Volume 31 Issue 1
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ZHANG Ze, TANG Zilai, 2021. Examination and Interpretation of the Quantitative Validity in China’s Corporate-based Urban Network Analysis. Chinese Geographical Science, 31(1): 41−53 doi:  10.1007/s11769-021-1175-y
Citation: ZHANG Ze, TANG Zilai, 2021. Examination and Interpretation of the Quantitative Validity in China’s Corporate-based Urban Network Analysis. Chinese Geographical Science, 31(1): 41−53 doi:  10.1007/s11769-021-1175-y

Examination and Interpretation of the Quantitative Validity in China’s Corporate-based Urban Network Analysis

doi: 10.1007/s11769-021-1175-y
Funds:  Under the auspices of the National Social Science Foundation of China (No. 16ZDA017)
More Information
  • Corresponding author: TANG Zilai. E-mail: zltang@tongji.edu.cn
  • Received Date: 2020-03-10
    Available Online: 2020-08-27
  • Publish Date: 2021-01-05
  • As a matter of expediency, most existing corporate-based urban networks can only be quantitatively measured by either counting the number of linkages or calculating the product of estimated service values. However, the impreciseness arising due to the limits of quantitative analysis may prove fatal to studies about non-market economies like China. Employing the capital investment dataset as an example, we build a capital-weighted intervention network as well as an unweighted control network to carry out an examination of the quantitative validity in China’s corporate-based urban network analysis. Both the overall spatial pattern and top city-dyads within the capital-weighted network witness Beijing, as the most dominant city, overshadow the performance of the others, and the unweighted network shows multilateral interactions between China’s top cities including Beijing, Shanghai, Shenzhen, and Guangzhou. To further interpret the noticeable differences, we divide the overall network into two subnetworks, inferred by focusing on state-owned enterprises (SOEs) and private enterprises. The results show that the public and private sectors have separately created vastly different subnetworks in China and that SOEs play a much more significant role in terms of capital. Besides fresh insights into China’s urban network, this study provides a cautionary tale reminding researchers of the essentiality and complexity when making a quantitative distinction between different linkages.
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Examination and Interpretation of the Quantitative Validity in China’s Corporate-based Urban Network Analysis

doi: 10.1007/s11769-021-1175-y
Funds:  Under the auspices of the National Social Science Foundation of China (No. 16ZDA017)

Abstract: As a matter of expediency, most existing corporate-based urban networks can only be quantitatively measured by either counting the number of linkages or calculating the product of estimated service values. However, the impreciseness arising due to the limits of quantitative analysis may prove fatal to studies about non-market economies like China. Employing the capital investment dataset as an example, we build a capital-weighted intervention network as well as an unweighted control network to carry out an examination of the quantitative validity in China’s corporate-based urban network analysis. Both the overall spatial pattern and top city-dyads within the capital-weighted network witness Beijing, as the most dominant city, overshadow the performance of the others, and the unweighted network shows multilateral interactions between China’s top cities including Beijing, Shanghai, Shenzhen, and Guangzhou. To further interpret the noticeable differences, we divide the overall network into two subnetworks, inferred by focusing on state-owned enterprises (SOEs) and private enterprises. The results show that the public and private sectors have separately created vastly different subnetworks in China and that SOEs play a much more significant role in terms of capital. Besides fresh insights into China’s urban network, this study provides a cautionary tale reminding researchers of the essentiality and complexity when making a quantitative distinction between different linkages.

ZHANG Ze, TANG Zilai, 2021. Examination and Interpretation of the Quantitative Validity in China’s Corporate-based Urban Network Analysis. Chinese Geographical Science, 31(1): 41−53 doi:  10.1007/s11769-021-1175-y
Citation: ZHANG Ze, TANG Zilai, 2021. Examination and Interpretation of the Quantitative Validity in China’s Corporate-based Urban Network Analysis. Chinese Geographical Science, 31(1): 41−53 doi:  10.1007/s11769-021-1175-y
    • Together with population size and settlement density, a city’s level of heterogeneity plays an extremely important role in urban life (Wirth, 1938). Cross-regional and transnational linkages bring tremendous non-local technology, information, talent, and capital into cities, which greatly enrich the diversity of urban society. Much of the existing literature on ‘space of flows’ has proposed that the power and position of cities derive from different kinds of flow between them rather than from what remains fixed within them (Derudder, 2006). With a more in-depth understanding of the ‘space of flows’, the central flow theory is also considered to be one of the two basic theories that is juxtaposed with the central place theory (Taylor et al., 2010). Within the past three decades, empirical studies of both global and national urban networks have become popular for interpreting regional configuration as well as for urban systems research (Taylor et al., 2013; Pan et al., 2017).

      By building on these former contributions to ‘space of flows’, we chose to examine capital flows as the starting point of this paper, which aims to further advance researches about urban networks from two points of view. On the one hand, we argue that network projections based on capital investment linkages may perform as a critical appraisal and a cautionary tale for existing network approaches which are far too soon to be abandoned (Derudder, 2020). Limited by a lack of datasets on flows (Beaverstock et al., 2000), the early work describing urban networks could only infer linkages between the departments of the same enterprise, such as advanced producer services (APS) enterprises (Taylor, 2001; Sassen, 2013) and global top 500 firms (Alderson and Beckfield, 2004). Shortly after these preliminary studies, recent literature has been turning to focus on inter-firm linkages as a supplemental perspective (Taylor, 2004; Jacobs et al., 2011; Martinus et al., 2015). Compared with the emerging and diverse perspectives concerning corporate-based network research, however, little work has been conducted to quantitatively optimize the existing methodology (Nordlund, 2004). Researchers could only count the number of inter-firm or intra-firm linkages (Alderson and Beckfield, 2004), or calculate the product of estimated service values (Taylor et al., 2014b), as they did decades ago. In recent years, the validity of existing network approaches has lately received great attention (Neal, 2012; Pažitka et al., 2020; Sigler et al., 2020) and it is worthwhile devoting much effort to this (Derudder and Taylor, 2020; Derudder, 2020; Neal, 2020). Just as with the accounting report on inter-firm deals and inter-organizational projects, intercity business linkages should be captured more directly and precisely (Pažitka et al., 2020), for example, in terms of capital (Anderson et al., 2004). On the other hand, we deem that viewing urban networks through the lens of capital flows can promote a more in-depth understanding of some non-market economies, such as China (Sutton and Costanza, 2002). Some Chinese state-owned monopolies, which are small in number but rich in capital, are the backbone of China’s economy. These state-owned monopolies will be considerably underestimated when building an urban network by either counting the number of linkages or adding up the product of service values rather than by calculating the capital volume of the investment (Wang, 2015).

      In this paper, we perform a comparative study of China’s urban network based on capital investment data to explore how the quantitative specification of corporate networks may affect empirical results. Capital is an essential element in both the free market economy and the state-regulated region. Capital flows can be precisely measured in monetary units, and it helps to highlight the critical role of state power in China’s urban network. By constructing an intervention network as well as a control network based on the same dataset, we clarify some of the quantitative biases of previous researches about China’s urban network and interpret the mechanism by which companies shape China’s urban network. In addition, given China’s increasing role in the international market, this may provide a cautionary tale for the world city network (WCN) analysis and lay the foundation for further optimizing existing quantitative methodologies.

    • In the last few decades, considerable attention has been paid to corporate-based urban networks (Taylor, 1997; Hennemann and Derudder, 2014; Neal et al., 2019). Despite the unavailability of relational data, scholars have been continually optimizing the underlying dataset. One compelling shift is that much of the recent literature has been moving away from studies of intra-firm networks and toward a focus on inter-firm networks. These inter-firm studies may appear to be directly observable flows to be sure rather than a ‘projection’ from a methodical ‘guesstimate’ of how different parts of the firm communicate with each other (Latapy et al., 2008). Together, these studies have enriched our understanding of the contemporary patterns of global urbanization (Zhang et al., 2018b).

      However, compared to the increasingly diversified perspectives of corporate-based urban network research, few studies have touched upon the use of quantitative algorithms. The connectivity between any two cities is assigned either to the number of linkages or to the product of estimated service values. These two assignments are indeed unavoidable choices (which most researchers studying urban networks have to face) since there is no extra available information on the specific roles that individual firms have played (Meyer, 2003; Zhang et al., 2018b). This reasoning entails the following assumption: the sample companies (e.g., 175 APS firms) are similar in size and the flows of information, money, or people indicated by each linkage are approximately equivalent. In the real world, however, many orders of magnitude difference in quantitative volume can exist between these linkages. The quantitative oversimplification of real-world linkages may lead to invalidity of empirical results. Along with the recent efforts to optimize the precision of quantitative analysis from other perspectives (Li and Phelps, 2018; 2019; Zhang et al., 2018a), the quantitative impreciseness of existing corporate-based network analysis is widely acknowledged, but researchers have not yet been able to identify the extent of this imprecision (Taylor et al., 2014b; Derudder, 2020).

      In a 2020 Geographical Analysis paper, Pažitka et al. (2020) present a pilot study by building networks based on different quantitative specifications. In particular, one weighted WCN is built based on inter-city business flows weighted by products of office sizes, while another binary WCN is produced using intercity business flows weighted by the number of overlapping firms. Similarly, networks produced by IOPA (inter-organizational project approach) consist of IOPA (count) and IOPA (revenue). Notwithstanding these efforts, Pažitka et al. (2020) acknowledge that the imprecision is only partially alleviated and encourage thorough discussions in further studies.

      Capital, as a necessary component of any economic activity, does best to precisely measure enterprises. A basic fact is that, in news reports and audit reports, the success of enterprises is commonly measured by its financial resources, including capital, money, and other assets. Capital was initially described as physical objects such as tools, buildings, and vehicles that are used in the production process. Since at least the 1960s, however, economists have increasingly focused on broader interpretations of the term ‘capital’ (Anheier et al., 1995). For example, investment in skills and education can be viewed as the development of human capital or knowledge capital, and investment in intellectual property can be viewed as building up intellectual capital. Drawing lessons from the Capital Asset Pricing Model (Fama and French, 2004), we conclude that any non-financial asset is priced in accordance with its participation in the economic operation of an enterprise. The fair value of non-financial assets is determined based on the highest and best use of the asset as determined by a market participant. The transaction records of various non-financial assets, like patents or business information, for example, provide good pieces of evidence. In this study, the collection of both financial and non-financial assets is defined as broad capital. Therefore, the intra-firm or inter-firm linkages used to construct urban networks could be seen as the process of broad capital being redistributed from one department to another, or from one enterprise to another. Thus, capital-measured networks, which are built based on capital-weighted linkages, provide a preliminary examination of existing quantitative specification of corporate-based networks.

      More importantly, we argue that our research aims to provide a quantitative test of previous research, rather than propose an alternative empirical approach. Urban network, just like any other urban system, is a theoretical representation and simplification of a complex and multilayered reality (Derudder, 2020). Despite the increasingly new available dataset, existing interlocking and ownership approaches are still the mainstream methods to elucidating urban networks in the short term. A clarification and examination of the quantitative validity are favorable to advancing the literature.

    • Along with the network approaches being introduced into China, the last decade has witnessed a growing literature on China’s urban network (Lai, 2012; Taylor et al., 2014a; Pan et al., 2018). Some of the recent studies discussed the limitations of applying the interlocking network approach to China’s urban network. Zhao et al. (2015), for example, point out the limitations to using Globalization and World Cities Study Group and Network (GaWC) data when conducting empirical research on APS firms and China’s urban network. More recently, scholars have been turning to illustrate China’s urban network from a perspective of inter-firm linkages, e.g., the cooperation between accounting, securities, law firms and IPO enterprise (Pan et al., 2017), and film co-production projects (Zhang et al., 2018b). Similar to previous research, the inter-city connectivity could be only assigned to the number of linkages. However, due to the significant size gap between state-owned enterprises (SOEs) and private firms, this kind of simplified quantitative method may prove fatal to studies about China’s urban network.

      Although there is still an argument whether China is a socialist market economy or state capitalism, the uniqueness of China’s economy has long been widely acknowledged. In China, the government uses a variety of SOEs to manage the exploitation of resources that they consider the state’s most valuable assets and to create and maintain large numbers of jobs (Bremmer, 2010). Therefore, many state-owned oligarchy enterprises and even state-owned monopoly enterprises are established and currently play a considerable role in China. In 2019, China (not including Chinese Taiwan, Hong Kong and Macao) is home to 112 corporations listed on the Fortune Global 500, but only 15% of those are privately owned. It should be noted that, although the SOE is a global phenomenon across the world (such as Norway, Singapore, France, United Kingdom, and the United States), both the size of SOEs and their high proportion in the national economy make China unique.

      In the case of China, unclear property rights between the government and enterprises and laggard company management systems mean that SOEs are generally not as productive and innovative as private firms. Nonetheless, the Chinese government is still keen on supporting SOEs and is committed to making them bigger, stronger, and more efficient (Chen et al., 2019). This is particularly relevant to certain strategic sectors where government oversight is essential, specifically in defense, energy, telecom, aviation, and railway systems. Hence, SOEs often have a hierarchical structure, while the SOE leadership sometimes focuses more on political goals rather than long-term company development or profits (Jones and Zou, 2017).

      In GaWC’s previous research on the WCN, the sample companies (comprising 175 APS firms) are similar in size. Therefore, it is feasible to convert the data of each firm using a simple coding system to enable cross-firm comparison for analysis (Taylor et al., 2014b). However, due to the significant size gap between Chinese SOEs and private firms, this kind of simplified quantitative method may lead to network distortion. One good example is the huge gap between the sizes of China’s state-owned banks and private banks (Tong, 2017); the underestimation of the size of China’s state-owned banks may lead to biases in understanding China’s financial system (Firth et al., 2009). The objective of this article is to examine, corroborate, and interpret this concern and pave a way for optimizing existing quantitative specifications.

    • Although lamenting the lack of genuinely relational data for cities has become common, rich sources of such data are available in the emerging era of big data (Neal, 2012). Publicly-listed firms, in particular, provide a useful dataset with two major benefits. First, publicly-listed firms are usually large corporations that dominate economic life throughout both the developed and leading developing countries (Chen, 2004). The annual ranking of leading companies released by Forbes magazine is a representative list of achievement-based, publicly-listed firms. Second, each listed company is commonly required to report its economic activities, major shareholders, and financial performance throughout the preceding year. These reports contain plentiful and comprehensive data on capital investment, which is genuinely relational data for cities. The urban network can be built by drawing on the investment linkages from the listed firms to their major shareholders and to their first-tier subsidiaries as well. Specifically, the annual reports provide records on each listed company’s activities and financial performance, in which the principal subsidiaries and branch offices are also revealed to the public. According to the past practice, both the major shareholders’ equity for each listed company and the investment volume from listed firms to their subsidiaries and other corporations are reported in terms of monetary measurement (Daude and Fratzscher, 2008).

      In common sense, the capital investment recorded in the annual reports represent the long-term strategies rather than the short-term, speculative capital investment of investors. In the mature securities market, investors may use both capital in a narrow sense (e.g., cash, loans, and bonds) or broad capital (e.g., trademarks and patents) to capture a larger share of the market and reap more revenue. There is no minimum or maximum volume of capital investment, and all the investments recorded in the annual reports can be precisely measured in monetary units.

      In China, with the development of the stock market, the proportion of listed companies in the national economy has also been increasing. As of the end of 2015, there were 2494 publicly-listed companies in the Shanghai and Shenzhen Stock Exchanges, which were headquartered in all provinces, municipalities, and autonomous regions of China. The total market value of listed companies reached 52.96 trillion yuan (RMB), which was almost the same as China’s GDP in 2015. China’s stock market is playing an increasing role in allocating capital across regions (Li, 2012; Bian, 2014), and it is a viable enterprise sample that can be used to conduct urban network research.

      Despite the above-mentioned benefits, we acknowledge the limitations of the capital investment dataset of 2494 publicly-listed firms. On one hand, those publicly-listed companies in the Shanghai and Shenzhen Stock Exchanges only account for a very limited share of all enterprises in China. The capital investment derived from some China-located but oversea-listed companies (e.g., Alibaba and Tencent) as well as some other unlisted but influential firms (e.g., Huawei) are not included in this work. On the other hand, investment is nothing but only one of the various kinds of capital flows. Other capital flows such as capital transfers and capital transactions are equivalent perspectives for shaping inter-city linkages but not discussed in this research.

      All in all, by collecting annual reports from 2494 listed firms, 3123 inter-city linkages from shareholders to listed firms and 15 027 inter-city linkages from listed firms to subsidiaries are screened out. Thus, 18 150 valid inter-city investment linkages comprise the final dataset, involving a total of more than 3 trillion yuan (RMB). Additionally, the 21 644 offices (including all listed firms, shareholders, and subsidiaries) are widely distributed across 356 prefectures and higher-level cities; these cities cover all parts of China (not including Chinese Taiwan, Hong Kong and Macao). Based on this investment dataset, we constructed a 356 by 356 city matrix.

      The inter-city connectivity (rab) between two cities a and b is thus given by aggregating intra-firm connections rabj across all firms:

      $$ {r}_{ab}={\sum }_{j=1}^{m}{r}_{abj} $$ (1)

      where rabj denotes the investment volume between cities a and b generated by firm j, and m is the total number of listed firms.

      Finally, the total network connectivity (TNC) of city a is generated by summing up the city’s connectivity to all other cities:

      $$ {TNC}_{a}={\sum }_{i=1}^{n-1}{r}_{ai}\left(a\ne i\right). $$ (2)

      For reasons of clarity, the connectivity of each city and dyad will be reported as standard connectivity, which is calculated by the percentages of the maximum connectivity.

    • Based on the same capital investment dataset, we developed two separate urban networks using two different quantitative approaches. The first is an intervention network based on the capital investment volume, which we call the capital-weighted urban network. The second is based on the number of investment linkages, named the unweighted network, which we used as a control network. The variable for intra-firm connections rabj was assigned as the number of investment linkages in the unweighted network, while rabj was assigned as the volume of investments with the monetary unit in the capital-weighted network. In this section, we will try to identify the quantitative biases of China’s urban network by comparing the capital-weighted and unweighted networks.

      According to the Jenks Natural Breaks Classification Method (McMaster and McMaster, 2002), the connectivity of cities and city-dyads were divided into five categories individually: high, relatively high, medium, relatively low, and low. We employed the Quadratic Assignment Procedure (QAP) correlation (Krackardt, 1987) varying between 0 and 1 to compare the similarity of the two subnetworks. The larger the correlation coefficient, the higher the network similarity. Fig. 1 presents the overall spatial patterns of two different urban networks based on unweighted and capital-weighted investment linkages; they show noticeable differences with QAP correlation of 0.664. In the network formed by unweighted investment linkages, the Beijing-Tianjin-Hebei Urban Agglomeration (BTH), Yangtze River Delta (YRD), and Pearl River Delta (PRD) have formed divergent network radiation at the national level as three major urban agglomerations in the coastal China areas (Lu and Wan, 2014). The economic core of western China, Chengdu-Chongqing Economic Zone (CCEZ), shows prominent connections with three major urban agglomerations in the coastal areas. Thus, a diamond-shaped spatial pattern, which consists of almost all most-connected cities and strongest dyads, is presented in the territory. As for the capital-weighted network, Beijing, as the single-center feature, is the most prominent spatial pattern. As the command center of the state administration, Beijing has strong connections with other major cities in China. Although cities such as Shanghai, Guangzhou, and Shenzhen also reflect the characteristics of specific central radiation, the intensity and spatial scale of the central radiation are far from being comparable to Beijing.

      Figure 1.  The spatial patterns of unweighted and capital-weighted urban networks in China (not including Chinese Taiwan, Hong Kong and Macao). a) The unweighted urban network; b) The capital-weighted urban network

      Additionally, a geographic concentration of city connectivity can also be observed in both urban networks along the eastern seaboard, which is consistent with our expectation (Zhang and Cai, 2020). Specifically, the average connectivity ratio of western, central, and eastern Chinese cities is 1.0∶1.5∶3.7 in the unweighted network, while the ratio of the capital-weighted network is 1.0∶1.6∶4.5 (Western Chinese cities include cities in Chongqing, Sichuan, Guizhou, Yunnan, Tibet, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang, Guangxi, and Inner Mongolia; Central Chinese cities consist of cities in Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, and Hunan; Eastern Chinese cities include cities in Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan). Cities in eastern China have a greater say in national capital policymaking and market control. In line with the persistent east-west divide in socioeconomic development in China, the Gini coefficient of both unweighted and capital-weighted networks also shows a downward trend from west to east. Moreover, this hierarchical structure is becoming increasingly evident from the unweighted urban network to capital-weighted urban network. In particular, the Gini coefficient of the unweighted urban network connectivity among cities in western, central, and eastern China is 0.67, 0.59, and 0.54, while the value of the capital-weighted urban network is 0.74, 0.71, and 0.68. This can be ascribed to the Matthew effect in network science (ital policymaking and market control. In line with the persistent east-west divide in socioeconomic development in China, the Gini coefficient of both unweighted and capital-weighted networks also shows a downward trend from west to east. Moreover, this hierarchical structure is becoming increasingly evident from the unweighted urban network to capital-weighted urban network. In particular, the Gini coefficient of the unweighted urban network connectivity among cities in western, central, and eastern China is 0.67, 0.59, and 0.54, while the value of the capital-weighted urban network is 0.74, 0.71, and 0.68. This can be ascribed to the Matthew effect in network science (Barabási and Albert, 1999) and the cumulative advantages of top Chinese cities in terms of economic capital (Dannefer, 2003).

      Table 1 lists the 20 most-connected Chinese cities in two different networks. Beijing, Shanghai, and Shenzhen are the top three cities, whereas Guangzhou is ranked fifth in both networks. Thus, we can verify China’s four tier-one cities’ leading positions in China’s urban network. It is also noteworthy that top cities hold much more dominant positions in the capital-weighted network. Beijing’s primacy index increases from 1.49 of the unweighted network to 2.38 of the capital-weighted network. As the second most-connected city of China’s network, Shanghai’s score is seven times larger than the tenth city in the capital-weighted network, which is in line with the comparison of the Gini coefficient. Furthermore, the different ranking order of China’s top 20 most-connected cities is likely to be a preliminary piece of evidence revealing potential quantitative biases. Ürümqi, as the most strategic place in the northwest border area of China, occupies a relative core position in both networks, which is a rather surprising result. This verifies the ‘regionality’ that exists within the city network (Taylor et al., 2014a), which is to say that a primary city of a large enough region is usually fully connected with other cities from and beyond its region. Additionally, a few cities with rich strategic resources—Taiyuan as the central city in the coal-producing area and Daqing as the main oil-producing area—are ‘punching above their weight’ in the capital-weighted urban network, which indicates an enhanced ‘strategic-ness’ (Taylor et al., 2014b).

      Urban networks based on two
      quantitative specifications
      The unweighted (control) urban networkThe capital-weighted (intervention) urban network
      CityRelative connectivityCityRelative connectivity
      Leading Chinese citiesBeijing1.000Beijing1.000
      Shanghai0.670Shanghai0.421
      Shenzhen0.505Shenzhen0.125
      Hangzhou0.278Tianjin0.103
      Guangzhou0.266Guangzhou0.097
      Chengdu0.223Taiyuan0.080
      Wuhan0.167Chengdu0.069
      Tianjin0.161Hangzhou0.061
      Suzhou0.152Wuhan0.059
      Changsha0.152Ürümqi0.059
      Chongqing0.125Changsha0.055
      Nanjing0.122Hefei0.054
      Fuzhou0.117Chongqing0.052
      Hefei0.117Nanjing0.049
      Xi’an0.095Daqing0.048
      Ürümqi0.094Dalian0.043
      Xiamen0.092Xi’an0.043
      Jinan0.088Fuzhou0.039
      Nanchang0.081Datong0.038
      Shenyang0.080Nanchang0.034

      Table 1.  Top 20 leading Chinese cities in two networks

      Table 2 ranks the 10 strongest city-dyads from the unweighted and capital-weighted networks. In addition to the high-frequency appearance of China’s four tier-one cities in the most-connected city-dyads, what interests us more is the difference between these two sets of city-dyads. The most compelling finding is the prominent links between neighboring cities (for example, Beijing and Tianjin, Guangzhou and Shenzhen, and Shanghai and Suzhou) in the unweighted network. As for the capital-weighted city-dyads, the 10 most-connected city-dyads are all the connections between Beijing and other cities, including outward gateway cities like Shanghai and Shenzhen, regional central cities like Chongqing and Guangzhou, and strategic cities like Ürümqi and Daqing. Given China’s unique institutional contexts (Pan and Xia, 2014), we can assume that the significant role played by the SOEs shapes the dominant position of some top cities in the capital-weighted network.

      Urban networks based on two
      quantitative specifications
      The unweighted (control) urban networkThe capital-weighted (intervention) urban network
      City-dyadRelative connectivityCity-dyadRelative connectivity
      Leading Chinese city-dyadsBeijing-Shanghai1.000Beijing-Shanghai1.000
      Beijing-Shenzhen0.667Beijing-Tianjin0.157
      Beijing-Tianjin0.470Beijing-Chongqing0.139
      Shanghai-Shenzhen0.459Beijing-Chengdu0.138
      Beijing-Guangzhou0.339Beijing-Guangzhou0.120
      Shanghai-Hangzhou0.333Beijing-Shenzhen0.119
      Beijing-Chengdu0.330Beijing-Ürümqi0.112
      Guangzhou-Shenzhen0.319Beijing-Wuhan0.100
      Shanghai-Suzhou0.302Beijing-Daqing0.097
      Beijing-Wuhan0.274Beijing-Changsha0.088

      Table 2.  Top 10 Chinese city-dyads in two different networks

    • Due to the political and historical reality of China’s developing economy, the public sector still accounts for a much more significant share of the national economy than the burgeoning private sector (Naughton and Tsai, 2015). The difference between SOEs and private enterprises in shaping China’s urban network is a key issue when discussing China’s urban network from the lens of corporate networks (Liu and Derudder, 2013; Zhao et al., 2015; Pan et al., 2017). Following the research of WCN by GaWC (Beaverstock et al., 2000), however, previous interpretations of China’s urban network were used to compare the subnetworks inferred by focusing on firms in specific sectors (e.g., banking and advertising) rather than firms of different ownership (Zhao et al., 2015; Pan et al., 2017).

      First, based on the ownership nature of the ultimate controllers given in annual reports, 2494 listed companies were divided into state-controlled and non-state-controlled companies to examine how corporate ownership influences China’s urban network. Although the number of listed SOEs was much smaller than that of listed private enterprises, the number of inter-city links formed by SOEs was essentially the same as those formed by private enterprises. More specifically, 948 SOEs contributed 8423 inter-city linkages, while 1546 private firms provided a further 9727. Additionally, the total investment volume of SOEs’ 8423 inter-city linkages was valued at 2.3 trillion yuan (RMB), which was more than three times the investment volume of private firms’ inter-city linkages, valued at 0.7 trillion yuan (RMB). One interpretation suggests that SOEs in the Chinese mainland usually maintain a monopoly in the domains of infrastructure, natural resources, and energy, as well as politically sensitive business, and they establish multiple subsidiaries nation-wide to serve the whole country.

      We mapped the public and private subnetworks using both unweighted and capital-weighted approaches. Fig. 2 shows clearly the different spatial patterns of networks formed by public and private sectors. Apart from the stable leading position of China’s four tier-one cities, interestingly, the differences between these two subnetworks are more significant than anticipated. Regardless if the inter-city connections were capital weighted or not, the public subnetwork seems to be highlighting the superior position of Beijing. The most striking result to emerge from the data is that nine of the top ten city-dyads in the public subnetwork are connections between Beijing and other cities. On the contrary, the private subnetwork reveals itself as a multilateral interaction between China’s top cities. The connectivity of Shanghai and Shenzhen separately accounts for more than 65% of Beijing’s connectivity in the private subnetwork. The QAP correlation between the private subnetwork and the public subnetwork is 0.342 using the unweighted method and 0.387 using the capital-weighted method. In addition to the different connectivity patterns of leading cities, some other cities hold different positions in public and private subnetworks. Tianjin, a strategic city in which many SOEs are located, is ranked fifth in the unweighted public subnetwork and third in the capital-weighted public subnetwork. Hangzhou, as a typical city where the private sector plays an increasingly important role and that is home to Alibaba’s headquarters, occupies fourth place in both private subnetworks.

      Figure 2.  Unweighted and capital-weighted subnetworks driven by public and private sectors. a) Unweighted public subnetwork; b) Capital-weighted public subnetwork; c) Unweighted private subnetwork; and d) Capital-weighted private subnetwork

      Second, the impreciseness of existing corporate-based network approaches is exemplified by the tremendous changes to China’s urban network after the investment linkages were weighted by capital. The considerable difference between the number of inter-city linkages and the total investment volume indicates the potential problem of quantitatively simplifying real-world situations. The most evident examples are the large number of shell companies in special economic zones that are established to enjoy tax preferences without themselves having any significant assets or operations (Sharman, 2010). As previous pieces of evidence have suggested (Li et al., 2016), in comparison with private firms, SOEs set up fewer shell subsidiaries because they do not share the same impetus private companies have, for example, to maintain anonymity or to significantly reduce their tax burden. Accordingly, in comparison with private firms, the inter-city linkages initiated by SOEs show greater consistency between their numbers and investment volume. The correlation coefficient between the unweighted connectivity and the capital-weighted connectivity is 0.849 in the public subnetwork, whereas it is only 0.543 in the private subnetwork. In short, the dominant role of a few state-owned monopolies in constructing cross-regional urban linkages, under traditional methods, is often submerged in a much larger number of private enterprises.

      Interestingly, SOEs fulfill entirely different roles in eliminating regional disparity when viewed comparatively between the unweighted and capital-weighted subnetworks. In the unweighted public subnetwork, the average connectivity ratio of western, central, and eastern Chinese cities was 1.0∶1.5∶2.9, which was a much more balanced cross-regional ratio than the overall network and suggests that SOEs contribute to the balance of regional connectivity in China’s urban network (Derudder et al., 2013). However, the average connectivity ratio between three regions rose to 1.0∶1.5∶4.4 after the linkages were capital weighted, showing that a vast inequality in capital still exists. In comparison, private firms demonstrated the same average connectivity ratio of western, central, and eastern China (1.0∶1.5∶4.5). This finding can be explained by the dual responsibilities of both public policy objectives and financial objectives of SOEs. In China, SOEs are required to not only respond to and support the country’s regional balance strategy—such as the Great Western Development Strategy—but also strive to increase profits and realize the added value of state-owned assets. SOEs are also required to establish enough subsidiaries in the economically-underdeveloped western regions to serve the whole country, but the capital investment in subsidiaries in the underdeveloped western regions is often cut to focus on their big customers in the developed eastern areas.

      Third, and finally, the different spatial patterns of unweighted and capital-weighted networks in China provide, to some extent, a cautionary tale for the need to pay attention to distinguishing quantitative differences between intra-firm or inter-firm linkages. On the one hand, shell corporations registered in tax havens are much more commonly used to support the international activities of multinational corporations (MNC) (Schleimer and Pedersen, 2014). It is questionable whether the connections of these tax haven cities (e.g., Hong Kong and Singapore) are overvalued (Sigler et al., 2020). On the other hand, advantages granted to SOEs by governments lead, at least to some extent, to the economic distortions in inter-city linkages worldwide (Drucker, 1997). To be sure, the high proportion of public sectors in China’s economy is unique among the world’s leading economies (Tsui and Lau, 2002). However, it should not be the reason for abandoning the comparative study of urban networks using different methods like the capital-weighted approach. While several countries underwent large-scale privatization in the 1980s and 1990s, SOEs remain significant actors in competitive markets, both domestically and globally (Bruton et al., 2015). Furthermore, state ownership has, in several instances, expanded over the last few decades. New policy strategies for selected firms and sectors have driven state ownership, particularly in emerging economies, such as the Chinese mainland and India (Hsueh, 2011; Gupta et al., 2015). In fact, with a growing integration via trade and investment, SOEs that have traditionally been oriented toward domestic markets increasingly compete with private firms in the global marketplace (Del Bo et al., 2017). Additionally, cross-border linkages initiated by SOEs are also a combination of both financial and political objectives. One strong example is the huge investments in Africa by China’s SOEs; it is not only the promotion of economic cooperation between the two but also an expansion of Beijing’s political influence in Africa (Kragelund, 2009).

    • By focusing on a quantitative formulation of corporate-based urban network approaches, this paper clarifies the potential network invalidity caused by the simplification of the real-world linkages and why this kind of quantitatively imprecise linkages may be fatal to the analysis of China’s urban network. Using a capital investment network as an example, we elucidate how Chinese cities’ centrality values can be differently produced under different quantitative specifications. The empirical evidence presented in this article corroborates our concerns and may pave a way for future research to extend our work by optimizing existing quantitative methodologies.

      The unweighted (control) urban network, based on investment linkages, primarily reflects the same characteristics with the interlocking network results from previous scholarship. In comparison, the capital-weighted (intervention) urban network reveals many unique characteristics, which indicates the potential problems caused by the quantitative simplification of real-world linkages. To further interpret the noticeable differences, the overall network was divided into two different subnetworks based on public or private sectors, rather than different specific industries. Though the number of private enterprises outweighed the SOEs, the public sector maintains a significant edge in shaping cross-regional linkages, measured in units of capital. The public subnetwork demonstrates Beijing’s political and economic dominance as well as the higher rankings of some other cities with higher political positions. On the contrary, private enterprises highlight the multilateral interactions between eastern Chinese cities because they are free from the direct controls of the government. China’s east-west gap widens in the private subnetwork; in fact, some economically developed prefectures in eastern coastal areas surpass the rankings of some central and western provincial capitals.

      Among the increasing discussions of China’s urban network, the different roles of public and private sectors have emerged as an interesting candidate to interpret the institutional uniqueness. This study enhances our understanding of the different roles of public and private sectors and reveals some new features of China’s urban network in terms of spatial patterns, connectivity, and hierarchy. We, therefore, see our research as providing new insights into China’s urban network and a beginning for interpreting China’s regional governance from the perspective of urban networks. In terms of advancing urban network literature, this study reveals that there is much room for improvement in the pursuit of optimizing precision in analyzing urban networks. Clearly, precisely recorded inter-city linkages would improve the authenticity of the corporate-based urban networks. Further in-depth case studies of inter-city linkages in the real world are required to optimize the existing quantitative approaches in urban network analysis.

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