Externalities of Urban Agglomerations: An Empirical Study of the Chinese Case

Abstract

Urban agglomerations are playing an increasingly important role in regional economic development, and economic externalities are the key factors in the formation and development of urban agglomerations. According to different mechanisms, agglomeration externalities can be divided into pecuniary externality and technological externality, but the literature has not paid enough attention to the differences between them. Based on the case of China’s five representative urban agglomerations, this paper analyzes and compares the origins, mechanisms, and factors of the two types of agglomeration externality. The results indicated that the pecuniary externality of urban agglomerations originates from the intercity flow and allocation of production factors, and its mechanisms include the specialized production brought by industrial division and the cost reduction caused by scale economy. While the technological externality originates from technological spillovers between cities, its mechanisms include knowledge sharing and technology cooperation. Among China’s five representative urban agglomerations, the key factor affecting their pecuniary externality is market size, and the key factor affecting their technological externality is economic density. In other words, the pursuit of a larger market and higher economic density are the two main driving forces for the formation of urban agglomerations in China. By distinguishing core cities from peripheral cities in China’s five representative urban agglomerations, we also find that there is no significant difference in their pecuniary externality. However, their technological externality presents complex differences. There is still much room to improve the externalities of agglomeration in China’s urban agglomerations. For example, the flow of capital does not show a shift to more productive cities. R&D activities are still mainly concentrated within a city, not intercity, in urban agglomerations.

1. Introduction

According to economic theory and practice, urban agglomerations will gradually become the focus and main mode of urbanization. Urban agglomerations can not only coordinate development of small towns and big cities but also strike a balance between efficiency and equity. Whether as a result of liberal economic development or governmental economic policies, urban agglomerations have played an increasingly important role in regional economic development. Development is neither smooth nor linear on a geographic scale. The report Reshaping Economic Geography, published by the World Bank in 2009, noted that the New York metropolitan area, which consists of 13 cities and 143 towns, was home to more than 18.7 million people with a GDP of $1133 billion. Just the 10 largest metropolitan areas in Mexico, which accounted for a third of the country’s population, generate 62 percent of its national value added. One of China’s most advanced urban agglomerations, the Pearl River Delta, consisting of nine cities, has a population comparable to that of Spain.

Urban agglomerations are structured economic entities characterized by industrial division and cooperation, infrastructure construction, and transportation, as well as employment and urban life. The externalities generated by the agglomeration economy are a major advantage of developing urban agglomerations compared to independent cities. It is worth noting that these externalities can be subdivided into two types based on their disparate mechanisms of function: pecuniary externality, which emphasizes interurban labor or capital allocation [1,2,3,4], and technological externality, which emphasizes interurban technology diffusion [5,6,7]. These two types of externalities are characterized by different manifestations, different mechanisms, and different factors, but the literature has not paid enough attention to their variants. Our literature review in Section 2 illustrates several points. First, many recent studies have consistently treated pecuniary externality and technological externality as a unified whole and have undertaken empirical analyses of their significance, but failed to disentangle their respective characteristics. Second, many other studies have placed great emphasis on pecuniary externality, regarding technological externality as something of a “black box” in the absence of in-depth study. With the development of communications technology, transportation networks, and high-tech industries, we believe that ignoring technological externality is a serious drawback. Third, different urban agglomerations may have different economic levels, geographical locations, and policy backgrounds. It is hardly a rigorous and objective method that studies only one case and applies the resulting conclusions to others.

Motivated by the shortcomings of the studies delineated above, we first present in this paper a theoretical analysis with a comprehensive perspective that accounts for pecuniary externality and technological externality of urban agglomerations. We then carry out an empirical study of the Chinese case by selecting five representative urban agglomerations.

Our study focuses on China for the following reasons. First, as of June 2021, China has more than 293 prefecture-level cities (located in 31 provinces). Its vast territory means that the agglomeration economy has a very important development significance in the economic development of China. China has formed numerous urban agglomerations, including five representative urban agglomerations and many potential small and medium-sized urban agglomerations. Second, the development of urban agglomerations has become the main mode of China’s new round of urbanization. Since the reform and opening up, China’s urbanization model has changed three times. The first model featured the development of small towns for their low construction costs. With an increasing focus on the advantages of scale, the second model was characterized by the development of large cities. However, both types of urbanization models have been stifled due to space constraints in small towns and resource shortages in large cities. Therefore, the Chinese government officially issued the National Plan on New-Type Urbanization (2014–2020), highlighting urban agglomerations’ function as new geographical units. However, urban agglomerations remain a weak link in academia and are in dire need of study.

The rest of our paper is organized as follows. In Section 2, we give a comprehensive review of the literature, noting its contributions and shortcomings. In Section 3, we use a theoretical model to identify pecuniary externality and technological externality, and then we propose two hypotheses for each type of externality. In Section 4, we give a brief introduction to China’s five representative urban agglomerations and then test their externalities by calculating Moran’s index. In Section 5, we empirically study pecuniary and technological externalities of China’s five representative urban agglomerations to identify their key factors and validate our hypotheses. Finally, in Section 6, we draw our conclusions and offer some discussion on accelerating the development of urban agglomerations in China.

2. Literature Review

According to the World Bank’s World Development Report in 2009, agglomeration economies are present in all large economic systems. A fundamental question in this area is why economic activities tend to cluster. This is an interesting topic that has attracted long-term attention and research. By measuring the prevalence of Silicon Valley-style clustering of individual manufacturing industries in the United States, Ellison and Glaeser [8] found that almost all manufacturing industries had different degrees of geographic agglomeration and identified that spatial spillovers and natural advantages are two important forces driving agglomeration. The diversity of natural endowments across regions was once thought to be a key factor driving this, but subsequent economic theories and practices had denied it a decisive role. As Fujita and Thisse [9] had remarked, agglomeration economies would be inevitably generated according to economic principles, social principles, and political principles even if the original states of regional natural endowments were comparable. Fujita and Mori [5] also pointed out that the effect of differentiation in interregional natural endowments could be explained only by traditional economic theories under the condition of perfect competition. Following the new economic geography’s discussion of externalities, Davis and Henderson [10] studied the determinants of headquarters agglomeration and the underlying economic basis of many larger metropolitan areas, concluding that the advantage of locating headquarters in metropolitan areas far from production facilities stemmed from the diversification of local services and the proximity to other headquarters. Headquarters of large firms are crucial to the economy of cities where they are located. They can obtain agglomeration economies not only by sharing common inputs and the same labor market but also by enjoying information spillover [11,12,13].

Under the condition of imperfect competition, new economic geography theories explain the evolutionary process of agglomeration economies based on Marshall’s externalities theory [14,15,16]—externalities that permit a firm to obtain an extra benefit from other firms without paying for it were the main motivation in forming agglomeration economies. Externalities can be subdivided in many ways. By their disparate mechanisms, they can be subdivided into two types: pecuniary, which refers to the effect of one firm on others through interurban labor or capital allocation, and technological, which refers to the effect of one firm on another through interurban technology diffusion. In fact, the division of externalities was first performed by Tibor Scitovsky in 1954. In his paper “Two concepts of external economies,” he noted that the first concept of external economies (referred to as pecuniary externality today) is that every economic influence from one economic participant’s behavior on another’s well-being is transmitted through its impact on market price. The second concept of external economies (which is distinct from modern technological externality) was much broader: that the profits of one economic participant are affected by the actions of others. Thus, under Tibor Scitovsky’s analytical framework, the first concept of external economies is included within the second concept of external economies. Today’s concept of pecuniary externality and technological externality were developed from new economic geography theory.

Since the explicit origins of pecuniary externality and clear welfare and facile modeling associated with it, more recent literature has placed greater emphasis on it. In general, studies on pecuniary externality have been carried out in two directions. One is the D-S analytical framework, which was proposed and developed by Dixit and Stiglitz [17] and based on the iceberg transport cost hypothesis and the general equilibrium of monopolistic competition. The other is the OTT analytical framework, which was proposed and developed by Ottaviano et al. [18,19,20,21,22] and based on quasilinear utility and linear transport costs. Subsequent scholars built diverse models according to these two frameworks, such as the core–periphery model and vertical linkage model, which analyze the effect of labor allocation [15,23,24,25], capital allocation [25,26], and industrial vertical linkage [23,27,28]. Both spatial skewness and agglomeration economies are important features in many countries. Wang [29] constructed a solvable core–periphery model to capture the two characteristics and explained why strong housing booms occurred only in large cities or metropolitan areas from an agglomeration externality perspective. Agglomeration and dispersion are not invariant, but in dynamic adjustment. Agglomeration is beneficial for reducing transportation cost, while dispersion is beneficial for reducing the burden of crowding cost. Zhou [30] paid special attention to wages and spotlighted how the urban wage inequality was determined by the interplay between urban costs and transport costs. The results implied that what mattered was neither agglomeration effect nor commuting costs, but the interaction between them.

In contrast, although empirical studies on the technological externality of urban agglomerations are abundant, their theoretical analysis has been stifled for a long time, especially the elaboration of their mechanisms. Due to the lack of microfoundations and the associated modeling difficulties, most scholars treat technological externality as a black box. Keller [31] and Koo [32] noted that studies of the agglomeration economy and studies of the technology spillover were distinct, and the endogenous mechanism analysis between them was lacking or ambiguous. Nevertheless, technological externality is attracting more attention as communications technology, transportation networks, and high-tech industries develop. Boix and Trullen [33] made an empirical study about the crucial effect of knowledge spillover in promoting regional economic growth, and the results also pointed out that knowledge accumulation was not only related to local factors but also to spatial factors, such as agglomeration and network externalities.

The existing research usually divides technological externality into the technology spillover within a department and the technology spillover across different departments, which correspond to specialization and diversification, respectively, in economic practice [34,35,36,37]. Ó Huallacháin and Lee [38] assessed technological specialization and diversity in urban inventions in the United States, and Wang et al. [39] measured regional industrial specialization and diversity in China. They both discussed the difference between Marshall technological externalities (which emphasize specialization) and Jacobs technological externalities (which emphasize diversification), and pointed out that specialization and diversity were not either/or competitive characteristics and that cities could have both. Kekezi et al. [40] examined the role of interregional and intersectoral knowledge spillovers on regional knowledge creation across US metropolitan counties, and the results indicated that although both within-sector (MAR) and between-sector (Jacobian) spillovers were important determinants of knowledge production, within-region MAR spillovers showed greater returns than the corresponding Jacobian spillovers. By separating the agglomeration effects and the spillover effects, Sun and Liu [41] investigated agglomeration externalities in China’s hi-tech industries and found that most hi-tech industries tended to be concentrated in the eastern coastal regions of China, while there were significant spillover effects from the eastern coastal regions to the central regions. However, Tran and La [42] argued that technology transfers were not an agglomerative force, based on an empirical study of the informal sector in Vietnam. Although the specialization effect and diversification effect both promote skill upgrading, Li and Zhu [43]’s empirical study based on China found that the effects of regional agglomeration externalities vary significantly among different regions, and the positive effects brought by specialization externalities usually dominate in less developed cities, inland cities or small cities, contrasting the diversification effect in developed cities or coastal cities. Traditional economic theories emphasize the role of agglomeration economies in promoting regional growth. However, urban networks have gradually become the dominant form of regional economic systems. Huang et al. [44] and Johansson and Quigley [45] analyzed the effect of urban network externalities on urban growth and compared it with that of agglomeration economies from the perspective of the externality theory, and found that cities with higher in-closeness centrality tended to enjoy higher economic growth due to their central position in the network, while urban network externalities did not depend on the geographical proximity of cities, but on the connections in the network.

Urban agglomerations rally loose urban centers as structured economic entities, and they are fast becoming platforms for promoting economic growth, international cooperation, and global competition [46,47,48]. Regarding the study of urban agglomerations’ externalities, Garcia-Lopez and Muniz [49] took an intrametropolitan approach to analyze the impact of urban spatial structure on local economic growth by estimating a municipal employment growth model in which the relationship between dynamic agglomeration economies and urban spatial structure was assessed. Their main conclusion was that urban spatial structure was important for economic growth in an intrametropolitan context. Kanemoto [50] examined the agglomeration benefits of improvement in transportation by modeling the microstructure of urban agglomeration based on monopolistic competition in differentiated intermediate products. The results indicated that the agglomeration benefits were positive if the increase in variety was procompetitive, but the net agglomeration benefits could be negative when other cities experiencing population reduction had larger agglomeration economies in multiple cities. Azari [51] used employment as a proxy for the agglomeration effect, and pointed out that agglomeration was an important type of externality mechanism in determining urban economic performance. Van Oort et al. [52] used a cross-sectional data set of 205 European regions during the 2000–2010 period to conduct an empirical study, and they found that variety was significantly related to employment growth and specialization significantly related to productivity growth.

In terms of studies of Chinese urban agglomerations, Li et al. [53] measured different tourism efficiencies and identified spatial characteristics of 61 cities in six coastal urban agglomerations in eastern China by employing DEA, bootstrap DEA, and Malmquist models. They concluded that there were significant differences in the efficiency of different urban agglomerations in China, but also showed a trend of convergence. By using an appropriate threshold of the digital number (DN) of nighttime light, Peng et al. [54] identified the boundary of urban agglomerations in China from 2000 to 2012, and explored the temporal evolution and spatial difference of urban agglomerations. However, their findings indicated that regional differences in urban agglomerations between southern and northern China, or between coastal and inland China, remained stable over the study period of 2000–2012. Tan [55] analyzed the features and spatial determinants of urban growth in the Wuhan urban agglomeration from 1988 to 2011 and indicated that spatial autocorrelations were common in the urban growth changes. Dong et al. [56] evaluated whether the economy of county units in the Changsha–Zhuzhou–Xiangtan urban agglomeration was growing as expected and analyzed the spatial economy pattern at the county level by using the exploratory spatial data analysis method. Their results showed that since 2008, the county-level economy of the Chang–Zhuzhou–Xiangtan urban agglomeration had exhibited a strong spatial autocorrelation and an accelerated integration trend. Jun et al. [57] analyzed the intensity of economic ties and structures based on an analytical approach to the intensity of central functioning and urban mobility. They concluded that a “multicenter” spatial framework was beginning to take shape in the urban agglomeration of the central delta with Wuhan, Changsha, and Nanchang.

The work of these scholars highlighted the role of urban agglomerations in China’s economic development, noting that externalities were the main advantage of developing urban agglomerations. However, they failed to conduct further comparative and comprehensive studies on the pecuniary externality and technological externality of Chinese urban agglomerations. As summarized by Fang [58], China was taking urban agglomeration as the main mode to promote its “new-type urbanization” (a concept proposed by the Chinese government in its urbanization plan, titled the National New-Type Urbanization Plan (2014–2020)). Fang (2017) did not define the concept of the new-type urbanization in detail, but he pointed out that it paid more attention to the match between rapid population urbanization and urban industrial structure adjustment, and urban agglomeration remained a weak link in academia and was in urgent need of study. Xu et al. [59] quantitatively evaluated the sustainability level of 20 urban agglomerations in the process of new urbanization in China by using a three-level index system based on six basic elements of cities and a comprehensive evaluation method based on a full array of polygons. According to their assessment, the urbanization of the 20 urban agglomerations had their own development patterns, and different urban agglomerations showed a polarization phenomenon in terms of sustainability. Liu et al. [60] selected China’s 19 urban agglomerations and portrayed comparatively their spatial differences in factors aggregating ability. They pointed out that the rank-size structure of factors aggregating capacity distribution in these 19 urban agglomerations was in line with Zipf’s law for urban systems. Urban agglomeration is an advanced spatial organization of cities that is still poorly understood, especially for the quantitative identification of the spatiotemporal evolution of urban agglomerations. Urban agglomerations are fundamental regional units of development and attract a large migrant population. Given that previous studies had only focused on migrant population distribution among cities, Zhou et al. [61] analyzed the spatiotemporal characteristics of migrant population distribution in China during 2000–2010 from the perspective of urban agglomerations. They found that large numbers of people had migrated into 19 urban agglomerations, which broadened regional differences in the distribution of the migrant population. Behind the population flow were the driving forces of the agglomeration economy and government planning, but the economic forces were more significant.

In summary, the current literature on agglomeration externalities and urban agglomerations is rich and has laid a solid foundation for our study. In this paper, we perform the following tasks to enhance academic research in these areas. First, we divide the externalities of urban agglomerations into pecuniary externality and technological externalities. Second, we conduct comparative theoretical studies of the two types of externalities. Third, we take five representative urban agglomerations in China as a sample to gain insight into the externalities and their effects.

3. Theoretical Analysis and Research Assumptions

3.1. Identification of Pecuniary Externality and Technological Externality

The same assumptions are made in both the D-S and the OTT analytical frameworks, which include two regions (north and south), two sectors (fully competitive agriculture and partially competitive manufacturing) and two factors of production (labor and capital). Their common conclusion is that one region will have a siphoning effect on the other and that industries and factors will then be concentrated in that region.

A typical urban agglomeration is a structured economic entity linked by industrial division and cooperation, infrastructure development and transportation, and employment and urban life. To simplify our analysis, we assume that each city in an urban agglomeration has the same production function and constraints. In this paper, the production function is described in Cobb–Douglas form, with constraint conditions including diminishing marginal yields of capital and positive returns on the scale, as shown in Equation (1):

$$\begin{array}{l}labp=f(k,A)=k^{\alpha }{A}^{\beta }\\ s.t.\alpha +\beta >1,\frac{\partial labp}{\partial k}>0,\frac{{\partial }^{2}labp}{\partial k^2}<0,\frac{\partial labp}{\partial A}>0\end{array}$$

(1)

where $labp$ denotes labor productivity and $k$ denotes capital stock per labor, with positive first-order partial derivative and negative second-order partial derivative. $A$ denotes technological level, and $\alpha +\beta >1$ denotes the positive return to scale.

Recent literature on pecuniary externality has focused on the input–output relationship between cities and analyzed the effects of labor migration, capital flows, and vertical links between industries. Meanwhile, recent literature on technological externality has focused on interurban technological relationships and analyzed the effects of technology spillover.

Alongside Equation (1), we define pecuniary externality and technological externality in this paper from an urban agglomeration perspective and note that urban agglomerations’ pecuniary externality manifests as interurban capital allocation and that their technological externality manifests as interurban technology spillover. Based on this, we further analyze how the pecuniary and technological externality of urban agglomerations are generated and function.

First, in terms of the pecuniary externalities of urban agglomeration, drawing on the assumptions of Desmet and Rossi-Hansberg [62] and Diamond [63], capital is free to move across locations without friction (In Desmet and Rossi-Hansberg’s work, they assumed that capital was freely allocated across cities at a nationally uniform interest rate $r_t$. Diamond also noted that a frictionless capital market supplied capital perfectly elastically at price ${\kappa }_t$, which was constant across all cities), but its utility is exclusive, meaning that if capital is used in one city, it cannot be used in others. Intercity capital allocation always chooses to transfer capital to cities with higher labor productivity, but its mobility must satisfy the constraint condition that the marginal cost of capital is lower than its marginal output. As in previous studies, we also take industrial structure into account to gain insight into the impact of diversification or specialization. Thus, interurban capital allocation can be described as follows:

$$\begin{array}{l}k=f(\underset{pecuniaryexternality}{\underbrace{\widehat{labp},MC,st}}),\\ s.t.\frac{\partial labp}{\partial k}\ge MC=f(c_0,ac,{\displaystyle \sum \raisebox{1ex}{$mk$}\!\left/ \!\raisebox{-1ex}{$d$}\right.})\end{array}$$

(2)

where $\widehat{labp}$ denotes the relative position of cities’ labor productivity and $MC$ denotes cities’ marginal cost, which is decided by factor cost $c_0$, congestion cost $ac$, and market size ${\displaystyle \sum \raisebox{1ex}{$mk$}\!\left/ \!\raisebox{-1ex}{$d$}\right.}$. Based on the theories of Adam Smith’s labor division, Alfred Marshal’s scale economy [64], and Allyn Abbott Young’s roundabout production [65], an increase in market size can reduce the average cost. In addition, the market size shows a negative relationship with geographical distance $d$.

According to Equation (2), the mechanism of urban agglomerations’ pecuniary externality can be described as follows. Urban agglomeration drives intercity capital allocation in the quest for higher productivity. An increase in market size will further optimize the intercity distribution of capital. These factors together promote the improvement of labor productivity in urban agglomerations.

Second, in terms of the technological externality, we assume that the intercity technology spillover has no cost and its utility is nonexclusivity, but the technology spillover is limited by the geographical accessibility. To simplify the analysis, the technical depreciation caused by technological upgrades is not considered in this paper.

We also take economic density into account, as in previous studies, to gain insight into the impact of economic clustering on the level of technology. Thus, the spillover of technology can be described as follows:

$$A=f(A_{t-1},rd,\underset{techno\log yexternality}{\underbrace{ds,{\displaystyle \sum \raisebox{1ex}{$rd$}\!\left/ \!\raisebox{-1ex}{$d$}\right.},st}})$$

(3)

where $A_{t-1}$ denotes the first-lagged technological level, $ds$ denotes cities’ economic density, $rd$ denotes cities’ R&D activities, and ${\displaystyle \sum \raisebox{1ex}{$rd$}\!\left/ \!\raisebox{-1ex}{$d$}\right.}$ denotes the spillover from other cities’ R&D activities, which is negatively related to geographical distance $d$.

According to Equation (3), the mechanism of urban agglomerations’ technological externality can be described as follows. Urban agglomerations create an environment for technological innovation by increasing economic density and pooling R&D resources. In addition, one city’s R&D activities will spread to other cities. Together, these factors contribute to the improvement of labor productivity in urban agglomerations.

Based on the above theoretical analysis, we argue that the pecuniary externality and technological externality of urban agglomerations have different function mechanisms and key factors. It is necessary to distinguish between them when studying the externalities of urban agglomeration.

3.2. Hypotheses

The above theoretical analysis gives insight into how pecuniary externality and technological externality arise and function in urban agglomerations. We now propose the following hypotheses and validate their validity through empirical analysis of China’s five representative urban agglomerations.

Hypothesis 1.

In urban agglomerations, capital tends to shift to cities with higher labor productivity.

Hypothesis 2.

In urban agglomerations, scale expansion and labor division will reduce the average cost and further optimize intercity capital allocation.

Hypothesis 3.

In urban agglomerations, rising economic density induces an aggregation of R&D resources that enhances technological innovation.

Hypothesis 4.

In urban agglomerations, R&D activities in one city can be more easily spread to other cities, thereby promoting technological innovation in the latter.

4. Urban Agglomerations and Spatial Correlation Test

4.1. Selection of Urban Agglomerations

China is immersed in rapid urbanization. The urban population has grown significantly from 170 million in 1978 to 914 million in 2021. During this period, the urbanization rate increased from 17.9% to 64.7%, representing an average annual growth rate of 1.09%, and the number of cities increased from 193 in 1978 to 661 in 2021 (including four municipalities directly under the central government, 283 prefectural cities, 374 county-level cities, and two special administrative regions (Hong Kong and Macao)).

With the rapid development of urbanization, Chinese urban agglomerations have also experienced vigorous development, forming a “5 + N” urban agglomeration distribution pattern, including five representative urban agglomerations and numerous potential small or medium-sized urban agglomerations. The National New Urbanization Plan (2014–2020) issued in 2014 clearly states that urban agglomerations are becoming the main form of China’s next stage of urbanization. As shown in Figure 1, China’s five representative urban agglomerations are the Beijing–Tianjin–Hebei urban agglomeration, the Yangtze River Delta urban agglomeration, the Pearl River Delta urban agglomeration, the Middle Reaches of Yangtze River urban agglomeration, and the Chengdu–Chongqing urban agglomeration.

Table 1. Typical characteristics of China’s five representative urban agglomerations.

Urban Agglomerations	Land Area (km2)	Population (Million)	Locations	GDP in 2014 (Billions of US Dollars)	Percentages in National GDP (%)
Beijing–Tianjin–Hebei	217,176.45	110.40	eastern	1254.40	8.54
Yangtze River Delta	259,509.02	196.54	eastern	3311.81	22.54
Pearl River Delta	54,977.65	78.23	eastern	1297.91	8.83
Middle Reaches of Yangtze River	418,404.37	155.15	central	1684.87	11.47
Chengdu–Chongqing Urban Agglomeration	186,243.38	89.34	western	877.32	5.97

Note: The statistics are from the National Bureau of Statistics of China.

reports the typical characteristics of these five representative urban agglomerations. The five representative urban agglomerations are located in eastern, central, and western regions, covering a total land area of 1,136,310.87 square kilometers. As the most active economic unit in China, they accounted for 44.59% of the country’s population and contributed 57.35% of the country’s GDP in 2020. Therefore, we believe that the five urban agglomerations are sufficiently representative of the overall development status of urban agglomerations in China. By studying the externalities of these five urban agglomerations, we can objectively obtain a wealth of information about how pecuniary externality and technological externality arise and function.

4.2. Spatial Correlation Test of Labor Productivity

Both pecuniary externality and technological externality can be expressed as the spatial correlations of labor productivity. In recent studies, Moran’s index ($Moran’sI$) is a common index for testing a variable’s spatial correlation. Here, we apply $Moran’sI$ to analyze the spatial correlation of labor productivity (in this paper, urban agglomerations’ labor productivity is measured by gross regional domestic product per labor unit) in China’s five representative urban agglomerations and then draw conclusions about their externalities. $Moran’sI$ can be calculated as follows:

$$\begin{array}{l}Moran’sI=\frac{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{w}_{ij}(lab{p}_i-\stackrel{-}{labp})(lab{p}_j-\stackrel{-}{labp})}}}{S^2{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{w}_{ij}}}}\\ Z(Moran’sI)=\frac{Moran’sI-E(Moran’sI)}{\sqrt{VAR(Moran’sI)}}\end{array}$$

(4)

where $n$ denotes the number of cities in an urban agglomeration and $i,j$ denote different cities. $\stackrel{-}{labp}$ denotes the average labor productivity and $w_{ij}$ denotes the spatial weight matrix, which is measured by geographical distances between cities. $Z(Moran’sI)$ is the Z statistic of $Moran’sI$, and $S^2=\frac{1}{n}{\displaystyle \sum _{i=1}^n(lab{p}_i-\stackrel{-}{labp})}$, $E(Moran’sI)=-\frac{1}{n-1}$.

Table 2. $Z(Moran’sI)$ labor productivity in China’s five representative urban agglomerations between 2010 and 2019.

Year	Beijing–Tianjin–Hebei Urban Agglomeration	Yangtze River Delta Urban Agglomeration	Pearl River Delta Urban Agglomeration	Middle Reaches of Yangtze River Urban Agglomeration	Chengdu–Chongqing Urban Agglomeration
2010	0.251 *** (3.702)	0.259 *** (5.880)	0.264 *** (4.397)	0.340 *** (7.332)	0.227 *** (3.741)
2011	0.112 *** (2.571)	0.194 *** (4.506)	0.208 *** (3.764)	0.339 *** (7.062)	0.224 *** (3.575)
2012	0.134 *** (6.781)	0.299 *** (6.794)	0.179 *** (3.073)	0.204 *** (4.676)	0.126 ** (2.517)
2013	0.219 *** (3.235)	0.385 *** (8.111)	0.179 *** (3.001)	0.241 *** (6.033)	0.149 *** (3.299)
2014	0.178 *** (2.889)	0.282 *** (6.349)	0.258 *** (5.131)	0.222 *** (4.906)	0.232 *** (3.690)
2015	0.137 *** (2.578)	0.248 *** (5.661)	0.182 *** (3.135)	0.193 *** (4.468)	0.215 *** (4.017)
2016	0.237 *** (3.463)	0.347 *** (7.354)	0.177 *** (3.159)	0.179 *** 4.096	0.220 *** (3.558)
2017	0.177 *** (2.804)	0.232 *** (5.283)	0.275 *** (4.444)	0.144 *** (3.572)	0.247 *** (3.948)
2018	0.295 *** (4.235)	0.242 *** (5.473)	0.234 *** (3.821)	0.101 *** (4.735)	0.114 *** (5.749)
2019	0.224 *** (4.418)	0.127 *** (4.017)	0.195 *** (3.406)	0.144 *** (3.944)	0.176 *** (3.274)

Note: The figures in parentheses are Z statistics; *** and ** denote the level of significance at 1% and 5% respectively.

reports $Moran’sI$ and $Z(Moran’sI)$ of labor productivity in China’s five representative urban agglomerations between 2010 and 2019. The value of $Moran’sI$ of each urban agglomeration in each year is significantly positive. That means that within each urban agglomeration, there is a spatial correlation of labor productivity between the cities.

In

Table 3. $Z(Moran’sI)$ of labor productivity at different geographical distances in 2010 and 2019.

Urban Agglomeration	Year	0–50 km	0–100 km	0–150 km	0–200 km	0–300 km	0–400 km	0–500 km	0–600 km
Beijing–Tianjin–Hebei	2010	0.876 ** (2.376)	0.805 *** (2.877)	0.416 *** (2.615)	0.247 ** (2.431)	0.083 ** (2.445)	−0.022 * (1.656)	-	-
	2019	1.198 *** (4.071)	0.328 * (1.739)	0.258 ** (2.319)	0.166 ** (2.377)	0.041 ** (2.336)	−0.043 (1.339)	-	-
Yangtze River Delta	2010	0.946 *** (4.431)	0.375 *** (2.801)	0.259 *** (3.061)	0.088 * (1.792)	0.054 ** (2.370)	−0.065 *** (4.357)	0.012 *** (3.600)	0.008 *** (11.029)
	2019	0.998 *** (5.810)	0.182 * (1.845)	0.037 (0.927)	−0.006 (0.520)	−0.031 (0.115)	0.015 *** (2.639)	0.002 *** (3.418)	0.000 *** (9.992)
Pearl River Delta	2010	0.557 ** (2.072)	0.180 *** (2.973)	-	-	-	-	-	-
	2019	0.871 *** (2.835)	−0.029 (−0.879)	-	-	-	-	-	-
Middle Reaches of Yangtze River	2010	0.946 *** (4.661)	0.551 *** (4.142)	0.433 *** (4.707)	0.342 *** (5.115)	0.181 *** (4.570)	0.014 (1.433)	−0.025 (0.124)	−0.037 (−0.808)
	2019	0.426 ** (2.494)	0.259 *** (2.362)	0.272 *** (3.521)	0.201 *** (3.648)	0.061 ** (2.227)	−0.001 (1.058)	−0.007 (1.207)	−0.006 (2.052)
Chengdu–Chongqing	2010	1.058 *** (2.809)	0.345 * (1.875)	0.279 ** (2.912)	0.006 (1.317)	-	-	-	-
	2019	0.694 ** (1.994)	0.243 (1.493)	0.140 * (1.891)	0.009 (1.405)	-	-	-	-

Note: The figures in parentheses are Z statistics; ***, ** and * denote the level of significance at 1%, 5% and 10% respectively.

, we further calculate $Moran’sI$ and $Z(Moran’sI)$ of labor productivity at different geographical distances in 2010 and 2019 by adjusting the upper bounds from 0 to 600 km. $Moran’sI$ in each urban agglomeration tends to decrease as the distance threshold increases. Some urban agglomerations’ $Moran’sI$ are not significant or become negative when the distance exceeds a certain threshold.

5. The Pecuniary Externality versus the Technological Externality

5.1. Modeling and Parameters

Based on the theoretical analysis in Section 3.1, the key factors for urban agglomerations’ pecuniary externality include the relative position of labor productivity $\widehat{labp}$, congestion cost $ac$, market size ${\displaystyle \sum \raisebox{1ex}{$mk$}\!\left/ \!\raisebox{-1ex}{$d$}\right.}$, and differentiation of intercity industrial structure $st$. The key factors for urban agglomerations’ technological externality include economic density $ds$, technology spillover from other cities’ R&D activities ${\displaystyle \sum \raisebox{1ex}{$rd$}\!\left/ \!\raisebox{-1ex}{$d$}\right.}$, and differentiation of intercity industrial structure $st$. We construct the empirical model as follows:

$$\begin{array}{l}\ln lab{p}_{it}=c+\alpha \ln k_{it}+\beta \ln A_{it}+{\epsilon }_{it}\\ \ln k_{it}=\underset{pecuniaryexternality}{\underbrace{{\gamma }_1\ln \widehat{lab{p}_{it}}+{\gamma }_2\ln a{c}_{it}+{\gamma }_3\ln {\displaystyle \sum _{j\ne i,j=1}^n\raisebox{1ex}{$m{k}_{jt}$}\!\left/ \!\raisebox{-1ex}{$d_{ji}$}\right.}+{\gamma }_4\ln s{t}_{it}}}+c+{\nu }_{it}\\ \ln A_{it}=\underset{techno\log yexternality}{\underbrace{{\eta }_1\ln d{s}_{it}+{\eta }_2\ln {\displaystyle \sum _{j\ne i,i=1}^n\raisebox{1ex}{$r{d}_{jt}$}\!\left/ \!\raisebox{-1ex}{$d_{ji}$}\right.}+{\eta }_3\ln s{t}_{it}}}+{\eta }_1\ln A_{it-1}+{\eta }_2\ln r{d}_{it}+c+{\mu }_{it}\end{array}$$

(5)

Taking the logarithm of Equation (1), we obtain the first regression in Equation (5), which describes the effect of capital stock $k$ and technological level $A$ in promoting cities’ labor productivity. The second regression and the third regression in Equation (5) describe the effect of the pecuniary externality’s key factors and the technological externality’s factors in promoting intercity capital allocation and technology spillover, respectively.

According to Equation (5), the pecuniary externality and the technological externality of urban agglomerations can be calculated by:

$$\begin{array}{l}PE=\alpha ({\gamma }_1\ln \widehat{lab{p}_{it}}+{\gamma }_2\ln a{c}_{it}+{\gamma }_3\ln {\displaystyle \sum _{j\ne i,j=1}^n\raisebox{1ex}{$m{k}_{jt}$}\!\left/ \!\raisebox{-1ex}{$d_{ji}$}\right.}+{\gamma }_4\ln s{t}_{it})\\ TE=\beta ({\eta }_1\ln d{s}_{it}+{\eta }_2\ln {\displaystyle \sum _{j\ne i,i=1}^n\raisebox{1ex}{$r{d}_{jt}$}\!\left/ \!\raisebox{-1ex}{$d_{ji}$}\right.}+{\eta }_3\ln s{t}_{it})\end{array}$$

(6)

where $PE$ denotes the pecuniary externality and $TE$ denotes the technological externality.

In this paper, labor productivity ($labp$) is still measured by gross regional domestic product per labor. The relative position of labor productivity ($\widehat{labp}$) is measured by the ratio of a city’s labor productivity to the average labor productivity of its urban agglomeration. Capital stock ($k$) is measured by capital stock per labor. Because of the absence of congestion cost ($ac$), we use a city’s population density to represent it. Following the method of Harrisa [66], the market size (${\displaystyle \sum \raisebox{1ex}{$mk$}\!\left/ \!\raisebox{-1ex}{$d$}\right.}$) of a city is calculated by summing the ratios of gross regional domestic product to geographical distances. We use total factor productivity (TFP) to represent technological level ($A$). Economic density ($ds$) is measured as GDP output per unit land area. A city’s own R&D activities ($rd$) are measured according to the working population in Scientific and Technical Services and the Geological Prospecting Sector. Following the International Research Center of the UNIDO (UNIDO is an acronym for the United Nations Industrial Development Organization) method, we define the differentiation of intercity industrial structure $st$ as Equation (7):

$$s{t}_{it}=\frac{1}{n}{\displaystyle \sum _{j=1}^n(1-\frac{{\displaystyle \sum _{k=1}^m(P_{it,k}{P}_{jt,k})}}{\sqrt{{\displaystyle \sum _{k=1}^m{(P_{it,k})}^2{\displaystyle \sum _{k=1}^m{(P_{jt,k})}^2}}}})}$$

(7)

where $n$ and $m$ denote the number of cities and the number of industrial sectors, respectively. $P_{it,k}$ denotes the ratio of the working population in the industrial sector $k$ to the entire working population in city $i$ at time $t$.

The data set in this paper covers the period of 2010 to 2019, and mainly extracts from the China City Statistical Yearbook. The Hausman test shows that the null hypothesis of using a random-effect model has been refuted at 1% level of significance, and we therefore choose the fixed-effect model for processing in Section 5.2. While in Section 5.3, when comparing the differences between core cities and surrounding cities, a mixed panel model is chosen due to the superposition between the dummy variable and the cross-section fixed effect.

5.2. Empirical Findings

According to Equation (5),

Table 4. Regression results of the pecuniary externality and technological externality in China’s five representative urban agglomerations.

	Beijing–Tianjin–Hebei Urban Agglomeration	Yangtze River Delta Urban Agglomeration	Pearl River Delta Urban Agglomeration	Middle Reaches of Yangtze River Urban Agglomeration	Chengdu–Chongqing Urban Agglomeration
Model (1)	explanatory variable: lnlabp
α	0.60 *** (6.09 × 109)	0.40 *** (33.61)	0.28 *** (4.43)	0.44 *** (28.16)	0.52 *** (22.10)
β	1.00 *** (3.01 × 109)	1.36 *** (24.04)	1.42 *** (9.29)	1.52 *** (31.78)	1.11*** (11.12)
constant	0.00 (−0.94)	−1.01 *** (−12.97)	−0.82 ** (−2.33)	−1.41 *** (−15.38)	−1.42 *** (−13.81)
Adj-R2	1.000	0.987	0.941	0.975	0.992
cross-section fixed	YES	YES	YES	YES	YES
Model (2)	explanatory variable: lnk
γ1	0.39 *** (4.09)	0.02 (0.67)	−0.01 (−1.26)	−0.01 (−0.64)	0.09 (0.99)
γ2	−0.31 (−0.52)	0.00 (0.03)	−0.46 (−1.51)	−0.02 (−0.95)	−2.34 (−1.57)
γ3	0.42 ** (2.31)	0.90 *** (14.11)	0.17 * (1.86)	1.11 *** (29.40)	1.22 *** (14.98)
γ4	0.17 ** (2.36)	0.01 (0.27)	0.03 (1.24)	−0.08 *** (−2.49)	0.00 (0.17)
AR(1)	0.90 *** (27.36)	0.85 *** (27.87)	1.25 *** (13.80)	0.81 *** (28.22)	0.81 *** (12.18)
constant	3.11 (0.78)	2.34 *** (5.03)	2.07 (0.25)	1.65 *** (6.10)	17.08 * (1.82)
Adj-R2	0.996	0.992	0.997	0.994	0.992
cross-section fixed	YES	YES	YES	YES	YES
Model (3)	explanatory variable: lnA
η1	0.24 *** (5.24)	0.13 *** (4.34)	0.53 *** (5.85)	0.52 *** (11.62)	0.15 *** (4.28)
η2	−0.07 (−1.45)	−0.07 (−1.16)	−0.54 *** (−3.09)	−0.91 *** (−6.27)	−0.19 *** (−2.76)
η3	−0.11 (−2.05)	−0.02 (−0.73)	−0.08 (−0.78)	−0.00 (−0.09)	0.02 (0.74)
η4	0.33 *** (4.05)	0.34 *** (7.16)	−0.01 (−0.12)	0.16 *** (3.03)	0.59 *** (6.10)
η5	−0.03 * (−1.68)	0.01 (0.17)	0.01 (0.13)	−0.08 * (−1.72)	−0.01 (−0.18)
constant	−1.31 (−2.63)	−0.20 (−0.70)	−3.74 *** (−3.69)	−0.58 *** (−7.20)	−0.91 *** (−3.09)
Adj-R2	0.972	0.955	0.948	0.925	0.980
cross-section fixed	YES	YES	YES	YES	YES

Note: The figures in parentheses are Z statistics; ***, ** and * denote the level of significance at 1%, 5% and 10% respectively.

reports the regression results of the pecuniary externality and the technological externality based on the five representative urban agglomerations in China. In Model (1), the elasticity coefficient of capital stock per labor ($\alpha$) is lower than the elasticity coefficient of technological level ($\beta$), and $\alpha +\beta >1$. The result indicates that there is a characteristic of increasing returns to scale in all five urban agglomerations, and technological level ($A$) has a much heavier effect in promoting labor productivity ($labp$) than capital stock ($k$).

Model (2) reports the effects of urban agglomerations’ pecuniary externality. First, the relative position of labor productivity ($\widehat{labp}$) has limited effects on capital stock ($k$), except in the Yangtze River Delta urban agglomeration. Meanwhile, the regression coefficient of congestion cost ($ac$) to capital stock ($k$) does not pass the significance test. These results suggest that congestion cost is not the key factor affecting intercity capital allocation, and the route of capital flow in most urban agglomerations is not aligned with the pursuit of higher labor productivity. Therefore, hypothesis 1 is not valid, and there are deep-rooted reasons for this, e.g., government intervention (in 1956, the Indian government issued an industrial policy resolution to try to direct investment to backward areas outside the metropolitan area. During 1970–1980, the Mexican government used financial incentives to promote industrial development outside the three major urban agglomerations. In 1989, Brazil set up constitutional funds to finance economic activity in the backward regions of the north and northeast. However, these government interventions all failed, resulting not only in wasted fiscal funds but also economic efficiency losses) or higher labor productivity cannot guarantee higher profits. Second, market size (${\displaystyle \sum \raisebox{1ex}{$mk$}\!\left/ \!\raisebox{-1ex}{$d$}\right.}$) has a positive effect on capital stock ($k$) in all five urban agglomerations. This suggests that the expansion of market size is a key factor in promoting intercity capital allocation. Therefore, hypothesis 2 is reasonable. Third, the differentiation of intercity industrial structure ($st$) has inconsistent results on capital stock ($k$) in the five key construction urban agglomerations. Specifically, the coefficient is positive in the Beijing–Tianjin–Hebei urban agglomeration, but negative in the Middle Reaches of Yangtze River urban agglomeration. In the other three urban agglomerations, the regression coefficients do not pass the significance test, indicating that specialization or diversification in the industrial structure does not affect the intercity capital allocation.

Model (3) reports the effects of urban agglomerations’ technological externality. First, economic density ($ds$) has a positive effect on the technological level ($A$). This suggests that the increase in economic density promotes the technological level of the city. Thus, hypothesis 3 is reasonable. Second, technology spillover from other cities’ R&D activities (${\displaystyle \sum \raisebox{1ex}{$rd$}\!\left/ \!\raisebox{-1ex}{$d$}\right.}$) has a negative effect on the technological level ($A$) in the Pearl River Delta urban agglomeration, Middle Reaches of Yangtze River urban agglomeration, and Chengdu–Chongqing urban agglomeration. In the other two urban agglomerations, however, the regression coefficients are not statistically significant. Thus, hypothesis 4 is not valid. Furthermore, cities’ R&D activities ($rd$) have a negative effect on promoting their technological level ($A$) in all five urban agglomerations. Third, the regression coefficient of differentiation of intercity industrial structure ($st$) to technological level ($A$) is not statistically significant in any of the five urban agglomerations, which indicates that there is no evidence to support the notion that specialization or diversification in industrial structure was beneficial in promoting cities’ technological level.

From the above discussion, we can draw the following conclusions. Market size is the main factor affecting the pecuniary externality, and economic density is the main factor affecting the technological externality of China’s five representative urban agglomerations. That is, the quest for a larger market size and higher economic density are the two main drivers of the formation of urban agglomerations in China.

5.3. Heterogeneity Test

Whether there are differences in externalities between the core cities and surrounding cities in urban agglomerations is another question that we are interested in. In this part, we introduce a dummy variable to group databases into core cities and surrounding cities (where $D=1$ denotes core cities and $D=0$ denotes surrounding cities) and apply similar models as used in part 5.2 to answer it. We define core cities as municipalities, provincial capitals, and vice-provincial cities, while other cities are labeled as surrounding cities [67] (this definition of core cities and surrounding cities is consistent with the definition criteria provided by the New-Type Urbanization Plan (2014–2020) issued by the Chinese government. In previous academic studies, the division by Han et al. is also consistent with our paper).

Table 5. Heterogeneity test of pecuniary externality between core cities and surrounding cities.

Explanatory Variable	lnk
	Beijing–Tianjin–Hebei Urban Agglomeration	Yangtze River Delta Urban Agglomeration	Pearl River Delta Urban Agglomeration	Middle Reaches of Yangtze River Urban Agglomeration	Chengdu–Chongqing Urban Agglomeration
γ1	0.36 *** (3.34)	0.07 ** (2.17)	−0.01 (−0.88)	−0.01 (−0.51)	0.10 (0.83)
D × γ1	0.28 (1.28)	−0.08 (−0.64)	−0.07 (−1.23)	−0.03 (−0.41)	0.04 (0.20)-
γ2	−0.27 (−0.96)	0.01 (0.53)	−0.21 (−1.19)	−0.03 (−1.27)	4.77 *** (−2.90)
D × γ2	−1.69 (−1.49)	0.05 (0.42)	−0.35 (−0.50)	0.14 (1.35)	3.53 (1.16)
γ3	0.34 (1.57)	0.69 *** (6.39)	0.28 ** (2.41)	0.45 ** (4.29)	0.22 (0.98)
D × γ3	−0.91 * (−1.91)	0.19 (0.59)	−0.27 (−1.59)	−0.17 (−0.56)	−0.15 (−0.29)
γ4	0.12 (1.44)	0.01 (0.38)	0.05 (1.48)	−0.04 (−1.08)	−0.01 (−0.68)
D × γ4	0.32 (1.46)	−0.10 (−1.04)	−0.08 (−1.52)	0.10 (−0.82)	0.01 (0.47)
constant	5.06 * (1.86)	−2.16 (−0.48)	−22.63 (−0.24)	−2.15 (−0.87)	12.45 (0.78)
D	16.77 * (1.84)	2.72 (0.48)	2.02 (0.26)	−3.29 (−1.53)	−28.71 (−1.31)
AR(1)	0.96 *** (69.80)	1.01 *** (113.5)	1.38 *** (11.90)	1.02 *** (144.80)	1.01 *** (157.42)
Adj-R2	0.996	0.989	0.997	0.992	0.993
cross-section fixed	NO	NO	NO	NO	NO

Note: The figures in parentheses are Z statistics; ***, ** and * denote the level of significance at 1%, 5% and 10% respectively.

and

Table 6. Heterogeneity test of the technological externality between core cities and surrounding cities.

Explanatory Variable	lnA
	Beijing–Tianjin–Hebei Urban Agglomeration	Yangtze River Delta Urban Agglomeration	Pearl River Delta Urban Agglomeration	Middle Reaches of Yangtze River Urban Agglomeration	Chengdu–Chongqing Urban Agglomeration
η1	0.00 (0.26)	0.01 (0.51)	0.42 *** (5.23)	0.06 *** (3.77)	−0.02 (−0.70)
D × η1	0.34 *** (3.04)	0.02 (0.37)	−0.40 (−3.46)	0.04 (0.18)	0.17 *** (3.34)
η2	0.05 (1.21)	0.00 (0.19)	−0.73 *** (−4.93)	−0.12 *** (−2.92)	−0.02 (−0.59)
D × η2	−0.12 * (−0.46)	−0.12 (−1.61)	0.69 ** (2.19)	−0.04 (−0.10)	−0.13 (−0.54)
η3	−0.07 (−1.38)	−0.01 (−0.41)	−0.00 (−0.05)	−0.05 (−1.22)	0.02 (0.51)
D × η3	−0.19 * (−2.04)	0.11 (0.71)	−0.01 (−0.06)	−0.12 (−0.37)	−0.03 (−0.66)
constant	0.02 (0.10)	0.07 (0.64)	−3.33 *** (−5.04)	−0.47 (−2.62)	0.10 (0.44)
D	−2.19 * (−2.08)	−0.09 (−0.14)	3.29 ** (2.34)	−0.64 (−0.27)	−1.11 (−1.05)
Adj-R2	0.961	0.930	0.915	0.837	0.976
cross-section fixed	NO	NO	NO	NO	NO

Note: The figures in parentheses are Z statistics; ***, ** and * denote the level of significance at 1%, 5% and 10% respectively.

report the regression results of their tests for heterogeneities in terms of pecuniary externality and technological externality, respectively.

In Table 5, first, the regression coefficients $D\times {\gamma }_1$, $D\times {\gamma }_2$, and $D\times {\gamma }_4$ all fail to pass the significance test in China’s five representative urban agglomerations, indicating that the differences in the relative position of labor productivity ($\widehat{labp}$), congestion cost ($ac$), and intercity industrial structure ($st$) between core cities and surrounding cities do not lead to any diversity concerning their pecuniary externalities.

Second, the regression coefficient $D\times {\gamma }_3$ is significantly negative in the Beijing–Tianjin–Hebei urban agglomeration, indicating that the market size of core cities (${\displaystyle \sum \raisebox{1ex}{$mk$}\!\left/ \!\raisebox{-1ex}{$d$}\right.}$) plays a weaker role in promoting intercity capital allocation than that of surrounding cities. The regression coefficients for the other four urban agglomerations are not statistically significant.

Table 6 reports the difference in the technological externality between the core cities and surrounding cities. First, the regression coefficients of $D\times {\eta }_1$ are significantly positive in the Beijing–Tianjin–Hebei urban agglomeration and the Chengdu–Chongqing urban agglomeration, which indicates that economic density ($ds$) demonstrates a heavier effect in promoting technological level ($A$) in their core cities than in their surrounding cities. In the other three urban agglomerations, however, the regression coefficients are not statistically significant.

Second, the regression coefficients $D\times {\eta }_2$ are significantly positive in the Beijing–Tianjin–Hebei urban agglomeration and the Pearl River Delta urban agglomeration, which indicates that technology spillover from other cities’ R&D activities (${\displaystyle \sum \raisebox{1ex}{$rd$}\!\left/ \!\raisebox{-1ex}{$d$}\right.}$) demonstrated a greater effect in promoting technological level ($A$) in their core cities than in their surrounding cities. However, the regression coefficients in the other three urban agglomerations fail to pass the significance test.

Third, the regression coefficient of $D\times {\eta }_3$ is significantly negative in the Beijing–Tianjin–Hebei urban agglomeration, which indicates that the differentiation of intercity industrial structure ($st$) demonstrates a weaker effect in promoting technological level ($A$) in its core cities than in its surrounding cities. In the other four urban agglomerations, however, the regression coefficients are not statistically significant.

In summary, there is no significant difference in pecuniary externality between the core cities and the surrounding cities in China’s five representative urban agglomerations. However, there are complex and significant differences in pecuniary externality between the core cities and the surrounding cities in China’s five representative urban agglomerations.

6. Conclusions and Discussions

In this paper, we provide an insight into pecuniary externality and technology externality of urban agglomerations based on the case of five representative urban agglomerations in China. Our results suggest that the pecuniary externality of urban agglomerations manifests as intercity capital allocation, and that the technology externality manifests as intercity technology spillover. The key factor of pecuniary externality in China’s five representative urban agglomerations is market size. That is, the pursuit of a larger market size is one of the main motivations in forming urban agglomerations in China, but the intercity capital allocation does not show a trend towards cities with higher labor productivity.

The key factor of technological externality in China’s five representative urban agglomerations is economic density. That is, the pursuit of higher economic density is another main motivation in forming urban agglomerations in China, but cities’ own R&D activities and the spread from other cities fail to improve the technological level of urban agglomerations.

Moreover, there is no evidence to suggest that the diversification or specialization of the industrial structure is related to the pecuniary externality or the technology externality of urban agglomerations. The regressions of dummy variables indicate that there are no significant differences in pecuniary externality between core cities and surrounding cities in the five representative urban agglomerations in China. However, their technological externality presents complex differences.

As urban agglomerations play an increasingly important role in regional economic development, our conclusions can provide many policy implications. First, our conclusions suggest that pecuniary and technological externalities should be distinguished when studying the externalities of urban agglomerations. These two types of externality have different manifestations, different mechanisms, and different factors. Understanding their respective characteristics is a prerequisite for advancing the development of urban agglomerations. Meanwhile, more attention must be paid to the technology externality of urban agglomerations. We believe technological externality will play a more important role in urban agglomerations as high-tech industries develop and transportation networks improve.

Second, policies should aim at enhancing the agglomeration capacity of China’s five representative urban agglomerations, and cultivating more small and medium-sized urban agglomerations. According to the 2019 World Development Report, the average population agglomeration index of urban agglomerations in China is around 0.4, while the index in the United States exceeds 0.7 and reaches 0.9 in Japan. The agglomeration capacity of Chinese urban agglomerations is still quite lacking.

Third, the intercity allocation of capital should shift to cities with higher labor productivity in pursuit of higher profits. However, our results do not lead to this conclusion in this paper. We argue that government intervention is one of the main deep-rooted causes. Government intervention may benefit the balanced development of the regional economy, but it will weaken economic efficiency. Thus, how to apply government intervention in the future to strike a balance between efficiency and equity will become an important issue.

Fourth, close attention should be paid to R&D activities. Our results suggest that it is immaterial to promote the technological level of urban agglomerations in China. By attracting people and firms, leading areas fuel agglomeration economies, becoming centers for innovation and growth and driving the national economy. However, in this paper, we conclude that cities’ own R&D activities and the spread from other cities fail to improve the technological level of urban agglomerations. Technological externality will play a more important role in urban agglomerations as high-tech industries develop and transportation networks improve. With patent citations, it is possible to identify a paper trail for some knowledge spillovers. United States patent citations are spatially concentrated, with citations 5–10 times more likely to come from the same standard metropolitan statistical area as originator patents. In additional, a staggering 96 percent of innovations occur in metropolitan areas in the United States. We argue that imitative innovation, rather than original innovation, has evolved into an obstacle to boosting technological development. Therefore, original innovation is a concern that needs urgent attention.