule, the fractal theory and the law of the primate city. We analyzed the spatial patterns, regional features, and implications for China from multi-scale and multi-dimension perspectives. The results show that: (1) There is an obvious pyramid structure of global city size distribution, but differences exist among countries and regions with different economic development types, suggesting a feature of “various types with pyramid dominated”; (2) The primate feature of global city size distribution is not very obvious. However, the primacy ratios of developed countries are much higher than others, and significant differences exist among different regions; (3) The global Zipf exponent and Hausdorff dimension are 0.66 and 1.29, respectively. Cities with middle ranks are in the majority, and the monopoly power of large and super cities is effective to a certain extent, indicating a decreasing concentration tendency in the city size distribution and a convergence trend in terms of relative population size, especially with regard to the medium and small cities; (4) The medium and small cities develop swiftly with limited agglomeration effect of large cities, and Chinese cities would significantly influence global urban progress and spatial patterns. Therefore, developing 780–800 cities will be reasonable for China's urbanization efforts by 2030.

Analisis Karakter Jalan Jalan Kombes H. Umar Kota Pagar Alam

As it is known that the road characteristics on a road are determined by road capacity, traffic volume and average speed. Road capacity is determined by the width of the road, side barriers which are influenced by activities and land use activities on the left and right of the road, besides being influenced also by other factors such as city size distribution factors, road shoulder construction. land use in determining road capacity. As it is known that MKJI (Indonesian Road Capacity Manual) has a procedure for calculating road capacity but traffic volume conditions that are often far above road capacity raise a question mark for the evaluation of the road capacity requirements. In this study the actual road capacity calculation is based on the approach of traffic volume and actual average speed which then the results of these calculations are compared with the results of MKJI calculations. Survey of traffic volume and speed at the research location.

An energy-centric theory of agglomeration

This paper sets out a simple spatial model of energy exploitation to ask how the location and productivity of energy resources affects the distribution of economic activity across geographic space. By combining elements from energy economics and economic geography we link the productivity of energy resources to the incentives for economic activity to agglomerate. We find a novel scaling law links the productivity of energy resources to population sizes, while rivers and roads effectively magnify productivity. We show how our theory's predictions concerning a single core, aggregate to predictions over regional landscapes and city size distributions at the country level.

Similarities and differences of city-size distributions in three main urban agglomerations of China from 1992 to 2015: A comparative study based on nighttime light data

Comparing the city-size distribution at the urban agglomeration (UA) scale is important for understanding the processes of urban development. However, comparative studies of city-size distribution among China’s three largest UAs, the Beijing-Tianjin-Hebei agglomeration (BTHA), the Yangtze River Delta agglomeration (YRDA), and the Pearl River Delta agglomeration (PRDA), remain inadequate due to the limitation of data availability. Therefore, using urban data derived from time-series nighttime light data, the common characteristics and distinctive features of city-size distribution among the three UAs from 1992 to 2015 were compared by the Pareto regression and the rank clock method. We identified two common features. First, the city-size distribution became more even. The Pareto exponents increased by 0.17, 0.12, and 0.01 in the YRDA, BTHA, and PRDA, respectively. Second, the average ranks of small cities ascended, being 0.55, 0.08 and 0.04 in the three UAs, respectively. However, the average ranks of large and medium cities in the three UAs experienced different trajectories, which are closely related to the similarities and differences in the driving forces for the development of UAs. Place-based measures are encouraged to promote a coordinated development among cities of differing sizes in the three UAs.

The size distributions of all Indian cities

We apply five distributions–lognormal, double-Pareto lognormal, lognormal-upper tail Pareto, Pareto tails-lognormal, and Pareto tails-lognormal with differentiability restrictions–to estimate the size distribution of all Indian cities. Since India contains numerous small cities, it is important to explicitly model the lower-tail behavior for studying the distribution of all Indian cities. Our results rigorously confirm, using both graphical and formal statistical tests, that among these five distributions, Pareto tails-lognormal is a better suited parametrization of the Indian city size data, verifying that the Indian city size distribution exhibits a strong reverse Pareto in the lower tail, lognormal in the mid-range body, and Pareto in the upper tail.

The post-Soviet evolution of the Russian urban system

ABSTRACTAn analysis of annual: city size data for more than 1000 cities in the period of transition from a planned to a market economy in 1991–2013 shows that: 1) predictions of the rapid growth of the urban system and of primary cities due to the introduction of market forces are not confirmed; 2) the city size distribution is almost unchanged; and 3) regression estimates reveal the significance of agglomeration economies. The results are consistent with the theories of random growth, increasing returns and locational fundamentals, but provide no convincing evidence for multiple spatial equilibria.

The size distribution and growth pattern of cities in China, 1982–2010: analysis and policy implications

ABSTRACTChina's urbanization in the late twentieth and early twenty-first centuries is a crucial process in transforming the country. Taking advantage of the de facto counts of city population in the last four censuses since 1982, this paper examines the city-size distribution and growth pattern of large cities in China in recent three decades. Combined with earlier data and work on the Mao era, the paper also presents some long-term trends and helps answer an important question: was China successful in controlling the growth of large cities? In addition, the paper analyzes the main features of China's urbanization policy in relation to the political economy and development strategy, and concludes with a discussion of the relevance of this study to the latest urbanization policy and the household registration system or hukou reforms in large cities.

Does Zipf’s lawhold for Polish cities?

AbstractIn this paper we study Zipf’s law, which postulates that the product of a city’s population and its rank (the number of cities with a larger or equal population) is constant for every city in a given region. We show that the empirical literature indicates that the law may not always hold, although its general form, the rank-size rule, could be a good first approximation of city size distribution. We perform our own empirical analysis of the distribution of the population of Polish cities on the largest possible sample to find that Zipf’s law is rejected for Poland as the city sizes are less evenly distributed than it predicts.

Spatial frictions

The world is replete with spatial frictions. Shipping goods across cities entails trade frictions. Commuting within cities causes urban frictions. How important are these frictions in shaping the spatial economy? We develop and quantify a multi-city general equilibrium model to address this question at three different levels: Do spatial frictions matter for the city-size distribution? Do they affect individual city sizes? Do they contribute to the productivity advantage of large cities and the toughness of competition in cities? The short answers are: no; yes; and it depends.

City size distribution and its spatiotemporal evolution in China

Based on the National Land Use/Cover Database of China (NLUD-C) in the end of the 1980s (the 1980s, hereafter), 1995, 2000, 2005, and 2010, 665 cities were selected to study the size distribution and its changes of urban lands in China. In this study, the spatiotemporal evolutions of urban land size distribution as well as the influence of administrative-level on these cities were explored by combining urban spatial positions and administrative-levels. Results indicate that: 1) City size distribution using urban lands was more practical and reasonable than using non-agricultural population. 2) In the 1980s, cities with ascending urban land rank were centralized in Eastern China, specially the Changjiang (Yangtze) River Delta, the Zhujiang (Pearl) River Delta, and Beijing-Tianjin-Hebei region. Cities in Central, Western, and Northeast China mainly indicated descending urban land rank. 3) The transfer of national development focus resulted in cities with ascending urban land rank becoming evenly distributed nationwide; however, this trend was slightly centralized around Chengdu, Chongqing, and Wuhan in different periods. 4) During the 1980s to 2010, the proportion of cities with ascending urban land rank in provincial capitals, municipalities, and special administrative regions (high-level cities, hereafter) was consistently higher than those in prefecture- and county-level cities except for 2005–2010. The ranks of the majority of the prefecture- and county-level cities were mainly descending, supported by ascending; the proportion of cities with unchanged rank is small. This study breaks through the bottleneck of traditional research in the area of city size distribution by examining urban land replacing the non-agricultural population. The current study also provides scientific explanation for the healthy and reasonable development of urban land as well as the coordinated development of population urbanization and land urbanization.

Walled cities in late imperial China

For thousands of years, the Chinese and many other nations around the world built defensive walls around their cities. This phenomenon is not well understood from an economic perspective. We rationalize the existence of city walls by developing a simple model that relates the dimensions and quality of city walls to a set of economic and geographic variables. We report an empirical analysis using hand-collected and previously unutilized data on city walls in the Ming (1368–1644) and Qing (1644–1911) Dynasties. We find that the circumference of a city wall is correlated with local economic and geographic conditions, that wall size is positively correlated with population size in the jurisdiction, and that frontier cities subject to a higher probability of attack tend to have stronger city walls. We examine the physical size distribution of walled cities in late imperial China and show that city sizes above a certain cutoff follow a Pareto law, although the Pareto coefficient decreases algebraically with the cutoff point. This result complements findings in the existing literature that focuses almost exclusively on the population size distribution of cities. We also find that cities with walls in the past have higher employment and population densities at the present time.

Zipf's Law: A Microfoundation

Existing explanations of Zipf's law (Pareto exponent approximately equal to 1) in size distributions require strong assumptions on growth rates or the minimum size. I show that Zipf's law naturally arises in general equilibrium when individual units solve a homogeneous problem (e.g., homothetic preferences, constant-returns-to-scale technology), the units enter/exit the economy at a small constant rate, and at least one production factor is in limited supply. My model explains why Zipf's law is empirically observed in the size distributions of cities and firms, which consist of people, but not in other quantities such as wealth, income, or consumption, which all have Pareto exponents well above 1.

The Size Distribution, Scaling Properties and Spatial Organization of Urban Clusters: A Global and Regional Percolation Perspective

Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms, and urban growth is one of the most eminent transformative processes. We analyze global land cover data and extract cities as defined by maximally connected urban clusters. The analysis of the city size distribution for all cities on the globe confirms Zipf’s law. Moreover, by investigating the percolation properties of the clustering of urban areas we assess the closeness to criticality for various countries. At the critical thresholds, the urban land cover of the countries undergoes a transition from separated clusters to a gigantic component on the country scale. We study the Zipf-exponents as a function of the closeness to percolation and find a systematic dependence, which could be the reason for deviating exponents reported in the literature. Moreover, we investigate the average size of the clusters as a function of the proximity to percolation and find country specific behavior. By relating the standard deviation and the average of cluster sizes—analogous to Taylor’s law—we suggest an alternative way to identify the percolation transition. We calculate spatial correlations of the urban land cover and find long-range correlations. Finally, by relating the areas of cities with population figures we address the global aspect of the allometry of cities, finding an exponent δ ≈ 0.85, i.e., large cities have lower densities.

China’s development policies and city size distribution: An analysis based on Zipf’s law

Since the establishment of the People’s Republic of China in 1949, China’s urban development policies have experienced dramatic changes, from anti-urbanisation before 1978, to anti-large-city-development during 1978–1999 and coordinated urbanisation in 2000–2012. Using city-level data from 1949 to 2012, this paper examines China’s development policies and city size distribution. Evidenced by the Zipf coefficient, we found that China’s city sizes became more evenly distributed before 2000, and this pattern was reversed after 2000. These findings suggest that China’s urban system is strongly affected by its shifting urban development strategies.

City size distribution across the OECD: Does the definition of cities matter?

This study provides new comparative evidence on city size distribution in OECD (the Organisation for Economic Co-operation and Development) countries, by using consistently defined functional urban areas (FUAs). FUAs are identified by an algorithm based on population density at grid level and commuting patterns and are thought to better approximate economic agglomerations and their internal spatial organisation. Results show that Zipf's law provides a better description of city size distribution when cities are measured in terms of FUAs rather than using traditional administrative definitions. In addition, Zipf's law describes well city size distribution both at country level and wider spatial scales, that is, by continent and for the whole OECD. Finally, the power law hypothesis – of which Zipf's law is a particular case – was not rejected in most of the countries.

Power Laws in Real Estate Prices? Some Evidence

Power law distributions have previously been observed in data like city-size distributions (Zipf’s Law), income distributions, and financial asset prices. In this paper we explore the distribution of real estate prices in Charleston County, South Carolina. We fit both a power law, lognormal and exponential distributions to the data and compare the goodness of fit among the distributions. We find that the best fit distribution lies somewhere between the lognormal and power law distributions. We estimate how the power law exponent changes over time and find a potential relationship between the shape of the power law distribution and the bursting of the real estate bubble in 2007.

An Evaluation of Pareto, Lognormal and PPS Distributions: The Size Distribution of Cities in Kerala, India

An Evaluation of Pareto, Lognormal and PPS Distributions: The Size Distribution of Cities in Kerala, India

Overall Size Distribution of Cities and Towns in India: 2011 Census

Overall Size Distribution of Cities and Towns in India: 2011 Census