Spatial and Temporal Evolution Characteristics of China’s City Size Distribution Based on New Criteria

Abstract

The distribution and evolution of city size are critical for town layout optimization. Based on the most recent classification standards and census data for 2010 and 2020, this paper aims to explore China’s city size distribution above the prefecture level. Using the rank-size law, Kernel density estimation, Spatial Gini coefficient, and Markov transition matrix, the newest city size distribution characteristics and spatial evolution patterns in China are shown from national and regional viewpoints. Our main findings are as follows: (1) Over the period from 2010 to 2020, China’s city size distribution follows the rank-size law but deviates from Zipf’s ideal. The distribution of city size is centralized in general. (2) China’s city-size hierarchy exhibits a good “olive” structure, with fewer megacities but larger populations. The growth rate of small and medium-sized cities is higher than the number of medium-sized cities. (3) China’s cities have grown greatly in size, with more than a third of them expanding. Over the last decade, high-ranking cities have become the primary driver of change. (4) There are disparities in city size between regions. A diminishing trend can be seen in three key economic zones.

1. Introduction

An urban system is a collection of cities with different divisions, hierarchies, and connections in a relatively complete region or country. Its formation, evolution, and development are historically dynamic processes [1]. The hierarchical scale structure includes the combination relationship, characteristics, and differences among cities, and is called the three major structures of the urban system together with the functional structure and the territorial structure. We need to correctly understand the characteristics of the hierarchical size structure of the urban system in China and the provinces. It plays a significant role in formulating urban system planning and spatial development strategies in the new era. Resultantly, it also promotes the coordinated development and rational layout of cities.

The study of the size of urban systems first originated in Europe and the United States. In 1913, the German geographer Auerbach [2] first found that the distribution of urban population data closely matched the Pareto distribution based on five European countries and the United States. On this basis, the researcher has given an exponential distribution of the rank variable in his study of city size in the United States. Similarly, Zipf [3] stated that the Pareto index of the city size distribution with an integrated urban system in an economically developed country is 1. This law is often referred to as Zipf’s law. Zipf’s law is supported by numerous early researches, Krugman [4] and Gabaix [5] found that the size distribution of urban systems in the United States follow Zipf’s law. Similar evidence is reported by Levy [6], Ioannides and Overman [7]. Several subsequent studies have shown that an appropriate definition of the city improves the fit of Zapf’s law [8,9,10]. After the 1970s, the data updating and the foreword of new theories brought a breakthrough in the study of the size structure of the urban system. In terms of the evolution of city size distribution, many scholars explored the mechanisms of the substance and Spatio-temporal evolution of city hierarchical size, respectively [11,12,13,14,15,16,17,18,19,20,21,22,23,24]. A large number of studies have found that the distribution of city size is relatively stable in developed countries, while it is more variable in emerging markets [25,26,27]. In recent work, the city size system has been researched more multidimensionally, with studies on the relationship between the new economy and city size [28], whether megacities undermine the urban hierarchy [29], the sensitivity of the city size distribution to the definition of a city [30], the relationship between development policies and city size distribution [31], etc.

The study of city size in China is divided into two phases. The first stage was from the 1980s to 2000, during which scholars such as Yan et al. [32] and Xu [33] pioneered the study of the hierarchical scale of China’s urban system, and they used Chinese urban population data to conduct a test of the rank-size law. Zhou et al. [34] also measured the size hierarchy characteristics of Chinese cities and proved that the Chinese urban system belongs to a relatively balanced type of rank-size structure. The second stage is entering the 21st century, when more scholars used new data to analyze the structure of China’s urban system, such as Wang [35], who calculated the law of the primate city, four-city index, and eleven-city index of China’s urban system from 1984 to 1995. Liu et al. [36] investigated the impact of rapid economic growth and changes in the urban management system on the size structure of China’s urban system. Using urban population data from cities above the county level countrywide, closest neighbor, and spatial autocorrelation analyses, Ye et al. [37] quantified the spatial distribution patterns of cities of various sizes. Ye and Zhuang [38] quantified the interprovincial differences in the size structure and the evolution pattern of spatial distribution of Chinese cities from 2000–2014 using the rank-size law. Chen et al. [39] assessed the distribution characteristics of urban size in China based on the Fifth and Sixth National Census, as well as resident population data from 312 cities and autonomous areas from 2015 to 2019. Recent studies have shown that scholars are trying to explore the causes of city size distribution from economic, cultural, and environmental perspectives, most notably Wang [40], Wang and Sun [41], and Wang and Feng compared the distribution and dynamic evolution characteristics of city size in China and 17 other countries to investigate the influence of spatial determinants in the evolution of city size. Based on the Land Scan Global Population Database, Wang et al. [41] and Sun et al. [42] investigate the relationship between regional income, environment, and city-size distribution. This conclusion was improved by You [43], Zhao and Liu [44] and others from the perspectives of regional economic development and the digital economy, respectively.

Numerous studies have pointed out that the city size distribution does not always fully conform to Zipf’s law and may have certain deviations [45,46], and that the city size system evolves dynamically. Specifically for China, Fang [31] and other scholars have pointed out that Chinese cities were more uniform in size before 2000. Sun [47] et al. point out that the distribution of city size in China is moving from decentralization to concentration from 2000–2014. Wan et al. [48] study the evolution of China’s urban system from 1990–2017 and point out that the distribution of Chinese cities is deviating from Zipf’s law. However, due to the differences in the definitions of cities among scholars and the inconsistent statistical calibers used, a number of different and even opposing research results have emerged. Wan et al. [49] examined the statistical distribution of urban size in China from the perspectives of the national, regional, and provincial levels by screening a sample of cities using internationally accepted urban population size threshold criteria. Wang and Zheng [50] used postal network data and studied by GIS tools and the bite-scale method to conclude that the bite-scale distribution of modern Chinese cities conforms to Zipf’s law. Yu et al. [51], Qi and Liu [52] analyzed the size of China’s cities based on the non-agricultural population data in the household population statistics. During the rapid urbanization of China from 2010 to 2020, a large number of the agricultural population converted to the urban population, which no longer accurately reflects the actual urban size.

Therefore, it has been controversial whether urban development follows Zipf’s law or not, and the possible reasons for these factors are differences in the scale of study, study area and study methods. According to Gabaix [1], Zipf’s law should be valid in all types of areas, and Giesen [14] verified and supports the hypothesis. However, this does not adequately explain whether Zpf’s law will remain stable in a country or region [17,22,53]. Although studies have been conducted to test this for some countries and regions, it is still insufficient. As a developing country, China is still in a stage of rapid urban development, and with its large population, the evolution of Chinese urban size can provide a good sample to test whether Zipf’s law has stability in a country or region.

Obviously, academic research on the structure of urban systems has been very rich in theory and mature methods. Among them, census data, because of its high authority, have been widely used in the study of city size system all over the world [25,26,54]. It is no exception in the study of the size of urban systems in China [55,56]. However, the urban population statistics used by scholars in the existing studies are as recent as the sixth census, and no studies have been conducted using the most recent data from the seventh census. China’s urbanization has experienced rapid growth in the past period [57,58]. Within this period, the State Council issued the Notice on Adjusting the Criteria for City Size Classification in November 2014, and the criteria for city size classification have changed significantly as a result. However, China’s sixth census was conducted in 2010, more than a decade ago now, and has clearly become difficult to reflect the latest structure of China’s urban system.

Based on the above background, the aims of this paper are to analyse two key questions. The first is to investigate what are the characteristics of the urban size structure in developing countries represented by China in recent years; the second is to test whether the urban size distribution is stable. Accordingly, this paper examines the spatial and temporal evolution of China’s urban size structure during the decade from the sixth census to the seventh census, in accordance with the latest Chinese urban size classification criteria.

Compared with the existing literature, the contributions of this paper are: first, using the latest data from the seventh census, we study the size structure of the Chinese urban system at the municipality level through the international common urban population size, which is an important complement to the changes in the size of the Chinese urban system in the past decade. Second, this paper takes into account the impact of changes in administrative divisions on the sample data, takes different samples for measurement, and examines the characteristics of China’s urban scale distribution at the national and regional levels, which is important for grasping the latest dynamics of China’s urban development and bridges the temporal and spatial discontinuity in China’s urban development. Third, by comparing the latest urban size structure with existing studies, it can provide evidence to support whether Zipf’s law is stable in a country or region.

2. Data and Methods

2.1. Methods for the Statistical Distribution of City Size

2.1.1. Kernel Density Estimation (KDE)

The kernel density estimation approach estimates arbitrary probability distributions without a priori knowledge of the data distribution, without attaching any assumptions to the data distribution, and by inferring the distribution of the total data from a small number of samples. Compared to general estimation methods and parameter estimation, KDE is more robust and obtains better continuity of the probability density function [59,60]. The trend of the city size distribution over time can be tested by non-parametric and density estimates, as shown in Equation (1):

$$f_{\begin{array}{c}h\end{array}}\left(x\right)=\frac{1}{nh}{{\displaystyle \sum }}_{\begin{array}{c}i=1\end{array}}^{n}K\left[\left(x-x_i\right)/h\right]$$

(1)

where $f_{\begin{array}{c}h\end{array}}\left(x\right)$ is the estimated probability density function; K(·) is the kernel function, which is essentially the weight function; h is the bandwidth, and the larger the bandwidth h, the smoother the estimated probability density function $f_{\begin{array}{c}h\end{array}}\left(x\right)$. In this paper, we estimate the optimal bandwidth h based on the commonly used Epanechnikov kernel, which is the bandwidth chosen by automatic adjustment in STATA 16.0 based on the sample data.

2.1.2. Rank-Size Law

The “rank-size” law examines the size distribution of an urban system from the relationship between the size and the rank of the city. A large number of studies within and across borders have shown that the rank-size law is the most comprehensive in portraying the size distribution of cities, and its expression is as follows:

$$R_i=K{P}_i^{-q}$$

(2)

Taking the logarithm of both sides of Equation (2), it can be converted to:

$$Log{R}_i=LogK-qLog{P}_i$$

(3)

where $R_i$ is the rank of the ith city; $R_i$ is the population size of the ith city in descending rank of city size; $K$ is a constant; $q$ is the size structure index, which can reflect the overall characteristics of the city size distribution. For $q$ = 1 (or the size structure index is not statistically different from 1), the city size distribution is close to the ideal model of Zipf’s law. That is, the second city in a country has half the population of the largest city, the third city is 1/3 the population of the largest city, and so on. Since q is the slope of the linear regression of the logarithmic function, the larger q indicates that the smaller the size of cities in the same class, the lower the centralization of cities, or the more evenly distributed the size of cities, with constant intercept. 0 < q < 1, indicating that the distribution of city size is centralized, the population flows to large cities, and the development of small and medium-sized cities is incomplete; q > 1, indicating that the distribution of city size is more dispersed, the development of low-rank cities is more prominent, and the centralization of large cities is not high.

Since the small-sample OLS (Ordinary Least Squares) estimates are biased and the regression after city size ranking may generate autocorrelation among the nuisance terms, thus biasing the standard error estimates of q. Gabaix and Ibragimov proposed a remedial method of regression using logarithms that vary by 1/2 rank. It has been demonstrated that the corrected OLS can reduce bias very well.

$$\log \left(R_i-\frac{1}{2}\right)=\log K-q\log P_i$$

(4)

Furthermore, the study of the modified OLS results revealed that all estimated q values were higher than classic OLS, but the pattern remained the same, with the value of q increasing as the sample size decreased. Combined with the scatter plot of ordinal size, it can be seen that the ordinal and population size have an inverted “U” shape, which indicates that the relationship between ordinal and city size may not be completely linear. Therefore, referring to the method of Xu and Zhu [61], the squared term of the logarithm of the city size is included in the regression.

$$\log \left(R_i-1/2\right)=\log K-q\log P_i+\beta \left(\log P_i\right) \left(\log P_i\right)$$

(5)

2.2. Methods for the Spatial Distribution of City Size

2.2.1. City Size Index

The city size index is a common indicator of city size distribution that represents, to some extent, the centralization of urban development elements in the largest cities in the urban system. The first degree, four-city index, and eleven-city index are commonly used to measure it. The first degree is the ratio of the largest city’s population size to the second-largest city’s population size, while the four-city index is the sum of the second, third, and fourth-largest cities’ population sizes, and so on. The city size index is determined as follows:

$$P{I}_N=\frac{P_1}{{{\displaystyle \sum }}_{i=1}^N{P}_{i+1}}$$

(6)

where P₁, P₂, and P_N are the resident populations of the first, second, and Nth largest cities in terms of population size, respectively.

2.2.2. Centralization (Spatial Gini Coefficient)

The spatial Gini coefficient is a measure of spatial agglomeration with the advantage of combining higher accuracy and less arithmetic, it has recently been used to quantify the centralization of population distribution across cities as a characteristic of city size distribution. A higher spatial Gini coefficient indicates a higher centralization of city size, i.e., a larger size gap between cities and migration to large cities. The narrower the gap in city size, on the other hand, the more distributed the population is throughout cities and the more developed small and medium-sized cities are. The spatial Gini coefficient calculation method proposed by Marshall [62] is used to measure the centralization of the spatial distribution of the size of cities in China.

$$G=\frac{1}{2n\left(n+1\right)\mu }{{\displaystyle \sum }}_i^n{{\displaystyle \sum }}_j^n|P_i-P_j|$$

(7)

where G is the spatial Gini coefficient; n denotes the number of cities; u denotes the average population size of cities in the region; P_i and P_j denote the population size of cities i and j, respectively.

2.3. Methodology for Analyzing the Dynamic Evolution of City Size

Spatial Gini coefficients, for example, describe the degree of centralization of city size distribution, but cannot portray the dynamics of the full range of cities during inter-temporal evolution, such as the impact of the growth of large cities on small cities. Black and Henderson [15], Anderson and Ge [63], and others, applied Markov transfer matrices to the analysis of the dynamic evolution of urban size structure across countries.

$$F_{t+1}=M{F}_t$$

(8)

where F_t+1 and F₁ denote the rank of a city at the end and beginning of the period, respectively. M is the Markov transfer matrix, and any element P_ij in M denotes the probability of a city in rank i switching to rank j in the next cycle, estimated by the expression M_ij = n_ij/n_i. n_ij denotes the composite of the number of cities with rank i in period t converted to cities with rank j in the next cycle, and n_i is the sum of the number of cities with rank i in period t.

2.4. Data

The size of the urban population is an extremely important and comprehensive characterization of a city. Studies of urban issues in China have differed in the selection of appropriate and continuous urban population measures. The difference is due to the frequent changes in the delineation of urban areas in China and the inconsistency of China’s urban population statistics over time. Two types of data are often used in national studies. One category is the household population or urban non-agricultural population in the China Statistical Yearbook to determine the size of the urban population. In the context of China’s rapid urbanization and massive population movement, the data ignore part of the household agricultural population and underestimate the size of cities. There is also a category of the urban resident population, which does not accurately reflect the true urban population size as this data includes the population of non-urban core areas, expanding the size of the city. City population data from the national census is based on the resident population in urban areas, which corrects the bias of ignoring population movement in the household population and is more accurate data on the size of the urban population compared to the household non-agricultural population.

The definition of urban population statistics in the census has changed relatively significantly. Since the founding of the PRC, China has conducted seven national censuses. Among them, the third to the seventh national census was conducted after the reform and opening up. It was not until the Sixth National Census that a uniform guideline for the urban population was constructed based on the principle of residence, consistent with the concept of urban physical territory. The data mentioned in the first five national censuses regarding the population of urban areas lack comparability with the results of the Sixth and Seventh National Census. Therefore, this paper sets the study period as 2010–2020, and the resident population of municipal districts of prefecture-level cities is used to measure the size of the urban population. The data on the resident population in the city are obtained from the National Bureau of Statistics, China’s Sixth National Census in 2010, China’s Seventh National Census in 2020, Tabulation on the 2010 Population Census of the People’s Republic of China by Country, and the census bulletins of various provincial and urban areas. The sample of prefecture-level cities with selection comes from the statistical table of administrative divisions of the Ministry of Civil Affairs of the People’s Republic of China.

Internationally, cities are usually defined using geographic units with a population size above a certain threshold. Among them, the most commonly used cut-off point is 100,000 people. In addition, the adjustment of urban zoning can also have an impact on the distribution of city size. Therefore, this paper deals with the data in two main ways: firstly, to classify the sample according to the population threshold, and secondly, to integrate the sample data according to the zoning adjustment.

3. China City Size Classification and Statistics

In November 2014, the State Council published the Notice on Adjusting the Criteria for the Classification of City Size to establish new criteria for the classification of city size. Cities are classified into five categories and seven classes using the resident population as the statistical caliber: cities below 500,000 are classified as small cities, with cities above 200,000 and below 500,000 as Type I small cities and cities below 200,000 as Type II small cities; cities above 500,000 and below 1 million are classified as medium cities; cities above 1 million and below 5 million are classified as large cities, with cities above 3 million and below 5 million as Type I large cities and cities above 1 million and below 3 million as Type II large cities; cities above 5 million and below 10 million are classified as large cities; cities above 5 million and below 10. According to the new standard, in 2010, there were 287 cities above the prefecture level in China, including four municipalities directly under the central government, 15 sub-provincial cities, and 268 prefecture-level cities. By 2020, China’s cities above the prefecture level will grow to 297, including four municipalities directly under the central government, 15 sub-provincial cities, and 278 prefecture-level cities.

Table 1. Population and city number distribution and growth by size class, 2010–2020.

	City Population (Millions)								Number of Cities (by Population Size)
Year	Total	<0.2	0.2–0.5	0.5–1	1–3	3–5	5–10	>10	Total	<0.2	0.2–0.5	0.5–1	1–3	3–5	5–10	>10
Population(millions)
2010	479.20	0	18.5	74.6	147.8	73.5	75.5	89.4	287	0	47	103	99	21	11	6
2020	661.52	0.58	12.3	64.7	215.9	65.4	119.2	183.5	297	6	30	86	129	17	18	11
Percentage distribution
2010	100	0	3.9	15.6	30.8	15.3	15.8	18.7	100	0.0	16.4	35.9	34.5	7.3	3.8	2.1
2020	100	0.1	1.9	9.8	32.6	9.9	18.0	27.7	100	2.0	10.1	29.0	43.4	5.7	6.1	3.7
Annual growth rate(percentage)
2010–2020	3.8	0.01	−0.2	−0.58	0.18	−0.54	0.22	0.9	0.34	0.2	−0.63	−0.69	0.89	−0.16	0.23	0.16

provides statistics on the distribution characteristics of the number of cities and population size in 2010 and 2020. The number of medium-sized and smaller cities has declined, while the number of large cities, supercities, and megacities has increased. Over the decade, the number of large cities (Type II) increased by more than 8.9%, and their population share increased to 32.6 percent. China’s city-size hierarchy in 2010 and 2020 is depicted (Figure 1). China’s city size in 2010 and 2020 is centralized between medium-sized cities and large cities, showing an “olive-shaped” structure with narrow ends and wide middle, which is a relatively well-structured city-size hierarchy. This is consistent with the findings of domestic and foreign scholars. Microscopically, in 2010, there were 150 medium-sized cities and smaller, as well as 120 major cities, which included 21 Type I large cities, 99 Type II large cities, 11 supercities, and six megacities. By 2020, there will be 122 medium-sized cities and smaller, 146 large cities (including 17 Type I large cities, 129 Type II large cities, 18 supercities, and 11 megacities), and 122 medium-sized cities and smaller. Chengdu, Xi’an, Wuhan, Hangzhou, and other regional Central cities are rapidly expanding in size and growing into megacities.

Between 2010 and 2020, China’s total urban population increases from 479.2 million to 661.5 million, with an average annual growth rate of 3.8%, while the average annual growth rate of China’s total population during the same period is only 0.53%. In contrast to the low rate of population growth, China’s cities have expanded rapidly over the past decade. This has been made possible by vigorous urbanization and productivity gains, with large-size population movements between urban and rural areas. The population share of medium-sized and below cities decreases more significantly, while the population share of large cities decreases from 46.1% in 2010 to 42.5% in 2020 despite a significant increase in the number of cities, and that of super cities and mega-cities increases from 34.5% in 2010 to 45.7% in 2020.

4. Empirical Analysis

4.1. Statistical Distribution Characteristics of City Size

4.1.1. Probability Density Distribution of City Size Structure in China

The change in city size over time can be examined using non-parametric kernel density estimates. With the logarithm of city size in the horizontal coordinate and probability density in the vertical coordinate, Figure 2 depicts the distribution and trend of relative city size in 2010 and 2020. The probability density curves all exhibit a single-peaked distribution, with the peak occurring near the mean city size, and the center of the kernel density function has not shifted considerably from the overall distribution. This represents the general characteristics of city size distribution, namely that the number of cities changes depending on the size class. The city size is centralized in the interval corresponding to large cities, and the overall structure is more stable. The occurrence of significant geographical unevenness characteristic of inter-city size is demonstrated by the fluctuation in wave width. When compared to the peak in 2020, the kernel density curve in 2010 is higher, and the right-hand curve decreases more quickly. It shows that the distribution of city size in China tends to be centralized from scattered in 2010, with a significant trend of population movement to large and medium-sized cities.

4.1.2. Validation of Zipf’s Law for the Size of Chinese Cities

The distribution of city sizes plays a significant role in a nation’s overall spatial pattern. A reasonable city size distribution is beneficial to the operation of the city system and the competitiveness of the country. It affects the overall development efficiency and economic growth of the country through the spatial allocation of resources and factors. When Zipf’s law is in effect, it is obvious that if the national population and the pace of urbanization are known, the population of any city can be simply projected or estimated. In the absence of Zipf’s law, the distribution of city sizes may be illogical, allowing the population to be better guided toward a more effective spatial pattern. For the creation of national and regional development strategies and plans, Zipf’s law research has theoretical and practical significance.

German geographer, Auerbach, first proposed in 1913 that the distribution of city sizes in a given territory follows a Pareto distribution. Zipf (1949) further developed this by stating that the size distribution of cities not only follows the Pareto distribution but also takes the Pareto index to be equal to one. Zipf’s law is a special law of rank size, which considers the size distribution of an urban system in terms of the relationship between the rank of cities and their size (

Table 2. Rank–size estimation of cities.

		Rank-Size Equation		Corrected Rank-Size Equation		Quadratic Rank-Size Equation
Year	Obs	q	R2	q	R2	Log (Size)	Log2 (Size)	R2
Full sample
2010	287	1.133 ***	0.956	1.162 ***	0.947	0.880 ***	−0.202 ***	0.991
		(0.000)		(0.000)		(0.000)	(0.000)
2020	297	0.872 ***	0.820	0.892 ***	0.810	0.513 ***	−0.150 ***	0.978
		(0.000)		(0.000)		(0.000)	(0.000)
Balanced panel
2010	285	1.130 ***	0.956	1.158 ***	0.947	0.885 ***	−0.202 ***	0.991
		(0.000)		(0.000)		(0.000)	(0.000)
2020	285	1.070 ***	0.952	1.096 ***	0.941	0.984 ***	−0.195 ***	0.988
		(0.000)		(0.000)		(0.000)	(0.000)
Sample with a threshold 100,000
2010	287	1.133 ***	0.956	1.162 ***	0.947	0.880 ***	−0.202 ***	0.991
		(0.000)		(0.000)		(0.000)	(0.000)
2020	294	1.024 ***	0.929	1.048 ***	0.918	1.091 ***	−0.205 ***	0.988
		(0.000)		(0.000)		(0.000)	(0.000)

Note: *** denotes significance at the 1% level.

). It is quite general for generalizing the size distribution of cities in countries and regions. In the period 2010–2020, China’s rank-size correlation coefficient is close to 1, indicating that the distribution of city size in China is compatible with the rank-size law. According to the table, the city size distribution in 2010 was fairly dispersed. Further, q was 0.872 by 2020, showing that the shifting trend in city size distribution is centralized. Large cities are becoming more agglomerated, and they are developing at a faster rate than small and medium-sized cities.

Figure 3 shows the scatter plot of the rank-size law, it can be seen that the slope of the curve increases slightly. The q value decreases, and the distribution of city size tends to be centralized. It means that the size of cities in the top rankings is growing faster, yet there is still room for growth. From 2010 to 2020, zoning changes will transform some county-level cities into prefecture-level cities, while some prefecture-level cities will be disbanded and divided into counties (districts). For example, the city of Chaohu was abolished in 2011 and the territory it governed was divided among the towns of Hefei, Wuhu, and Maanshan. The city of Laiwu was absorbed into Jinan in 2019. The overall pattern of city size distribution may be affected by these sample modifications. This paper re-measures the balanced panel data after omitting these prefecture-level cities to explain the shift. The results reveal that the ordinal size law’s correlation coefficient is still dropping, with a correlation coefficient greater than 1 in 2020. It shows a more dispersed distribution of city size. As new cities arrive and exit, this means a more centralized distribution of city size. The original city has grown in size due to administrative changes and the extension of the metropolitan area, but the overall trend of population migration to large cities is considerable. A major role is played by policy variables in the conclusion. Some Chinese regional governments have implemented the development model of strong provincial capitals and built regional Central cities since the reform and opening up. When the Central city reaches a certain scale, the regional authority gains greater resources through zoning changes to support regional development.

Cities that are formally recognized but smaller in size have emerged in the process of fostering coordinated regional development. Cities are usually defined internationally by geographic units with certain population size criteria. The most common cut-off point among them is 100,000 individuals. The sample size is reduced to 294 in this paper by removing small cities with populations under 100,000. The rank-size law’s correlation coefficients are all greater than one, indicating that the city size distribution is closer to the Zipf ideal than the full sample and balanced panel.

The rank corrected model is employed to measure, due to the biased nature of small sample OLS. The corrected OLS results are all higher than the standard OLS results, and the upward trend in correlation coefficients continues. The balanced panel’s regression results with small cities excluded imply that there may not be a perfect log-linear relationship between city size and rank. The inverted “U” shaped link between the population logarithm and the place rank in Figure 3 also supports this. The concave regression line is formed when the squared term is included in the positive coefficient of the logarithm of city size and the negative coefficient of the squared term. The R2 is greater than traditional OLS and corrected OLS, indicating the model fits better.

In conclusion, the city size distribution satisfies the Pareto distribution but falls short of the Zipf ideal. At the same time, the overall size distribution of Chinese cities is trending towards centralization. What is the cause? With economic development, the government’s policy of adjusting administrative divisions has led to the expansion of urban areas in some Central cities to meet the needs of regional development. The population of cities has grown as well. On the other hand, cities with greater size classes have relatively higher economic, cultural, medical, educational, and wage levels, creating a “siphon effect”. The Central city of a region attracts people and resources from surrounding areas and continues to expand outward, resulting in a transition from the “lower” to the “upper” level of China’s urban system. Along with the constant resource centralization and the implementation of “talent introduction plans” in each city. The “Matthew effect” is forming as the appeal of the center city grows stronger. In China, the population loss from surrounding small and medium-sized cities has resulted in a shift from dispersed to centralized city sizes.

4.2. General Characteristics of City Size Distribution

4.2.1. City Size Index for City Size Distribution

Based on the definition of cities and the selection of city samples in this paper, the size of China’s first cities in 2010 and 2020 is 22.32 million and 25.38 million, respectively. According to the principle of rank-size, ideally, the first place should have a value of 2, and the four-city and eleven-city indices should have a value of 1. However, according to

Table 3. The law of the primate city in China.

Year	PI2	PI4	PI11
2010	1.1853	0.4893	0.4168
2020	1.0204	0.3878	0.3210

, in 2010 and 2020, the first degree, four-city index, and eleven-city index are all lower than the theoretical value of the rank-size law, and the city size is concentrated on the first city. After the redistricting, Shanghai became the top city in 2010, and Chongqing became the top city in 2020. These two cities consistently rank first and second in terms of urban population size, and their populations are reasonably close. The results of the four-city index and the eleven-city index are both significantly lower than the theoretical value of the city size index. This validates the preceding conclusion: China’s city size distribution follows the Pareto distribution, indicating decentralization. However, there is a trend toward centralization. There could be two explanations for this. On the one hand, China’s government has traditionally promoted regional development coordination. The development of medium-sized cities and above has been aided by policies such as “China’s Western Development”, the “Metropolitan Area” strategy, and the designation of regional center cities. It made the gap between high-rank cities smaller. On the other hand, cities of higher rank, such as Beijing, Shanghai, and Chongqing, are comparable in size and do not have a discontinuity between them, resulting in a lower than ideal city size index.

4.2.2. Spatial Gini Coefficient of City Size Distribution

The spatial Gini coefficient of China’s city size in 2010 and 2020 is 0.519 and 0.550, respectively (

Table 4. The spatial Gini coefficient of China’s city size in 2010 and 2020.

Year	Obs	All City	Small City (Type II)	Small City (Type I)	Medium City	Large City (Type II)	Large City (Type I)	Supercity	Megacity
Full sample
2010	287	0.519	0	0.125	0.113	0.162	0.069	0.112	0.196
2020	297	0.550	0.345	0.092	0.111	0.168	0.077	0.121	0.193
Balanced panel
2010	285	0.519	0	0.125	0.110	0.163	0.069	0.112	0.196
2020	285	0.539	0	0.086	0.110	0.168	0.077	0.121	0.193
Sample with a threshold 100,000
2010	287	0.518	0	0.125	0.113	0.162	0.069	0.112	0.196
2020	294	0.546	0.131	0.086	0.111	0.168	0.077	0.121	0.193

). The existing spatial Gini coefficient for Chinese cities is often low when compared to the spatial Gini coefficient under the Zipf ideal. This is in line with the fact that the size distribution of China’s cities is not centralized. In terms of time series, the spatial Gini coefficient is greater in 2020 than in 2010 for the full sample, balanced panel, and considering the 100,000-population threshold case. It demonstrates that the overall size distribution of Chinese cities is growing. The centralization of large cities is increasing, but the size gap between them is widening. When we exclude cities that have changed because of administrative divisions, we find that the spatial Gini coefficient in 2010 is not much different from the full sample. In 2020, the spatial Gini coefficient will decrease slightly. This suggests that administrative divisions have influenced the degree of centralization of city size distribution in China, but that they are not the dominant factor. When cities with populations under 100,000 are excluded, the spatial Gini coefficient is lower relative to the full sample. Small cities have little impact on the centralization of China’s city size distribution. Urbanization gives China’s cities the ability to go from fragmentation to centralization. Population mobility between cities is unrestricted. Because of their superior resources, large cities attract a significant number of mobile people, resulting in a much higher population growth rate than small cities.

4.3. Evolutionary Characteristics of City Size Structure

The rank-size law describes the distribution of city sizes. The city size index reflects the macro trend toward a more balanced distribution of city size and structure. However, data on the dynamics of city size distribution is scarce.

Table 5. The Markov transition matrix of China’s city size from 2010 to 2020.

	Year 2020
	Rank	Megacity	Supercity	Large City (Type I)	Large City (Type II)	Medium City	Small City (Type I)
Year 2010	Megacity	100%	0	0	0	0	0
	Supercity	45.5%	45.5%	9.1%	0	0	0
	Large city (Type I)	0	57.1%	38.1%	4.8%	0	0
	Large city (Type II)	0	1.0%	8.2%	88.8%	2.0%	0
	Medium city	0	0	0	35.3%	56.9%	8.2%
	Small city (Type I)	0	0	0	8.5%	48.9%	42.6%

shows the probability matrix of city size rank transfer obtained using the Markov transfer matrix.

In this study, we select the balanced panel with a 100,000-population threshold to eliminate the effect of administrative divisions. As can be observed, the most prominent aspect is that most diagonal values are around 50%. This shows that city size has most likely changed in the recent decade. The lower values in the upper middle part of the diagonal reflect the fact that relatively larger cities are driving China’s city size changes. Most city sizes are transformed to the size of the next hierarchical levels, as the diagonal closeness values are nearly always non-zero. This indicates that within the urban system, the flow of city size tends to be in the neighborhood hierarchy.

From 2010 to 2020, Figure 4 depicts the spatial distribution of cities in China with grade changes. The dots on the graph represent the rank of the city after the change in size. Microscopically, 45.5% of supercities are promoted to megacities, while 9.1% are demoted to large cities from 2010 to 2020. More than half of Type I large cities grow into super cities, but only 4.8% of Type II large cities degenerate. This is the foundation of China’s trend to centralize city size distribution. Further, 1% of Type II large cities produced crossover promotions and expanded into super cities, while 2% shrank to become medium-sized cities. More than one-third of medium-sized cities are elevated to Type II large cities. Those cities in Type I that have grown in size have “broken out” upward. Nearly half of these cities were upgraded to medium-sized cities, while 8.5% jumped to large cities. These trends suggest that the distribution of city size in China saw varying degrees of expansion between 2010 and 2020. The majority of cities grow to a larger size. Type I large cities and medium cities have a higher probability of upgrading. Degradation has occurred in some city sizes, but the probability of degradation is relatively low.

4.4. Sub-Regional City Size Distribution Characteristics

Is China’s city size distribution stable across economic regions, as described in the preceding paper, from decentralization to centralization? Three major economic zones are researched in depth to learn more about the features of the size distribution among Chinese cities. Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Guangxi, and other provinces and cities make up the Eastern Economic Zone. Heilongjiang, Jilin, Shanxi, Anhui, Jiangxi, Henan, Hubei, Hunan, Shaanxi, Inner Mongolia, and Sichuan are among the 11 provinces and autonomous areas that make up the Central Economic Zone. Xinjiang, Tibet, Qinghai, Yunnan, Guizhou, Ningxia, and Gansu are among the provinces and autonomous areas that make up the Western Economic Belt.

Table 6. The descriptive statistics of cities in Eastern, Central, and Western China.

	Number	Average Size (10,000s)	Standard Deviation (10,000s)	Min Size (10,000s)	Max Size (10,000s)
2010
Total	287	167.0	247.6	21.1	2232
East	113	231.2	326.5	31.7	2232
Middle	138	122.9	133.6	21.1	978.5
West	33	90.66	87.65	21.1	354.5
2020
Total	297	222.7	339.7	0.233	2538
East	112	323.1	420.7	39.5	2487
Middle	137	163.5	213.4	22.4	1233
West	43	105.9	126.0	8.2	595.1

shows the results of descriptive statistics. From 2010 to 2020, the average city size in the Eastern, Western, and Central regions all increased significantly. The Eastern region’s fastest city growth, from 2.312 million in 2010 to 3.231 million in 2020. Cities in the Eastern area are significantly larger than those in the Central and Western regions, and their growth rate outpaces that of the country. Due to excessive growth and proximity to the threshold, the top city in the Eastern region is shrinking in size. Start shifting your focus from quantity to quality. Due to their strong development potential, the leading cities in the Central and Western areas have risen significantly within a decade with reasonably fast growth rates.

The findings of the statistical distribution of city sizes in Eastern, Central, and Western China in 2010 are shown in

Table 7. Rank–size estimation of cities in Eastern, Central, and Western China.

		Rank-Size Equation		Corrected Rank-Size Equation		Quadratic Rank-Size Equation
Year	Obs	q	R2	q	R2	Log (Size)	Log2 (Size)	R2
East
2010	113	1.008 ***	0.951	1.056 ***	0.935	1.251 ***	−0.218 ***	0.992
		(0.000)		(0.000)		(0.000)	(0.000)
2020	297	1.010 ***	0.944	1.056 ***	0.926	1.596 ***	−0.236 ***	0.989
		(0.000)		(0.000)		(0.000)	(0.000)
Middle
2010	285	1.380 ***	0.948	1.441 ***	0.939	1.090 ***	−0.261 ***	0.976
		(0.000)		(0.000)		(0.000)	(0.000)
2020	285	1.273 ***	0.950	1.331 ***	0.943	0.552 ***	−0.183 ***	0.969
		(0.000)		(0.000)		(0.003)	(0.000)
West
2010	287	1.086 ***	0.956	1.201 ***	0.914	1.283 ***	−0.280 ***	0.949
		(0.000)		(0.000)		(0.026)	(0.000)
2020	294	0.817 ***	0.875	0.888 ***	0.847	1.262 ***	−0.254 ***	0.978
		(0.000)		(0.000)		(0.000)	(0.000)

Note: *** denotes significance at the 1% level.

. The Eastern region’s size distribution was determined to be similar to the Zipf ideal, with q values near 1. With the addition of the squared term, the corrected OLS gets larger, and the rank-size law’s correlation coefficient is more than 1 and increases significantly in 2020. This could be attributed to the east’s higher level of centralization, where large cities confront growth constraints and a lack of expansion momentum. Simultaneously, the Eastern region’s second-ranking cities have aggressively embraced policies in recent years to accomplish rapid urban development with the benefits of location and policies. This has hampered the Eastern region’s centralization of large cities. In the Central region, the q value is bigger than 1, with a downward tendency. These figures show a significant shift in the size of cities in the Central area. In general, the Central region’s city size distribution is more spread. Cities in the Central region, on the other hand, have become more appealing to cities in the region as a result of initiatives such as “strong provincial capitals” and “metropolitan areas”. Cities’ agglomeration capacity has grown, and the population has become increasingly concentrated. The correlation coefficient for the Western area in 2020 is less than one, indicating a downward trend. The Western region is poorly situated, and the centralization of resources and population benefits the region’s overall level. Under the national policy of “The development of the western region in China”, “The Belt and Road” and “Paired Assistance”, the distribution of cities in the Western region tends to be centralized and the agglomeration capacity is enhanced.

The scatter plot of the rank-size law is shown in Figure 5. The trend graph for the Eastern, Central, and Western areas in 2010 compared to 2020 deviates to some extent from the Zipf trend graph of the Zipf ideal state, as seen in the graph. Cities in the Eastern, Central, and Western regions are still too small. The slope of the trend graph reveals a definite propensity in the Eastern Mid-Western region to focus on city size. This supports the previous conclusion. Scatter plots for the Western region show fewer dots and lower logarithmic horizontal coordinate values.

5. Driving Factors

Referring to the literature review and earlier discussions, a variety of factors, both environmental and societal ones, affect the city size distribution [64]. These driving factors could vary depending on the nation. The following important factors impacting the city size distribution in China are taken into account in this work by combining the existing research experience.

The first is policy. The impact of policy on the city size system is decisive. China’s institutions determine the key role of government. For example, China’s household registration policy largely restricts the free movement of population and prevents over-concentration in Central cities such as Beijing and Shanghai, which deeply affects the city size system [65]. Moreover, new policies can directly determine the future of a city. The development of Shenzhen, Guangzhou and some of China’s coastal cities today is due to China’s reform and opening-up policy back then. The current distribution of city sizes is also influenced by China’s growth philosophy, which advocates that “the rich first will lead the rich later”. This is clearly illustrated by the fact that many of China’s provincial capitals are growing well due to their greater political advantages.

The second is the economy [66]. There is no doubt that the economy has a significant impact on the system of city size, and it is clear that, as is typical around the world, large-scale cities are typically the ones that have more developed economies. Examples of this include the Atlantic coast and Great Lakes region of the northern United States, the Pacific Coast of Japan, and the Eastern Seaboard of China. Experience shows that the more developed the economy, the more reasonable the city size system generally is. This is due to the economy’s importance, which shows that the nation has a sensible resource allocation, developed industries, and effective factor flows—all of which are directly tied to the city size system. Of course, this may not necessarily apply to all nations, as some have particular resources that have contributed to their special development.

The third is geography. Although geographic restrictions on city size continue to be weakened by technology advancements, their impact is still important. According to China’s distribution of city sizes, major cities are more likely to develop in plain areas, whereas small and medium-sized cities are the only ones that can grow in hilly regions due to land constraints. There are more hilly areas and less plain areas in China, which is one of the reasons for the small number of large cities and the large number of small and medium-sized cities in China. In addition, some important geographical resources, such as the density of rivers [67] and the number of harbors, are also closely related to the development of cities, thus influencing the overall size system.

The fourth is the level of industrialization. Some researchers found that the level of industrialization also affects the city size system [68], which is also easy to understand. A higher level of industrialization means a more developed industrial structure, which is more conducive to population clustering and the agglomeration effect is easier to play. Therefore, secondary, and tertiary industries are more advanced in nations and regions with a high level of industrialization, and city scale systems are often more rational. On the other hand, cities that are less industrialized tend to be more dispersed and to diverge from Zipf’s law. The level of industrialization in China has been increasing, which is consistent with the fact that the distribution of city sizes is evolving toward balance.

The fifth is transportation. Transportation is also one of the key driving factors being discussed, with well-developed transportation facilitating the movement of factors and urban development. In general, developed nations have excellent transportation systems. In the past, China’s sustained urban expansion has been supported by its advanced transportation system. However, there is also a clear imbalance in transportation construction in the Eastern and Western parts of China. The Yangtze River Delta city cluster and the Beijing-Tianjin-Hebei city cluster are two examples of the Eastern region’s highly developed economy and transportation infrastructure. Contrarily, the Central and Western regions’ transportation infrastructure is more antiquated, which results in stark regional disparities in city size and has an impact on the generally acceptable distribution of city size.

6. Discussions and Conclusions

6.1. Discussions

The results show that the size distribution of the above-territory city system in China during 2010–2020 is consistent with the law of dislocation size, but deviates from the Zipf ideal. This supports some existing research experience [69,70], but also contradicts some existing research [71]. Although previous studies have shown that city size systems evolve dynamically [47,48], no study has revealed what causes the evolution of city size distribution, specific to a particular country or region, which may also be a direction worth thinking about. The research in this paper is helpful in identifying the changing patterns of city size distribution, which have been studied to point out that differences in city size distribution patterns affect economic [72,73], environment [74], and many other aspects. Similarly, another conclusion of this paper, the “olive-shaped” structure of China’s urban size distribution, is supported by a large body of evidence [42], and this growth pattern of Chinese cities may be maintained by China’s urban development policies and economic development patterns.

This study examines the intra-regional variation in city size, following up on the previous study by Wan et al. [49] and reaching different conclusions. Although both studies support the existence of large differences in city size distribution between regions, the findings of this paper show a gradient of decreasing city size in all three major regions of China, which is different from Wan’s study, but there is not yet a good theory to explain the difference in findings. In future studies, we will conduct more rigorous research.

In addition, although the authority of census data has been widely tested [17,53,54], the long intervals between census data can neglect changes in city size distribution in the intervening years. Some studies have now been conducted with some innovations in data [64,75], and a better combination of data and methods for a more rigorous study might lead to different findings.

6.2. Conclusions

According to the most recent city size classification standards, this paper analyses the characteristics of the hierarchical scale structure of all Chinese cities above the prefecture level. Using the rank-size law, spatial distribution measurements, and Markov transfer matrices, we derived the following conclusions based on the most recent 2010 and 2020 census data:

• The prefecture-level and above city-size structure in China is a relatively balanced type of rank-size structure. A further progression toward equilibrium occurs, but it departs from the Zipf ideal. The population size of large, medium, and small cities varies unpredictably, forming an “olive-shaped” pattern. Small and medium-sized cities are more numerous but smaller in size, while large cities are fewer in number but larger in size. Large cities have a faster rate of growth than small and medium-sized cities. In the process of fostering the development of large cities, the government should pay attention to the balanced development of small and medium-sized cities. The head city has a high level of primacy, the overall city size has a low level of primacy, and megacity population growth is slowing.
• The size hierarchy of Chinese cities is quite varied. Between 2010 and 2020, the population of 101 Chinese cities changed. Twelve cities have shrunk in size, while 89 have increased in size. With over 90% of China’s medium and large cities, it is apparent that high-grade cities have been the primary driver of the country’s city size adjustments over the last decade.
• The distribution of city sizes varies significantly by region. As agglomeration capacity declines, the Eastern region approaches the Zipf ideal. The Central region’s city size distribution is more dispersed, but it still tends to be centralized. And the Western area has become more centralized as a result of the policy to enhance city size distribution. The distribution of city sizes in the Eastern, Central, and Western provinces show gradient differences. That is, the Eastern region’s growth rate of city size is substantially larger than the Central and Western areas, and the Central region’s growth rate is higher than the Western regions.

The implications of our empirical results for the practice of building a rational city size system are relatively straightforward.

• China’s city size distribution deviates from Zipf’s ideal state, which indicates that there are some irrationalities in China’s city size system and needs to adjust the future urban development strategy. First, while encouraging the growth of large cities, consideration should be given to the balanced growth of small and medium-sized cities. They have a significant role in China’s administrative structure due to their huge number of small and medium-sized cities, extensive land, and concentration of resources, industries, and other growth elements. Secondly, transforming the development mode and improving the development quality are of global and decisive significance for China to optimize the urban size system, build a moderately prosperous society in all aspects and achieve national rejuvenation. Thirdly, the growth of small and medium-sized cities is the primary symbol used by both the “National New-type Urbanization Plan” and the “two sessions” to gauge the overall condition. Small and medium-sized cities ought to follow the path of distinctive development, take full advantage of the benefit of relatively low total costs, take the initiative to carry out the industrial transfer and function decentralization of megacities, and solidify the basis of true economic development.
• Urban development initiatives should place a strong emphasis on top-level design. Small- and medium-sized cities’ slow population growth is a significant contributor to the urban system’s imbalance and a pressing issue that has to be addressed. In order to solve this issue, the government will be crucial. On the one hand, the central government should reinforce the policy predilection for small and medium-sized cities and assist them in achieving rapid population growth by implementing relevant institutional measures when it formulates policies for the coordinated development of urban population size. For example, enhance the linkages between small, medium, and large cities, and fully utilize the spatial spillover effect of major cities. On the other hand, local governments should implement equivalent protective measures, such as creating preferential population policies, enhancing public services, raising welfare benefits for citizens, and encouraging infrastructure development. Small and medium-sized cities can be encouraged to experience a healthy economic development while also ensuring population expansion through these policy initiatives.
• High levels of government power are a distinctive feature of the Chinese system. China’s household registration system is restricting the free movement of people, especially in large cities. This is an important factor in avoiding the over-concentration of population in metropolitan areas, but it is also an important factor in the irrationality of the population size system, although these restrictions are being weakened. In this regard, China should continue to support reform and opening up, support reform of the household registration system, support free movement of people, fully utilize the central government’s macro control capabilities, support the flow of capital, people, and goods, and create a “national unified market”. Additionally, encourage the Eastern regions to make the most of their financial advantages, advance industrial modernization, raise the happiness level in cities, and draw in more highly qualified workers. The Central and Western areas should exploit their cost advantages and resource advantages to establish competitive industries and draw in a flow of human capital.

6.3. Research Limitations and Future Directions

Although this study has drawn some remarkable conclusions, the limitations of this paper are also obvious. First, this paper analyzes the urban size structure and evolutionary trends, but neglects to examine the underlying drivers and mechanisms, and attention to these issues may help us enrich our study and conclusions, which is the direction we will focus on to improve our work in the future. Second, although we use a variety of methods in this study, and we also explain why we use census data to study urban size distribution, HILL estimator and maximum likelihood estimator can be used as alternative methods for this study, in addition to OLS methods. Although existing studies have generally measured city size using population data, many other data can actually be used to study city size systems, including nighttime lighting data and land use data. In future studies, we will consider different methods and data to improve and enrich our research. Finally, this paper is developed in China; although China is the largest developing country and has certain representativeness, it also has special characteristics: will the same conclusion be obtained by using other developing countries as the research object? This is also one of the future works for further research.