An Empirical Evaluation of the Critical Population Size for “Knowledge Spillover” Cities in China: The Significance of 10 Million

Abstract

In advanced countries such as the USA and China, some cities are characterized by “knowledge spillover industries”, which play crucial roles in driving innovation, entrepreneurship, and economic growth. However, the excessive expansion of megacities in China has led to the overabsorption of labour from other cities. The unchecked growth of individual megacities causes metropolitan malaise and regional imbalance, further limiting the emergence of new “knowledge spillover” cities, which is detrimental to overall economic development. This study analyses China’s employment population structure to identify the critical population size required for the formation of “knowledge spillover” cities. The results show that 10 million is the unique threshold for which cities with populations above this size see a significant improvement in the prominence of “knowledge spillover” industries. Therefore, a population base of approximately 10 million is essential for these cities to thrive. This result suggests that China should pay more attention to the construction of urban agglomerations as geographic or administrative units to better distribute resources and promote balanced regional development. This approach can help foster the emergence of more “knowledge spillover” cities, thereby enhancing national innovation capacity and economic growth.

1. Introduction

The emergence of cities is a symbol of the maturity and civilization of human beings [1,2]. Inevitable urbanization processes result in the accumulation of various material resources, such as capital, materials, commodities, and labour. The concentration and proper distribution of resources reduce various production and living costs, improve the social efficiency of a city, and promote the further concentration and distribution of material resources. As the economy and technology develop and progress, more emerging industries and employment opportunities appear in cities. This situation directly leads to rapidly expanding urban size [3] and complex economic activities [4].

The growth of the urban population is not random but follows a structured pattern [5]. Different industries have varying contributions to urban economic growth and exhibit different employment growth rates [6,7]. In urban scaling theory, the relationship between employment in different industries and the urban population is often described by the power-law function $Y_i\sim N^{{\beta }_i}$ [8,9], where N represents the city population, and $Y_i$ represents the employment in industry i. Industries that exhibit superlinear growth in employment relative to the urban population (${\beta }_i>1$) are generally considered to be driven by “knowledge spillovers”, whereas urban infrastructure industries (${\beta }_i<1$) show the opposite trend [8,10]. This relationship suggests that the population dependencies during urbanization may underpin the urban economic structure and promote its evolution [5], as the output and employment share of knowledge spillover industries continue to increase compared with those of infrastructure industries [11,12]. The employment structure of metropolitan regions has evolved in the postindustrialization era [13,14,15]. Cities with more pronounced production advantages in “knowledge spillover” industries (with ${\beta }_i>1$) are referred to as “knowledge spillover” cities. Some scholars argue that the emergence of “knowledge spillover” cities is contingent upon a sufficiently large population. The most recent quantitative analyses indicate that in the United States, “knowledge spillover” cities begin to emerge only when the population exceeds 1.2 million [7].

China’s large population and abundant regional labour flows [16] provide a strong basis for rapid urbanization [17,18] and the construction of several international metropolises [19,20]. Moreover, China’s urbanization process has exhibited patterns of shifting from manufacturing to service industries as well as the gradual emergence of knowledge spillover industries as key drivers of urban growth. However, some megacities, even those with populations exceeding those of major international metropolises in the developed countries, still have dominant industries that are basic in nature and contribute limited value to GDP growth. This situation has sparked debates among scholars regarding whether China should restrict the size of its superlarge cities [21,22]. The emergence of “knowledge spillover” cities, which are expected to drive economic innovation and sustainable growth, has been hindered. This issue is characterized by the excessive expansion of a few megacities, which not only leads to “metropolitan malaise” and unbalanced regional development but also limits the emergence of other “knowledge spillover” cities [5,23]. Addressing this issue requires an analysis of the coevolutionary patterns between urban population size and industrial structure transformation.

This research aims to examine the mechanism by which population distribution characteristics promote urban evolution in China, with a focus on the emergence of “knowledge spillover” cities. It specifically investigates how urban population distribution impacts urban evolution. Hypothesis testing has confirmed that cities with populations exceeding 10 million have significantly more prominent “knowledge spillover” industries than those with populations below 10 million, and this threshold value is unique. The study identifies the labour conditions necessary for the emergence of “knowledge spillover” cities and demonstrates that the longitudinal changes in urban economies follow a universal process governed by changes in population size. This study intends to comprehend the underlying mechanisms driving urban development and provide insights into fostering a more balanced and sustainable urbanization process in China. Additionally, it aims to pinpoint the population thresholds and labour conditions required for the emergence of knowledge spillover cities.

2. Literature Review

The labour force and contributing individuals—represented by producers, consumers, and members of society in the urban area—are the most fundamental resources for any urban area. Generally, the population distribution among urban areas is uneven, where N is the urban population and $P\left(N\right)$ is the distribution function. Urban populations typically follow a Pareto distribution $P\left(N\right)=C{N}^{-(\alpha +1)}$ [24,25], Zipf’s law, or a log-normal distribution $P\left(N\right)=C{N}^{-1}exp\left(-{\displaystyle \frac{{(lnN-\mu )}^2}{2{\sigma }^2}}\right)$ [26,27,28]. Urban areas are ranked by population size in descending order. The population of the urban area ranked r is proportional to $r^{-1}$. For example, the largest urban area has twice the population of the second-largest urban area, three times that of the third-largest urban area, and so on. Although Zipf’s law is not expressed as a probability density function, it also indicates that the population of top-ranked urban areas is much larger than is that of lower-ranked urban areas. These distributions all feature a negative exponent of N, suggesting that population concentration results in a few large metropolises standing out from many smaller urban areas [29,30]. However, the quality of urbanization and industrial structure differ significantly among urban areas of varying sizes [5]. According to Zhao (2017), the shift from manufacturing to the service industry as the leading economic sector is an important reason for the continuous growth of urban areas [31]. However, not all expanding urban areas can leverage “knowledge spillovers” to become centres of superlinear growth industries and thus gain competitive advantages. Therefore, understanding how the distribution characteristics of urban populations influence the evolution of urban areas and how urban expansion can be effectively managed to better support the economic structure and foster “knowledge spillover” urban areas are questions of great interest to scholars and policy-makers.

Scholars have explored the general patterns by which increasing urban population sizes drive structural transformations in urban areas. Friedmann (2006) notes that disparities in urban size lead to great inconsistencies between the quality of spatial development in urbanization and the quality of social development [32]. According to Frank and Balland (2018, 2020), small urban areas heavily rely on manual labour, whereas large urban areas rely on cognitive labour [4,33]. The authors suggest that as the urban population increases, industries transform from labour- to capital- and knowledge-technology-intensive or from agriculture- to manufacturing- and modern-services-led [11]. Recent quantitative analyses in the United States show that “knowledge spillover” urban areas emerge only when the population exceeds 1.2 million [7].

China’s early rapid urbanization process [34,35] and subsequent “polarization” problem [36,37,38] have inspired comprehensive analyses of the mechanisms by which population promotes urban evolution. China’s large population base and substantial migrant population have enabled the rapid formation of multiple international metropolises. From 2020–2021, China had 21 urban areas with populations exceeding 5 million [39] and 17 urban areas with populations exceeding 10 million [40]. However, insufficient “knowledge spillover” urban areas have emerged. Therefore, it is necessary to investigate whether similar general patterns exist in China, where population size drives urban transformation, and to identify the population threshold for such transformations. This research demonstrates that the longitudinal change in urban economies follows a universal process governed by changes in population size.

In summary, while significant progress has been made in understanding the relationship between urban population dynamics and economic evolution, gaps remain in identifying the specific mechanisms and thresholds that drive the emergence of knowledge spillover in urban areas. Future research should focus on bridging these gaps, particularly in the context of China’s unique urbanization trajectory. The remainder of this study is arranged as follows. Section 3 introduces the data source and methods. Section 4 describes the scaling characteristics of employment in different industries and indicates that urban areas have different comparative advantages, which is the basic assumption used to discuss urban development and innovation, analyses the evolution of knowledge spillover industries, and illustrates the labour demand and its limitations for “knowledge spillover” urban areas in China. Section 5 provides the conclusion and discussion.

3. Data & Methods

3.1. Data Sources and Preprocessing

The dataset encompasses the urban population of cities in China at the prefecture-level and higher, along with their employment across various industries. Given the substantial floating population in China, studies on urban evolution typically utilize resident population data. The resident population accurately reflects the mobility characteristics of the current Chinese population and provides a precise depiction of urbanization levels on the basis of resident population standards. For example, China’s census data are based on the resident population.

3.1.1. Resident Population Data for Cities from 2004 to 2019

In January 2004, the National Bureau of Statistics mandated that all provinces, autonomous regions, and municipalities calculate the gross regional product (GRP) per capita using the resident population data. (According to the spirit of the 28th executive meeting of the State Council, the National Bureau of Statistics issued the Notice on Improving and Standardizing Regional GDP Accounting on 6 January 2004, which required provinces, autonomous regions, and municipalities to uniformly calculate per capita GDP using the resident population (i.e., the registered population minus the outflow population of more than half a year plus the inflow population).) Owing to the lack of publicly available and reliable resident population data, the urban population of each city was estimated using formula ${\displaystyle \frac{GRP}{GR{P}_{\mathrm{per}\mathrm{capita}}}}$ from 2004 onwards. The effectiveness of this estimation method is discussed. A reliability analysis of the estimated data for four typical cities is provided in Appendix A.1.2.

The GRP and GRP per capita data are sourced from the “China City Statistical Yearbook” [41]. Since the Yearbook ceased reporting industry-specific employment data for prefecture-level cities starting in 2020, the dataset is confined to the period up to 2019. To extend the dataset to 2020, data from the 7th National Population Census were incorporated. Given that the census is conducted decennially and that the employment population distribution in prefecture-level cities was significantly influenced in the short term by the COVID-19 pandemic in 2020, the supplementary data for 2020 are presented exclusively in Appendix A.2.1. Given the altered characteristics of the urban population distribution, the implications for the conditions under which “knowledge spillover” cities emerged in 2020 are examined.

3.1.2. 280 Cities and 19 Industries

As of 2019, China had 4 municipalities and 293 prefecture-level cities. The employment data for 19 industries for the period 2004–2019 were selected from the “China City Statistical Yearbook” [41]. The industries are defined according to the Industry Classification of the National Economy (GB/T 4754) [42]. However, employment data for certain industries were missing in some cities. Although these cases are rare, they required rigorous preprocessing. Interpolation was employed for non-endpoint missing values, and regression prediction was used to interpolate endpoint vacancy values (details in Appendix A.2.2).

The detailed data are provided in

Table 1. Data description.

Variable	Variable Description	Data Source
Employment in China	The employment of 19 industries in prefecture-level and above cities, annual data during 2004–2019, from “China City Statistical Yearbook” [41], 10 thousand people.	https://data.oversea.cnki.net/en/trade/yearBook/single?zcode=Z009&id=N2025020156&pinyinCode=YZGCA (accessed on 20 May 2025)
GRP, GRP (per capita) in China	The gross regional product and gross regional product per capita in prefecture-level and above cities of China, the annual data during 2004–2012 and 2014–2019 are from “China City Statistical Yearbook” [41], and the annual data in 2013 is from “China Statistical Yearbook for Regional Economy” [43], yuan.	https://data.oversea.cnki.net/en/trade/yearBook/single?zcode=Z009&id=N2025020156&pinyinCode=YZGCA (accessed on 20 May 2025); https://data.oversea.cnki.net/en/trade/yearBook/single?zcode=Z009&id=N2015070200&pinyinCode=YZXDR (accessed on 20 May 2025)
Sales of commodities in China	Total retail sales of consumer goods + total sales of commodities of enterprises above designated size in wholesale and retail trades prefecture-level and above cities of China, annual data in 2019, from “China City Statistical Yearbook” [41], 10,000 yuan.	https://data.oversea.cnki.net/en/trade/yearBook/single?zcode=Z009&id=N2025020156&pinyinCode=YZGCA (accessed on 20 May 2025)
GDP (per capita) in the United States	CAGDP1 gross domestic product (GDP) summary by metropolitan area, from U.S. Bureau of Economic Analysis [44], annual data during 2004–2019, thousands of chained 2012 dollars.	https://www.bea.gov/data/gdp/gdp-county-metro-and-other-areas (accessed on 20 May 2025)
Population in the United States	Annual estimates of the resident population for metropolitan statistical areas in the United States, from U.S. Census Bureau, Population Division [45], annual data in 2019, people.	https://www.census.gov/data/datasets/time-series/demo/popest/2010s-total-metro-and-micro-statistical-areas.html (accessed on 20 May 2025)
Sales of commodities in the United States	Real personal consumption expenditures by States, real personal income by metropolitan area, annual data in 2019, from U.S. Bureau of Economic Analysis, millions of constant (2012) dollars [46].	https://www.bea.gov/data/consumer-spending/real-consumer-spending-state (accessed on 20 May 2025)

. To ensure statistical consistency, 18 cities lacking a significant amount of data were excluded (Specifically, 16 cities lacked GRP data for several years, which poses problems for obtaining permanent resident population data (Sansha, Zhangzhou, Bijie, Zunyi, Tongren, Lasa, Rikaze, Changdu, Linzhi, Shannan, Naqu, Longnan, Haidong, Zhongwei, Tulufan, and Hami), and 2 cities lacked all employment population data for certain industries (Ziyang and Hengshui), so these 18 cities were excluded from the analysis. Additionally, Laiwu was merged with Jinan in January 2019, and the city was retained in the analysis to maintain consistency). The effective sample thus includes 276 prefecture-level cities and 4 municipalities directly under the central government, totalling 280 cities. According to the classification of China’s four major economic regions (see

Table A5. China’s four major economic regions.

Region	Provinces
Eastern Region	Beijing, Tianjin, Hebei, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Hainan, Taiwan, Hong Kong SAR, Macao SAR
Central Region	Shanxi, Anhui, Jiangxi, Henan, Hubei, Hunan
Western Region	Inner Mongolia Autonomous Region, Guangxi Zhuang Autonomous Region, Chongqing Municipality, Sichuan, Guizhou, Yunnan, Tibet Autonomous Region, Shaanxi, Gansu, Qinghai, Ningxia Hui Autonomous Region, Xinjiang Uygur Autonomous Region
Northeast Region	Liaoning, Jilin, Heilongjiang

Classification based on the standards of the National Bureau of Statistics of China.

in Appendix C.4), there are 86 cities in the eastern region, 80 cities in the central region, 80 cities in the western region, and 34 cities in the northeast region.

3.2. Investigate How the Comparative Advantage Evolves with Population Size

For city c, the revealed comparative advantage ($RCA$) of industry i in all employment is quantified as [7,47,48]

$$RC{A}_{ci}={\displaystyle \frac{Y_{ci}/{\sum }_i{Y}_{ci}}{{\sum }_c{Y}_{ci}/{\sum }_{c,i}{Y}_{ci}}},$$

(1)

where $Y_{ci}$ denotes the employment of industry i in city c. Specifically, an industry i is considered characteristic in city c if $RC{A}_{ci}>1$, whereas $RC{A}_{ci}<1$ indicates a lack of specialization [7].

To verify that a population of 10 million is the appropriate threshold for “knowledge spillover” cities, in addition to plotting the evolution curves of $RCA$ for different industry types with respect to city size and making intuitive judgements on the basis of these curves, this paper further conducted hypothesis testing to provide a more rigorous validation and explanation. This approach aims to substantiate the significance of the 10 million population scale in the context of urban development in China.

Define the sets

$$G_1=\{N_c<p_1\}$$

$$G_2=\{p_2\le N_c<p_3\}$$

where $N_c$ is the population of city c.

Null Hypothesis ($H_0$): The proportion of cities with an $RCA$ value greater than 1 is the same for cities in $G_1$ and cities in $G_2$.

Alternative Hypothesis ($H_1$): The proportion of cities with an $RCA$ value greater than 1 is higher for cities in $G_2$ than for cities in $G_1$.

Mathematically, these hypotheses can be expressed as

$$\begin{array}{cc}\hfill H_0:{\theta }_{G_1}& ={\theta }_{G_2}\hfill \\ \hfill H_1:{\theta }_{G_1}& <{\theta }_{G_2}\hfill \end{array}$$

where ${\theta }_{G_1}$ and ${\theta }_{G_2}$ denote the proportions of cities with $RCA$ values greater than 1 in sets $G_1$ and $G_2$, respectively.

To test the above hypotheses, we use a logistic regression model to predict the probability that the $RCA$ value is greater than 1. The steps are as follows:

1. Construct the Logistic Regression Model:

Divide the population size into two groups: $p_1>N_c$ and $p_2\le N_c<p_3$. Assume that y is a binary variable indicating whether the $RCA$ value is greater than 1 (1 if greater than 1, 0 otherwise). The logistic regression model can be expressed as:

$$log\left({\displaystyle \frac{P(y=1)}{1-P(y=1)}}\right)={\beta }_0+{\beta }_1·G$$

where ${\beta }_0$ is the intercept, ${\beta }_1$ is the coefficient for the population size group, and G is a categorical variable representing the population size group: 0 for $G_1$ and 1 for $G_2$.

2. Fit the Logistic Regression Model:

Use maximum likelihood estimation (MLE) to fit the logistic regression model. The model outputs the coefficients, standard errors, z values, and p values for each independent variable.

3. Output the Results:

Output the summary of the logistic regression model, including the coefficients, standard errors, z values, and p values. Check if the p value for the population size group is less than the significance level (0.01).

If ${\beta }_1$ is significantly greater than 0 (p value less than 0.01), cities with a population between $p_2$ and $p_3$ have a significantly higher proportion of $RCA$ values greater than 1 compared to cities with a population less than $p_1$. Confidence intervals not including 0 further support the conclusion that population size has a significant effect on the proportion of $RCA$ values greater than 1.

To ensure that the sample sizes of the two groups are the same and to avoid bias due to different group sizes, we performed stratified sampling by randomly selecting an equal number of samples from each group. This balanced sampling approach helps to eliminate potential biases in the analysis.

In practical applications, whether this difference is significant also needs to be judged in conjunction with the specific research background and domain knowledge. For example, if an $RCA$ value greater than 1 indicates that a certain industry has a competitive advantage in a certain city, then an increase in population size might lead to a significant increase in competitive advantage.

3.3. The Comparative Advantage of Industries and Its Critical Point Analysis

Some studies use scaling exponents to explore employment distribution and reflect the technical level of industries [11,12]. Other scholars analyse a city’s growth model by examining the distribution of the urban population using scaling exponents [49,50]. However, few studies consider urban population and employment together. Some scholars explored the relationships between urban size growth and urban innovation using the scaling exponent $\beta$ [7]. The authors reported that superlinearity ($\beta >1$) is typically associated with knowledge spillover industries, whereas sublinear scaling ($\beta <1$) is often attributed to infrastructure industries [7,10].

$$Y_{ci}\approx Y_{io}{N}_c^{{\beta }_i}.$$

(2)

Although a power-law distribution is common in urban populations and other socioeconomic systems [51,52,53], not all countries or regions follow this pattern [54,55]. Some of the literature suggests that China’s urban population does not follow a power-law distribution [49] but obeys a log-normal distribution [56]. Here, on the basis of the data for urban residents, it is verified that China’s urban population satisfies the log-normal distribution (see Figure A2 in Appendix A.1.3). In the range of relatively small or large N, it can be assumed that the distribution function is linear under double logarithmic coordinates, as $P\left(N\right)\sim N^{-\gamma }$ in $N\in [N_{min},N_{max}]$, where $\gamma$ is the coefficient of the explanatory variable [48,57,58].

The function of comparative advantage $RCA$ is then derived as follows, with the details provided in Appendix B.1 and Appendix B.2:

$$RCA(\beta ,N)=N^{\beta -1}\left({\displaystyle \frac{\beta -\gamma +1}{N_{max}^{\beta -\gamma +1}-N_{min}^{\beta -\gamma +1}}}\right).$$

(3)

According to Equation (3), the change in $RCA$ with respect to the scaling exponent $\beta$ and population N is quantified. This calculation allows for the analysis of the universal development path and labour demand of cities in China by comparing the evolution of the employment advantages among industries.

In physics, a critical point $({\beta }^{*},N^{*})$ of the function $RCA(\beta ,N)$ is a point in the function’s domain at which it is either not holomorphic or the derivative is equal to zero [59]. On the surface of the graph of the function $RCA(\beta ,N)$ (a two-dimensional surface composed of $\beta$ and N), the critical point is defined by $\left({\displaystyle \frac{\partial RCA}{\partial \beta }}=0\mathrm{and}{\displaystyle \frac{\partial RCA}{\partial N}}=0\right)$. This definition indicates that regardless of how the two parameters change near this point, the value of $RCA$ will remain unchanged. Thus, it is defined as a fixed point in mathematics. Whether the critical point is stable depends on whether the point is a minimum or a maximum. For a one-dimensional function, the critical point is relatively easy to judge. For example, for function $f\left(x\right)=x^2-3$, $x^{*}=0$ is a critical point with ${\displaystyle \frac{\partial f}{\partial x}}=0$, and it is stable with ${\displaystyle \frac{{\partial }^{2}f}{\partial x^2}}>0$, indicating a minimum. The critical point of a multidimensional function is more complex because each dimensional state may differ.

In this study, on the basis of empirical analysis, the critical points are identified as saddle points, with the Hessian matrix having one positive eigenvalue and one negative eigenvalue. Through a schematic diagram of this two-dimensional surface, the evolution of $RCA$ for different industrial employment with parameter changes is analysed (see Figure 1). When $N>N^{*}$, for industries with $\beta >{\beta }^{*}=1$, $RCA$ increases with increasing $\beta$, while for industries with $\beta <{\beta }^{*}=1$, $RCA$ decreases with the growth in $\beta$. This result demonstrates that $N^{*}$ is an important critical point. The advantages of knowledge spillover industries can be realized only when the urban population reaches a certain scale.

4. Results

4.1. Distribution and Evolution of Scale Characteristics

4.1.1. Evolution of Scale Characteristics

The hypothesis posits that the employment population in different industries $Y_{ci}$ and the urban population $N_c$ adhere to a power-law relationship, described by $Y_{ci}\approx Y_{io}{N}_c^{{\beta }_i}$. Here, ${\beta }_i$ varies across industries, reflecting different scaling effects. To test this hypothesis, a log-linearized model $ln\left(Y_{ci}\right)=ln\left(Y_{io}\right)+\beta ·ln\left(N_c\right)$ is employed for the regression analysis. Additionally, a null model $ln\left(Y_{ci}\right)=ln\left(Y_{io}\right)$ is introduced for comparison, which assumes that the employment population is determined solely by a constant term and is independent of the urban population. Both the actual and the null models are fitted using ordinary least squares (OLS), and an F test is conducted to compare them. If the p value of the F test is less than the significance level (e.g., 0.05), the actual model significantly outperforms the null model, thereby supporting the hypothesis that a power-law relationship exists between the employment and the urban populations, with distinct ${\beta }_i$ values for different industries.

For the period 2004–2020, only the scaling relationships in the agriculture and mining industries are insignificant. This result indicates that most industries have a logarithmic linear relationship between employment $Y_{ci}$ and the urban population $N_c$, supporting the hypothesis. For two special industries, agriculture and mining, the scaling characteristics are not considered in subsequent research. Figure 2 shows that in China, approximately 50% of industries have ${\beta }_i>1$. The distribution of ${\beta }_i$ was wider in 2019 than it was in 2004. Specifically, in 2004, ${\beta }_i$ fell within a narrower range of [0.7, 1.1], whereas in 2019, the range expanded to [0.7, 1.4]. The resident service, public facilities, and manufacturing industries are representative of those whose ${\beta }_i$ increased rapidly. There was no obvious decrease in ${\beta }_i$ from 2004 to 2019.

Different factor endowments and technology levels cause the same industry to have varying ${\beta }_i$ across different countries. Although scaling characteristics cannot be used to judge the advantages of an industry between China and the United States, ${\beta }_i>1$ indicates that the employment structure of that industry in large cities is more advantageous. The economies of scale in large cities show that industries with ${\beta }_i>1$ tend to be more important and often represent the driving force of the country’s economic development. Therefore, the development of “knowledge spillover” cities should focus more on industries with ${\beta }_i>1$.

The analysis compares the changes in scaling characteristics across industries and shows their longitudinal dynamics from 2004 to 2019, with manufacturing, finance, education, and public administration as four typical examples (see Figure A5 in Appendix A.2.3). The results show that the manufacturing industry has become more concentrated and that the scaling effect has strengthened; the education and public services industries have become more decentralized, with more equal resource allocation; and the financial industry has maintained a relatively stable relationship. The regression results for 2019, including ${\beta }_i$ and $R^2$, indicate that the scaling relation captures the patterns of most cities.

4.1.2. Distribution of Scale Characteristics in Different Cities

Cities of different sizes have various advantageous industries. On the basis of the average population during 2004–2019 (omitting 2009 because of its instability), 280 cities were divided into three groups: small, medium, and large cities (each comprising 33% of the total). Figure 3 shows the probability distributions of the characteristic industries in the three groups. For all cities, more of the characteristic industries exhibit sublinear scaling with $\beta <1$. For scaling exponent $\beta$, the mean value ($\mu$) of large cities is greater than that of medium cities, and the $\mu$ of medium cities is greater than that of small cities. However, the standard deviation follows the opposite trend.

This analysis confirms that the advantageous industries in large cities are more likely to be knowledge spillover industries, whereas small cities have more significant infrastructure industries.

4.2. Labour Demand of “Knowledge Spillover” Development

4.2.1. Evolution of Knowledge Spillover Industries

The literature indicates that population dependencies may underpin the urban economic structure and its evolution, as small cities heavily rely on infrastructure industries, whereas large cities rely on knowledge spillover industries [4,33,60]. This finding is shown in Section 4.1.2. Furthermore, some scholars have analysed data from the United States and propose that knowledge spillover industries (referred to as cognitive industries) become characteristic only when the urban population reaches a certain scale [7]. Does this rule also apply to other economies? Here, Chinese cities of different sizes are shown to have distinct characteristic industries. Although industrial scaling characteristics vary across countries, do they follow similar universal laws in “knowledge spillover” development? As a populous country with rapid economic development, China’s urban evolution has attracted widespread attention. Chinese cities with characteristic knowledge spillover industries are defined as “knowledge spillover” cities, and the paths of “knowledge spillover” development and labour demand are studied using both empirical analysis and theoretical models.

Population size is not used to define “knowledge spillover” cities here. However, the subsequent analysis shows that the structural advantages of knowledge spillover industries often appear only in cities with sufficiently large populations, with the premises that the urban population of the country follows log-normal distribution characteristics and that the employment structures of infrastructure and knowledge spillover industries exhibit different growth (or scale) characteristics. Especially in China, compared with infrastructure industries, cities with advantageous knowledge spillover industries often require a population size of more than 10 million. This is a universal rule for the emergence of “knowledge spillover” cities in China, as detailed below.

Figure 4 shows the average $RCA$ of 19 industries in cities with different population sizes in 2019. Here, the line colour indicates the industry $\beta$: blue for infrastructure industries, red for knowledge spillover industries, and grey for agriculture and mining industries. To clarify, the average evolutionary trends are highlighted for several typical knowledge spillover and infrastructure industries. On the basis of the previous assumption, only the effective region where the urban population and employment share a logarithmic linear relationship is discussed, i.e., the regions between $N_{min}$ and $N_{max}$.

First, for small- and medium-scale cities in China, infrastructure industries (in blue) are usually more characteristic. With the expansion of the urban scale, the $RCA$ of knowledge spillover industries (in red) increases, whereas the $RCA$ of infrastructure industries gradually decreases. When the population size reaches ${10}^7$, the comparative advantage of cities shifts to knowledge spillover industries, whose $RCA$ values exceed those of infrastructure industries. This result is similar to the urban development pattern in the United States, where the emergence of “knowledge spillover” cities is based on a certain population size. “Knowledge spillover” cities in the United States require less labour than Chinese cities do, with a threshold of approximately $1.2\times {10}^6$ [7].

The results of hypothesis testing provide a more rigorous validation and explanation for 2019 (

Table 2. The hypothesis testing results in 2019.

No.	${\mathit{p}}_1$ Million	${\mathit{p}}_2$ Million	${\mathit{p}}_3$ Million	LLR p-Value	Population $\mathit{p}>\left|\mathit{z}\right|$
1	10	11	∞	0.007 *	0.008 *
2	6	7	10	0.205	0.206
3	5	6	10	0.012	0.012
4	4	5	10	0.022	0.023
5	3	4	10	0.061	0.062
6	2	3	10	0.539	0.539

(*) indicates a significance level of 0.01.

). Here the analysis is confined exclusively to industries with ${\beta }_i>1$. In the initial experiments, $H_0$ is rejected, indicating that for those industries with $\beta >1$, the proportion of cities with $RCA>1$ is higher for cities in $G_2$ ($p_2\le N_c<p_3$) than it is for cities in $G_1$ ($N_c<p_1$). For the other experimental groups, $H_0$ cannot be rejected, implying that the significance of “knowledge spillover” industries does not differ significantly between the two groups.

Overall, cities with a population greater than 10 million show significantly greater significance in “knowledge spillover” industries than do those with a population less than 10 million. In cities with populations less than 10 million, no clear boundary demonstrates a significant difference between the two city groups. Therefore, the significance of 10 million as a critical threshold for the prominence of “knowledge spillover” industries is further clarified. This property occurred from 2004 to 2019 (

Table A3. The results of hypothesis testing in 2004–2020.

Year	${\mathit{p}}_1$ Million	${\mathit{p}}_2$ Million	${\mathit{p}}_3$ Million	LLR p-Value	Population $\mathit{p}>\left|\mathit{z}\right|$
2004	8	9	∞	0.002 *	0.000 *
2005	8	9	∞	0.000 *	0.000 *
2006	8	9	∞	0.000 *	0.000 *
2007	8	9	∞	0.000 *	0.001 *
2008	8	9	∞	0.008 *	0.010 *
2009	8	10	∞	0.001 *	0.003 *
2010	8	10	∞	0.007 *	0.009 *
2011	8	10	∞	0.000 *	0.001 *
2012	7	10	∞	0.005 *	0.008 *
2013	10	11	∞	0.002 *	0.005 *
2014	10	11	∞	0.003 *	0.005 *
2015	10	11	∞	0.001 *	0.002 *
2016	10	11	∞	0.005 *	0.007 *
2017	10	11	∞	0.002 *	0.004 *
2018	10	11	∞	0.002 *	0.003 *
2019	10	11	∞	0.007 *	0.008 *
2020	8	10	∞	0.009 *	0.010 *

(*) indicates a significance level of 0.01.

).

After this phenomenon was observed from the empirical data, it was analysed with a theoretical model. On the basis of the analysis of Equation (3), two critical points were identified, both of which are saddle points. Especially at the critical point where the urban population is approximately $1.07\times {10}^7$, the advantages of knowledge spillover industries become prominent, with $RCA>1$. Meanwhile, the advantages of infrastructure industries disappear, with $RCA<1$. The competitive strengths of these two types of industries reverse at this point.

Here, $RCA$ has a maximum in one dimension and a minimum in the other dimension. The details are provided in the Appendix B.2. According to the theoretical model, around the critical point, the $RCA$ of knowledge spillover industries increases with urban population growth, whereas that of infrastructure industries decreases. Moreover, crossing the critical point indicates that the significance of knowledge spillover industries exceeds that of infrastructure industries. This result also implies that the emergence of “knowledge spillover” cities is based on a certain urban population size, such as ${10}^7$ in China.

Therefore, both the empirical data and the theoretical model identify and verify the critical points, confirming the theoretical hypothesis and deduction process and revealing several statistical rules for a comparative advantage in China’s urban evolution.

4.2.2. Comparison with the Optimal City Size Model

The critical point in China is approximately ${10}^7$, whereas in the United States, it is approximately $1.2\times {10}^6$. As analysed in Section 4.2.3, in addition to the differences in absolute population (i.e., the various $N_{min}$ and $N_{max}$ in different countries), this difference stems from the distribution characteristics of urban size in different countries, as indicated by $\gamma$. This idea is similar to traditional optimal city size theory [61]. For a single city, finding the optimal size is a typical optimization problem that considers economic externalities or agglomeration benefits as well as commuting and rental costs [62,63,64]. The optimal size of multiple cities in an urban system is usually measured by the rank-size rule [17,65,66], which is typically described by the Pareto distribution, Zipf’s law, some improved models [24,25,67], or log-normal distributions [27,28].

Some scholars have calculated the optimal size of a single city in China and the United States. From the perspective of maximizing net income, Wang and Xia noted that the optimal city size in China is approximately ${10}^7$ [68]. Carlino studied the relationship between agglomeration economies and the increasing coefficient of scale returns from the perspective of increasing returns to scale and noted that the optimal city size in the United States is approximately $3.4\times {10}^6$ [69]. Using Carlino’s method as a reference, Jin noted that the optimal city size of Beijing, Shanghai, and Tianjin is approximately ${10}^7$ [70]. Of course, some studies that incorporate environmental pollution and energy efficiency suggest that the optimal city size obtained is significantly smaller than that suggested by previous research and that the optimal urban size in China should not exceed $0.5\times {10}^7$ [71,72]. The literature considers output as a whole, without discussing the dependence and impact of changes in output structure on city size.

Using one typical optimal size model of a single city (as there are many empirical models of the optimal city size, which cannot be tested individually this study takes only a representative model as an example to compare such methods with the empirical results of our study), this study quantifies the optimal city size in China and the United States that maximizes benefits through the analysis of personal income and expenditure [61]. The results show that, on the basis of empirical data from 2019, the optimal city size in the United States is $1.22\times {10}^6$, whereas that in China is $1.13\times {10}^7$. The optimal size model differs from the method used in this study, but both yield similar quantitative results (details in Appendix C.3).

In the optimal size model, $ϵ$ represents the exponential rate of per capita GDP growth with urban population size. Both $\gamma$ and $ϵ$ describe the population-based scale effect, and urban endogenous agglomeration benefits from different perspectives. China has a smaller $\gamma$ and a larger $ϵ$ (see

Table A4. Optimum city size of China and the United States in 2019.

	a	$\mathit{ϵ}$	$\mathit{\rho }$	${\mathit{n}}^{*}$
China	245.471	0.1064	0.3528	1.13 × 107
United States	131.978	0.0994	0.3393	1.22 × 106

in Appendix C.3). A smaller $\gamma$ indicates that the population is more concentrated in a few large cities, whereas a larger $ϵ$ indicates that per capita output or personal income is relatively higher in large-scale cities. These factors make China’s optimal city size much larger than that of the United States. Because the population is highly concentrated in a few large cities, fewer Chinese cities can cross the critical transition point compared to cities in the United States.

The traditional optimal city size model describes the benefits of urban growth through economies of scale and analyses the problems associated with congestion costs. Adding to the discussion on changes in economic structure with urban scale growth would provide a valuable supplement and verification to the theory of optimal city size. The employment structure reflects a city’s production characteristics. The predominance of knowledge spillover industries often means higher per capita output under the same size. Thus, the evolution of the employment structure is related to changes in a city’s optimal scale, as illustrated by the consistency of the results derived from the two models.

4.2.3. Limitations of Urban Innovation in China

For the cities located near the critical point, industries with $\beta >1$ significantly increase, whereas those with $\beta <1$ decrease. Therefore, cities near $N_2^{*}$ are selected to analyse their evolution trends. As shown in Figure 5, some of these cities are on the verge of surpassing $N_2^{*}$ and have the potential to transform into “knowledge spillover” cities; these include Guangzhou, Baoding, Shijiazhuang, Suzhou, Linyi, Shenzhen, Chengdu, and Wuhan. In addition, three cities—Beijing, Shanghai, and Chongqing—have already surpassed the critical point in terms of population size, despite not being located near it. Here, subinnovative cities refer to the emergence stage of the innovation cycle. Compared with subinnovative cities that have leading technologies and highly skilled jobs, cities in the “knowledge spillover” stage have more mature technologies and a greater density of skilled jobs [11]. Moreover, $94.3\%$ of cities in China still need to further improve their technical levels and work proficiency to achieve “knowledge spillover” development.

Figure 6 analyses the geographical distribution of cities near the critical point. Dark red indicates cities that have crossed $N_2^{*}$, whereas light red indicates cities with population gaps of less than 20% from $N_2^{*}$. In terms of spatial distribution, all “knowledge spillover” cities are concentrated east of the Hu Huanyong Line, which indicates regions with relatively high population density in China. Moreover, most of the dark and light red cities are located in China’s major urban agglomerations, including the Central Plains, Jing-Jin-Ji, Shandong Peninsula, Yangtze River Delta, Yu-Rong, Middle Yangtze, and Greater Bay areas (marked here).

This result indicates that the proportion of Chinese cities crossing or near the critical point is relatively low. According to the 2019 statistics from the United States Census Bureau in [45], among the 384 metropolitan areas, 49 have populations exceeding the critical population size of 1.2 million [7], accounting for $12.8\%$. Therefore, China does not have enough cities likely to complete the transformation from subinnovative to “knowledge spillover” cities. Moreover, most of these cities are located near existing “knowledge spillover” cities. When these cities complete the transformation, they can form urban agglomerations of a certain scale, which will facilitate further regional expansion.

China is a populous country. In terms of absolute population size, most Chinese cities have larger populations than their U.S. counterparts do. Even in 2019, 256 cities at the prefecture level and above had populations exceeding the critical point of the United States (i.e., 1.2 million). However, owing to differences in urban population distribution and industrial employment scaling characteristics, the demand for population resources in “knowledge spillover” cities varies significantly between the two countries. This situation is related to factors such as production technology and other economic conditions. Only 16 cities in China meet the population demand for “knowledge spillover” development, and the innovation rate of population demand is far lower than that of the United States.

4.2.4. Influence of Population Distribution Characteristics

In addition, to compare economies of different population sizes, this study theoretically analyses the changes in $log(N^{*}/N_{max})$ according to different values of $\gamma$. $\gamma$ represents the distribution characteristic of the urban population in a country and has a significant effect on the proportion of “knowledge spillover” cities. The $\gamma$ of the United States is less than 2 [7], whereas the $\gamma$ of China is located in the range $[1.10,1.35]$. Consequently, $log(N^{*}/N_{max})$ is closer to 0 in China than it is in the United States. Therefore, the population demand of China’s “knowledge spillover” cities is closer to that of the largest cities, indicating a limited number of such cities in China (Figure 7b).

In addition, the trend of urban population growth in China is not encouraging [73]. China’s population has already experienced three consecutive years of negative growth [74]. According to the latest data, the total population peaked in 2022 and has since decreased. In 2024, the total population decreased by 139 million compared with that in the previous year, with a natural growth rate of −0.99%.

Furthermore, according to the latest projections, China’s working-age population is expected to continue to decrease at an accelerated pace, with a projected decrease of 200 million people by 2050 [75]. The slow or even negative growth of China’s population will lead to significant changes in population structure, which will greatly impact urban innovation capabilities [76]. Moreover, China’s large cities face challenges related to industrial agglomeration and innovation agglomeration [77].

5. Conclusions and Suggestions

Exploring the conditions for the emergence of cities dominated by “knowledge spillover” industries is of great significance. These cities leverage superlinear growth factors to achieve advanced development and utilize resources more efficiently. Focusing on China, this study identifies a development path in urban evolution and the labour demand characteristics of “knowledge spillover” cities through the analysis of industrial employment and comparative advantage. It uncovers a critical population size.

5.1. The Comparative Advantage of “Knowledge Spillover” Industries Requires a Critical Urban Population Size

The relationship between industry employment and the urban population reveals distinct growth patterns for different industries. Superlinear growth industries, such as “knowledge spillover” industries, accelerate their growth in larger cities, which can be interpreted as a more efficient aggregation of resources. This phenomenon is reflected in the statistical patterns of the urban population and number of employees in prefecture-level cities in China. The analysis from a modelling perspective further elucidates the underlying mechanisms involved.

The log-normal distribution of the urban population indicates that only a small number of large-scale cities exist. Industries have different scaling effects: sublinear growth industries typically dominate in smaller cities, whereas superlinear growth industries thrive in larger cities. The comparative advantage of superlinear over sublinear growth industries emerges when the urban population reaches a certain scale. This critical population size varies across economies, depending on urban population distribution characteristics and the scaling properties of different industries.

5.2. The Critical Population Size of 10 Million for China

The specific superlinear growth industries vary across countries due to differences in economic endowments, production technologies, and other factors. For example, in the United States, administrative and financial services exhibit superlinear growth characteristics, whereas in China, manufacturing and retail trade are more prominent. The underlying principle is the same: each country has industries that can grow at an accelerated rate, aggregating resources more efficiently and driving economic development more effectively. These industries can thrive as “knowledge spillover” and dominant sectors only in cities that reach a certain population size.

The labour demand for “knowledge spillover” cities varies across economies, and in China, it is $1.0\times {10}^7$. It is influenced by the overall population size and the characteristics of the urban population distribution. China’s urban population distribution has a large negative power index, indicating a relative insufficiency in the number of large cities. Although China is a populous country, only 5.7% of its cities have become “knowledge spillover” cities.

5.3. Future Prospects for China

The critical population size of 10 million in China represents a significant threshold. However, this threshold is particularly high given the current trends in China’s demographic and urban development. China’s population growth has been slowing, and the further expansion of megacities could lead to several challenges. The expansion of large cities may result in urban problems such as traffic congestion, housing shortages, and environmental pressures, commonly referred to as “metropolitan malaise”. The population concentration in a few megacities could exacerbate the imbalance in the urban population distribution, potentially increasing the threshold.

To address these challenges and leverage the advantages of superlinear growth industries, China needs to adopt a balanced urban development strategy. This strategy should focus on promoting the growth of medium-sized cities and improving the connectivity and integration of urban agglomerations. By doing so, China can create a more balanced urban population distribution, reduce the pressure on megacities, and provide more opportunities for the emergence of knowledge spillover cities. Additionally, policies should be designed to encourage the development of superlinear growth industries in a wider range of cities, ensuring that the benefits of these industries are more evenly distributed across the country.