Urban scaling in rapidly urbanising China

Abstract

Chinese

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

Keywords

agglomeration effects Chinese urban system economies of scale rapidly urbanising country urban scaling laws

Introduction

The world is becoming increasingly urbanised: today 55% of the population lives in cities and this figure is expected to reach 68% by 2050 (United Nations, Department of Economic and Social Affairs, Population Dynamics, 2018). Our planet is experiencing the greatest urbanisation of its population, the extent of which is unlikely to occur again in the future. More than 90% of new urban residents will be concentrated in developing countries, especially in Asia and Africa (Sahasranaman and Bettencourt, 2019) and this will be both the impetus and pressure for urban development. In view of the rapid urbanisation in developing countries, a deeper quantitative and scientific understanding of urban processes and their practical significance is urgently needed. The size of a city is an important determinant of socio-economic, infrastructure strength and knowledge production activities (Bettencourt et al., 2007, 2010; Lobo et al., 2013). Thus, understanding how different urban attributes develop with an increase in urban population size and coordinating their relationship is crucial to the realisation of sustainable urban development goals in a rapidly urbanising country.

Benefiting from the emergence of available data and the introduction of complexity science theories and methods, a new science of cities has been established as a quantitative approach to gain systematic insight into cities (Batty, 2013; Meirelles et al., 2018; West, 2017). As one of the cornerstones of exploration of the new science of cities, urban scaling shows how urban attributes vary with size and the relationship between them (Rybski et al., 2018). Empirical evidence has shown that an urban indicator referring to a material resource or measure of social activity, Y(t), scales with urban population size N(t) across cities at time t, obeying the form of Y(t) = Y₀N(t)^β, where Y₀ is a normalisation constant. Empirical studies have shown that generally attributes related to socio-economic activities associated with innovation and creativity (such as GDP, income, patents, etc.) scale in a super-linear manner with population size (β>1) because of increasing returns to urban population size. Infrastructure and public service attributes (such as built-up area, road length, gas stations, etc.), demonstrate a sublinear scaling regime with urban population (β<1). This condition is analogous to living organisms and represents the economies of scale from an increase in efficiency. Such an efficiency gain, in turn, promotes sustainability in large cities. Variables associated with individual needs (such as jobs, housing, household water consumption, etc.) scale linearly with population size (β ≈ 1) (Bettencourt et al., 2007).

Urban scaling theory emphasises the basic function of urban population size in the growth of socio-economic activities and infrastructure (Lobo et al., 2013). It also shows that urban growth brought by urban population size is nonlinear, which also determines the agglomeration effects or economies of scale of urban attributes in the process of urban development (Bettencourt et al., 2010). But in recent years the interpretation of the paradigm of urban scaling has been found to be incomplete, as urban size is not the only determining factor in agglomeration effects (Keuschnigg et al., 2019). Intra-urban social interactions represented by urban population size can only explain half of the scaling exponent of urban wage income. In addition, the scaling relationships actually reflect the difference in urban sociodemographic composition. But there is no doubt that urban population size is critical and significant in urban development. Therefore, the simple but unified scaling framework constructed by urban population size and urban attributes is still significant and applicable to urban studies.

Urban growth is an endogenous process and can be described as an emergent property of urban life (Keuschnigg et al., 2019). Scaling regimes may be dependent on the locality and the feedback of social interconnectivity and interaction as urban density increases (Arbesman and Christakis, 2011) since the essence of a city is interaction (Batty, 2013; Glaeser et al., 1995; Lobo et al., 2019; Pumain, 2000; Smith, 2019). Mathematical models have been proposed to demonstrate and explain that the scaling phenomenon is the result of the network of infrastructure and human social interactions embedded in space (Lobo et al., 2019; Ortman et al., 2014). The likelihood of encounters and interactions increases as individuals move spatially closer to each other, and transaction and communication costs decrease (Bettencourt and Lobo, 2016; Ribeiro et al., 2017). These general dynamics lead to network effects, with some fractal-dimension and distance-dependent interactions associated with the structure ofnetworks and spatial densities (Bettencourt et al., 2020; Molinero and Thurner, 2019; Ribeiro et al., 2017).

The empirics and the theory of urban scaling are sufficiently mature to be formulated and measured in many urban systems around the world (Bettencourt and Lobo, 2016; Bettencourt et al., 2007; Meirelles et al., 2018; Sahasranaman and Bettencourt, 2019; Van Raan et al., 2016; Zünd and Bettencourt, 2019). Urban scaling provides a unified framework for understanding the general and extensive properties of various urban systems in time and space (Cesaretti et al., 2016; Lobo et al., 2019; Ortman et al., 2015). Nevertheless, the scaling characteristics of urban systems in contemporary developing countries have been studied less than those of developed countries (Bettencourt and Lobo, 2016; Bettencourt et al., 2007). As a typical developing country, China has been experiencing rapid urbanisation since the 1980s with a complex urbanisation pattern that has attracted the world’s attention. It is necessary and interesting to focus on the comprehensive characteristics of urban growth in a rapidly urbanising country and to analyse the dynamic evolution of cities (Pumain and Raimbault, 2020) by verifying Chinese cities as social entities by whether they conform or not to the predictions of the scaling framework. This study intends to capture how the unique scaling characteristics in China vary from those in developed countries to reveal the distinct development pattern of rapidly urbanising countries which can be explained by evolutionary theory. It should be borne in mind that it is more meaningful to pay attention to differences and deviations rather than the universal pattern.

Initially, studies focused mainly on the common attributes of socio-economic activities and infrastructure, such as built-up area, GDP, crime and patents. Limited indicators such as built-up areas and GDP are used in the few existing studies of China (Jiao et al., 2020; Lang et al., 2019; Zünd and Bettencourt, 2019). If we intend to use a scaling framework in our future policy-making, we need to test the universality and applicability of urban scaling theory through a comprehensive multi-indicator verification. The theory of hierarchical diffusion of innovation (Hägerstrand, 1952) explains how new socioeconomic activities are first adopted by large cities in the early stages of development and spread as an innovation wave, resulting in different scaling exponents of specific economic sectors in developed and developing countries. This process has been reinforced by rapid urbanisation and globalisation (Pumain et al., 2006; Pumain and Rozenblat, 2019; Strano and Sood, 2016; Zdanowska et al., 2020). Scaling exponents are predicted to be static on a theoretical basis, usually changing slowly on a timescale of several decades, which has been proven in the urban properties of the developed world (Bettencourt, 2013; Bettencourt et al., 2007, 2010, 2020). Thus, taking China as the subject of study provides an opportunity to systematically explore the linking of urban scaling with the urbanisation process, and to test the dynamic evolution in rapidly urbanising urban systems.

It is noted that scaling relationships are highly dependent on urban ontology and measurement contexts and methods (Arcaute et al., 2015; Batty and Ferguson, 2011; Fragkias et al., 2013). Properly defining the urban boundary and choosing appropriate statistical data are important prerequisites for a systematic quantitative analysis of urban scaling. Previous studies were mostly based on the adoption of a functional city as the urban extent, such as metropolitan statistical areas (MSAs) in the USA and large urban zones (LUZs) in Europe (Zhao et al., 2018), as all of them are defined as comprehensive economic and social units containing urban cores and administrative divisions. A recent study appeared to apply voice-call interactions within the cities of Chile to distinguish and define urban boundaries and provide a practical implementation of urban scaling (Sotomayor-Gómez and Samaniego, 2020). China has a unique statistical system with diverse sources and various statistical criteria for defining urban territory (Lang et al., 2019). The lack of well-defined and standardised terms for urbanised areas in China has led to some confusion, compounded by the fact that the official urban population is divided into registered and permanent residents. If these characteristics are ignored, serious deviations in results can easily occur.

We collected more than 90 urban indicators in ten categories, including infrastructure, land use, education, medical and healthcare, energy, employment, economy, company, innovation and environmental press, from 275 Chinese cities to systematically explore the integrated characteristics of the Chinese urban system using scaling analysis. These attributes characterise well the economic activity, individual demand, infrastructure and public services covering most of the unexplored indicators and three typical and theoretic scaling regimes (super-linear, linear and sublinear). Our statistical unit is Chinese prefecture-level cities (Dong et al., 2017; Xu et al., 2019). A prefecture-level city in China is typically a place where social interactions occur with a certain population size (Zhao et al., 2018; Zünd and Bettencourt, 2019). There is a higher urbanisation rate and more mature infrastructure in urbanised areas (municipal districts) within prefecture cities (Swerts and Liao, 2018). Fundamentally, the urbanised area of Chinese prefecture-level cities is consistent with the definition of functional cities and this choice is adequately justified and measured (Xu et al., 2019; Zhao et al., 2018; Zünd and Bettencourt, 2019). Since the floating population accounts for a considerable proportion of the population of China’s major cities, the permanent population, including registered and temporary residents, is more representative of the true city size because they participate in social interactions and shape urban functions.

In this wider context, the aim of this paper is to make sense of the urban scaling in rapidly urbanising China, aggregating quantitative assessments of a large number of urban attributes. We attempt to situate an original approach of applying urban scaling laws to a developing country where urban growth is very strong and to recognise the characteristics of a rapidly urbanising urban system reflected by scaling. We characterise these unique features in detail by considering the spatial disparities and temporal evolution of scaling exponents from 2000 to 2017. Spatial disparities of scaling can provide a uniform and comparable basis for the evaluation of social and economic development among regions. Scaling exponent variations over time reflect the temporal evolution of the urban system and can measure the coordination and balance of urbanisation. We do not simply put scaling analysis into the Chinese context but, using many practical considerations, effectively ensure the spatial consistency of the statistical data. To the best of our knowledge, this work will aid in the scientific understanding of the scaling characteristics and evolution of the urban system in rapidly urbanising countries, and provide support for urban development and planning.

Data and methods

Study area and data sources

In this study we took 275 Chinese prefecture-level cities, including four national direct-controlled municipalities, as our unit of analysis. Hong Kong, Macau and Taiwan are excluded because of the absence of data. We collected urban population data and attributes from 2000 to 2017 and the data for 2017 are selected to explore cross-sectional scaling. All data are available from the China Urban Statistical Yearbook and China Urban Construction Statistical Yearbook. The number of patents for Chinese cities is taken from the National Intellectual Property Office (SIPO) (available at: pss-system.cnipa.gov.cn).

To compare spatial disparities of the urban scaling exponent, we identified four major regions (Figure 1), namely Western, Central, Eastern and Northeast China (National Bureau of Statistics of China, 2011). Urban agglomeration is created as an emerging state-space to manage inter-city cooperation and competition (Cui et al., 2020; Fang, 2015; Wu, 2015) and will be the ultimate urban spatial form of China’s new urbanisation (Fang and Yu, 2017). Following The 13th Five-Year Plan for Economic and Social Development, we also selected 19 urban agglomerations as research samples, including five national-level urban agglomerations, eight regional medium-sized urban agglomerations and six regional economic cooperation organisations, namely a ‘5+8+6’ spatial structure for China’s urban agglomerations, to provide a larger sample to test urban scaling effects. Detailed descriptions for these 19 urban agglomerations are presented in Table S1 in the Appendices (available online). Five major national-level urban agglomerations among them were selected as typical urban agglomeration analysis units, including the Beijing-Tianjin-Hebei (BTH), Chengdu-Chongqing (CY), Pearl River Delta (PRD), Yangtze River Delta (YRD) and Yangtze River Middle-Reach (MYR) Urban Agglomerations.

Figure 1.

The spatial distribution of the urban population of 275 Chinese cities in 2017 and the location map of four typical regions and five typical national-level urban agglomerations.

Urban scaling laws

Urban scaling laws reflect the quantitative scaling relationship between urban indicators and urban population size at a given time. Urban indicators (Y) with population size (N) at time t is given by the form of power law:

Y_{i} (t) = Y_{0} N_{i} (t)^{β}

(1)

where β is the scaling exponent, i represents different cities within the urban system and Y₀ is a normalisation constant (Bettencourt and Lobo, 2016; Bettencourt et al., 2007). To derive the scaling exponent, we take linear ordinary least squares (OLS) regression by logarithmic transformation:

\log Y_{i} (t) = β \log N_{i} (t) + \log Y_{0} + ξ_{i} .

(2)

β corresponds to the slope of the linearised model and ξ_i is a normally distributed error with zero mean. Considering the quality of the statistics, quality checks were done before fitting and double standard deviations are taken to remove outliers.

Some studies have criticised the applicability of the traditional logarithmic linear regression model, as there is a systematic error in parameter estimation and an ignored error in the independent attributes (Gudipudi et al., 2019a; Leitão et al., 2016). To solve this problem, recent studies have sought a more rigorous statistical fitting approach to ensure the robustness of the scaling exponent, such as orthogonal or total least squares regression (ORTH) (Zhao et al., 2018), quantile regression (Lang et al., 2019) and the urban Kaya relation which is applied to urban emission scaling (Gudipudi et al., 2019b). There is still no doubt that classic OLS is a popular and common approach in urban scaling analysis because of its simplicity and feasibility. Consequently, OLS is chosen in this study as fitting approach to keep the model as simple as possible, since we introduce a large number of diverse urban attributes into our framework, complicating the interpretation. Additionally, only in this way can we ensure that the results are comparable with other urban systems and can correctly measure the integrated characteristics in the Chinese urban system.

The quantities ζ_i(t), namely Scale-Adjusted Metropolitan Indicators (SAMIs), represent deviations of individual cities from the predicted scaling values. ζ_i(t) can measure the performance of an individual city and provide a direct comparison among different cities (Alves et al., 2015; Jiao et al., 2020; Lobo et al., 2013).

ζ_{i} (t) = \log \frac{Y_{i} (t)}{Y_{0} N {(t)}^{β}}

(3)

We attempt to aggregate data from different units and compare the differences between larger samples in a simple and efficient manner. Equation (1) allows us to express the average dynamics of a set of units in a normalised way for the data on logarithmic urban size and attributes magnitude (〈logY(t)〉, 〈logN(t)〉) (Bettencourt, 2020; Bettencourt and Lobo, 2016; Sahasranaman and Bettencourt, 2019), defined by the average of a set of units as

\begin{matrix} 〈 \log Y (t) 〉 = \frac{1}{N_{c}} \sum_{i = 1}^{N_{c}} \log Y_{i} (t) \\ = \log Y_{0} + β 〈 \log N 〉 \end{matrix}

(4)

〈 \log N (t) 〉 = \frac{1}{N_{c}} \sum_{i = 1}^{N_{c}} \log N_{i} (t)

(5)

where N_c is the total number of units (cities or regions) in a given urban system and where we have used the fact that 〈ξ〉 for a well-posed fit.

Regression analysis

The regional variation in the scaling exponent is the result of quantitative and attribute factors. In order to better study the regional differences of scaling exponents in China, we added regional dummy variables into the regression model to investigate the spatial influence of urban population size on urban attributes, and then explored the significance of regional differences in scaling exponents. As we have grouped Chinese cities into four regions, a category variable (Region) is introduced to capture the regional difference statistically (Liu and Wang, 2016).

\begin{matrix} \log Y_{i} (t) = \log Y_{0} + β \log N_{i} (t) \\ + α^{*} Region + ξ_{i} \end{matrix}

(6)

Empirical results

Urban scaling in China

We summarise the scaling exponents of all statistically significant urban attributes in Figure 2. Detailed explanations of abbreviations of urban attributes are presented in Table S2 in the Appendices (available online). Analysis of these scaling exponents indicates that power-law distributions describe well a multitude of the indicators in China. The general proposition of increasing returns to size for social-economic attributes and economies of scale for infrastructure holds true for our urban attributes in the Chinese urban system. In general, the scaling exponent values of attributes related to education, medical and healthcare, land use and public services indicators are less than one, following the sublinear regimes and indicating that there is a higher infrastructure sharing rate in Chinese large cities, which has also been confirmed in the existing literature (Swerts and Denis, 2017). Urban attributes related to economy and company present super-linear regimes as expected. These results enrich the choice of a new set of attributes compared with previous studies, such as the number of employees in different sectors (manufacturing, service), different types of urban construction land area, finance and economy development (revenue, tax, expenditure).

Figure 2.

Urban scaling exponents for 97 indicators across Chinese urban system in 2017.

Figure 3a shows the scaling exponents of 12 main representative sets of indicators from ten categories covering typical indicators of three paradigms and the unexpected attributes that can reverse the unique characteristics of rapid urbanisation. These scaling exponents, derived from OLS regression on logarithmic indicators, broadly agree quantitatively with the simplest predictions from the scaling regimes. All indicators related to social interactions (i.e. patents, GDP) and numerous indicators for infrastructure follow the empirical super-linear and sublinear scaling regimes, respectively. However, several indicators related to infrastructure and individual needs, such as the number of buses and length of gas supply pipelines, deviate from the general expectation.

Figure 3.

Scaling of main urban attributes across Chinese cities in 2017. (a) Scaling exponents for a representative 12 urban indicators in ten categories within the Chinese urban system. (b) Comparison of scaling exponents about built-up area and (c) GDP in diverse systems of cities.

Socioeconomic indicators scale super-linearly against population, which is in line with other urban systems. The scaling exponent of patents is noisy, with confidence intervals remaining broad (but clearly super-linear), as expected. This result demonstrates that with the increase in urban size, both positive (i.e. GDP, patents and the number of industrial enterprises) and negative (i.e. annual quantity of wastewater discharged) social output attributes have increased significantly.

Indicators related to individual needs, which are expected to exhibit a linear scaling regime, slightly deviate from the expectation. Employment (the number of employees) scales super-linearly against population, with β = 1.06. Household water consumption also scales super-linearly against population, with β = 1.06. Urban residents living in large cities have superior living conditions, which means they have higher per capita household water consumptions.

Built-up area, pupil, hospital bed and road length follow sublinear regimes, as expected. However, other indicators such as the number of buses and the length of gas supply pipelines surprisingly scale super-linearly against population. These public resources in China tend to be gathered in large cities and fail to reflect economies of scale. It is surprising but common in rapidly urbanising countries that large cities have comparative advantages in public service construction, resulting in an uneven development of infrastructure among districts.

We compare the scaling exponents of built-up area and GDP with those of previous empirical analysis to elicit the different scaling characteristics in Chinese urban system (Figure 3b, c). Built-up area and GDP scale sublinearly and super-linearly, respectively, against population in our study, which is in accordance with previous results and validates the hypothesis of urban scaling theory (Bettencourt and Lobo, 2016; Bettencourt et al., 2007; Meirelles et al., 2018; Sahasranaman and Bettencourt, 2019; Van Raan et al., 2016). Comparatively speaking, China has a relatively lower land use efficiency but a more significant agglomeration effect for economic productivity than those of developed countries (Bettencourt and Lobo, 2016; Bettencourt et al., 2007; Van Raan et al., 2016). Urban population agglomeration also contributes more to economic development in China than it does in other developing countries such as India and Brazil (Meirelles et al., 2018; Sahasranaman and Bettencourt, 2019). It merits mention that there is a stronger super-linear scaling relation between GDP and urban registered population in a previous study (Zünd and Bettencourt, 2019) than between the permanent resident population. Both results have confirmed that there is a significant economic productivity efficiency in Chinese large cities. While it is obvious that the registered population underestimates the real urban population size and leads to overstating the agglomeration effects of GDP and other attributes in a sense.

Spatial disparities of scaling

We selected three main representative urban indicators (built-up area, employment and GDP), and obtained the scaling exponents by regions, to explore spatial disparities of scaling exponents in China (Table 1 Model III–VI). Built-up area in four regions scales sublinearly with population size (β<1) as expected. As for individual-needs indicators, the expected scaling exponent value of employment should equal 1. However, there are some exceptions in different regions in China. Employment in the Northeast China (NE) shows a super-linear scaling behaviour with β = 1.12, contrary to the prediction, while employment in Central China shows a significant sublinear relationship with the urban population (β = 0.95), showing a slower growth with an increase of urban population. Scaling exponent values of GDP in all regions are greater than one, which is consistent with the expected super-linear scaling behaviour. Among all regions, the NE shows the most significant agglomeration effects for economic outputs, with β = 1.44.

Table 1.

Estimation of built-up area, employment and GDP among regions under logarithmic conditions.

Independent variable	Dependent variable
	Log built-up area			Log employment			Log GDP
	I	II	III–VI	I	II	III–VI	I	II	III–VI
Log Pop	0.901***(0.014)	0.892***(0.015)		1.067***(0.021)	1.041***(0.020)		1.189*** (0.031)	1.145***(0.029)
Log Region_ C		0.017(0.020)			0.098***(0.027)			0.197***(0.037)
Log Region_ E		0.041*(0.019)			0.161***(0.026)			0.313***(0.036)
Log Region_ W		0.016(0.019)			0.079** (0.027)			0.187***(0.037)
Log C_ Pop (III)			0.785***(0.031)			0.954***(0.051)			1.043***(0.067)
Log E_ Pop (IV)			0.928***(0.024)			1.069***(0.299)			1.154***(0.045)
Log W_ Pop (V)			0.886***(0.026)			1.024***(0.037)			1.087***(0.040)
Log NE_ Pop(VI)			0.946***(0.041)			1.119***(0.056)			1.439***(0.116)
Intercept	0.686***(0.083)	0.714***(0.088)		2.967***(0.123)	3.020***(0.121)		3.848***(0.186)	3.898***(0.174)
R-squared	0.940	0.941		0.914	0.926		0.849	0.884

Notes: Standard errors in parentheses. Model I is scaling across the whole urban system. Model II is a full model taking categorical variable (Region) to capture regional differences. Model III–VI are the scaling exponents fitting by region to characterise the spatial disparities of scaling.

p < 0.05. **p < 0.01. ***p < 0.001.

Model II in Table 1 also summarises the effects of urban population size among different regions statistically. Built-up area, employment and GDP are all positively associated with population size. For employment and GDP, the impact of an increase in population size among different regions is significant, but less so in built-up areas. Conditioning on urban population size for cities in Eastern China, one unit increase in logarithm of population size is significantly associated with a 0.041, 0.161 and 0.313 unit increase of the degree of built-up area, employment and GDP, respectively (p<0.05), especially for employment and GDP (p<0.001).

Table 2 Model III–VII shows that built-up area in MYR presents a significant sublinear scaling relationship with urban population (β = 0.77). From small cities to large cities, there is a greater average population density within MYR. When it comes to individual-needs indicators, employment in BTH unexpectedly shows a super-linear scaling behaviour with β = 1.22. Large cities in BTH are more attractive to labour resources. Relatively, employment in the MYR and PRD scale sublinearly against population size, with the scaling exponent values less than one. As for social outputs, there is a clear sublinear and linear scaling behaviour of GDP in the PRD and CY, respectively. These results stand in stark contrast to the expected super-linear scaling regime. In contrast, GDP of BTH strongly scales super-linearly against population size with β = 1.21, indicating a significant agglomeration effect of economic productivity.

Table 2.

Estimation of built-up area, employment and GDP among urban agglomerations under logarithmic conditions.

Independent variable	Dependent variable
	Log Built-up Area			Log Employment			Log GDP
	I	II	III–VII	I	II	III–VII	I	II	III–VII
Log Pop	0.888***(0.120)	0.871***(0.020)		1.120***(0.038)	1.076***(0.036)		1.138***(0.050)	1.079***(0.048)
Log UA_ BTH		0.009***(0.026)			−0.031 (0.051)			−0.011(0.064)
Log UA_ CY		0.006 (0.023)			−0.069(0.046)			−0.066(0.059)
Log UA_ PRD		0.068*(0.031)			0.189** (0.058)			0.193*(0.076)
Log UA_ YRD		0.075***(0.020)			0.085*(0.041)			0.189***(0.054)
Log BTH_ Pop (III)			0.926***(0.043)			1.224***(0.062)			1.213***(0.122)
Log CY_ Pop (IV)			0.914***(0.030)			1.107***(0.060)			1.003***(0.079)
Log MYR_ Pop (V)			0.772***(0.043)			0.953***(0.070)			1.174***(0.096)
Log PRD_ Pop (VI)			0.827***(0.076)			0.827**(0.159)			0.801**(0.228)
Log YRD_ Pop (VII)			0.912***(0.033)			1.156***(0.065)			1.105***(0.075)
Intercept	3.239***(0.120)	3.172***(0.117)		1.331***(0.230)	1.092***(0.217)		4.214***(0.304)	4.519***(0.284)
R-squared	0.960	0.966		0.912	0.930		0.857	0.887

Notes: Standard errors in parentheses. Explanations of models as above, with model III–VII being the scaling exponent values fitting by region.

p < 0.05. **p < 0.01. ***p < 0.001.

Similar to regions, we also compare the significance of spatial disparities of scaling on different urban agglomerations (Table 2 Model II-VII). There are significant regional disparities of scaling exponents among PRD and YRD. For cities in YRD, one unit increase in logarithm of population size is significantly associated with 0.075, 0.085 and 0.189 unit increase of the degree of built-up area, employment and GDP, respectively (p<0.05), especially for built-up area and GDP (p<0.001). Employment and GDP are more sensitive to urban population in PRD with coefficients of 0.189 and 0.193, respectively.

The above analysis focuses more on the differences between different-sized cities within an individual urban agglomeration by analysing spatial disparities of scaling exponents. In order to make a horizontal comparison of urban agglomeration development, we normalised the data for each urban agglomeration by the average logarithmic city size and attribute magnitude within the sample. These comparisons take urban agglomerations as units for fitting, giving us a sense of their convergence or divergence across the urban system (Bettencourt and Lobo, 2016). Scatter points show a strong correlation between the two average logarithm attributes (p<0.001), and is still consistent with urban scaling laws (Figure 4).

Figure 4.

The average logarithm indicators and population size of cities in 19 different urban agglomerations across the Chinese urban system.

Results show that there is a more significant agglomeration effect at the urban agglomeration level. There is an average land-use efficiency across urban agglomerations as the scaling exponent value for centred built-up area is close to theoretical expectation (β = 0.85). Tracing a horizontal line of approximately the same average logarithmic built-up area, there is more urban land supplement in smaller cities within the SDP compared with the CY. MYR has a relatively lower per capita land area and a higher land-use efficiency compared with other urban agglomerations.

There is a significant comparative advantage in working conditions and bonus in mature PRD, YRD and BTH national-urban agglomerations, with β = 1.25. These urban agglomerations are more attractive to the labour force, especially to senior talent, quality companies and advanced production, because of their ability to provide better conditions and benefits for the labour force, including providing work not available in smaller areas.

Economic output performance of different urban agglomerations varies greatly. Along a horizontal line, to achieve a similar economic output performance, YRD requires cities to improve the efficiency of their economic productivity, while BTH’s is driven by size. Similarly, tracing a vertical line from the JZ, CY to SDP, with a similar average size, SDP has the greatest economic efficiency. PRD, YRD and BTH have comparative advantages both in employment and GDP with obvious positive deviations from theoretical values.

Temporal evolution of scaling

The scaling exponent is not fixed as it does not always stay at a particular value and evolves over time. The temporal evolution of scaling exponents can reflect the variation in urban development efficiency and regional differences (Figure 5). It is found that scaling exponent values of GDP were always greater than one during 2000–2017, which is in line with expectations. The agglomeration effect of economic outputs of large cities was most significant in 2009; it weakened slightly and then maintained an average level in recent years, as scaling exponent values have been around 1.14–1.16. Generally speaking, large Chinese cities show a strong agglomeration effect of economic output, and will continue to maintain this higher economic productivity in the future.

Figure 5.

Temporal evolution of scaling for main indicators from 2000 to 2017 in China.

Scaling exponent values of employment have increased since 2000 in general and have exhibited a robustness without obvious fluctuations in recent years, resulting in a slightly super-linear behaviour. From 2000 to 2008, the β of the built-up area exhibited an overall upward trend. There was a relatively lower land-use efficiency in large cities with a higher per capita land-use area during 2000–2008. After 2008, β decreased slightly and the economies of scale for land use in large cities have strengthened. The expansion rate of the built-up area of large cities in China is slightly faster than that of developed countries, where the scaling exponent value is generally 0.6–0.8 (Bettencourt et al., 2007).

The above analysis of the evolution of scaling shows that although scaling exponent values are dynamic, scaling behaviours are generally stable over time. GDP and built-up area maintain super-linear and sublinear, respectively, scaling regimes over time. The scaling behaviour of employment has transformed from linearity to super-linearity and has been maintained in the past ten years. Exponent values are not the same in developed and developing countries because of the hierarchical diffusion of the innovations hypothesis. When we look at the temporal evolution of scaling exponents we should pay more attention to long-term trends than specific numerical values.

Conclusion and discussion

Urban scaling theory establishes a systematic and quantitative framework for urban organisation and sustainable development research. These nonlinear relationships reveal the physical constraints on complex systems and emphasise the relationship between urban functions, urban size and innovation cycle (Finance and Swerts, 2020; Pumain et al., 2006). This study contributes to urban scaling laws by testing the universality hypothesis against a broad range of diverse attributes of urban systems in rapidly urbanising China and measuring its unique scaling characteristics combined with its underlying socioeconomic process and development path. We extend a comprehensive understanding of urban scaling in China by quantifying spatial disparities and temporal evolution of scaling exponents. Chinese cases provide new narratives for urban scaling studies. Given the leading external policies from the government over the past years, China’s urban development has followed urban scaling theory during the rapid urbanisation process. Furthermore, China’s emerging urbanisation is dominated by both top-down urbanisation and bottom-up evolution (self-organisation) (Friedmann, 2006; Lang et al., 2019), which is different in many ways from the developed capitalist pattern. It is not unexpected therefore that unique scaling behaviours are demonstrated, even deviating from those expected.

The underlying signals of some of these peculiar characteristics of Chinese urbanisation may express stronger local contexts and interventions of different-sized cities and regions (Zünd and Bettencourt, 2019). In a rapidly urbanising country, the progress of hierarchical diffusion of information and innovation is still concentrated in large cities until equality is reached across the whole system (Meirelles et al., 2018;Pumain, 2012; Pumain et al., 2006). The economic and social cycle sustains urban growth. China has realised significant urbanisation in a relatively short time by giving priority to developing economic and infrastructure construction in large cities (Brelsford et al., 2017). Central government has become a key actor in urban guidance and policy implementation (Jonas, 2020; Yeh and Chen, 2020). Large cities have a greater capacity to continuously capture, and keep growing through, the benefits of superior resources (Keuschnigg et al., 2019). Similarly, urban residents living in large cities enjoy superior living conditions, which results in an unexpected super-linear behaviour for several attributes closely tied to population. Under the influence of this unique economic structure, local governments also have a greater responsibility for the provision of local public services and the construction of infrastructure. Urban areas with higher population density ensure sufficient tax revenues by making earmarked and comprehensive regulations and policies to invest in infrastructure construction for the future (a sign of rapid urbanisation) or preferential treatment by the central government to selected areas (intergovernmental fiscal relations) (Hannay and Wachs, 2007; Zhao et al., 2021). In this way, basic infrastructure and public services in large cities are more generally accessible, with super-linear behaviours presenting as the products of government decision-making (Meirelles et al., 2018).

The spatial disparities of scaling exponents are supposed to measure the regional difference of urban development. The difference between cities is an important reason for the imbalance and lack of coordination in urban development (Li et al., 2020). For districts, unbalanced opportunities and unequal resources brought about by policy orientation and development needs are most prominent in BTH. Large cities in BTH have a stronger development drive and a more intensive attraction for highly skilled resources. Nevertheless, the PRD urban agglomeration novelty shows sublinear scaling behaviour against population in terms of individual needs and economic outputs. The development of the PRD over the past two decades has completed the development of market space, and the transformation to technological innovation and a land-intensive economic pattern. In this way, spatial diffusion effects brought by information innovation are relatively common in the PRD and adjustment of the industrial structure and spatial effects are presented gradually through the specific perspective of production networks (Li et al., 2020; Wu, 2020). Urban agglomerations are created by specific local contexts, thereby showing different levels of economic development and spatial allocation, but are not just products of economic cooperation and linkages of state control and governance – they also reflect the urbanisation process (Wu, 2020). For most urban agglomerations in China, cities with high productivity cluster together, resulting in an obvious inter-regional inequality and intra-cluster differentiation. Some UAs such as PRD may resort to market-based regional cooperations with Hong Kong and Macao, while the development of BTH is driven by policy and governance, with the creation of the Xiong’an New Area. Cities in Eastern and Northeastern China have the advantages of land supply for urban expansion resulting from local extensive land-use policies (Deng et al., 2020). It will be necessary to strengthen control of land expansion in the future (Xu et al., 2020).

Variations in scaling exponents over time reflect the evolution of urban systems (Xu et al., 2019) and measure the coordination and balance of urbanisation. It is noted that although the actual scaling exponents are unstable, they are within the normal range over a long period, which is consistent with the situation that China is facing. Large cities continue to grow and maintain their attraction as they offer more benefits than disadvantages. Interestingly, the variation trend for built-up area is now almost consistent with GDP. China joined the WTO in 2001 and the 10th Five-Year Plan (2001–2005) was launched in the same year. Rapid urban expansion and rapid economic growth mainly took place in large cities during the first decade of the 21st century (2000–2008). In this way, urban land-use efficiency in large cities has decreased while the economic output efficiency has increased. After the 2008 economic crisis, China’s economic development strategy was adjusted. Economic focus has shifted to the small and medium-sized cities of the interior, and Chinese economic development has also entered a new stage (Xu et al., 2019). In recent years, China’s economic growth targets have been lowered, resulting in stable economic growth. This process evidences the dynamics of urbanisation at different stages are in accordance with policy adjustment by central government (Lang et al., 2019), resulting in the dynamic evolution of scaling exponents in the short term. It is proven that the scaling exponents are predicted to be stable in long-time-series research (Bettencourt et al., 2020). Owing to the relatively short research period in this study, the historical and long-period characteristics of the scaling exponent are not fully manifested.

China’s socioeconomic development has strong stability and sustainability from the perspective of the actual process of China’s economic growth. China’s economy has successively gone through two stages: labour-driven and capital-driven, such as infrastructure and real estate industrial investment. It will further transform to a technology, production and business-driven pattern, resulting in higher economic value-added but a relatively slower speed of economic growth. This process is consistent with the theory of hierarchical diffusion of innovations (Hägerstrand, 1952; Pumain et al., 2006). Urban transformation and industrial structure adjustment will be the emphasis in further economic development. Scaling exponent values will vary steadily over time and large cities will maintain the agglomeration effects of production. Given that China’s urban expansion has slowed in recent years, more attention should be focused on the quality of land stock within cities (Deng et al., 2020). Although the pace of economic growth and urban expansion has slowed in recent years, the regional disparities of the agglomeration effects of wealth production and urban expansion are still very obvious. We propose differentiated plans formulated and implemented in different regions to promote coordinated development.

The existing quality issues of statistical data and the lack of definition of functional cities have meant that a set of systems for urban studies in China is not yet formed (Zünd and Bettencourt, 2019). This can be illustrated by the concept that cities in China are different from those of developed countries, and the statistical extent is not consistent. Scaling exponents are unstable under different sizes of cities because of complex and fuzzy boundaries. The means of defining a city and the density of commuting flows also influence the scaling behaviours and scaling exponent values (Arcaute et al., 2015). As Chinese statistical data come from a variety of sources and formulations, particular care is needed in choosing urban units and processing methods for research on Chinese cities. Certainly, the absence of officially defined functional cities limits present studies. In this study, we take official statistical data from urbanised areas in prefecture-level cities as samples, which fully conform to the definition of functional cities, assuring the consistency and comparability of data as much as possible. We have shown that urban attributes also scale with urban population size by taking urban agglomerations as urban units. Perhaps this is also an effective way to consider statistical units for further research about urban scaling in China.

Supplemental Material

sj-pdf-1-usj-10.1177_00420980211017817 – Supplemental material for Urban scaling in rapidly urbanising China

Supplemental material, sj-pdf-1-usj-10.1177_00420980211017817 for Urban scaling in rapidly urbanising China by Weiqian Lei, Limin Jiao, Gang Xu and Zhengzi Zhou in Urban Studies

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by National Natural Science Foundation of China, No. 41971368 and National Key R&D Program of China, No. 2017YFA0604404.

ORCID iDs

Weiqian Lei

Gang Xu

Supplemental material

Supplemental material for this article is available online.

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