Evolution of the Spatial Network Structure of the Global Service Value Chain and Its Influencing Factors—An Empirical Study Based on the TERGM

Abstract

With the rapid advance of digital technologies, the service industry has become a key driver of sustainable economic growth and the restructuring of international trade. Drawing on value-added trade flows for five pivotal service industries—construction, air transportation, postal telecommunications, financial intermediation, and education—over 2013–2021, this study examines the spatial evolution of the global service value chain (GSVC). Using social network analysis combined with a Temporal Exponential Random Graph Model (TERGM), we assess the dynamics of the GSVC’ core–periphery structure and identify heterogeneous determinants shaping their spatial networks. The findings are as follows: (1) Exports across the five industries display an “East rising, West declining” pattern, with markedly heterogeneous magnitudes of change. (2) The construction industry is Europe-centered; air transportation exhibits a U.S.–China bipolar structure; postal telecommunications show the most pronounced “East rising, West declining” shift, forming four poles (United States, United Kingdom, Germany, China); financial intermediation contracts to a five-pole core (China, United States, United Kingdom, Switzerland, Germany); and education becomes increasingly multipolar. (3) The GSVC core–periphery system undergoes substantial reconfiguration, with some peripheral economies moving toward the core; the core expands in air transportation, while postal telecommunications exhibit strong regionalization. (4) Digital technology, foreign direct investment, and manufacturing structure promote network evolution, whereas income similarity may dampen it; the effects of economic freedom and labor-force size on spatial network restructuring differ significantly by industry. These results underscore the complex interplay of structural, institutional, and geographic drivers in reshaping GSVC networks and carry implications for fostering sustainable services trade, enhancing interregional connectivity, narrowing global development gaps, and advancing an inclusive digital transformation.

1. Introduction

With the deepening of digital globalization and the accelerated servicification of global trade, the service sector has become an increasingly crucial driver of economic growth, playing a pivotal role in global industrial specialization and international trade. According to data from the United Nations Conference on Trade and Development (UNCTAD), the value-added contribution of the global service sector accounted for 66.6% of global GDP in 2022. Meanwhile, statistics from the World Trade Organization (WTO) indicate that the total value of global service trade reached $15.25 trillion in 2023, reflecting an 8.8% year-on-year increase, in stark contrast to a 4.9% decline in global goods trade. While developed economies have historically played a leading role in advancing the liberalization and integration of the global service sector, the continued expansion of service trade openness has increasingly positioned services as a key engine of economic growth in developing countries. Moreover, services have become a focal point in the restructuring of international trade frameworks and economic governance mechanisms. More importantly, as the next wave of technological innovation and industrial transformation gains momentum, emerging technologies, business models, and service formats are reshaping the global service industry landscape at an unprecedented pace. This ongoing transformation is not only expanding the scope of service trade liberalization and international cooperation but also unlocking new opportunities for global economic integration within the service sector.

Driven by technological advancements and economic globalization, international industrial specialization has transcended national and regional boundaries, evolving into a globally integrated system of resource optimization and cross-border collaboration. Countries now engage in industry segments where they possess comparative advantages, thereby maximizing their industrial potential and enhancing global production efficiency. With rapid advancements in transportation and communication technologies, production processes have become increasingly fragmented, enabling various stages to be outsourced across borders to countries or regions with cost advantages and technological expertise. Against this backdrop, sociologists and economists introduced the concept of the Global Value Chain (GVC) to examine the structure of global production and value distribution [1]. Although GVC research has traditionally focused on manufacturing, the service sector has emerged as a critical component of global value chains. Beyond its expanding economic significance, services play a pivotal role in facilitating global market integration, promoting trade liberalization, and deepening international cooperation. Notably, with the rapid proliferation of information technology, service production and delivery models are undergoing digitalization, standardization, and remote transformation. This shift increasingly aligns global service trade with goods trade, allowing service “production” to be geographically dispersed, thereby accelerating the formation and expansion of the global service value chain.

The existing literature on global service value chain can be broadly divided into three parts. The first part analyzes the rise of global service trade as a result of the expansion of the service outsourcing market on the demand side. In the early stages of international service outsourcing, the focus was primarily on IT outsourcing [2,3], corresponding to the global distribution of low-end stages in the value chain. With the development of international service outsourcing, business process outsourcing (BPO) began to emerge [4,5], leading to the globalization of mid-tier stages in the value chain. Notably, the large-scale outsourcing of knowledge services [6,7,8] has facilitated the global segmentation of the entire service value chain, further enhancing resource allocation efficiency [9]. Most prior studies emphasize a “scale–outsourcing-mode” expansion path—stressing aggregate volumes and business-model evolution—while paying limited attention to how cross-national spatial network structures are reorganized. Using value-added trade to construct cross-national networks for five major service industries, and combining social network analysis (SNA) with a Temporal Exponential Random Graph Model (TERGM), we identify structural shifts in the core–periphery order and the move toward multipolarity. In doing so, we address a gap in the demand-side literature regarding the mechanisms of spatial pattern evolution. The second part of the literature analyzes how different economies join the global service division network based on their existing comparative advantages from the supply side. Arnold et al. [10], by focusing on the cases of India and the Czech Republic, demonstrated the welfare gains from service liberalization, which ranged from 2% to 7%, with developing countries experiencing greater benefits than developed countries [11,12]. Developing countries typically possess abundant low-cost labor. Countries like India and the Philippines, which have a service-driven development model, have initiated the process of human capital accumulation by improving the educational level of their workforce. This has attracted foreign investment, which in turn has increased the demand for educated labor [13,14]. By leveraging globalization, digitalization, and other technological advances, developing countries have been able to fully realize their comparative advantages. This is reflected in the reduction in service trade costs brought about by digitalization, which has enabled developing countries to increase their participation in the global service value chain [15]. Existing studies largely emphasize macro welfare outcomes or participation metrics, with limited attention to endogeneity in network formation and to structural heterogeneity. In TERGM, we jointly include node-level covariates—digital technology, FDI, manufacturing structure, economic freedom, and labor-force size—while controlling for endogenous network effects such as reciprocity, transitivity, degree distribution, and temporal dependence. Estimating the model separately by industry, we reveal cross-industry structural differences and the supply-side channels through which these factors reconfigure the spatial network. The third part examines service trade resilience by exploring the adaptation and recovery mechanisms of global service trade under external shocks. It analyzes how different economies, industries, and firms enhance the stability and sustainability of service trade through structural adjustments, innovation-driven upgrades, and network collaboration. The resilience of economies is influenced by the nature of external shocks and regional characteristics [16]. Regional cooperation has been shown to mitigate service quality deterioration, but its effectiveness in improving response speed remains limited [17]. Moreover, the impact of external shocks varies significantly across service industries [18,19]. Industries with higher levels of digitalization demonstrate greater resilience, whereas sectors that heavily rely on physical delivery are more severely impacted by external shocks [18]. Against this backdrop, advancing service sector digitalization and fostering business model innovation have emerged as critical pathways to strengthening service industry resilience. At the firm level, resilience-building is essential for the sustainable development of service trade. Market orientation, supply chain optimization, and employee innovation capacity are identified as key strategies to enhance business resilience [20,21]. By establishing multi-level resilience mechanisms [22], the global service trade system can more effectively respond to external shocks and achieve sustainable growth. Existing resilience research largely proceeds from shock effects and recovery paths, with limited dynamic testing that quantifies the resilience—structure reconfiguration nexus in cross-national networks. We operationalize “structural resilience” using indicators such as core expansion/contraction, intensified regionalization, and the emergence of multipolarity, and we examine—within a TERGM framework—the effects of digitalization, FDI, and industrial structure on network reconfiguration. This provides an integrated evidence chain from “structural evolution → determinants,” thereby addressing gaps in the literature regarding spatial-network structure and causal identification.

In essence, the global service value chain is a dynamic network ecosystem, enabled by digital transformation, where multiple stakeholders engage in collaborative innovation and adaptive resilience to transcend spatial and sectoral boundaries, facilitating value co-creation, capture, and redistribution [23]. Among the key industries, the postal and telecommunications industry plays an irreplaceable role in the evolution of the global service value chain by enhancing global data flows and driving the digital transformation of services. As a critical enabler of digital infrastructure, this industry has become increasingly essential for value creation and transmission within the global service network. The financial intermediation industry serves as the core pillar of the global service value chain by facilitating cross-border investment and industrial coordination through financing, settlement, and risk management provided by banks, securities, and insurance institutions. Given its central role as a global service network node, finance not only operates as an independent industry but also exerts a decisive influence on the functioning of other service industries. The air transport industry functions as a key facilitator of global economic connectivity. The efficient operation of cross-border business activities, high-end service industries (such as finance, consulting, and education), and global production networks heavily relies on aviation. Consequently, the air transport industry is indispensable to the global service value chain. The construction industry (The classification of the construction industry differs across statistical frameworks. According to the Asian Development Bank (ADB) industry classification, construction is categorized as a service sector under traditional international trade statistics (BOP statistics). However, in China, based on the National Economic Industry Classification (GB/T 4754-2011), construction is classified as part of the manufacturing sector. This discrepancy arises because China’s industry classification system distinguishes manufacturing and services based on physical production activities. Real Estate industry in China: Includes land development, property management, leasing, and sales, which are classified as services. Construction industry in China: As a provider of infrastructure for the real estate industry, construction is classified as manufacturing to reflect its contribution to fixed asset investment.) serves as the physical infrastructure backbone of the global service value chain, fostering the development of financial centers, technology hubs, and aviation gateways, which, in turn, shape the spatial distribution and expansion of other service industries. Meanwhile, the education industry acts as a key driver of global service value chain upgrading and knowledge spillovers. Through high-end human capital development, it directly enhances the international competitiveness of high-value-added service industries, including postal and telecommunications, finance, and aviation. The formation and expansion of the global service value chain have been primarily driven by digital connectivity (postal and telecommunications), capital flows (finance), spatial mobility (aviation), infrastructure development (construction), and human capital (education) [24]. Based on these fundamental drivers, this study selects five key industries for analysis, as their strong economic interconnectivity and spatial network evolution significantly impact the global service value chain’s overall structure and distribution. Therefore, by analyzing the spatial network evolution and key influencing factors of these five industries, this study offers valuable insights into the dynamic transformation of the global service value chain. Moreover, understanding the structural shifts within these industries can help economies enhance their competitiveness in the global service value chain, offering policy implications for sustainable service industry development.

The marginal contributions of this study are reflected in three key dimensions: In the field of research, The global service value chain is characterized by an increasingly complex and interconnected network structure [23]. However, existing network-based studies have primarily focused on value chain networks [25], supply chain networks [26], and global production networks [27]. This study extends the literature by analyzing the spatial evolution patterns of five key service industries, offering new insights into the comparative advantages of different economies. By quantifying each economy’s role within these industries, this research provides a novel perspective to help economies better understand their positioning and actively integrate into the global service value chain. Utilizing Origin software for visualization analysis, this study quantifies the share of different economies across service industries, offering theoretical support and empirical insights into the division of labor and specialization patterns within the global service value chain. From a research perspective. This study systematically analyzes the network structure evolution of five key service industries within the global service value chain from a global perspective, addressing a gap in the literature, where existing studies often focus on individual service industries in isolation [28,29]. By providing structural data and analytical support, this study enhances understanding of interconnections among economies within the global service value chain [30]. Through Gephi-based network analysis, the study explores both macro-level network characteristics and micro-level interactions between economies. These findings offer policy insights to promote global service cooperation and integration. In terms of research methodology, the technological complexity of different service industries results in significant variations in trade structure characteristics [31]. Common methodologies used to analyze trade network formation mechanisms include the Gravity Model, Quadratic Assignment Procedure (QAP) Model, and Exponential Random Graph Model (ERGM) [32,33]. However, unlike traditional static network models such as ERGM, this study employs the Temporal Exponential Random Graph Model (TERGM), which is particularly well-suited for analyzing dynamic networks [34]. By examining the spatial network evolution of five key service industries, this study applies TERGM to conduct an in-depth investigation into the factors influencing the structural evolution of the global service value chain network. These findings provide empirical evidence to support the high-quality development of global service value chain, offering a valuable supplement to existing academic research on global service value chain dynamics and transformations.

The remainder of this paper is organized as follows: Section 2 introduces the data sources and the construction of the global service value chain value-added trade network model, further explaining the network analysis methods and the factors influencing the network evolution using the TERGM. Section 3 presents the research findings, focusing on two aspects: the evolution of trade patterns and the factors influencing the formation of trade networks. The final section presents the discussion, conclusion, and policy implications.

2. Data and Methodology

2.1. Data Description

With the increasing globalization of service trade, the cross-border flow of intermediate service products has become a prevalent phenomenon. However, under traditional trade accounting frameworks based on gross trade value, the value of many service products is often attributed solely to the country or region exporting the final service product, failing to reflect the contribution of multiple economies involved in intermediate production stages. To overcome this limitation, this study employs a value-added-based trade accounting framework to trace the value-added creation process at each stage and in each participating country. The value-added trade data is sourced from the ADB-MRIO global service value chain dataset provided by the UIBE GVC Index database. The variables for TERGM analysis are primarily drawn from the World Bank database and CEPII database. Regarding the selection of the time frame, this study focuses on 2013–2021, considering two primary factors. First, data availability constraints prevent extending the dataset beyond this period. Second, 2013–2021 represents a critical phase of rapid digital economy development, making it an appropriate period for capturing the evolution and structural dynamics of the global service value chain. Within this timeframe, countries with significant data deficiencies were excluded from the analysis. As a result, the final dataset covers 52 major economies (Table S1), each playing a pivotal role in the global service value chain.

2.2. Network Construction and Analysis Methods

2.2.1. Network Construction Model

This paper constructs a directed global service value chain network using the value-added bilateral service trade data between these countries. Based on complex network theory, the network is represented as G = (V,A,E,W), where $V=\left(v_{1,}{v}_{2,}\dots ,v_n\right)$ denotes the set of nodes representing the countries; $A=\left\{a_{ij}\right\}\left(i=1,2\dots 52;j=1,2\dots 52\right)$ is the adjacency matrix for each period, indicating whether a trade relationship exists between two countries; $E=\left\{e_{ij},i=1,2\dots n;j=1,2\dots n\right\}(i\ne j)$ is the set of edges representing trade relationships between countries; and $W=\left\{w_{ij},i=1,2\dots n;j=1,2\dots n\right\}(i\ne j)$ is the set of weights for each edge connecting the two countries, representing the value-added trade volume between the exporting and importing countries.

Due to the significant variation in trade values between countries, it is necessary to apply a threshold in the data preprocessing stage to more clearly and effectively preserve the structural characteristics of the global service value chain network [35,36,37]. By examining the value-added share of world trade, a threshold of the 75th percentile is used to retain trade relationships. This threshold ensures the relative completeness of the trade network and is well representative.

2.2.2. Network Characteristic Analysis Methods

For the overall network structure analysis, social network analysis methods are primarily employed. Various indicators, such as the number of nodes, number of edges, average degree, network density, and average clustering coefficient, are used to depict the overall topological characteristics of the network from different dimensions, and to measure the scale and connectivity of the trade network. Specifically, the number of nodes represents the number of trading countries, while the number of edges refers to the number of bilateral trade relationships between nodes. The average degree indicates the average number of trade partners for each economy. Network density is the ratio of actual edges to the maximum possible edges in the network; a higher network density implies greater influence on the actors within the network. Additionally, the average clustering coefficient is the mean value of the clustering coefficients for all countries in the network. A higher value indicates stronger agglomeration effects [38,39].

Core–periphery structure analysis, In the global service value chain network based on value-added trade data, the coupling interactions among heterogeneous economies lead to a non-homogeneous relationship between economies within the network, resulting in a hierarchical structure of the global service value chain network. By analyzing the association characteristics between economies and the structural features of the network, the global service value chain network is divided into a tightly connected core and a sparsely connected periphery, which helps to understand the position of different economies within the trade network [40]. This paper uses Gephi (Gephi Consortium v0.10.1) to perform degree centrality and modularity analysis, and based on these analyses, divides the global service value chain network into its core–periphery structure.

2.3. Network Influencing Factors Analysis Methods

The Exponential Random Graph Model (ERGM) overcomes the independence assumption in traditional regression methods, allowing for the integration of different types of micro-level network configurations and estimating their impact on network formation and evolution [41]. Its greatest advantage lies in its ability to simultaneously study both endogenous and exogenous mechanisms of network formation. The general form of the ERGM is as follows [41,42]:

$$\mathrm{Pr}(Y=y\mid \theta )={\displaystyle \frac{1}{K}}\exp \left\{{\theta }_{\alpha }{g}_{\alpha }(y)+{\theta }_{\beta }{g}_{\beta }(y,X)+{\theta }_{\lambda }{g}_{\lambda }(y,Z)\right\}$$

(1)

In this model, Y_ij represents the trade relationship between economy i and economy j, and y_ij denotes the observed value of Y_ij, $\mathrm{Pr}(Y=y\mid \theta )$ represents the probability of observing y in Y under the condition θ. K is a normalizing constant, and ${\theta }_{\alpha },{\theta }_{\beta },{\theta }_{\lambda }$ is the parameter estimating the strength of the influence of each covariate. $g_{\alpha }(y)$ denotes the network statistic corresponding to the endogenous network structure, capturing the pure structural effect of network formation; $g_{\beta }(y,X)$ represents the network statistic associated with the node attribute X, testing the attribute effect generated by the network; and $g_{\lambda }(y,Z)$ denotes the network statistic corresponding to another network Z, testing the network embedding effect of network formation.

Traditional Exponential Random Graph Models (ERGM) simulate and study network relationships from a static perspective. In contrast, this study adopts the Temporal Exponential Random Graph Model (TERGM). The unique advantage of the TERGM is its consideration of the temporal dependency in network data, making it suitable for the study of dynamically observed networks [34]. The model is specified as follows [43]:

$$P\left(Y^t=y^t\mid Y^{t-K},\cdots ,Y^{t-1},\theta \right)={\displaystyle \frac{1}{C\left(\theta ,y^{t-K},\cdots ,y^{t-1}\right)}}\exp \left[{\displaystyle \sum _H{\theta }_H}g\left(y^t,y^{t-1},\cdots ,y^{t-K}\right)\right]$$

(2)

$$P\left(N^{k+1},\cdots ,N^T\mid N^1,\cdots ,N^k,\theta \right)={\displaystyle \prod _{t=k+1}^{T}P}\left(N^T\mid N^{t-K},\cdots ,N^{t-1},\theta \right)$$

(3)

In the equation: P(·) represents the probability of observing network y among all possible networks Y; C(·) is the normalizing constant, ensuring that the probability lies between 0 and 1; H is the set of variables influencing network formation and evolution, including structural endogenous effects, temporal dependence effects, attribute effects, and network embedding effects; θ_H is the coefficient vector of the observed network’s influencing factors; and g(·) represents the network statistic corresponding to H. N is the adjacency matrix, where N_ij = 1 if a relationship exists between nodes i and j, and N_ij = 0 otherwise.

To investigate the endogenous mechanisms of global service value chain network formation and dynamic evolution, this study uses one-year intervals, resulting in a longitudinal observation network covering 9 periods from 2013 to 2021. If the specific observation of the global service value chain network in year t is denoted by N^t, a K-order Markov-dependent TERGM is constructed using the discrete-time Markov chain principle [44]:

$$\begin{array}{l}\mathrm{P}\left({\mathrm{N}}^{\mathrm{t}}\mid {\theta }^{\mathrm{t}},{\mathrm{N}}^{\mathrm{t}-1}\right)=(1/\mathrm{c})\exp \left({\theta }_0 \mathrm{edges} +{\theta }_1 \mathrm{mutual} +{\theta }_2 \mathrm{gwodeg} +{\theta }_3 \mathrm{stability} +{\theta }_4 \mathrm{variability} +{\theta }_5 \mathrm{dof} +\right.\\ {\theta }_{\mathrm{r}1}\log \mathrm{dt}+{\theta }_{\mathrm{r}2}\log \mathrm{fdi}+{\theta }_{\mathrm{r}3}\mathrm{peo}+{\theta }_{\mathrm{r}4}\log \mathrm{m}+{\theta }_{\mathrm{r}5}\mathrm{lowincome}+{\theta }_{\mathrm{r}6}\mathrm{upincome}+{\theta }_{\mathrm{s}1}\log \mathrm{dt}+{\theta }_{\mathrm{s}2}\log \mathrm{fdi}+{\theta }_{\mathrm{s}3}\mathrm{peo}+{\theta }_{\mathrm{s}4}\log \mathrm{m}\\ +{\theta }_{\mathrm{s}5}\mathrm{lowincome}+{\theta }_{\mathrm{s}6}\mathrm{upincome}+\left.{\theta }_{\mathrm{s}} \mathrm{continent} +{\theta }_{\mathrm{d}}\log \mathrm{dist}+{\theta }_{\mathrm{c}} \mathrm{comlang} \right)\end{array}$$

(4)

In this model, N^t and N^t−1 represent the global service value chain networks in years t and t − 1, respectively. θ corresponds to the unknown parameters, and 1/c is the normalization constant. “edges” represents the edge variables in the global service value chain network, which corresponds to the intercept term in traditional regression models. The explanatory variables include: mutual, gwodeg, stability, variability; logdt, logfdi, logm, dof, peo, lowincome, upincome, continent; logdist and comlang serve as control variables. The subscript r of θ represents the recipient, while s represents the sender.

3. Results

3.1. Evolution of Trade Patterns in Typical Industries of the Global Service Value Chain

3.1.1. Evolution of the Spatial Pattern of Typical Industries in the Global Service Value Chain

By comprehensively analyzing the spatial pattern evolution of the five key industries within the global service value chain, this study clarifies the roles of different economies within specific service industries. This helps economies identify their competitive advantages within the global service value chain and facilitates the optimal allocation of resources, promoting more efficient industrial division and global cooperation. The analysis clearly shows that, over the past decade, export trade in the five key industries of the global service value chain has exhibited a distinct “East rising, West declining” trend, particularly with India’s significantly strengthened core position in the construction, postal telecommunications, and education industries, making it a typical representative of this trend. Overall, variations in industry functional roles, levels of digitalization, market demand structures, economic cycles, and external shocks have led to substantial differences in the magnitude of change across industries, highlighting pronounced heterogeneity (Figure 1).

The overall trade pattern in the construction industry has remained relatively stable, with Europe continuing to serve as the core region. Germany (GER), the Netherlands (NET), the United Kingdom (UKG), and Poland (POL) hold substantial market shares, forming a highly concentrated European cluster. Within this cluster, strong cooperative relationships are evident, reflecting the deep economic integration and regional collaboration within the European Union. As a core node, Germany maintains close ties with several European countries, highlighting its regional dominance in the construction industry. In contrast, the Asia-Pacific cluster was relatively weak in 2013, with only sporadic trade links between China (PRC) and Japan (JPN). However, by 2021, China had become the central node in the Asia-Pacific cluster, with a significantly increased number of international connections, demonstrating its growing participation in the global construction market. This shift may be attributed to China’s advancements in construction technology exports and international project collaborations, particularly under the Belt and Road Initiative, which has fostered closer cooperation with more countries. Additionally, by 2021, emerging markets such as India (IND) and Vietnam (VIE) saw a noticeable increase in international connections, reflecting their rising influence in the construction industry. This trend is likely tied to the growing demand for infrastructure development and increased reliance on international construction resources, marking the rise of emerging powers in the global construction industry.

The air transport industry is highly concentrated, exhibiting a distinct “The United States and China” dual structure. Compared to 2013, the air transport network in the Asia-Pacific region expanded significantly by 2021, with countries such as China, South Korea, and Singapore strengthening their air transport connections. This reflects the growing prominence of Asia-Pacific economies in the global aviation market. Notably, China’s influence in the region became more pronounced, as it established denser air links with multiple countries, signaling its rapid rise in both the Asia-Pacific and global aviation markets. The United States (USA) and European regions maintained strong clustering relationships in both 2013 and 2021, with stable bilateral and multilateral air transport connections between major European countries. It is worth noting that the United Kingdom’s market share significantly declined, dropping from the fourth-largest global position in 2013 (5.04%) to the fourteenth position in 2021 (1.77%). This change is likely linked to market adjustments following the UK’s formal departure from the European Union in 2020. However, air connections between the United States and European countries, such as the United Kingdom, Germany, and France, remained stable from 2013 to 2021, demonstrating sustained demand in the transatlantic aviation market. Despite changes in the global air transport landscape, transatlantic and transpacific routes continue to be the core of the global aviation network. This suggests that traditional routes maintain a foundational position in the global aviation market, supporting air transport demand between regions and internationally.

The spatial pattern change in the postal and telecommunications industry exhibits the most pronounced “East rising, West declining” pattern. This transformation is likely driven by both the expansion of the digital economy and e-commerce as well as changes in Western market demand and regional economic cooperation. Asia—particularly China and Southeast Asia—has rapidly strengthened its global competitiveness through technological upgrades, market expansion, and policy support. In contrast, Western economies have experienced a relative decline in competitiveness due to market saturation, shifts in demand structure, and the decline of traditional postal services. Overall, the industry’s global center of gravity has evolved into a quadrilateral structure dominated by the United States, the United Kingdom, Germany, and China. The United States remains the core node in the global postal and telecommunications network, with its connections spanning not only North America but also extending to transatlantic and transpacific communication networks, continuing to play a key bridging role in global postal telecommunications. European countries still dominate the postal telecommunications network, with strong links among the United Kingdom, Germany, France (FRA), and the Netherlands, forming a core cluster within Europe. These countries not only maintain frequent postal and telecommunications exchanges within Europe but also maintain close ties with the United States across the Atlantic. Meanwhile, the postal and telecommunications network in the Asia-Pacific region further expanded by 2021. The regional connections among countries such as China, Japan, and South Korea significantly increased, reflecting the rapid growth of communication demand within the Asia-Pacific region. Notably, India’s importance in the global postal and telecommunications network has risen significantly, moving from the 14th position (1.92%) in 2013 to the 7th position (4.66%) in 2021, becoming a core node in the Asia-Pacific region. This indicates that India is playing an increasingly important dual role in both the regional and global postal and telecommunications networks, further highlighting its rise in this industry.

Compared to other industries, the decline in trade volume within the financial intermediation industry has been particularly pronounced. This trend is likely influenced by the global financial crisis and multiple economic cycles, which have prompted countries to tighten financial regulations to mitigate systemic risks. These regulatory measures have not only constrained global financial liquidity but have also curbed cross-border capital flows, limiting the expansion of certain international financial intermediation activities. Overall, the global trade landscape of the financial intermediation industry has consolidated into a five-pillar structure centered on China, the United States, the United Kingdom, Switzerland, and Germany. Meanwhile, the market shares of certain economies have undergone significant adjustments, reflecting the dynamic evolution of the global financial network in response to changing market conditions. In 2013, the top 10 global economies accounted for 71.93% of global trade, with the top five—China, the United States, the United Kingdom, Switzerland, and Germany—accounting for 51.81%. By 2021, the share of the top 10 economies increased to 76.02%, but the share of Switzerland and Germany declined. Switzerland’s share decreased from 7.04% in 2013 to 5.52% in 2021, while Germany’s share fell from 6.61% to 4.99%. Meanwhile, the shares of China, the United States, and the United Kingdom increased, with their combined share reaching 47.92% in 2021. Asian economies’ share in global financial intermediation trade also rose from 32.30% in 2013 to 35.85%. China has maintained its leading position, with its share growing from 15.75% to 19.75%. Japan moved up from 9th place in 2013 to 5th place in 2021, while Singapore rose from 10th place (3.58%) to 7th place (3.73%). As a financial hub in Southeast Asia, Singapore’s position in both the Asia-Pacific and global financial networks has been further strengthened, continuing to serve as an important bridge between the Asian and Western financial markets. Additionally, Canada’s ranking improved, rising from 11th place in 2013 (3.25%) to 9th place in 2021 (3.36%). The shares of other countries generally showed a noticeable decline.

The education industry has shown a trend of multipolar development, gradually expanding from Europe-dominated to a more globally distributed pattern. In 2013, the top 10 countries in the global education industry accounted for 69.28% of the total market share, with European countries holding 48.65%, led by the United Kingdom, Germany, France, the Netherlands, and Switzerland. However, by 2021, the share of the top 10 education countries increased to 77.3%, but Europe’s overall share declined to 42.83%, while the shares of China, Australia, and India significantly increased, reflecting the rise of emerging economies in the global education market. At the same time, the United States also saw a significant increase in its share, reinforcing its position as a global leader in the education industry. Specifically, the United States performed exceptionally well, with its global share rising from 4th place (6.41%) in 2013 to 1st place (13.34%) in 2021, highlighting its sustained advantage in higher education and international student attraction. China also showed strong performance, moving up from 9th place (4.29%) in 2013 to 4th place (9.22%) in 2021, due to the rapid development of its high-quality education system and the deepening of international educational cooperation under the Belt and Road Initiative. Australia, similarly, improved its position from 7th place (5.12%) in 2013 to 5th place (8.86%) in 2021, further consolidating its role as a key educational hub in the Asia-Pacific region. Notably, Switzerland’s global share dropped significantly from 6th place (5.17%) in 2013 to just 0.55% in 2021, possibly due to its relatively stable education market size and intensified competition from emerging markets. Meanwhile, India’s share increased rapidly from 0.54% in 2013 to 10th place (3.05%) in 2021, reflecting its rapid growth in vocational education, information technology training, and online education, further strengthening its competitiveness in the global education market.

3.1.2. Evolution of the Network Structure of Typical Industries in the Global Service Value Chain

Through a comprehensive analysis of the network structure evolution of the five key industries in the global service value chain, this study clarifies the interrelationships between economies within the global service value chain. it will help to enhance the flexibility and resilience of the global service value chain and promote the construction of a more efficient and stable global service value chain.

• Overall network characteristics

By analyzing the network structure characteristics of the five key industries in the global service value chain from 2013 to 2021, several observations can be made: First, there is a degree of variation in the number of economies participating in the network (

Table 1. Changes in the size of global service value chain networks.

Year	Number of Economies					Average Degree
	Con	Air	Pos	Fin	Edu	Con	Air	Pos	Fin	Edu
2013	49	46	47	46	44	13.796	14.696	14.383	14.696	15.364
2014	49	46	48	47	44	13.796	14.696	14.083	14.383	15.364
2015	49	47	48	47	47	13.796	14.383	14.083	14.383	14.383
2016	49	47	50	47	44	13.796	14.383	13.52	14.383	15.364
2017	49	47	49	48	44	13.796	14.383	13.796	14.083	15.364
2018	48	49	46	48	46	14.083	13.796	14.696	14.083	14.696
2019	49	49	47	46	48	13.796	13.796	14.383	14.696	14.083
2020	48	50	47	48	49	14.083	13.52	14.383	14.083	13.796
2021	48	48	48	48	47	14.083	14.083	14.083	14.083	14.383

Note: Con indicates that the construction industry, Air indicates the air transport industry, Pos indicates postal telecommunications industry, Fin indicates financial intermediation industry, Edu indicates the education industry.

). The number of nodes in the construction industry network remained relatively stable, ranging from 48 to 49. In contrast, the air transport and financial intermediation networks showed a growth trend, both increasing from 46 nodes in 2013 to 48 nodes in 2021. The postal telecommunications network experienced more fluctuation, rising slightly from 47 nodes in 2013 to 49 nodes in 2017, but declining back to 48 nodes by 2021. The education industry network started with 44 nodes in 2013, increased to 47 nodes in 2015, and has remained relatively stable, increasing thereafter to 47 in 2021. Second, the number of global value-added trade relationships remained generally stable. All five industries consistently exhibited 676 edges in their networks. This indicates that while the spatial distribution of nodes in the global service value chain has changed, the overall number of trade connections has not undergone significant alteration. This phenomenon may reflect that, against the backdrop of rapid advancements in digital technology, the evolution of the global service value chain is more evident in the depth and quality of trade relationships rather than in a simple increase in the number of nodes or edges. This suggests that international cooperation and value chain integration in the service sector are progressing toward higher levels of sophistication.

In terms of network density changes (

Table 2. Global service value chain network density and average clustering coefficient.

Year	Network Density					Average Cluster Coefficient
	Con	Air	Pos	Fin	Edu	Con	Air	Pos	Fin	Edu
2013	0.287	0.327	0.313	0.327	0.357	0.715	0.686	0.772	0.744	0.686
2014	0.287	0.327	0.300	0.313	0.357	0.722	0.660	0.729	0.721	0.691
2015	0.287	0.313	0.300	0.313	0.313	0.697	0.647	0.731	0.737	0.674
2016	0.287	0.313	0.276	0.313	0.357	0.706	0.647	0.700	0.722	0.725
2017	0.287	0.313	0.287	0.300	0.357	0.724	0.646	0.718	0.711	0.734
2018	0.300	0.287	0.327	0.300	0.327	0.709	0.695	0.780	0.721	0.744
2019	0.287	0.287	0.313	0.327	0.300	0.687	0.650	0.754	0.740	0.709
2020	0.300	0.276	0.313	0.300	0.287	0.730	0.636	0.731	0.731	0.708
2021	0.300	0.300	0.300	0.300	0.313	0.733	0.666	0.712	0.752	0.700

), while there have been some fluctuations in the value-added trade network density of the five key industries in the global service value chain, the overall variation has been relatively small. With the exception of the construction industry, which showed an upward trend in network density, all other industries exhibited a downward trend. Specifically, the network density in the construction industry increased slightly from 0.287 in 2013 to 0.300 in 2021. The network density of the postal and telecommunications industry fluctuated significantly: it decreased from 0.313 in 2013 to 0.276 in 2016, experienced a slight rebound in 2017–2018, and then declined again to 0.300 in 2019–2021. The network density in the financial intermediation industry remained relatively stable, mostly staying between 0.300 and 0.327. The air transport and education industries, which were more significantly affected by the COVID-19 pandemic, exhibited greater fluctuations. The network density of the air transport industry decreased steadily from 0.327 in 2013 to a low of 0.276 in 2020, before rebounding slightly to 0.300 in 2021. The network density of the education industry dropped to its lowest value of 0.287 in 2020, while it frequently reached its highest level between 2013 and 2017. Given that the global service value chain network size dynamically evolves over time, the average degree metric was further used to describe the sparsity of the network (Table 1). In terms of numerical values, the education industry had a higher average degree index than the other industries, but the changes in the construction and financial intermediation industries were notably smaller, indicating that trade connections between economies in these industries are becoming more stable and closely interconnected. Regarding the average clustering coefficient (Table 2), although there were some fluctuations during the sample period, the overall changes were minimal. The construction, financial, and education industries showed an upward trend, while the air transport and postal telecommunications industries exhibited a downward trend. Overall, the average clustering coefficient remained around 0.7, indicating a significant clustering effect in the global service value chain network, reflecting the increasingly close trade cooperation between economies within the global service value chain.

2.

“Core–periphery” structural characteristics

This study divides economies into “core and periphery” layers, with Figure 2 illustrating the evolution of the “core–periphery” structure in the value-added trade networks of the five key industries in the global service value chain. The results indicate that the global service value chain’s value-added trade network exhibits a distinct “core–periphery” hierarchical structure, with the majority of economies situated in the periphery. Between 2013 and 2021, the “core–periphery” system of global service trade underwent significant changes, with some peripheral economies gradually advancing toward the core, exerting pressure on and challenging the position of certain core economies. At the same time, there was also notable iteration and restructuring within the core itself, reflecting dynamic evolutionary characteristics.

The core circle of the construction industry network is relatively large, with Germany, China, the United States, the United Kingdom, the Netherlands, Belgium, and Italy consistently remaining within the core circle from 2013 to 2021. Notably, India, with its rapid economic growth and infrastructure development, managed to transition from the periphery to the core circle. Meanwhile, Japan, Poland, and France were pushed out of the core circle due to their declining relative influence in the global construction industry. This may be attributed to intensifying overseas competition, constrained financing capacity, and rising labor costs. At the same time, the rapid rise of China and other emerging economies in the construction industry has accelerated the restructuring of the global construction market landscape. The core circle of the aviation transport industry network shows a trend of expansion. The United States, China, and France maintained stable positions as core economies between 2013 and 2021. Germany and Japan, through continuous strengthening of their international air transport networks, successfully moved from the periphery to the core. However, the United Kingdom’s core position was challenged, and due to a decline in market share and reduced competitiveness of international routes, it dropped to the periphery by 2021.The core circle of the postal telecommunications network exhibits regional characteristics, with European and Asian economies dominating both in 2013 and 2021. However, during the evolution, Russia, due to a decline in its competitive position, fell from the core circle to the periphery. This decline is closely linked to the economic sanctions imposed by Western countries following the 2014 Crimea crisis, which significantly constrained Russia’s international cooperation and market expansion in the postal and telecommunications industry. On the other hand, India and the Netherlands showed significant improvement in cross-border postal telecommunications services, successfully transitioning from the periphery to the core circle. The core circle of the financial intermediary industry noticeably shrank during this period, from 9 members in 2013 to 5 members in 2021. The United States, China, Germany, the United Kingdom, and France maintained their core positions due to stable financial systems and strong influence in global capital markets. Conversely, Italy, the Netherlands, Switzerland, and Japan have shifted from the core to the periphery, possibly due to the implementation of the 2013 Basel III Accord, which raised capital adequacy ratio requirements. This regulatory change may have weakened their competitiveness in the process of financial globalization, limiting their ability to maintain a dominant position in the global financial network. This change reflects the intensifying competition within the global financial intermediary network and the trend of resources concentrating in fewer but more influential core economies. The core circle of the education industry network also saw a notable change, shrinking from 10 members in 2013 to 7 members in 2021. Germany, the United Kingdom, France, the United States, China, and the Netherlands retained their core positions. India, with its rapid growth in international education demand, successfully entered the core circle. However, a relative decline in their international education cooperation capacity led to Italy, Australia, Belgium, and Switzerland falling from the core to the periphery. This change reflects the increasing competition within the international education services network and the concentration of resources in a few countries with strong attraction and educational resource advantages.

3.2. Analysis of Factors Affecting the Evolution of the Spatial Network Structure of Global Service Value Chain

Generally speaking, the formation of network relationships is influenced by various social processes, incorporating both endogenous and exogenous mechanisms, each of which can affect the evolution of network structures [41]. This paper employs the TERGM to further explore the factors that influence the evolution of the spatial network structure of global service value chain. The main factors correspond to endogenous structural variables of economies, exogenous attribute variables, and relational variables between economies. The factors considered in constructing the TERGM are shown in

Table 3. Statistical variables of the TERGM.

Categories	Variables	Variable Meaning	Description and Data Sources
Exogenous node attribute covariates	Nodecov (logdt)	Countries with stronger attributes (level of digital technology, economic freedom, foreign direct investment, size of labour force and structure of manufacturing sector) have more expansive trade networks	Using the digital technology section of the TIMG2023 report prepared by the Institute of Finance, Chinese Academy of Social Sciences, reported in logarithmic form.
	Nodecov (dof)		Adoption of the Indicators of Global Economic Freedom report issued by the Heritage Foundation of the United States of America
	Nodecov (logfdi)		Expressed in logarithmic terms using the stock of foreign direct investment (World Bank database).
	Nodecov (peo)		Measured using services employment as a percentage of total employment as estimated by the International Labour Organization model.
	Nodecov (logm)		Measured using industrial value added as a share of GDP (World Bank database)
	Nodematch (continent)	Whether countries belonging to the same continent are more likely to have trade relations.	Whether belonging to the same continent (CEPII database)
Endogenous network structural variables	edges	The effect of network density on the formation of network relationships is similar to the intercept term in the regression model.	Network Graphic Variables
	mutual	Whether economies in the network favour reciprocal trade.
	gwodeg	Trends in the distribution of export services of economies in the network
Exogenous network covariates	Edgecov (distcap)	The effect of other network relationships (distance, language) on trade network relationships.	Geographical distance expressed as the actual distance between national (regional) capitals (CEPII database)
	Edgecov (comlang_off)		If two economies share a common official language, the value is 1; otherwise, it is 0 (CEPII database).
Time-dependent variables	stability	It reflects whether the dependency relationship connection status at time t remains unchanged at time t + 1.
	variability	To examine whether trade dependency relationships change over time, specifically in terms of the disappearance or emergence of dependencies.

.

3.2.1. Endogenous Structural Variables

The endogenous hierarchical structure characteristics of trade networks play a crucial role in the formation and evolution of the overall trade network [45]. To this end, this paper introduces endogenous structural variables to observe the overall and local features of the network and their dynamic evolution patterns. These mainly include edge, reciprocity, and expansiveness. Specifically, reciprocity (mutual) reflects whether economies and their trade partners have a preference for establishing mutually beneficial trade relationships; expansiveness (gwodeg) depicts the changing distribution trends of a country’s export service trade relationships. However, introducing triangular structural variables into the TERGM may lead to model non-convergence [40]. Therefore, based on relevant studies, this paper selects edge, reciprocity, and expansiveness as endogenous structural variables for analysis.

3.2.2. Exogenous Node Attribute Variables

The global service value chain network consists of numerous economies, and the differences in the attributes of these economies drive them to make distinct choices within the network, thus fostering the formation of complex relational networks. Research has shown that various factors, such as digital technology level, economic freedom, capital investment, and market size, significantly influence different types of trade networks [46,47,48,49,50]. Specifically, the level of digital technology enhances market competitiveness and is a key factor in influencing international trade; economic freedom forms an essential foundation for international trade; labor force size, to some extent, reflects labor costs, which have a crucial impact on the development of the service sector, further influencing trade structures. In addition, foreign direct investment (FDI) growth has driven the construction of the global service value chain network, while the optimization of manufacturing sector structures has further facilitated the stratification and evolution of service value chain. Therefore, this paper selects digital technology level, economic freedom, FDI, labor force size, and manufacturing sector structure as specific node attribute variables. Based on the previous analysis, we observe that global service trade exhibits distinct regional characteristics. As a result, this paper further introduces an attribute variable based on the continent to which each economy belongs in order to analyze the convergence characteristics of the network structure.

3.2.3. Exogenous Network Variables

According to the embeddedness theory, economic activities are embedded within complex socio-cultural systems, and multi-dimensional proximity mechanisms have garnered significant attention in the process of network formation [51,52], with evidence showing their significant impact on international trade. Proximity here refers to the broader concept of closeness, encompassing various forms such as institutional proximity, organizational proximity, linguistic proximity, and geographical proximity. Due to trade costs, geographical distance often acts as an obstacle to trade development. The geographical distance network objectively determines the transportation costs between economies in the global service value chain network and is a crucial factor affecting trade volume and convenience. At the same time, regions with linguistic and cultural similarities typically share similar values and consumption concepts, which help strengthen trade ties and cooperation. Therefore, this paper takes an “embeddedness” perspective from the exogenous network and focuses on a detailed analysis of the geographical distance network and the common language network.

3.2.4. Time-Dependent Variables

Like all things, networks evolve over time. In the case of the global service value chain network, the interdependencies between economies are continuously changing, and the formation and evolution of these relationships exhibit path dependence characteristics. This network shows both a trend of stable development and the possibility of variation. Stability refers to the tendency of the network to maintain its overall structure over time; a network is considered stable if the probability of connections between economies remains relatively constant, and the network relationships in the current period are influenced by the network from the previous period. Variation, on the other hand, refers to the randomness or unpredictability in the network’s evolution, indicating whether the network relationships between economies in the current period will increase or decrease. Consistent with the earlier conclusions drawn from the comparative analysis of the global service value chain network’s visualization, both stability and variation jointly drive the dynamic evolution of the network.

3.2.5. Estimation Results of the TERGM

Based on the value-added trade data of the five major service industries from 2013 to 2021, this study employs the TERGM to estimate and fit the influencing factors of the evolution of the global service value chain’s spatial network structure. The empirical results are presented in

Table 4. TERGM estimation results.

Variable	Model 1	Model 2	Model 3	Model 4	Model 5
edges	−15.19 ***	−21.89 ***	−25.38 ***	−27.95 ***	−23.45 ***
	(1.77)	(1.67)	(1.84)	(2.27)	(1.80)
nodeicov.logdt	2.41 **	3.45 ***	1.75 *	0.57	2.12 **
	(0.75)	(0.64)	(0.75)	(0.88)	(0.72)
nodeocov.logdt	2.62 ***	4.19 ***	4.75 ***	4.72 ***	2.50 ***
	(0.73)	(0.65)	(0.74)	(0.88)	(0.70)
nodecov.dof	−0.12	−0.31 ***	−0.09	−0.26 *	−0.23 **
	(0.10)	(0.08)	(0.09)	(0.11)	(0.09)
nodeicov.logfdi	0.41 *	0.51 ***	0.51 **	0.64 ***	0.40 *
	(0.16)	(0.13)	(0.16)	(0.18)	(0.15)
nodeocov.logfdi	0.22	0.49 ***	0.63 ***	1.90 ***	1.13 ***
	(0.15)	(0.13)	(0.15)	(0.17)	(0.14)
nodeicov.peo	−0.43	−0.94	−0.41	0.01	0.55
	(0.69)	(0.57)	(0.63)	(0.77)	(0.62)
nodeocov.peo	−2.85 ***	−1.07	−2.45 ***	−0.83	−1.09
	(0.67)	(0.59)	(0.65)	(0.76)	(0.58)
nodeicov.logm	1.52 ***	1.15 ***	1.61 ***	1.65 ***	1.57 ***
	(0.19)	(0.15)	(0.18)	(0.20)	(0.18)
nodeocov.logm	0.81 ***	0.74 ***	1.00 ***	0.39 *	0.73 ***
	(0.20)	(0.16)	(0.19)	(0.18)	(0.16)
nodeifactor.income lower middle income	0.83 **	0.57 *	0.69 *	0.67 *	1.19 ***
	(0.30)	(0.23)	(0.27)	(0.31)	(0.24)
nodeifactor.income Upper-middle income	0.49 **	−0.27	0.35 *	−0.02	0.06
	(0.19)	(0.15)	(0.17)	(0.20)	(0.18)
nodeofactor.income lower middle income	−0.84 **	−0.50 *	0.27	0.82 *	0.05
	(0.29)	(0.24)	(0.26)	(0.32)	(0.25)
nodeofactor.income Upper-middle income	−0.77 ***	0.03	−0.56 **	−0.13	−0.90 ***
	(0.19)	(0.15)	(0.18)	(0.20)	(0.18)
nodematch.income	0.05	−0.00	−0.01	−0.01	−0.26 *
	(0.13)	(0.10)	(0.12)	(0.14)	(0.13)
nodematch.continent	−0.04	0.40 **	0.38 *	0.68 ***	0.55 ***
	(0.15)	(0.13)	(0.15)	(0.18)	(0.15)
edgecov.comlang_off	0.43 *	0.06	0.32	0.24	0.21
	(0.20)	(0.16)	(0.18)	(0.22)	(0.17)
edgecov.logdistcap	−1.63 ***	−0.43 **	−1.06 ***	−0.67 ***	−0.50 **
	(0.18)	(0.15)	(0.17)	(0.20)	(0.17)
mutual	0.53 ***	0.48 ***	1.16 ***	0.83 ***	0.65 ***
	(0.12)	(0.10)	(0.11)	(0.14)	(0.11)
gwodeg.fixed.0.1	−2.19 ***	−2.00 ***	−1.22 **	−0.59	−1.26 ***
	(0.35)	(0.32)	(0.38)	(0.35)	(0.32)
edgecov. stability	2.70 ***	2.31 ***	2.43 ***	2.73 ***	2.44 ***
	(0.05)	(0.04)	(0.04)	(0.05)	(0.04)
edgecov. variability	−0.07 ***	−0.09 ***	−0.09 ***	−0.13 ***	−0.10 ***
	(0.02)	(0.02)	(0.02)	(0.02)	(0.02)

*** p < 0.001; ** p < 0.01; * p < 0.05; ( ) is a standard robust error.

. Specifically, Model 1 represents the construction industry, Model 2 represents the air transport industry, Model 3 represents the postal telecommunications industry, Model 4 represents the financial intermediation industry, and Model 5 represents the education industry.

In terms of endogenous network structural variables, the edge coefficient shows a significant negative effect on the global service value chain network. This indicates that the value-added trade network in the global service value chain is not random, supporting the earlier analysis of the characteristics of the value-added trade network. The coefficient of reciprocity is positive and significant, suggesting that when economy i exports service products to economy j, economy j is also inclined to export service products to economy i, highlighting the positive impact of reciprocity on the formation of relationships within the global service value chain network. The coefficient for expansiveness is significantly negative, with the exception of the financial intermediation industry, where the coefficient is not significant. This implies that there is no phenomenon in the global service value chain network where a few countries dominate a large portion of export service trade relationships. This result may stem from advances in digital technology, which have weakened the distance decay effect between global economies and enhanced spatial proximity effects, thereby promoting a more balanced and diversified distribution of service trade worldwide.

In terms of node attribute covariates, the level of digital technology shows a significant sending effect with a positive coefficient, indicating that a higher level of digital technology facilitates the export of global services. At the same time, the level of digital technology also exhibits a significant receiving effect with a positive coefficient, suggesting that it promotes the import of global services. However, the receiving effect of digital technology on the financial intermediation industry is not significant, possibly due to the industry’s strong localization characteristics, which rely more on local markets and customer relationship networks. Foreign direct investment (FDI) displays significant sending and receiving effects, with a positive coefficient, indicating that economies with higher levels of FDI are more likely to establish both import and export trade relationships in global services. FDI typically accompanies capital inflows and outflows, promoting the deep integration of multinational corporations with local markets, which in turn strengthens economic ties. This connection not only enhances export capabilities but also stimulates the growth of import demand. The manufacturing sector’s structure shows a significant sending effect with a positive coefficient, suggesting that economies with a larger share of manufacturing are more inclined to export services. This is mainly because such economies possess strong industrial production capacities, with a more prominent ability to servitization of manufacturing, which reflects comparative advantage in service exports. At the same time, the manufacturing sector structure also exhibits a receiving effect with a significantly positive coefficient, indicating that economies with a larger share of manufacturing are more likely to establish more service import relationships. This phenomenon can be attributed to the deepening of global supply chains and the increasing specialization of labor. Manufacturing economies often need to collaborate with international service providers to optimize production efficiency, reduce costs, and enhance product quality, leading to a stronger tendency to import specialized services in order to maintain competitiveness in global markets. In particular, lower-middle-income economies exhibit more pronounced receiving effects, while upper-middle-income economies show more significant sending effects. The coefficients for the construction, postal telecommunications, and education industries are significantly negative, possibly because these industries have already matured in upper-middle-income economies, meaning there is limited growth potential within the industries, which hinders the formation and evolution of the global service value chain. The effects of economic freedom, labor force size, and regional affiliation on the global service value chain network show heterogeneity. In terms of economic freedom, the coefficients for the air transport, financial intermediation, and education industries are negative and pass the significance tests, while the coefficients for the construction and postal telecommunications industries are negative but do not pass the significance tests. This is related to the share of countries in these industries, indicating a “The strong get stronger” phenomenon in the global service value chain network. The labor force size has a significant impact on the global service value chain network only in the construction and postal telecommunications industries. This may be because larger labor forces imply that production and service provision rely more on manual labor rather than technological innovation or efficiency improvements, which in turn limits the competitiveness and expansion ability of these industries in the global service value chain. The coefficient for regional affiliation is positive and significant, indicating that economies belonging to the same continent are more likely to choose trade partners within the same continent.

In terms of exogenous network covariates, the coefficient for geographic distance is significantly negative, indicating that geographic distance suppresses the formation of service trade relationships. This suggests that transportation costs remain a crucial factor affecting the global service value chain network. The coefficient for linguistic proximity is positive, but only the coefficient for the construction industry is significant. This may be because international markets typically communicate in dominant languages (such as English), thereby diminishing the importance of linguistic proximity. In the construction industry, the significance of linguistic proximity reflects the industry’s high reliance on language and culture, whereas in other industries, factors such as international standards, technical regulations, and institutional dependencies have led to linguistic proximity not showing the same level of significance.

In terms of temporal dependence covariates, the stability coefficient is significantly positive, indicating that the global service value chain network exhibits a certain degree of stability. This suggests that existing value-added trade relationships remain stable over time. The variability coefficient is significantly negative, indicating that, while trade cooperation relationships generally remain stable, their significance gradually declines, and some trade relationships may even disappear over time. This phenomenon may be linked to the global economic downturn and the adoption of trade protectionist policies by various economies.

3.2.6. Robustness Test

To verify the robustness of the TERGM estimation results, this study substitutes the Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC MLE) method with the Maximum Pseudo-Likelihood Estimation (MPLE) method. The empirical analysis results are shown in

Table 5. TERGM robustness test results.

Variable	Model 6	Model 7	Model 8	Model 9	Model 10
edges	−15.16 *	−22.64 *	−26.00 *	−28.59 *	−23.52 *
	[−21.71; −8.01]	[−29.09; −18.07]	[−34.24; −20.05]	[−35.30; −23.31]	[−30.26; −19.42]
nodeicov.logdt	2.50 *	3.75 *	1.84	0.76	2.24
	[0.00; 4.87]	[1.49; 5.57]	[−0.02; 3.80]	[−1.70; 3.53]	[−0.03; 4.25]
nodeocov.logdt	2.58 *	4.68 *	4.84 *	4.81 *	2.48 *
	[0.06; 4.49]	[2.81; 7.43]	[2.47; 7.14]	[2.17; 7.29]	[1.51; 3.83]
nodecov.dof	−0.15 *	−0.33 *	−0.09	−0.27	−0.23
	[−0.26; −0.03]	[−0.60; −0.02]	[−0.29; 0.06]	[−0.61; 0.03]	[−0.58; 0.19]
nodeicov.logfdi	0.44 *	0.59 *	0.54 *	0.71 *	0.40
	[0.20; 0.60]	[0.35; 0.91]	[0.17; 0.92]	[0.17; 1.20]	[−0.20; 0.91]
nodeocov.logfdi	0.30	0.47 *	0.65 *	1.93 *	1.13 *
	[−0.09; 0.65]	[0.22; 0.78]	[0.22; 1.00]	[1.60; 2.31]	[0.71; 1.47]
nodeicov.peo	−0.46	−1.14	−0.41	−0.05	0.50
	[−1.54; 0.67]	[−2.15; 0.03]	[−1.45; 0.69]	[−1.39; 1.53]	[−1.04; 2.57]
nodeocov.peo	−2.95 *	−1.32	−2.47 *	−0.88	−1.06
	[−4.18; −1.44]	[−2.32; 0.04]	[−3.44; −1.68]	[−2.10; 0.40]	[−2.50; 0.45]
nodeicov.logm	1.54 *	1.17 *	1.64 *	1.64 *	1.58 *
	[1.14; 1.98]	[0.95; 1.54]	[1.16; 2.19]	[1.32; 1.98]	[1.24; 2.27]
nodeocov.logm	0.76 *	0.72 *	1.05 *	0.40 *	0.71 *
	[0.52; 1.18]	[0.33; 1.20]	[0.61; 1.60]	[0.08; 0.76]	[0.29; 1.13]
nodeifactor.income lower middle income	0.83 *	0.54 *	0.72 *	0.69	1.21 *
	[0.38; 1.24]	[0.09; 1.08]	[0.15; 1.06]	[−0.15; 1.75]	[0.38; 2.26]
nodeifactor.income Upper-middle income	0.48 *	−0.29	0.35	−0.03	0.06
	[0.12; 0.85]	[−0.60; 0.03]	[−0.25; 0.73]	[−0.62; 0.57]	[−0.46; 0.63]
nodeofactor.income lower middle income	−0.89 *	−0.58	0.26	0.80 *	0.06
	[−1.63; −0.35]	[−1.67; 0.56]	[−0.32; 0.76]	[0.14; 1.65]	[−0.90; 1.26]
nodeofactor.income Upper-middle income	−0.78 *	0.01	−0.53 *	−0.12	−0.86 *
	[−1.07; −0.54]	[−0.53; 0.62]	[−0.90; −0.18]	[−0.75; 0.52]	[−1.48; −0.17]
nodematch.income	0.07	−0.02	0.00	−0.00	−0.25 *
	[−0.24; 0.36]	[−0.15; 0.11]	[−0.24; 0.25]	[−0.36; 0.32]	[−0.42; 0.02]
nodematch.continent	−0.00	0.40 *	0.38 *	0.70 *	0.55 *
	[−0.19; 0.22]	[0.07; 0.83]	[0.19; 0.59]	[0.55; 0.94]	[0.26; 0.92]
edgecov.comlang_off	0.46 *	0.08	0.37 *	0.26	0.20
	[0.15; 0.84]	[−0.14; 0.27]	[0.15; 0.66]	[−0.25; 0.64]	[−0.12; 0.46]
edgecov.logdistcap	−1.63 *	−0.50	−1.12 *	−0.69 *	−0.50 *
	[−2.17; −1.14]	[−1.05; 0.00]	[−1.53; −0.81]	[−1.14; −0.20]	[−0.75; −0.26]
mutual	0.54 *	0.37 *	1.05 *	0.72 *	0.61 *
	[0.26; 0.74]	[0.11; 0.63]	[0.84; 1.27]	[0.42; 1.03]	[0.34; 0.94]
gwodeg.fixed.0.1	−2.34 *	−2.77 *	−1.31 *	−0.64 *	−1.91 *
	[−3.18; −1.52]	[−4.23; −1.17]	[−2.49; −0.15]	[−1.00; −0.31]	[−2.89; −1.01]
edgecov. stability	2.69 *	2.32 *	2.42 *	2.73 *	2.45 *
	[2.49; 2.92]	[1.96; 2.81]	[1.99; 2.87]	[2.51; 3.01]	[2.06; 2.91]
edgecov. variability	−0.07 *	−0.07 *	−0.10 *	−0.14 *	−0.10 *
	[−0.13; −0.03]	[−0.12; −0.04]	[−0.15; −0.06]	[−0.21; −0.09]	[−0.17; −0.04]

*** p < 0.001; ** p < 0.01; * p < 0.05; [ ] denotes the confidence interval of the estimated parameters.

. By comparing the model estimation results before and after the change in estimation method, it can be observed that, with the exception of the sign of the Postal telecommunications industry’s coefficient in the income matching variable, the coefficient signs in the MPLE results are consistent with those in the MCMC MLE estimation results. This suggests that the empirical findings of the TERGM are robust.

To further verify robustness, the following three steps are implemented: (1) Report backbone sensitivity by re-estimating the network at the 70% and 80% percentile thresholds and using the difference and hypergeometric filters, and present the effects on the TERGM coefficients. we reconstructed the backbone network at the 70% and 80% percentile thresholds and additionally reported the baseline 75% threshold. We also re-estimated the network using both the difference and hypergeometric filters, recalculated centrality measures, and re-estimated the TERGM. The main findings (see Supplementary Materials Tables S2–S6) are as follows: across alternative backbone constructions, the signs and economic interpretations of the key coefficients are consistent, and the main conclusions remain unchanged. Within the 70–80% percentile range, coefficient estimates and statistical significance are most stable (the 75% threshold closely matches the results at the two endpoints). Under the difference/hypergeometric filters, the network becomes sparser and information more conservative; as expected, standard errors increase and significance weakens, but coefficient directions are unchanged, and the conclusions are unaffected. Overall, our results are robust to the choice of backbone extraction: the percentile-threshold approach (70%/75%/80%) and the difference/hypergeometric filters align in direction and economic meaning, with the primary difference being the attenuation of significance under stricter sparsification. For ease of review, we present side-by-side comparisons in the Supplementary Materials. (2) Clarify and test temporal dependence by incorporating tests for K > 1 (higher-order Markov dependence) and lagged covariates, and by comparing stability and volatility effects across specifications. In the main text, we adopt a TERGM with first-order Markov dependence as the baseline specification. We estimate three models sequentially: M0 (including one-period lags of dyadic covariates), M1 (adding one-period lags of node attributes to M0), and M2 (further adding two-period lags of dyadic covariates to M1). The principal results (Supplementary Materials Tables S7–S11) show broadly consistent coefficients and standard errors across specifications, with three exceptions: (i) the coefficient on logdt turns from positive to negative; (ii) the coefficient on logm increases slightly with model order; and (iii) the coefficients and standard errors for peo and its one-period lag are larger. Given the high within-sample correlation between peo and its lag, this pattern indicates a risk of multicollinearity. Overall, changes in model order have limited impact on our conclusions. To balance parsimony and robustness, we adopt K = 1 as the main specification and relegate higher-order results to the Supplementary Materials as robustness checks. (3) We introduce the interaction between digital technology and distance (digdist). To mitigate potential multicollinearity, models that include this interaction omit the separate main-effect terms for digital technology and distance. In view of the notion that digitalization relaxes geographic and income constraints in cross-border trade, we further replace gwodeg with gwesp to test the robustness of the transitivity specification. The main results (Supplementary Materials Tables S12–S16) are as follows: coefficient signs and significance levels are broadly consistent across specifications; the only exception arises in finance, where peo displays a significant sign opposite to the other settings under the difference-filter specification. Overall, the coefficient on digdist is negative and statistically significant, indicating a steeper distance decay—i.e., greater digitalization strengthens the distance penalty, shifting the network toward short-range/intra-regional ties (heightened regionalization and relatively muted long-distance links). Building on this, we estimate three specifications: M0 (including one-period lags of dyadic covariates), M1 (M0 plus one-period lags of nodal covariates), and M2 (M1 plus two-period lags of dyadic covariates). We primarily report results at the 75th-percentile threshold (Supplementary Materials Tables S17–S21); results for alternative percentiles and filtering schemes are available upon request. The main findings are as follows: overall, M0 exhibits stronger statistical significance, whereas in M1 and M2 the nodal covariates and their one-period lags are less significant than in M0. These patterns further support our use of a first-order Markov TERGM as the main specification.

3.2.7. Goodness-of-Fit Test

To assess the validity and suitability of the TERGM for the observed network, this study examines whether the observed network deviates significantly from the distribution implied by the model. We simulated 5000 networks using the fitted model to generate the distribution intervals of network features, which are presented using grey box line diagram. Four typical statistics—Outdegree, Dyad-wise shared partners, Edge-wise shared partners, and Geodesic distances—were selected as measurement indicators. The fitting results are shown in Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7. Overall, the model fitting meets expectations and demonstrates good performance.

4. Discussion, Conclusions, and Policy Implications

4.1. Discussion

Among the five major industries analyzed, the heterogeneous impact of income compatibility on different sectors of the global service value chain is particularly noteworthy. Conventionally, a higher degree of income compatibility is expected to foster trade development [53,54]. However, our findings suggest that greater income compatibility may, paradoxically, hinder the spatial network evolution of the global service value chain. One possible explanation is that high-income compatibility reduces market complementarity, thereby dampening incentives for technology transfer and innovation, weakening the role of international specialization, and potentially leading to fragmentation within the global value chain. This fragmentation, in turn, restricts the expansion of the global service value chain network. Conversely, service trade between economies with larger income disparities appears more likely to drive global service integration and upgrading through complementarity, technology transfer, and cooperative specialization. The development of lower-middle-income countries, facilitated by trade with high-income economies, can further accelerate the structural evolution of the global service value chain.

This study examines value-added trade flows within the global service value chain network, providing an initial exploration of the spatial network structure’s evolution and its key influencing factors. However, several areas warrant further investigation. First, this research primarily analyzes international service trade using value-added trade data, with a focus on the period up to 2021 due to data availability constraints. Future studies should extend the analysis beyond this timeframe to capture the post-pandemic restructuring of the global service value chain and its long-term spatial dynamics. Second, while the global service value chain spans multiple industries, this study focuses on representative sectors such as financial intermediation and postal telecommunications. Expanding the analysis to a broader set of service industries could provide a more comprehensive understanding of the evolving structure of global service trade networks. Finally, multinational enterprises play a pivotal role in shaping global service trade, and their strategic decisions significantly influence the spatial network structure of the service value chain. Future research should integrate firm-level value chain analysis to better capture the micro-level mechanisms driving the evolution of the global service value chain network.

4.2. Conclusions

This study examines the evolution of the spatial distribution of value-added trade across five key industries—construction, air transportation, postal telecommunications, financial intermediation, and education—within the global service value chain from 2013 to 2021. By doing so, it identifies the competitive advantages of different economies and their positioning within global service trade networks. Additionally, this study explores the roles and structural positions of various economies across these service industries and investigates the key factors shaping the spatial network structure of the global service value chain. Based on these analyses, the following conclusions can be drawn:

The export trade across the five key industries within the global service value chain exhibits a clear “East rising, West declining” trend. Notably, India has significantly strengthened its central position in the construction, postal telecommunications, and education industries, making it a representative example of this shift. Overall, variations in industry functional roles, levels of digitalization, market demand structures, economic cycles, and external shocks have led to substantial differences in the magnitude of change across industries, highlighting pronounced heterogeneity.

The overall trade pattern in the construction industry has remained relatively stable, with Europe maintaining its position as the core region. The air transport industry exhibits a high degree of concentration, forming a distinct bipolar structure dominated by the United States and China. Among all industries, the postal telecommunications sector has undergone the most pronounced transformation, reflecting an “East rising, West declining” trend. The industry’s focal points are now distributed in a quadripartite pattern, centered around the United States, the United Kingdom, Germany, and China. Meanwhile, trade flows in the financial intermediation industry have declined considerably, with its network now characterized by a five-point structure encompassing China, the United States, the United Kingdom, Switzerland, and Germany. Lastly, the education industry has exhibited a multipolar expansion, shifting from a traditionally Europe-dominated structure to a more diversified regional distribution.

Between 2013 and 2021, the “core–periphery” structure of the global service value chain network underwent significant transformations. Some peripheral economies have challenged and displaced the core positions of certain economies while gradually integrating into the core circle. Specifically: Construction Industry: The core network remains relatively broad, with Germany, China, the United States, the United Kingdom, the Netherlands, Belgium, and Italy consistently occupying central positions. Air Transport Industry: The core network has expanded, with the United States, China, and France maintaining stable core positions throughout the period. Meanwhile, Germany and Japan have successfully transitioned from the periphery to the core, driven by the continuous strengthening of their international air transport networks. Postal Telecommunications Industry: The core network exhibits distinct regional characteristics, with European and Asian economies dominating in both 2013 and 2021. Financial Intermediation Industry: The core circle has notably contracted, with the United States, China, Germany, the United Kingdom, and France retaining their core positions due to their stable financial systems and strong influence in global capital markets. Education Industry: The core network has experienced the most substantial changes; however, Germany, the United Kingdom, France, the United States, China, and the Netherlands have maintained stable core positions throughout the period. These findings highlight the dynamic nature of the global service value chain, with evolving regional dominance and shifting core–periphery relationships across industries.

The formation of value-added trade networks across various industries within the global service value chain is shaped by four key factors: network self-organization, exogenous endowment attributes, exogenous network embedding, and temporal dependence. Trade in different service industries exhibits strong mutual dependence and expansionary effects, with intra-continental trade relationships being more prevalent. Several structural and institutional factors influence service trade patterns: Digital technology advancement, foreign direct investment, and the composition of manufacturing sectors play crucial roles in facilitating trade across service industries. The impact of economic freedom and labor force size varies significantly across industries, reflecting sector-specific sensitivities to institutional and demographic conditions. Geographical distance exerts a significant negative effect on trade relationships, whereas a shared language positively enhances trade connectivity. These findings highlight the complex interplay between structural, institutional, and geographic factors in shaping the evolution of value-added trade networks within the global service value chain.

4.3. Policy Implications

Drawing on the analysis of the spatial network evolution of the global service value chain and its determinants from 2013 to 2021, this study presents the following targeted policy recommendations aimed at optimizing the spatial structure of the global service value chain and enhancing the competitive positioning of economies within the global service network.

Enhancing Interregional Connectivity and Optimizing the Global Service Trade Landscape: Developed economies should expand their presence in emerging markets, particularly in high-value-added service industries such as postal telecommunications, finance, and education, to mitigate the risk of market share erosion resulting from trade contraction. Simultaneously, emerging economies should deepen high-end service trade cooperation with developed economies, fostering cross-regional industrial chain integration to prevent market fragmentation and strengthen global market connectivity. To advance service sector liberalization, economies should actively leverage free trade agreements (FTAs), bilateral investment treaties (BITs), and multilateral cooperation frameworks (e.g., RCEP, CPTPP) to streamline market entry for multinational service enterprises into emerging economies. Furthermore, service enterprises should be encouraged to accelerate their global expansion through foreign direct investment (FDI), cross-border mergers and acquisitions (M&As), and strategic joint ventures, fostering deeper international collaboration and enhancing the resilience of the global service value chain.

Supporting High-Growth Industries to Strengthen National Service Sector Competitiveness:

Governments should accelerate the development of digital infrastructure and advance comprehensive digital transformation to eliminate barriers between physical spaces (construction industry), cloud space (air transport industry), and virtual networks (postal and telecommunications industry). By fostering cross-industry intelligent integration, economies can establish a more cohesive and efficient global service network, thereby enhancing the international competitiveness of their service industries. Moreover, deepening the liberalization of financial services and facilitating cross-border capital flows will drive synergies across service industries. To adapt to the evolving global financial landscape, policymakers should reinforce cross-regional financial regulatory cooperation, enhancing the resilience and inclusiveness of financial systems. This approach not only ensures financial stability but also optimizes global financial resource allocation, thereby supporting the continuous upgrading of the global service value chain.

Fostering Synergistic Development Between Core and Peripheral Economies to Accelerate Regional Integration into the Global Core Network: A three-dimensional strategy—“Institutional Interface Innovation–Technology-Driven Iteration–Spatial Node Restructuring”—should be implemented to enhance the integration of core and peripheral economies within the global service value chain. To facilitate greater alignment in core–periphery service trade, a “gradient compliance mechanism” should be established to ensure differentiated compatibility in service industry technical standards and data flow regulations. This will reduce institutional friction and enhance the adaptability and feasibility of cross-border cooperation. Core economies should develop an AI-powered dynamic assessment system, utilizing machine learning algorithms to identify high-potential service industries in peripheral economies, evaluate their competitive positioning within the global service value chain, and provide targeted technological support and industry collaboration strategies. Peripheral economies, in turn, should establish “modular digital service hubs” to optimize industrial structures, enhance absorptive capacity for external resources, technology, and capital, and facilitate adaptive alignment and iterative upgrading of digital service technologies and workforce development. Ultimately, this approach will drive the inclusive restructuring of the global service value chain, supporting the progressive integration of regional economies into the global core network.

Leveraging Digital Technologies to Optimize Talent Allocation in the Global Service Value Chain: The strategic application of digital technologies is crucial for enhancing global talent allocation and improving cross-border coordination efficiency within the service value chain network. To this end, economies should collaborate with multilateral institutions, such as the United Nations Development Programme (UNDP), to establish a global talent supply-demand intelligent matching platform. By integrating big data and artificial intelligence, this platform would optimize cross-border talent allocation, facilitating precise and efficient talent-business matching on a global scale. Additionally, a regional talent mobility framework should be developed to streamline the migration of highly skilled professionals in the service sector. Key initiatives include optimizing global high-skilled talent visa systems, facilitating mutual recognition agreements between core and peripheral economies, and reducing bureaucratic barriers by simplifying visa approval processes. These measures will significantly enhance cross-border mobility for highly skilled professionals, fostering a more fluid and dynamic service talent network. Furthermore, online education platforms and remote vocational training systems should be leveraged to promote international skill enhancement programs, equipping peripheral economies with advanced digital competencies and market adaptability. Strengthening workforce technological capabilities will enable these economies to better integrate into the core network of the global service value chain, thereby facilitating the optimization and upgrading of the global service industry structure.