An expected rank-size rule: A theoretical relationship between the rank size rule and city size distributions

This paper investigates a theoretical relationship between the rank-size rule and city size distributions. First, a method of relating a certain city size distribution to ranked city size is formulated by employing order statistics. Second, it is shown that there do not exist city size distributions which satisfy the rank-size rule. Third, an alternative rank-size rule is proposed as $\text{E(P}{}_{\mathrm{r}}\text{)?(r)}\text{?(r?y)}\text{=c}$, which is equivalent to the Pareto city size distribution. Last, an alternative statistical test for the rank-size rule is proposed to overcome a shortcoming of the conventional test. Along this line, the Hokkaido region data is analyzed.     

Rank-size rule for rural settlements

A new rank-size rule for rural settlements is presented. It replaces the urban rank-size P_n = P₁/n by P_n = P₁ δⁿ⁻¹ where P_n is the population size of the nth settlement. A graphic presentation of this rule is the straight line on a semilogarithmic grid. The basis for checking the proposed rule is a case-study based on population records for Samarian villages for 1596, 1931, and 1975. The explanation for the rural rank-size rule is that there is a certain optimal size of a rural settlement. This optimum shows itself in the form of a concentration of settlements within a relatively narrow range of sizes. It is suggested that each region and each culture has its own specific range of preferred sizes. The optimum level is thus the major factor which accounts for the special case of the rural rank-size rule. But variations in the range of concentration reflect the relative importance of dynamic factors: the development of urban centers, at one end, and the establishment of new off-shoots in marginal areas, at the other.     

The size distribution of cities: An examination of the Pareto law and primacy

This paper examines the Pareto and primacy measures of the size distribution of cities. The mean Pareto exponent for a sample of 44 countries is 1.136, somewhat greater than the exponent of one implied by the rank-size rule. We find that value of the Pareto exponent is quite sensitive to the definition of the city and the choice of city sample size. The significance of non-linear terms in variants of the Pareto distribution also indicate that the rank-size rule is only a first approximation to a complete characterization of the size distribution of cities within a country. The relatively low correlation between primacy and Pareto measures confirms the need for a variety of measures of city size distributions. This paper also suggests that large cities are growing faster than small cities in most of the countries in our sample. This is indicated by the positive coefficient on the first non-linear term introduced into the Pareto equation. Finally, variations in the Pareto exponent and measures of primacy are partly explained by economic, demographic, and geographic factors.     

基于分形理论谈安徽沿江环湖城市群的建立

简要介绍了分形理论的原理,运用分形理论,借助于罗特卡公式分析安徽省城市体系规模分布的分形特征,发现安徽省城市体系规模分布符合位序—规模率,存在城市体系规模分布过于均衡及首位城市、大城市规模过小的问题。提出建立安徽省沿江环湖城市群规模体系的发展对策。     

邯郸地区城镇规模体系的演变

使用首位度指数、位序——规模律及基尼系数的方法对邯郸地区1996、2001、2004、2006年四个年份的城镇规模分布的演变进行了分析,结果显示邯郸地区首位城镇垄断性较强,城镇体系首位度较高;城镇规模级别不合理,存在中间层次的断层现象;城镇体系的基尼系数远离平衡状态,产业梯度转移链条断裂。     

中国城市规模分布实证研究

选择1994-2004年中国城市规模位于前200住的地级及地级以上城市,分剐采用人口和建成区面积来表征城市规模,借助于分形理论进行研究发现,无论是从人口规模还是从用地规模来看,中国城市规模的分布符合"位序一规模"法则;外来人口的增加和2000年之后城市规模的加速增长使城市发展表现出向高位次城市集聚的倾向;但由于中国城市体系规模结构比较成熟,其基本特征并没有因时间、外来人口和城市规模的变化而改变;高位次城市仍有较大的发展空间.认为如何更好地识别城市的实际规模,促进城市的理性增长和城市规模结构的健康优化,是中国城市发展亟待解决的问题.     

A new interpretation on the optimal density regulations: Closed and open city

Optimality of urban density regulations differs between a closed city and an open city. We demonstrate, by examining optimal floor area ratio (FAR) regulation, how to control building size to mitigate traffic congestion externality in a monocentric city. Results show that a closed city requires not only downward adjustment to the market density at boundary locations using maximum FAR regulation but also upward adjustment at central locations using minimum FAR regulation. On the other hand, an open city requires only the former. The common practice of imposing only maximum FAR regulation is thus insufficient for closed cities although it is effective for open cities.     

1990-2004中国城市体系演变研究

通过考察人口在各级别城市的分布,利用住序-规模法则验证,对各省城市体系类型聚类分析,考察城市体系等级规模的变化,分析人口经济总量的分布现状及其演变,发现我国城市化的总体趋势是城市化进程比较快,呈现出特大城市和中小城市优先发展的事实.城市体系演变的趋势是城市体系由低级向高级、低水平向高水平、由不平衡向平衡型的演变.整体看我国城市的发展势头良好,但无论从绝对差距还是从相对差距看,东部地区相对快速发展的趋势还会持续下去.我国城市等级规模及人口经济规模分布极不均衡,在一定程度上影响区域经济的发展,应当分区域采取不同的发展战略.今后国家城市建设应当集约利用土地,重点扩大城市人口规模.国家在投资鼓励、区域发展政策等方面应当对中西部地区有实质性的扶持,努力使中西部地区城市人口与经济实力增强.     

The Rank-Size rule in the absence of growth

This paper makes a discovery in comparing Steindl's model of a growing system of cities to Champernowne's model of a stationary one: While the so-called Pareto coefficient (a measure of size concentration) of the city size distribution for a growing system is determined by the ratio of the average rate of growth in the sizes of cities to the rate of growth in the number of cities, and is thus independent of the variance in growth rates across cities, and also, to a large degree, independent of their behavior over time, the coefficient is directly proportional to this variance in the case of stationarity. This has interesting policy implications: As long as the urban system is growing as a whole, efforts to reduce rates of growth in high-growth areas and to raise them in low-growth areas, i.e., to reduce the dispersion in growth rates across cities, will have no effect on the shape of the size distribution of cities. However, if the system were to cease to grow, these same efforts would have a potentially great effect on this distribution. This suggests that the customary pessimism expressed by students of urban phenomena in the efficacy of legislation to alter the form of the size distribution of cities, a pessimism induced by their observation of the persistence of the current distribution over time in many countries, is primarily due to the circumstances in which these systems are observed, i.e., in periods of growth and expansion.     

The Structure of Sprawl: Identifying and Characterizing Employment Centers in Polycentric Metropolitan Areas

This paper applies a consistent framework to four comparably sized metropolitan areas to identify and characterize their employment centers. Employment centers are identified as places that exceed a threshold employment density and a threshold employment level. They are also characterized as specializing on the basis of location quotient analysis. We find clear evidence of specialization in every employment center in the four metropolitan areas studied. Our interpretation is that what we are observing is a systematic change in metropolitan structure rather than a random sprawling of firms. We also find some evidence that the size distribution of employment centers follows the rank-size rule. This suggests that there is structure not only in the distribution of economic activity among the employment centers but also in their size distribution. Because less than 50 percent of metropolitan employment is within employment centers, future research should focus on understanding the more diffuse employment patterns. The rank-size rule gives some guidance as to the expected size distribution of employment throughout the metropolitan area.     

Determinants of urban population density functions: a procedure for efficient estimates

A model of urban population density functions is proposed that uses all available data on densities in urban areas. "This model postulates that population density at each census tract in each city is determined by city size, transportation costs, land supply, income and age of city." The model is applied to data on cities in Israel.     

Growth in a Cross-section of Cities: Location,Increasing Returns or Random Growth?

Abstract

This article analyses empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we consider a large database of urban, climatological and macroeconomic data from 1,173 US cities observed in 1990 and 2000. The econometric model is robust to the presence of spatial effects. Our analysis shows the existence of increasing returns and two distinct equilibria in per-capita income and population growth. We also find important differences in the structure of productive activity, unemployment rates and geographical location between cities in low-income and high-income regimes.     

Comparative statics analysis of a fully closed city

This paper extends the existing comparative statics analysis about open or semiclosed cities, notably that of W. Wheaton [J. Econom. Theor., 9 (2), 223–237 (1974)], to a fully closed city, where urban land rent is redistributed to the city population. Specifically, we examine the effects on changes in exogenous variables, such as population size, agricultural rent, and initial endowments, on endogenous variables such as welfare level, city size, and rent schedule. Most, but not all, of the existing results are reestablished. Surprisingly, it is shown that, in contrast to the existing literature, and perhaps to intuition, the city area may shrink when the city population increases. The paper also extends the existing literature by analyzing the effect of the exogenous variables on the endogenous income and the demand for transportation. It is shown that, under plausible assumptions, the quantity of transportation demanded declines with its price.     

城市制度:城市发展的核心构架

讨论了城市制度的本质、结构、功能及我国城市的发展模式 ,提出城市制度不完善是我国城市发展滞后的重要原因 ;建构与转换城市制度是城市发展进入自觉阶段的根本标志。我国城市要实现跨越式发展 ,应以制度创新为先导     

城市的脆弱性及其规避措施

在城市安全问题上引入"脆弱性"这一概念,初步构建城市脆弱性的研究框架:概念界定、影响因素和评价方法。城市规模、密度和形态,经济社会发展和基础设施水平以及应急管理水平,是影响城市脆弱性的结构性因素。突发事件是城市脆弱性产生的主要胁迫因素。城市规划和建设应以安全为基点,将城市脆弱性分析作为新依据,建立城市规模、密度和形态三位一体的关系,做好城市安全基础设施规划和建设,增强城市突发事件的综合应对能力。     

The golden rule of urban transportation investment

The purpose of this paper is to find an optimal taxation rule for transportation investment in an ever growing urban economy. First we dynamize a standard circular-city model with identical residents by introducing population growth and transportation improvements over time. Assuming that utility functions are of a constant-elasticity form and transportation investment is financed by an income tax, we prove the existence, uniqueness and stability of a balanced growth equilibrium for each given tax rate. Then, an optimal tax rate is determined so as to maximize the balanced growth equilibrium level of utility for every resident in the city. It is also shown that our simple rule remains valid in the case of two income classes.     

Sequential city growth: Empirical evidence

Using two comprehensive datasets on populations of cities and metropolitan areas for a large set of countries, I present three new empirical facts about the evolution of city growth. First, the distribution of cities’ growth rates is skewed to the right in most countries and decades. Second, within a country, the average rank of each decade’s fastest-growing cities tends to rise over time. Finally, this rank increases faster in periods of rapid growth in urban population. These facts can be interpreted as evidence in favor of the hypothesis that historically, urban agglomerations have followed a sequential growth pattern: Within a country, the initially largest city is the first to grow rapidly for some years. At some point, the growth rate of this city slows down and the second-largest city then becomes the fastest-growing one. Eventually, the third-largest city starts growing fast as the two largest cities slow down, and so on.     

京津冀区域空间格局及其优化整合分析

本文以京津冀区域空间结构为研究对象,从点、线、网络和域面四个基本空间要素入手,研究提升区域竞争力的空间整合规律.研究认为,京津冀区域人口和城镇体系的空间分布不均衡,一方面,以自然条件为基础,呈现东南集中特征,另一方面,中小城镇分布以京广、京九、京哈铁路等为依托,呈现以北京为中心的强向心分布;城镇带分布大体可划分为京广线...     

二代优先:当前城市户籍政策调整的一种思路

城市户籍政策调整对于统筹城乡发展、促进社会和谐有着至关重要的战略意义.本文在充分剖析当前户籍制度改革困境的基础上,提出了“二代优先”的户籍政策调整新思路,即允许流动人口子女先于父母双方获得城市常住户口,其基本前提是其父母已经在该城市就业、居住达到一定的年限.这一政策可以较好地与现有落户政策衔接,具有较高的可行性,并且有...     

基于网络分析法的广义宜居城市概念

长期以来,我国城市发展遵从于一种单纯以GDP的增长,作为唯一评价尺度的发展模式.宜居城市概念的提出是基于对我国城市发展模式的反思--变单一评价指标为综合评价指标的城市发展模式.其目的在于通过发展模式的转变,而达到转变发展方向的效果.然而,这样的宜居城市理念并没有改变城市发展的行为范式--不同的城市仍在统一的评价体系的导向下发展,仍然无法避免"千城一面"的城市发展误区.城市是文明的产物,不同的城市有着不同的文化积淀,从而决定不同城市居民的价值观.城市是否宜居只能由城市居民去判断,故而,必须重视不同城市文化影响下,城市价值观对宜居城市评价体系的个性化要求.传统宜居城市的评价基于层次分析法不能反映城市文化对评价体系的反作用.这里提出基于网络分析法的广义宜居城市的概念,可以充分考虑不同城市文化对城市宜居程度评价指标的具体要求,方便的得到更合乎逻辑的评价结果.