Abstract
In this article, the socioeconomic determinants on urban population in China are empirically investigated with a theoretical equilibrium model for city size. While much of the research on urban size focuses on the impact of agglomeration economies based on “optimal city size” theory, this model is eschewed in our research due to its theoretical paradox in the real world, and we turn instead toward an intermediate solution proposed by Camagni, Capello, and Caragliu. This equilibrium model is estimated on a sample of 111 prefectural cities in China with multiple regression and artificial neural networks. Empirical results have shown that the model explains the variance in the data very well, and all the determinants have significant impacts on Chinese city sizes. Although sample cities have reached their equilibrium sizes as a whole, there is substantially unbalanced distribution of population within the urban system, with a strong contingent of cities that are either squarely too large or too small.
Introduction
About two decades after engaging on the path of economic reform, China has not only experienced sizzling economic growth, it has also undergone an almost equally dramatic growth in urbanization. Urban population has increased over 200 percent between 1990 and 2015 (Gu, Kesteloot, and Cook 2015), and by the end of 2018, almost 60 percent of the population lived in urban areas according to the World Bank (https://data.worldbank.org/indicator/SP.URB.TOTL.IN.ZS?locations=CN&view=chart), which increased 4 percent within the past three years. Questions about the size of Chinese cities have also multiplied as part of a broad-based debate in urban economics and economic geography on optimal city size. Along this line, the study by Au and Henderson (2006) stands out as it concluded that Chinese cities are too small. More important, Chinese urban system has been fluctuated between divergence and convergence in accordance by the urbanization policy at the different stages of history. For example, scholars have found that Chinese urban system was balanced at two periods: before 1949 and 1990–2000. After 2000, with the policy concentration on the big and mega cities, urban system is argued to be unbalanced that big cities are sprawling and congested, while small and medium cities are lagged of development (Sun, Jin, and Lin 2019). Therefore, our aim here is to holistically revisit this contention in the light of a more recent data series that describes urbanization across China’s prefectural cities.
While disciplinary research in economics and geography has expounded theoretically and empirically on specific aspects of city size, cities have been argued by other urban scientists to be complex systems whose sizes are affected by a range of intertwined dimensions (Batty 2008). These substitutable factors not only influence urban agglomeration economies but also other contextual conditions, thus affecting urban costs and benefits (Camagni, Capello, and Caragliu 2013). Against this backdrop, modern China has followed a rather singular path to urbanization, although its profile is that of a developing country with high pace of modern urbanization. There is still scant research on the determinants of city growth and on the structures of the urban system of contemporary China from an integrated perspective (Thill, Son, and Chen 2017), which makes it an interesting case in point. Also, there is a pressing need to examine China’s urban system from this broader perspective at this juncture because of various national policies and plans being rolled out regarding urbanization (see, for instance, Taylor, O’Brien, and O’Keefe 2015; Farrell and Westlund 2018). This article is a contribution aimed at understanding the existence of other determinants influencing urban agglomeration beyond sheer physical size and therefore the structure of China’s urban system in response to the urbanization policy since 2000s, and at reexamining if cities are still too small?
The quest for reasonable city size has been a provocative, yet puzzling, research area since last century (Alonso 1971; González-Val et al. 2015). In the years since Alonso’s seminal research on “the economics of urban size,” a strand of conceptual research has emerged to tackle the issue of optimal urban population built upon the “optimal city size” theory. Meanwhile, the sceptic view about the inconsistency between the theoretical “optimal city size” and the urban system in the real world has shifted the scientific debate toward the determinants of urban costs and benefits (Camagni, Capello, and Caragliu 2013). In particular, there is a large body of literature on the impacts of conventional elements on city size, such as agglomeration, urban land rent, quality of life, and social conflicts (David et al. 2013; Evans 1972; Henderson 1986; Parr & Jones 1983; Segal 1976). Beyond these conventional effects, more recent theoretical research has focused on the importance of city connectivity, urban functions, and urban sprawl (Camagni, Stabilini, and Diappi 1994; Capello and Nijkamp 2005; Meijers, Burger, and Hoogerbrugge 2016). As a more radical departure, Camagni, Capello, and Caragliu (2013) proposed a model of equilibrium city size that takes both conventional and unconventional factors into account. Their effort provides a pathway to resolving the long-standing challenges in the search for theoretically feasible city size, which abandons the paradigm of “optimal city size,” and instead leads to an “equilibrium” size for cities.
Despite considerable effort on the theorization of city size, few papers have assessed the relationship between conventional or unconventional elements and city size in developing countries such as China. Fewer still try to explain the impact of social conflict, network, and urban function on the size of cities in China. To fill this gap in the literature, we apply the conceptual framework of Camagni’s equilibrium model and initially test the theoretical hypothesis of traditional and unconventional with improved estimation framework for Chinese cities. To this end, this article applies techniques of multiple regression and artificial neural networks (ANNs) for the prediction of equilibrium city size. We find that the relationship between a range of elements and city size can be explained very well by our model and that all the elements have reliable roles in the growth of urban population in China. In addition, comparing the predicted urban population with actual population allows us to identify city-specific variability in China’s urban system: specifically, the actual population of some cities is found to be notably lower (higher) than the equilibrium city size, and these cases are discussed in more detail.
The rest of this article is organized as follows. The second section reviews the city size theory and theories focusing on the relationship between city sizes. The third part describes the equilibrium model and the data set used in the empirical analysis. Fourth section comprises the results of multiple regression and ANN estimations and predictions, and the comparison between actual population and predicted equilibrium urban size. Finally, conclusions in fifth section suggest future strategies in urban planning and urbanization policy as well as pathways for improving the economic and social environment.
Literature Review
When it comes to the question of city size, one of the reference bodies of literature is the theory of optimal city size. This theory claims that urban population is the fundamental determinant of location costs and benefits. The economies of scale in cities exist within a certain range of urban size, beyond which diseconomies of scale take place and the average revenues of a city decrease. Thus, the optimal condition for urban population is reached as the result of the maximization between a location cost curve of land rent and the aggregate agglomeration curve (Capello and Camagni 2000). Since the theoretical work on optimal city size proposed by Alonso (1971), a large number of empirical estimations have been done, and these studies can be divided into two groups. The first group tries to build relationship between city size and urban agglomeration economies, such as the relationship between wages, employment, and city size (Kelley 1977). The second group of empirical investigations studies optimal city size based on the Henry George Theorem. These studies, for example, consider the urban rent and congestion as the cost of agglomeration externalities, and optimal city size is obtained when agglomeration economies equal the urban rent (Albouy et al. 2019; Henderson 1974).
Although the optimal city size theory has been demonstrated by a large body of empirical estimations, many scholars have criticized it on various grounds (Camagni, Capello, and Caragliu 2016). First, it assumes all the cities have similar cost and production functions, whereas it has been argued the estimation of optimal city size from the same urban production function for all cities is extremely restrictive (Capello and Camagni 2000). Second, cities with different specializations perform different production functions, and their optimal city size may therefore be different depending on their specific characteristics. As Alonso (1971) himself admitted, optimal sizes vary from city to city with different cost and production curves, which makes the theory of optimal size unfeasible in practice. Third, due to the blending of pure physical size and potential welfare in the model, empirical studies on optimal city size provide no theoretical explanations as to why certain variables are chosen and others are not. Thus, results of optimal city size vary from study to study based on different considerations. In addition, as optimal size estimation only considers the relationship between traditional economic benefits and physical size, there are no studies in which social benefits and costs have been taken into account (Mizutani, Tanaka, and Nakayama 2015).
As a result, another strand of literature takes a critical view of theoretical work on city size and employs an approach that estimates the equilibrium size from benefit and cost functions, including both economic and social costs (Camagni, Capello, and Caragliu 2016; Mizutani, Tanaka, and Nakayama 2015). Camagni, Capello, and Caragliu (2013) proposed an intermediate solution that preserves the inherent economic rationality of cities while permitting cities with heterogeneous cost and production functions. Rooted in location choice theory, this equilibrium model of city size is comprised of benefits and costs that critically summarize different theoretical and empirical works. These factors include agglomeration, urban amenities, industrial diversity, network, and urban function as city benefits attracting and retaining firms. On the other side of the ledger, urban rent, social conflict, and land consumption (urban sprawl) are regarded as costs that foster the loss of population. As a result, city size can be separated from physical size that is used in the new theoretical model, and the model recognizes its dual role in urban costs and benefits. The model stems from neoclassical location theory, where the locational choice of single firms is driven by profit maximization; thus, the equilibrium size is achieved when marginal city costs equal marginal city benefits (Camagni, Capello, and Caragliu 2013).
In this research, we follow the new theoretical model of equilibrium city size (Camagni, Capello, and Caragliu 2013) as the basic framework to examine this critical issue in developing countries. Our study faces both a great challenge and opportunities in several ways. First, the topic of city size has been extensively discussed in the context of advanced economies, while there is so far limited research directed toward developing countries, which extends beyond the purely economic perspective. We apply state-of-the-art analytical techniques to test the theoretical model and incorporate broader and deeper considerations on the issue of urbanization. Second, in recognition of the specificities of urban development in China, we include some variables tailored to the socioeconomic context of this developing economy while preserving the fundamental principles of the theoretical model. Adjustments of the model specification to China’s context are discussed hereunder.
First, in advanced economies, it is argued that cities with managerial functions are larger in population than cities with production functions (Duranton and Puga 2005; Ioannides 2013). The concept of urban function was coined to capture this specificity. In empirical research, the workforce in International Standard Classification of Occupations (ISCO) professions is a good indicator of the prevalence of high-level functions including legislators, managers, and other professionals. In China, as in many developing countries, however, the degree of urbanization is still apprehended in terms of sectoral specialization of industry (Li and Phelps 2018), and no data directly pertaining to urban function are available. Given this context and in order to shed light on the emerging response of Chinese urban economies to socially and culturally advanced urban functions, we use the adjusted number of university professors as a proxy measure to differentiate the intensity of urban function of a city (Camagni, Capello, and Caragliu 2013).
Urban sprawl is the second factor that needs to be critically thought out to tightly articulate the theoretical and empirical perspectives. In physical terms, it is increasingly argued to present challenges for the environmental costs and socioeconomic benefits of urbanization. On the one hand, a number of Chinese scholars and policy makers still ascribe to the preponderance of economic benefits brought by built expansion in countries with large population like China. On the other hand, there is a growing consensus that urban sprawl has been an uncontrolled and disorderly phenomenon in China, which is threatening the country’s eco-environmental quality and socioeconomic sustainability (Li and Li 2019; Wang and Zhang 2010; Wei 2018). Urban sprawl is typically measured by either of two methods, namely, a multidimensional set of urban sprawl metrics or a single index. Both approaches have their own advantages and disadvantages. Whereas the single index has limited capability to capture the multiple aspects of urban sprawl, it is appropriate to make comparisons among different cities at the large scale of a national sample of cities (Lopez 2010). Therefore, in this study, we use the single measure to focus on the relationship between urban sprawl and urban population.
Lastly, social cost has been valued as a significant contribution to the theory of city size. Specifically, a large literature focuses on the relationship between social conflict and urban size. Many empirical studies from Western societies use crime prevalence as the measurement of social conflict. In China, social conflicts may be expressed differently and exhibit different considerations associated with stages of social change. The core issue of social conflict can be ascribed to the problem of social equity (Perry and Selden 2003). Compared with the large volume of qualitative work that has been done on social conflict in China, empirical studies that quantify its impact on urban population are rather scarce, due in no small part to data scarcity. Instead, we will resort to proxies. In the analysis of location choice of foreign direct investment (FDI) and regional institutions in China, it has been found that FDI is more likely flowing to an urban location with strong public institutions, such as law enforcement, governmental corruption, and transparency (Du, Lu, and Tao 2012; He and Zhu 2017). Therefore, seeking to integrate social costs into the framework of urban equilibrium population in China, we use a measure derived from the work on FDI location to quantify the social costs.
Model Specification and Data Sources
The theoretical equilibrium model proposed by Camagni, Capello, and Caragliu (2013) is an intermediate solution—neither single size for all nor infinite sizes for each—that allows cities to share the same complex cost and production functions with heterogeneity across the urban system. Therefore, each city preserves its specificity with its equilibrium size on the one hand, while cities are still comparable on the other hand, which provides the opportunity to develop policy strategies for urban growth or containment as suggested by authors.
The equilibrium urban model is comprised of urban costs (1) and urban benefits (2), as defined above, which stems from the neoclassical von Thunen–Alonso–Fujita location theory:
In such framework, the location choice of any firm is motivated by profit maximization; thus, urban cost (equation [1]) should be equal to urban benefit (equation [2]). In this model, a standard Cobb–Douglas formulation is adopted for both functions of cost and benefit (equations [3] and [4]), which is analytically more tractable than others (Camagni, Capello, and Caragliu 2013):
and
where α, β, γ, δ, ε, η, θ, σ, ø, and v are parameters. Each parameter in the two functions (equations [3] and [4]) is assumed to be bounded in the interval (0, 1), except for the size (α) in the cost function (equation [3]), for which an exponential cost effect is hypothesized when α is greater than one. Then, the equilibrium size is satisfied when marginal location costs (equation [5]) equal marginal benefits (equation [6]), so that the maximized profit of firms is obtained. Logically, these assumptions produce the following form:
and
The equilibrium condition is given by
By substitution, it can be implied that:
or
Then, equation (11) is log-linearized to compute the equilibrium for city size:
As can be seen, the physical equilibrium city size depends on benefit and cost functions with conventional and unconventional elements. The model assumes spatial equilibrium across the urban system, so that people can freely move between city regions across space in search of a better life. This assumption may face criticism under China’s residency registration principle, the Hukou system, which can be an administrative impediment to population migration from rural to urban areas, as well as between urban areas. However, a large wave of labor migration including rural-to-urban, inter- and intraprovincial population flow for better living conditions has been emerged along with the urbanization (Fu and Gabriel 2012; Gu, Kesteloot, and Cook 2015). Theory also indicates that persistent population flows can be triggered by even a small proportion of labor and capital mobility accompanied by small changes in local productivity or quality of life (Rappaport 2004). Given these conditions, this model not only captures the impact of conventional and unconventional elements on the location costs and benefits, but more importantly, it tackles the endogenous interaction with population and urban function across the urban system.
The analysis is performed at the level of prefecture cities of which there are about 300 nationwide, according to China City Statistical Yearbook 2011–2016 (there are new cities upgraded from lower administrative level by central government every year). For the purpose of data integrity, some cities are excluded from our study. First, cities with missing values for some variables have to be dropped (e.g., cities in Tibet); second, newly established county-turned-prefectural cities after 2011 are also omitted for the sake of data consistency; third, since a group of minority nationality regions from western China is not listed in the China City Statistical Yearbook, these cities are also excluded from our analysis. In order to control for reverse causality, we apply a time lag to the dependent variable: population is measured as an average of years 2014–2016, while all independent variables are the averages during 2011–2013. As a result, we have a sample of 111 cities (see Figure 1) that are considered in the empirical analysis.
Map of Chinese cities in the study.
For the purpose of data reliability, except for urban sprawl, all the variables are measured based on cities including districts and counties as shown in the China City Statistical Yearbook. Because urban sprawl is only provided at the level of city district in the statistical yearbook, this is the single variable measured by city districts. There might need some explanations about why we use data at the city level (including districts and counties) rather only at districts. From a theoretical perspective, the development of counties is a significant component of the distribution of population and of sustainable urbanization. They not only provide labor force that contributes to industrial production but also support the social and ecological environment of the city as a system (Chan 2012). Besides, in the context of China’s urbanization process, the concentration of political and institutional power and of capital in urban districts has engendered tremendous conflicts at the urban–rural interface for some time, including political, environmental, cultural, and resource issues (Yu et al. 2014). Therefore, we argue that it is very important to consider both districts and counties into the analysis to examine the Chinese city size from a holistic research view. From an empirical point, it would be one-sided to leave counties out of our research. Since some variables are reported only at the city level, we decide to account for all the variables at the same spatial level in order to avoid creating an implicit bias. For instance, the Statistical Yearbook reports on city amenities as “the total revenue of domestic tourism,” without apportionment to urban and rural parts of the city territory.
Table 1 presents a summary of the data set assembled for our empirical analysis based on prefectural cities in China. On the benefit side (expected positive effect), first, agglomeration economies are measured by the population density in each city; second, diversity economies are calculated as the employment in private enterprises and self-employed sector (Renski 2011); third, a measure of urban amenities is computed as the total revenue of domestic tourism in order to represent urban attractiveness of each city (Camagni, Capello, and Caragliu 2013). At the same time, city network and urban function are taken as the nonconventional factors in urban benefits. Considering the selective availability of data on Chinese prefectural cities, we apply the annual average number of highway, railway, and airline passengers as a composite network index measuring city network strength. The higher the volume of passengers, the higher the interconnectivity of the city with the rest of the urban system of China. Finally, because there is no ISCO occupational classification in China (Li 2015; Zhang 2009), looking for an indicator of urban function is an extreme challenge. Given the critical role of high-level educational institutions and their relations with high-level functions (Camagni, Capello, and Caragliu 2013), we use the number of professional faculty per university weighted by the number of “211 Project” university to indicate the functional impact in China. Nationally, since 1995, there are 116 universities described as “211 Project,” which are considered as flagship provincial universities for the purpose of promoting development. These universities are treated in priority to receive financial support from the government and grow faster than others (Luo, Guo, and Shi 2018). As a result, two cities with the same number of faculty members per university will have different functional levels according to the number of “211 Project” universities they house.
Variables and Indicators.
Source: China City Statistical Yearbook.
On the cost side (expected negative effect), urban land rent indicates the pure location costs associated with urban size and is measured by the average sale price per square meter of residential apartments in urban areas. Second, urban sprawl is calculated by the percentage of non-build-up land area within each city. Moreover, the social distress associated with urban life is measured by the number of FDI contracts in each city. Finally, the dependent variable population is the total population at the end of each year, as reported in China City Statistical Yearbook. Consistently with the theoretical model, all variables are nature-log transformed. Descriptive statistics of the dependent and independent variables are presented in Table 2.
Descriptive Statistics of Natural-log Transformed Variables.
Empirical Results
Regression Analysis
We first report on bivariate relationships among variables in the model using correlation analysis (Table 3). Pearson’s correlation coefficients between the dependent variable (lnpop) and the independent variables are given in the table. All the benefit variables show strong positive correlation with the dependent variable; on cost side, sprawl and closeness significantly show negative relationship with population, whereas rent fails to be statistically significant, which is at odd with previous studies. Overall, the correlation analysis confirms the soundness of the selection of factors of city size and of the choice of direct and proxy measures. Potential independent variables exhibit a certain degree of collinearity.
Correlation Matrix.
** Correlation coefficient is significant at .01 level; *Correlation coefficient is significant at .05 level.
The multiple regression model of city population is estimated via ordinary least squares (OLS) on the potential factors listed in Table 1. Final estimation results are reported in Table 4 for the final specification, which includes only the subset of factors found to be statistically significant. There is no evidence of multicollinearity from the variance inflation factor (VIF), which is below the cutoff of 3 in all cases. In addition, the assumption of normality is met, as conveyed by the Q-Q Plot. The multiple regression model statistically predicts the average city population during 2014–2016, with the following statistics: F (8, 102) = 18.82, p < .001, adj. R2 = .56. Five variables are significant predictors of city population at p < .05 (the urban amenities and sprawl factors are significant at p < .1). All the benefit variables exhibit consistent direction and strength with the dependent variable; land rent plays a statistically significant negative role in the model. Considering the results from correlation and regression analyses, it is clear that the theoretical model is empirically validated, although collinearity prevents all the tested factors from entering the multivariate model. This provides the ground for using the complete set of eight factors (Table 1) in the subsequent neural network analysis aimed at predicting population size of Chinese cities.
Empirical Results of the Model of Equilibrium City Population.
Note: B = unstandardized regression coefficient; SEB = standard error of the coefficient; β = standardized coefficient.
**p < .05.
***p < .001.
ANN Analysis
ANNs (Anderson and Ge 2005) are known as soft computing techniques. As techniques of supervised machine learning, they have been applied with great success in many domains of application, particularly for forecasting and prediction. Neural network models provide an alternative approach to analyze data with the advantage of not being bound to estimate linear relationships only, to assume normality of data series or other, not other strong conditions on data structures. We use a feed-forward network with the back propagation algorithm, one of the most popular and most effective forms of ANN, to predict urban population based on the equilibrium model presented above (equation [12]).
The architecture of feed-forward networks is composed of input, output, and one or more hidden layers of sigmoid nodes. In this study, the input layer has eight nodes corresponding to the predictors in our model of city size; the output layer consists of a single node, city population size. Hidden layers of nodes with nonlinear transfer functions allow the network to learn nonlinear and linear relationships between input and output vectors (Tiryaki 2008). The scaled conjugate gradient (SCG) and Levenberg–Marquardt (LM) optimization methods are used for ANNs training. To avoid overfitting, a single hidden layer is used; also, this layer has tangent sigmoid transfer function nodes. The number of nodes on the hidden layer is a critical factor of the model performance, following the common practice of a trial-and-error scheme to choose the appropriate number of hidden nodes. The neural networks were coded using the MATLAB Neural Network Toolbox.
Twenty independent runs having different initial random weights are performed, and the results are compared by statistical methods in order to achieve a good solution. We use the determination coefficient (R2; Asiltürk and Çunkaş 2011) to identify the predictive performance with lowest error:
where ti is the observed vector and oi is the predicted vector. The LM and SCG search methods are compared with nine or ten hidden nodes for eight independent variables. We find the model using LM, and nine hidden nodes produce the best results with an R2 = 99.81 percent (see Table 5 for the detailed results).
Predictive Performance Statistics.
We also compare the performance of the ANN with nine hidden nodes and eight input nodes to the OLS regression results produced with five independent predictors. For this purpose, we use the R2 as well as Pearson’s correlation coefficient. Results (Table 6) indicate that the ANN model outperforms the OLS model, and ANN is a robust method to reliably predict most of the variance in the city population size.
Artificial Neural Network (ANN) and ordinary least squares (OLS) Regression Peformance.
**p < .05.
We further exploit the analytical results produced by the neural network model by comparing the actual population of each city to their predicted population. It allows us to sort out cities as either beyond or below their theoretically estimated equilibrium size given the current level of development, which is given their valuation on the factors of city size put forth by the theoretical model. The gap between the actual and estimated city populations is measured by the value of actual average population from 2014 to 2016 over its predicted population. This ratio is referred to as the population oversize ratio (POR). If the POR values equal to 1 (within the margins of error of 5 percent on the predicted population, i.e., 0.95 ≤ POR ≤ 1.05), cities are said to be in equilibrium; if the values are greater (or smaller) than 1, cities are considered as over (or under) their equilibrium sizes. The cities are sorted according to their POR value and plotted as undersized cities, equilibrium cities, and oversized cities in Figures 2 –4, where cities in equilibrium are depicted by gray bars (0.95 ≤ POR ≤ 1.05). A table detailing the POR of each city is also given in the Table 7 in Appendix.
Population oversize ratio when actual urban population is lower than predicted urban equilibrium size.
Population oversize ratio when actual urban population is within margins of error of predicted urban equilibrium size.
Population oversize ratio when actual urban population is higher than predicted urban equilibrium size.
Population Oversize Ratio (POR).
Overall, it is a major challenge for the process of urbanization to maintain a balanced relationship between urban productivity and the growth of population. Only 15 of the 111 cities (13.5 percent) studied in this research have actual population within 5 percent of their predicted value, while 48 cities have an oversized population and 48 are undersized. The average value for 111 sampled cities is 1.05. However, there is big variance among these cities, with a range from 0.52 (Xiaogan city) to 2.03 (Fuzhou city). According to the theoretical hypothesis, all the city benefit factors have a significantly positive impact on the equilibrium size, while cost elements negatively influence the population. In other words, given the social and economic development measured in our model, these undersized cities still have capacities for more population. Guiyang, whose population growth rate was rapid by the end of 2018, is a good example of this. Also, Beijing is still somewhat undersized when the model investigates the problem at the city level. It is commonly known that Beijing’s population is highly clustered in two districts (Chaoyang and Haidian districts), and its urban problems are largely affected by the wicked urban planning and transportation design. Considering the indicators in the equilibrium model in terms of city benefits and costs, the model does not show any evidence that Beijing is beyond its equilibrium population.
In contrast, in the oversized cities, the development of current socioeconomic conditions lags behind population growth. The ten cities whose population exceeds the predicted size the most mainly belong to the group of wealthier coastal cities. The large urban–rural development gaps experienced by the cities may be one of reasons for these cities to be oversized, as our model holistically examines the issue by considering both districts and counties. Along the most developed cities, Shanghai and Chongqing are slightly beyond their equilibrium size; Shenzhen and Tianjin are close to their equilibrium population. In general, small and medium cities from more developed regions of the country and big cities from the western region are still below their equilibrium urban size.
Our estimations and forecasts reveal that China’s urban system is quite imbalanced, with a number of cities that are oversized, while some others are well below their equilibrium size. The discrepancy between the predicted population and the real urban population demonstrates the magnitude of the inadequacy of urban and regional economic policies of China to harness the complexities of contemporary urban environments. For those cities whose population is under the equilibrium line (POR value under 0.95), there is an opportunity to grow, and such possibilities need to be further explored by other efficiency characteristics that are not captured by the model. Especially, the distribution of Chinese urban system is largely affected by national policy of urbanization development. Reviewing the history of urbanization policy in China, it has been wavering from concerning the small cities in late twentieth century to support the big cities since twenty-first century. This change of the policy has significantly lead to the concentrated growth in small amount of big cities and the convergence and unbalance of urban system in China in twenty-first century (Sun, Jin, and Lin 2019). After close examination of the undersized cities, we find that they are mainly the medium cities across nation. Our study reveals that these cities need to pay more attention on the development of economic and social benefits and costs to improve the urban environment so that to attract more population. In addition, although some large cities with concentrated political and economic power argue that they are oversized, we do not find evidence to support that big cities are excessively big. These cities are either slightly over or under the equilibrium size.
Conclusions
China’s remarkably fast speed of urbanization has offered an opportunity as well as a challenge to the country’s effort to improve welfare of society. Some scholars have argue that Chinese cities are too small, while others think they are overpopulated. We believe the discourse on the matter is too often influenced by received ideas on how large cities should be that lack evidentiary support. Under the optimal city size framework, Au and Henderson (2006) argued that Chinese cities generally were undersized on the basis of research modeling net agglomeration economies and diseconomies in the period of 1990–1997. On the other hand, Chinese national policies on urbanization assume that the big cities are too big and try to disperse the growth of population through a variety of central regulations. Most of the research on urban size in China tends to focus on a single element, such as agglomeration economies, while little attention has been turned toward the integrated effect of economic and social elements on urban population and productivity. Thanks to recent improvements to the equilibrium model of city size, which comprises both the neoclassical and nonconventional approaches within the framework of urban benefits and costs, we can enhance our understanding of the determinants of city size and of the case of the Chinese urban system a decade after Au and Henderson’s seminal argument in search of the answer to the universal question—are cities too small or too big?
By employing the theoretical model proposed by Camagni, Capello, and Caragliu (2013), updated estimation techniques, the evidence suggests that indeed, both the neoclassical and more recent approach matter not only in Western countries but also make a difference in developing nations such as China. Especially, population of prefectural cities is likely to rely heavily on the modern economic paradigms at the foundation of Camagni, Capello, and Caragliu’s (2013) model. Furthermore, our revised social cost of closeness as the measurement of equity also shows significant impact and improves the performance of population prediction. ANN and multiple regression models are developed to predict the equilibrium city size for each city in our data sample; our results clearly and consistently reveal that urban agglomeration, diversity, function, and the physical connection to other cities allow cities to achieve a larger equilibrium size. Conversely, urban sprawl, rent, and closeness decrease the equilibrium size, and rent still represents the single highest cost associated with urban size.
At last, by comparing the estimated equilibrium population with actual urban size, the analysis further suggests that although the sample of 111 cities reached their equilibrium size on average, there is a big gap in the Chinese urban system between oversized cities and undersized cities. While some cities have a size that is consistent with their equilibrium, many others either have lower or larger population than predicted size. Small- and medium-sized cities are more likely to be undersized, while big cities are not disproportionately beyond their equilibrium population and some of them are even smaller. This convergent urban system in China provides an important evidence that government’s urbanization policy plays a significant role in controlling and allocating urban population. Also, the established national development policy that determines how many cities are allowed to grow and the fiscal allocations to carefully selected growth centers figure unmistakably among the causes of unbalanced urban development. Therefore, it is critical for the government to conduct the consistent and stable policies in city development (Sun, Jin, and Lin 2019).
The analysis of this article has certain limitations. First, due to restrictions on data access, some of the proxy indicators of factors of urban size may be less desirable, and alternative specifications may be in order in the future. Second, we argue that social and environmental benefits and costs are playing increasingly urgent roles in modern society. Therefore, such determinants need to receive more attention when considering the overall welfare. Our study is an initial effort to bring such issues to the forefront, and future empirical work should focus on the priorities to establish the robustness of our empirical results.
Footnotes
Authors’ Note
They have significantly contributed to the enhancement of the scientific contribution made by this research.
Acknowledgments
The authors wish to thanks the reviewers for their perspective comments on an earlier version of the manuscript.
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) received no financial support for the research, authorship, and/or publication of this article.
