Modeling the Synergistic Integration of Financial Geographic and Virtual Agglomerations: A Systems Perspective

Abstract

Digital technologies have transformed the spatial organization of finance. As a result, geographic and virtual agglomerations co-exist. In this paper, we model the synergistic integration of geographic and virtual agglomerations within China’s financial industry from a systems perspective. Using provincial panel data from 2011 to 2023, we develop an entropy-weighted coupling coordination model to measure the interaction between the two agglomerations. Furthermore, we employ spatial and convergence analyses to reveal their evolutionary characteristics. Our findings reveal three key results. First, financial geographic agglomeration shows an overall increasing trend, with regional levels ranked as follows: eastern region, northeastern region, western region, and central region. It exhibits significant positive spatial correlation and convergence characteristics. Second, financial virtual agglomeration also continues to strengthen, with regional levels ranked as eastern, central, western, and northeastern regions. Its convergence patterns display regional heterogeneity, and no significant spatial correlation is observed. Third, the coupling coordination degree between the two agglomerations has steadily improved nationwide and across all four major regions with convergent trends. By 2023, the eastern region has entered a stage of primary coordination, while the central, western, and northeastern regions remain in a near-dysfunctional state. In terms of driving patterns, most provinces are primarily driven by geographic agglomeration. Hunan, Hainan, and Guizhou are driven by virtual agglomeration, whereas Beijing, Anhui, Shandong, Guangdong, and Yunnan demonstrate a synchronized pattern driven by both agglomeration types. Overall, our findings highlight the systemic nature of financial agglomeration in the digital economy and enrich the theoretical understanding of financial dual-agglomeration synergy. They provide an analytical framework and empirical evidence for designing differentiated regional financial development policies.

1. Introduction

The digital transformation of industry is a global phenomenon, fundamentally reconfiguring traditional models of agglomeration. Internationally, the rise in platform-based ecosystems and virtual clusters demonstrates a shift towards dematerialized and networked forms of industrial organization [1,2]. In strategic alignment with this trend, the Chinese government explicitly proposes the establishment of virtual industrial parks and clusters that transcend physical boundaries, aiming to promote the virtualization, phantomization, and networked collaboration of industrial resources [3,4]. This strategic convergence of a global paradigm and national policy provides a critical lens for analyzing the profound organizational transformation within the financial sector, where fintech and platform models are reshaping its fundamental structure [5].

Against this backdrop, the financial industry has evolved into a new form characterized by the synergistic integration of geographic and virtual agglomeration [6]. On the one hand, this form inherits the advantages of geographical proximity, enabling economies of scale and reductions in transaction costs. On the other hand, it relies on digital interconnectivity to overcome spatial constraints, facilitating remote collaboration and the cross-regional optimization of financial resources. As an inevitable outcome of digital technological iteration and market structural evolution, the synergistic integration of financial geographic and virtual agglomeration represents not only a critical theoretical lens for understanding organizational innovation in the financial industry under the digital economy, but also a key determinant of the sector’s service efficiency, which directly influences the quality of economic growth. Therefore, it is of great theoretical and practical significance to scientifically define the conceptual connotations of this synergistic integration, measure its coordination level, and reveal its spatio-temporal evolutionary characteristics. For simplicity, the synergistic integration of financial geographic and virtual agglomeration is hereafter referred to as financial dual agglomeration synergy.

Current studies on the evolutionary mechanisms of financial dual agglomeration synergy can be broadly divided into two categories. The first stream focuses on the evolutionary patterns of financial geographic agglomeration and has formed a relatively mature analytical framework from multiple perspectives [7,8]. The second category of research primarily focuses on the evolution and development of virtual agglomeration and its applications across various industries [9,10]. However, two main research gaps remain. First, systematic studies specifically targeting the financial dual agglomeration synergy are still scarce. Second, the quantitative measurement and evolutionary dynamics of financial dual agglomeration synergy remain largely exploratory. In response, this study takes the perspective of financial dual agglomeration synergy to clarify its conceptual framework, construct an evaluation index system, and measure the level of synergy across provincial regions in China. Furthermore, it explores its evolutionary characteristics and regional disparities and proposes corresponding policy recommendations.

The contributions of this study are threefold. First, it establishes a systems-based conceptual framework that defines the synergistic integration of financial geographic and virtual agglomerations as an interacting dual system. It positions the financial industry as a coupled system composed of physical and digital subsystems. It provides a new analytical lens for understanding complex financial spatial structures. Second, this study conducts empirical analysis of system evolution and systematically examine how the two subsystems—geographic and virtual agglomeration—develop, interact, and converge across different regions. This analysis uncovers heterogeneous temporal and spatial dynamics that conventional single-dimensional studies cannot capture. Third, it develops a quantitative evaluation and modeling framework based on entropy weighting and coupling coordination methods. It measures the strength and balance of interaction between the two agglomeration subsystems. Overall, this research enriches the systems-oriented understanding of financial agglomeration and provides an operational model for analyzing coupled economic systems.

2. Literature Review and Theoretical Connotation

2.1. Literature Review

2.1.1. Research Framework on Financial Geographic Agglomeration

The evolutionary patterns of financial geographic agglomeration have been examined from multiple perspectives in the existing literature. From the perspective of industrial economics, scholars emphasize efficiency improvement as the core mechanism, explaining that the internal driving force of financial geographic agglomeration lies in the formation of external economies of scale and the reduction in transaction costs [11]. From the perspective of financial geography, geographical, socio-cultural, and informational factors are incorporated into an integrated analytical framework, highlighting information asymmetry as a key cause of financial agglomeration [12].

Chinese scholars, drawing on domestic financial practices, have further expanded the analytical dimensions of financial geographic agglomeration. Drawing on evolutionary and institutional economic geography, Zhao et al. [8] analyzed the agglomeration process and evolutionary mechanisms of the financial industry within a specific spatial context, with a case study of the financial industrial cluster in Zhengzhou, a central city in inland China. Yue et al. [7] empirically investigated the relationship between financial geographic structure and innovation quality, and further examined the moderating role of economic policy uncertainty in this association. Xie et al. [13] examined the impact of financial agglomeration on the ratio of domestic value added in exports to gross exports (DVAR) of firms. Zhang et al. [14] analyzed the relationship between financial geographic structure and corporate financialization. Although the existing studies have established a multi-perspective analytical framework for understanding financial geographic agglomeration, they have paid insufficient attention to the transformation of financial industry agglomeration patterns induced by digital technology. Consequently, they have not adequately explained the adaptive adjustments and functional transformations of financial geographic agglomeration in the digital economy era.

2.1.2. Evolution of Virtual Agglomeration Research

Virtual agglomeration, as a novel spatial organizational form in the digital economy era, traces its theoretical origins to the late 20th century. In 1997, an EU research team first proposed the concept of virtual industrial agglomeration [15]. With the deepening of the information technology revolution, early international studies focused on how information technology reshapes agglomeration patterns. Brown and Lockett [16] argued that Internet platforms provide a vehicle for firms’ digital interconnections, giving rise to virtual agglomeration as a new spatial organizational form.

Research in China has followed a systematic trajectory from theoretical construction to quantitative application. During the theoretical framework development stage, Chen et al. [9] identified the causal factors of virtual agglomeration in the creative industries and based on this analysis, constructed a driving force model to explain its formation. Zhang et al. [10] investigated the characteristics of virtual agglomeration through an analysis of China’s manufacturing sector and uncovered the inter-industrial connections and network structures facilitated by digital platforms by applying social network analysis.

In the quantitative application stage, Deng et al. [17] examined the synergistic development between digitalization and manufacturing through a dual analytical framework integrating geographical and virtual agglomeration, and analyzed its spatiotemporal evolutionary patterns. Yang et al. [18] employed the entropy method to measure the level of regional virtual agglomeration and examined the impact of digital transformation on corporate sustainable development among Chinese listed companies, as well as the moderating role of regional virtual agglomeration.

Overall, research on virtual agglomeration has evolved from initial explorations of technology enablement to a multidimensional system encompassing conceptual definition, measurement methods, and industry applications, thereby providing a multidisciplinary perspective for understanding the evolutionary patterns of virtual agglomeration in the digital economy era.

2.1.3. Theoretical Origins of the Synergistic Integration of Financial Dual Agglomeration

The deep integration of digital technology and the financial industry has given rise to financial virtual agglomeration, characterized by network-based and platform-based operations. This new form of agglomeration exerts a systematic impact on economic and social development, reshaping industrial boundaries, organizational forms, and everyday practices.

At the financial industry level, financial virtual agglomeration (a new form enabled by digital technology) has driven a fundamental restructuring of the internal architecture of finance. Hendrikse et al. [19] and Lai et al. [20] note that fintech not only challenges traditional international financial centers but also reshapes their development trajectories. This shows that financial virtual agglomeration is altering the allocation pattern of financial resources across the globe. At the level of industrial convergence, virtual agglomeration promotes deeper integration between finance and the real economy. As Tsai and Peng [21] illustrate, Foxconn’s provision of financial guarantees and loan services via e-commerce platforms demonstrates how virtual agglomeration reshapes inter firm networks and power relations. Moreover, financial virtual agglomeration is deeply embedded in daily practices, not only shaping new financial behaviors and habits [22] but also enabling socio-cultural factors such as national sentiment to trigger cross-regional financial synchronization through digital networks [23]. Thus, financial virtual agglomeration has become a significant force driving the transformation of socio-economic structures.

Against this backdrop, the financial industry has evolved into a new “dual agglomeration” form, where geographic agglomeration and virtual agglomeration coexist. Notably, financial virtual agglomeration does not simply replace financial geographic agglomeration. Lin and Viswanathan [24] show that even in Internet-based financial scenarios, the diversity and complexity of financial services still lead many to prefer conducting transactions within a close geographic proximity. Therefore, the relationship between financial virtual and geographic agglomerations tends to be synergistic. Hence, systematically analyzing the synergistic mechanisms of financial dual agglomeration represents not only an important extension of financial geography theory, but also a key theoretical entry point for understanding the operations of financial systems in the digital age and the sources of regional financial competitiveness.

However, the existing studies exhibit certain limitations. First, in terms of research focus, most work concentrates on the creative industries [9] or manufacturing sectors [10,18], while the synergistic mechanisms of financial dual agglomeration remain unclear. Second, regarding empirical measurement, the quantitative assessment of the synergistic effects between the two agglomerations is still exploratory. This research gap hinders a comprehensive understanding of financial industry agglomeration patterns in the digital era.

To address these gaps and advance empirical research, this paper introduces a coupling coordination degree model to analyze the synergistic level between financial geographic and virtual agglomerations. This model has been widely applied in studies on industrial linkages, regional economic synergy, and related fields, to effectively quantify the coordinated development degree among two or more subsystems. For example, prior research has employed this model to measure the coupling coordination between digital finance and common prosperity [25], as well as between green finance and renewable energy industries [26], providing methodological reference for its application to the study of financial dual agglomeration. This paper treats financial geographic and virtual agglomerations as a composite system. By constructing a rigorous indicator system and a coupling coordination degree model, it quantitatively reveals the synergistic degree and evolution characteristics of the two. Thus, it offers a novel research perspective and empirical evidence for understanding financial industry agglomeration in the digital age.

2.2. Financial Dual Agglomeration: Theory and Measurement

2.2.1. Theoretical Connotations of Financial Dual Agglomeration Synergy

Financial geographic agglomeration refers to the spatio-temporal dynamic process in which financial resources are coordinated, allocated, and combined with regional conditions, thereby promoting the growth of the financial industry and forming a dense system within a specific geographic space [27]. Its essence lies in the geographic clustering of financial institutions, capital, talent, and other key elements. Through geographic proximity, it reduces information asymmetry, transaction costs, and regulatory costs, thereby establishing a financial ecosystem.

Lai et al. [20] examines the role of financial technology (FinTech) and digital platforms in reshaping financial geographies and propose the conceptual model of the “FinTech Cube”. This model consists of three dimensions—financial products, technology, and key actors—and highlights their interactions within digital platforms to generate financial solutions. Representative platforms such as Alipay illustrate this mechanism by integrating financial products, technologies, and diverse participants. This achieves a systematic clustering of financial activities in digital space. Building on this, the paper introduces the concept of financial virtual agglomeration, defined as a dynamic process that relies on digital platforms, digital technologies, and data networks to enable the clustered allocation of key elements such as capital and data within virtual space. Its core mechanism lies in digital connectivity, which breaks geographical constraints to facilitate remote integration of financial resources and the cross-regional provision of financial services.

It is important to clarify that financial virtual agglomeration differs fundamentally from earlier forms of financial “virtualization”. The latter, exemplified by online banking, primarily represents the migration of offline operations to online channels. It constitutes a technological adaptation of existing financial services. In contrast, financial virtual agglomeration signals a structural transformation of the financial ecosystem. It is a shift toward a new organizational form centered on digital platforms [20,28]. Under this emerging structure, digital platforms can transcend geographical boundaries, coordinate complex transactions, facilitate data flows, and organize multi-sided market interactions [20]. In this way, it is profoundly reshaping the spatial logic and organizational patterns of financial activities.

On this basis, the paper further proposes the synergistic integration of financial dual agglomeration. This refers to a systemic framework in which financial geographic and virtual agglomerations interact and cooperate within a digital technological architecture. Through the dynamic coupling of physical elements (e.g., financial institutions, professional talent) and data elements (e.g., data assets, algorithmic models), this framework gives rise to a novel organizational form that merges the physical and virtual dimensions. This process is driven by institutional innovation, facilitated by spatial structural reconstruction, guided by the shared flow of elements, and oriented toward functional coordination and complementarity. Ultimately, Pareto improvements in the efficiency of financial resource allocation can be achieved.

The core characteristics of financial dual agglomeration synergy include the following:

(1)

Institutional Innovation Synergy. Based on the theory of institutional complementarity, different institutional arrangements can form systemic synergy through functional complementarities, generating mutual support and reinforcing effects [29]. Accordingly, institutional innovation synergy can be deconstructed as follows: financial geographic agglomeration provides the foundation for the effective implementation of institution (example, financial institution entry rules, prudential regulatory frameworks), thereby establishing a stable operational framework for financial activities [30]; financial virtual agglomeration, on the other hand, offers a practical environment for the innovation of digital rules (e.g., data flow standards, algorithmic governance norms), driving the expansion of institutional boundaries [31,32]. The two dimensions interact through a dynamic complementary mechanism of “anchoring the foundation, breaking boundaries,” jointly constructing an institutional innovation system that spans both geographic and digital spaces. This complementarity reduces institutional friction costs, stimulates institutional innovation, and ultimately optimizes the efficiency of financial resource allocation. A typical example is the joint issuance by the China Banking and Insurance Regulatory Commission and the Shanghai Municipal Government in June 2025 of the Action Plan to Support the Construction of Shanghai as an International Financial Center. The plan exhibits a clear dual-layered synergy: the first article, “Promoting the Clustering of Financial Institutions”, strengthens the anchoring function of institution; the third article, “Expanding Institutional Openness”, highlights the breakthrough effect of digital rule innovation. This institutional paradigm provides a systematic solution that balances stability and innovation for financial development in the digital economy era.

(2)

Spatial Structure Reconstruction. Based on the research of Wójcik and Macdonald-Korth [33] on the agglomeration of British financial resources toward national financial centers, spatial structure reconstruction can be deconstructed as follows: credit anchors established through localized institutional networks, including formal rules and social trust networks, form the foundation for the formation and maintenance of financial geographic agglomeration. The deep application of digital technologies, in turn, drives financial virtual agglomeration, breaking the constraints of traditional geographic boundaries. The two dimensions evolve synergistically, forming a core–periphery network topology.

In the context of national-level strategic layouts, the core geographic agglomeration areas (example, Shanghai, Beijing) serve a dual function: acting both as hubs of physical element aggregation and as key nodes in the virtual agglomeration network. Through the integration model of geographic-space physical carriers + digital-space virtual scenarios, technologies such as blockchain and API interfaces enable the digital representation and efficient transmission of financial resources. Consequently, core regions can establish close digital connections with hub nodes in central and western regions (example, Chengdu, Chongqing, Guizhou). This spatial structure not only maintains the scale and scope economies of financial geographic agglomeration but also extends the reach of financial services through technological spillovers and radiation effects from virtual agglomeration. This is consistent with the dual agglomeration integration framework for digital industries proposed by Zhao and Zhang [34], ultimately constructing a hierarchical, wide-reaching system for the coordinated allocation of financial resources.

(3)

Element Flow and Sharing. Based on the research of Zhao and Zhang [34] on how dual agglomeration in digital industries promotes cross-temporal and cross-spatial sharing of physical and digital elements, element flow and sharing can be deconstructed as follows: leveraging digital technologies, it drives the bidirectional transformation and cross-enablement of physical elements (e.g., financial institutions, talent) and digital elements (e.g., data assets, algorithmic resources), thereby enhancing the efficiency of financial resource allocation. An example of the transformation from physical to digital elements is the codification of tacit knowledge and experience in the physical domain. For instance, risk control experience in traditional financial institutions can be modeled algorithmically to establish platform rules, realizing the effectiveness of physical elements in digital space. Conversely, the transformation from digital to physical elements occurs when digital tools optimize decision-making and operational processes in physical institutions. For example, digital credit scoring models based on big data can be deeply integrated into the credit decision-making processes of financial institutions, creating feedback effect from digital elements to the real economy. It is noteworthy that this bidirectional transformation does not occur in isolation but operates through deep coupling to form a cross-enablement mechanism. By reducing information asymmetry and risk identification costs, this mechanism ultimately improves the precision of financial resource allocation.

(4)

Functional Coordination and Complementarity. Drawing on industrial agglomeration theory and digital economy theory, financial geographic agglomeration and financial virtual agglomeration jointly construct a risk-control and governance framework through functional complementarity, thereby strengthening financial security and enhancing resource allocation efficiency. In financial geographic agglomeration, localized social networks and geographic proximity facilitate repeated interactions and the formation of reputation mechanisms among financial institutions, effectively mitigating information asymmetry and its associated problems such as adverse selection and moral hazards. In financial virtual agglomeration, digital risk-control systems dynamically identify and manage information asymmetry and related risks from a technological perspective. The synergistic effect of these two dimensions provides a composite risk governance foundation for the financial system. Furthermore, by leveraging digital platforms and algorithmic optimization capabilities built within financial virtual agglomeration, financial institutions can achieve efficient cross-domain allocation of financial resources and risk diversification, significantly enhancing the efficiency of financial resource allocation. This functional complementarity mechanism contributes to a dynamic balance between financial security and allocation efficiency.

2.2.2. Construction of the Evaluation Indicator System

The evaluation indicator system for the synergistic integration of financial dual agglomeration constructed in this study is presented in

Table 1. The evaluation index system of financial dual agglomeration synergy.

Dimension	Indicator	Indicator Calculation or Description	Unit	Attribute
Financial Geographic Agglomeration	Financial Industry Location Entropy	$LQ=(E_{it}/P_{it})/(E/P)$	-	Positive
	Financial Institution Density	Number of financial institutions in the province/provincial population	Institutions per 100 million	Positive
Financial Virtual Agglomeration	Level of Digital Financial Development	Peking University Digital Inclusive Finance Index	-	Positive
	FinTech Enterprise Density	Number of FinTech enterprises in the province/provincial population	Enterprises per 100 million people	Positive

. The underlying logic lies in capturing the essential attributes of the two types of agglomeration. Indicators are selected from a dual perspective of core characteristics and spatial carriers, thereby enabling a scientific and systematic measurement.

Indicator Selection for Financial Geographic Agglomeration

The selection of indicators for financial geographic agglomeration closely aligns with the core characteristics of geographic agglomeration and the spatial attributes of physical carrier support.

Drawing on Fracasso and Vittucci Marzetti [35], this indicator is selected to represent the core characteristic of geographic agglomeration in a province’s financial industry. The calculation formula is shown in Table 1, where $LQ$ denotes the financial industry location entropy, $E_{it}$ represents the financial industry’s added value of province $i$ in year $t$, $P_{it}$ denotes the population of province $i$ in year $t$, $E$ refers to the national financial industry’s added value in year $t$, and $P$ denotes the national population in year $t$.

The core logic is as follows: when the location entropy $LQ>1$, it indicates that the level of financial geographic agglomeration in the province exceeds the national average, thereby intuitively reflecting the concentration of financial resources within the geographic space.

Financial Institution Density. Financial institutions (bank branches, securities firms) constitute the core physical carriers of financial geographic agglomeration, and their spatial distribution density directly reflects the accessibility of financial services within a geographic space. The calculation formula is presented in Table 1. Essentially, this metric measures the scale of offline financial service nodes per unit of population. The underlying logic is as follows: a higher financial institution density indicates a more sufficient provision of face-to-face financial services within a province, reflecting the strength of geographically anchored financial service supply.

Indicator Selection for Financial Virtual Agglomeration

The selection of indicators for financial virtual agglomeration closely aligns with the core characteristics of virtual agglomeration and the spatial attributes of technological carrier support.

Digital Financial Development Level. Drawing on Wei et al. [36], this indicator is used to capture the core characteristic of virtual agglomeration within a province’s financial industry, measuring three dimensions: coverage breadth (e.g., the penetration rate of mobile financial accounts), usage depth (e.g., the scale of online lending), degree of digitization (e.g., the proportion of mobile payment transactions in terms of both number and transaction volume) [37]. This indicator evaluates the scope and efficiency of financial activities conducted via virtual carriers (e.g., the Internet and mobile terminals), directly reflecting the breadth and depth of financial virtual agglomeration.

FinTech Enterprise Density. FinTech enterprises constitute the core technological carriers of financial virtual agglomeration, and their spatial distribution density directly reflects the technological support capacity of financial virtual agglomeration. The calculation formula is presented in Table 1. Essentially, this metric measures the scale of virtual financial service providers per unit of population. The underlying logic is as follows: a higher density of FinTech enterprises indicates a greater concentration of technological providers supporting the digital financial infrastructure within a province, which in turn facilitates the development of a more sophisticated virtual financial service network.

In summary, the proposed indicator system scientifically measures the two forms of agglomeration by distinguishing between geographic and virtual spaces, as well as physical and technological carriers. This provides a reliable quantitative foundation for analyzing the evolutionary characteristics of financial dual agglomeration synergy.

3. Materials and Methods

3.1. Entropy Method

To avoid subjectivity in the process of assigning weights to indicators, this study adopts an objective weighting approach, the entropy method. The entropy method determines the weight of each indicator based on the amount of information it contains and its degree of variation. Following the approach of Wei et al. [38], the entropy method is employed to assign weights to the indicators representing financial geographic agglomeration and financial virtual agglomeration.

The calculation of indicator weights follows Equations (1)–(5), while the computation of the Financial Geographic Agglomeration Index and Financial Virtual Agglomeration Index is based on Equation (6).

Step 1: Data Standardization. To eliminate the effects of differing measurement units across indicators, all indicators are standardized prior to analysis.

$$\mathrm{Positive} \mathrm{indicators}: b_{ijt}={\displaystyle \frac{a_{ijt-\underset{1\le t\le T}{\min }\underset{1\le i\le m}{\min }\left(a_{ijt}\right)}}{\underset{1\le t\le T}{\max }\underset{1\le i\le m}{\max }\left(a_{ijt}\right)-\underset{1\le t\le T}{\min }\underset{1\le i\le m}{\min }\left(a_{ijt}\right)}}$$

(1)

$$\mathrm{Negative} \mathrm{indicators}:{ b}_{ijt}={\displaystyle \frac{\underset{1\le t\le T}{\max }\underset{1\le i\le m}{\max }\left(a_{ijt}\right)-a_{ijt}}{\underset{1\le t\le T}{\max }\underset{1\le i\le m}{\max }\left(a_{ijt}\right)-\underset{1\le t\le T}{\min }\underset{1\le i\le m}{\min }(a_{ijt})}}$$

(2)

where $i=\mathrm{1,2},\dots ,m$, $m$ denotes the number of provinces; $j=\mathrm{1,2},\dots ,n$, $n$ denotes the number of indicators, $a_{ijt}$ is the original value of indicator $j$ for province $i$ in year $t$; $\mathrm{m}\mathrm{a}\mathrm{x}\left(a_{ijt}\right)$ and $\mathrm{m}\mathrm{i}\mathrm{n}\left(a_{ijt}\right)$ represent the maximum and minimum values of indicator $j$ across all provinces and years, respectively; $b_{ijt}$ is the standardized value of $a_{ijt}$ after normalization.

Step 2: Calculation of Information Entropy

$$e_j=-k{\sum }_{t=1}^T({\displaystyle \frac{b_{jt}}{{\sum }_{t=1}^T{b}_{jt}}}ln{\displaystyle \frac{b_{jt}}{{\sum }_{t=1}^T{b}_{jt}}}), k=[1/lnT]$$

(3)

Step 3: Calculation of Redundancy Degree

$$g_j=1-e_j$$

(4)

Step 4: Determination of Indicator Weights

$$w_j=g_j/{\sum }_{j=1}^n{g}_j$$

(5)

Step 5: Calculation of Financial Geographic Agglomeration ${FG}_{it}$ and Financial Virtual Agglomeration ${FV}_{it}$,

$${FG}_{it}\left({FV}_{it}\right)=\sum _{j=1}^n{w}_j{b}_{ijt}$$

(6)

3.2. Coupling Coordination Degree Model

The coupling coordination degree model is employed to measure the synergistic integration of the financial dual agglomerations. Originally derived from physics, the concept of coupling refers to the degree of interdependence and interaction between systems. In the context of economics, it describes the extent to which different subsystems interact and evolve in a coordinated manner. In this study, financial geographic agglomeration and financial virtual agglomeration are regarded as two distinct subsystems. The coupling coordination degree between them is then calculated using Equations (7)–(9).

Step 1: Coupling Degree

$$C_{it}={\displaystyle \frac{2\times ({FG}_{it}\times {FV}_{it}{)}^{1/2}}{{FG}_{it}+{FV}_{it}}}$$

(7)

where $C_{it}$ represents the coupling degree between the two subsystems, financial geographic agglomeration and financial virtual agglomeration, of province $i$ in year $t$. A smaller value of $C_{it}$ indicates that the two systems tend to evolve in a more disordered and uncoordinated manner.

Step 2: Comprehensive Coordination Index

$$R_{it}=l_1{FG}_{it}+l_2{FV}_{it}$$

(8)

where $R_{it}$ denotes the comprehensive coordination index of financial geographic agglomeration and financial virtual agglomeration for province $i$ in year $t$. $l_1$ and $l_2$ are coefficients reflecting the relative importance of the two subsystems. In this study, financial geographic agglomeration and financial virtual agglomeration are considered equally important across provinces; therefore, $l_1=l_2=0.5$.

Step 3: Coupling Coordination Degree

$$D_{it}={(C_{it}\times R_{it})}^{1/2}$$

(9)

where $D_{it}$ represents the coupling coordination degree of financial geographic agglomeration and financial virtual agglomeration for province $i$ in year $t$, that is, the level of synergistic integration of the financial dual agglomerations. Its value ranges from 0 to 1.

3.3. Coefficient of Variation

To measure the convergence characteristics of the Financial Geographic Agglomeration Index, Financial Virtual Agglomeration Index, the synergistic integration level of financial dual agglomerations, this study employs the coefficient of variation ($CV$) for σ-convergence testing. The $CV$ allows for the observation of temporal trends in variation across provinces, thereby assessing whether inter-provincial differences exhibit convergence. It is calculated as follows:

$${CV}_{it}={\displaystyle \frac{{\sigma }_{it}}{\overline{x_{it}}}}={\displaystyle \frac{\sqrt{\frac{1}{m}{\sum _{i=1}^m(x_{it}-\overline{x_{it}})}^2}}{\overline{x_{it}}}}$$

(10)

where $x_{it}$ represents the value of the Financial Geographic Agglomeration Index, Financial Virtual Agglomeration Index, or the synergistic integration level of financial dual agglomerations for province $i$ in year $t$; $m$ denotes the number of provinces; $\overline{x_{it}}$ is the mean value of $x_{it}$; ${\sigma }_{it}$ is the corresponding standard deviation; and ${CV}_{it}$ represents the coefficient of variation.

3.4. Kernel Density Estimation

This study employs the kernel density estimation ($KDE$) method to analyze the distribution patterns of financial geographic agglomeration and financial virtual agglomeration. The calculation formula is as follows:

$$f\left(x\right)={\displaystyle \frac{1}{mh}}\sum _{i=1}^{m}K({\displaystyle \frac{\overline{x}-x_i}{h}})$$

(11)

where $x_i$ represents the Financial Geographic Agglomeration Index or Financial Virtual Agglomeration Index for province $i$; $\overline{x}$ denotes the mean value; $m$ is the number of provinces; $h$ represents the bandwidth; and $K(·)$ is the kernel function. This study employs the Gaussian kernel function to estimate the dynamic distribution characteristics of financial geographic and virtual agglomeration.

3.5. Spatial Correlation Analysis

Global spatial correlation analyses and local spatial correlation analyses are employed to identify the spatial interdependencies of financial industry agglomeration as well as the differences in agglomeration among provinces. Specifically, the Global Moran’s I and Local Moran’s I indices are calculated. Global Moran’s I is used to assess whether financial geographic agglomeration or financial virtual agglomeration exhibit spatial correlation, while Local Moran’s I is used to analyze the spatial distribution characteristics among provinces.

The calculation formulas for Global Moran’s I, and Local Moran’s I_i are as follows:

$$\mathrm{Global} \mathrm{Moran}’\mathrm{s} I, I={\displaystyle \frac{m\sum _{i=1}^m\sum _{z=1}^m{w}_{iz}(x_i-\overline{x})(x_z-\overline{x})}{{\sum _{i=1}^m(x_i-\overline{x})}^2\sum _{i=1}^m\sum _{z=1}^m{w}_{iz}}}$$

(12)

$$\mathrm{Local} \mathrm{Moran}’\mathrm{s} I_i, I_i={\displaystyle \frac{m(x_i-\overline{x})\sum _{z=1}^m{w}_{iz}(x_z-\overline{x})}{{\sum _{i=1}^m(x_i-\overline{x})}^2}}$$

(13)

where $m$ represents the number of provinces; $x_i$ and $x_z$ denote the Financial Geographic Agglomeration Index or Financial Virtual Agglomeration Index for province $i$ and province $z$, respectively, and $i\ne z$; $\overline{x}$ is the mean value of financial agglomeration across all provinces; and $w_{iz}$ represents the spatial weight matrix.

3.6. Data Sources

Considering data availability, this study focuses on 31 provinces in China (excluding Hong Kong, Macao, and Taiwan). The financial industry value added and population data at the national and provincial levels are obtained from the National Bureau of Statistics of China, the China Statistical Yearbook, and the respective provincial statistical yearbooks. Data on financial institutions are sourced from the China National Financial Regulatory Administration website. Data on digital inclusive finance are obtained from the Digital Inclusive Finance Index compiled by the Digital Finance Research Center at Peking University. Data on fintech enterprises are collected from the Tianyancha database. Following Song et al. [39], relevant data were retrieved using keywords such as financial technology, cloud computing, blockchain, and artificial intelligence. For instances of missing data, linear interpolation was applied to fill gaps.

4. Evolutionary Paths in Financial Geographic and Virtual Agglomerations

In analyzing the evolutionary characteristics of financial geographic agglomeration and financial virtual agglomeration, comparisons are made across the national level, four major regions (Eastern, Central, Western, and Northeastern China), and individual provinces. Specifically, the Eastern region includes Beijing, Tianjin, Hebei, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan; the Central region includes Shanxi, Anhui, Jiangxi, Henan, Hubei, and Hunan; the Northeastern region includes Liaoning, Jilin, and Heilongjiang; and the Western region includes Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang, Inner Mongolia, Guangxi and Tibet. During the analysis, regional data are averaged to facilitate comparative evaluation.

4.1. Evolutionary Characteristics of Financial Geographic Agglomeration

4.1.1. Temporal Characteristics

(1)

Changes in Financial Geographic Agglomeration

At the national level, as shown in Figure 1, the Financial Geographic Agglomeration Index increased from 0.1024 in 2011 to 0.2995 in 2023, indicating a sustained growth trend. At the regional level, the indices for the Eastern, Central, Western, and Northeastern regions all exhibit growth trends consistent with the national trajectory. Comparing regional averages, the Eastern region clearly leads both the national average and the other three regions, followed by the Northeastern region, the Western region, and lastly the Central region, which slightly lags behind the Western region.

At the provincial level, as shown in

Table 2. Financial geographic agglomeration index of Chinese provinces, 2011–2023.

Province	2011	2023	Province	2011	2023
Beijing	0.6963	0.9654	Hainan	0.0403	0.2295
Shanghai	0.5345	0.8204	Shanxi	0.0380	0.2643
Tianjin	0.3392	0.5252	Heilongjiang	0.0253	0.2553
Zhejiang	0.2423	0.3969	Guangxi	0.0245	0.1767
Guangdong	0.1601	0.2967	Gansu	0.0244	0.2316
Jiangsu	0.1593	0.3606	Hebei	0.0237	0.2008
Chongqing	0.1237	0.3197	Yunnan	0.0221	0.1453
Fujian	0.1112	0.3346	Sichuan	0.0199	0.2419
Ningxia	0.0929	0.2497	Hubei	0.0195	0.2321
Inner Mongolia	0.0797	0.2990	Henan	0.0189	0.1534
Liaoning	0.0678	0.2939	Guizhou	0.0148	0.1575
Xinjiang	0.0614	0.2124	Tibet	0.0142	0.2935
Shandong	0.0531	0.2236	Hunan	0.0090	0.1963
Qinghai	0.0518	0.2585	Anhui	0.0059	0.1920
Jilin	0.0512	0.2897	Jiangxi	0.0047	0.2108
Shaanxi	0.0446	0.2567

, the top five provinces in terms of the Financial Geographic Agglomeration Index in 2011 were Beijing, Shanghai, Tianjin, Zhejiang, and Guangdong, while in 2023, the top five were Beijing, Shanghai, Tianjin, Zhejiang, and Jiangsu. Comparing 2011 and 2023, the overall ranking remained relatively stable, with only Jiangsu moving up in rank and Guangdong declining slightly.

(2)

Convergence Characteristics of Financial Geographic Agglomeration

To clearly depict the convergence characteristics of financial geographic agglomeration, this study employs the coefficient of variation ($CV$) for analysis. Economically, a smaller $CV$ indicates stronger convergence and smaller relative differences, whereas a larger $CV$ suggests weaker convergence and greater relative differences.

As shown in Figure 2, from 2011 to 2023, the Financial Geographic Agglomeration Index at the national level and across the Eastern, Central, Western, and Northeastern regions exhibits a clear convergent trend. At the national level, convergence is particularly pronounced, with the $CV$ decreasing from 1.5326 in 2011 to 0.5913 in 2023, indicating a continuous reduction in relative differences in financial geographic agglomeration across the country. At the regional level, the $CVs$ of the Eastern, Central, Western, and Northeastern regions all show a downward trend, suggesting that relative differences among provinces within each region are also narrowing. However, the Eastern region consistently exhibits the highest CV $CV$, indicating that relative disparities in the distribution of physical financial resources among provinces within this region remain the most pronounced, and its convergence process lags behind that of the other regions.

4.1.2. Spatial Characteristics

(1)

Kernel Density Analysis

Figure 3 employs kernel density estimation to depict the dynamic distribution of the Financial Geographic Agglomeration Index nationwide. First, regarding the distribution location, the kernel density curve exhibits an overall rightward shift, indicating a gradual increase in the national level of financial geographic agglomeration. Second, analyzing peak characteristics, the height of the main peak decreases while its width expands, suggesting an increasing dispersion of financial geographic agglomeration levels within the sample; that is, in terms of absolute differences, the gap among provinces is gradually widening. Third, in terms of distribution skewness, the kernel density curve shows a right-tail feature, reflecting that a few provinces exhibit significantly higher financial geographic agglomeration levels than others. Finally, regarding the number of peaks, the kernel density curves maintain a three-peak distribution pattern from 2011 to 2023, with the side peaks in 2023 slightly lower than in 2011, indicating that while the overall differentiation pattern remains unchanged, the degree of disparity has marginally decreased.

(2)

Spatial Correlation Analysis

According to the “First Law of Geography,” “everything is related to everything else, but near things are more related than distant things.” In practice, regions that are geographically closer tend to have more frequent flows of production factors, such as digital infrastructure, technology, and talent. Therefore, it is hypothesized that financial geographic agglomeration exhibits spatial correlation. To verify whether financial geographic agglomeration has spatial correlation and to identify its spatial distribution pattern, spatial correlation analysis is conducted.

First, the global Moran’s I index is used to analyze the financial geographic agglomeration across 31 provinces, providing an overall assessment of spatial correlation. The results are presented in

Table 3. Global Moran’s I of financial geographic agglomeration.

Year	Global Moran’s I	Z	p
2011	0.282	4.091	0.000
2012	0.300	4.305	0.000
2013	0.302	4.331	0.000
2014	0.286	4.129	0.000
2015	0.247	3.655	0.000
2016	0.231	3.460	0.000
2017	0.237	3.544	0.000
2018	0.243	3.637	0.000
2019	0.226	3.428	0.000
2020	0.220	3.342	0.000
2021	0.186	2.916	0.002
2022	0.227	3.400	0.000
2023	0.232	3.475	0.000

. The global Moran’s I generally range between −1 and 1, where a value greater than 0 indicates positive spatial correlation, a value less than 0 indicates negative spatial correlation, and a value equal to 0 indicates no spatial autocorrelation. As shown in Table 3, the global Moran’s I for financial geographic agglomeration from 2011 to 2023 is consistently positive and significant at the 1% level, indicating a strong spatial positive correlation among provinces. Historically established financial centers, such as Beijing and Shanghai, continue to attract financial resources geographically through institutional advantages, economies of scale, and knowledge spillovers.

Table 4. Regional distribution of Local Moran’s I_i for financial geographic agglomeration.

Year	High–High (HH) Regions	Low–High (LH) Regions	Low–Low (LL) Regions	High–Low (HL) Regions
2011	Beijing, Tianjin, Jiangsu, Shanghai, Zhejiang, Fujian	Hebei, Shandong, Liaoning, Inner Mongolia, Anhui	Shanxi, Jilin, Heilongjiang, Jiangxi, Henan, Hubei, Hunan, Guangxi, Hainan, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang, Tibet	Guangdong, Chongqing
2023	Beijing, Tianjin, Jiangsu, Shanghai, Zhejiang, Fujian	Hebei, Shandong, Anhui	Shanxi, Jilin, Heilongjiang, Jiangxi, Henan, Hubei, Hunan, Guangxi, Hainan, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang, Tibet	Chongqing

presents the regional distribution characteristics of the Local Moran’s I_i for financial geographic agglomeration in 2011 and 2023. The Local Moran’s I divides regions into four quadrants: High–High (HH) regions: provinces with high financial geographic agglomeration levels surrounded by neighbors with similarly high levels, representing promotion zones; Low–High (LH) regions: provinces with low levels surrounded by neighbors with high levels, representing transition zones; Low–Low (LL) regions: provinces with low levels surrounded by neighbors with similarly low levels, representing low-level zones; and High–Low (HL) regions: provinces with high levels surrounded by neighbors with low levels, representing radiation zones.

Comparative analysis indicates that the spatial distribution pattern of financial geographic agglomeration remained largely stable between 2011 and 2023. Beijing, Tianjin, Jiangsu, Shanghai, Zhejiang, and Fujian consistently fall within the promotion zones; Hebei, Shandong, and Anhui remain in the transition zones. In 2023, Liaoning and Inner Mongolia show a trend of evolving from transition zones toward promotion zones, lying at the boundary of the two categories. Chongqing remains in the radiation zone, while Guangdong in 2023 is located at the boundary between low-level and radiation zones. All other provinces consistently fall within the low-level zones.

4.2. Evolutionary Characteristics of Financial Virtual Agglomeration

4.2.1. Temporal Features

(1)

Changes in Financial Virtual Agglomeration

At the national level, as shown in Figure 4, the financial virtual agglomeration index increased steadily from 0.0084 in 2011 to 0.2365 in 2023, indicating a sustained growth trend. At the regional level, the indices for the Eastern, Central, Western, and Northeastern regions also exhibited growth trends that converged with the national trajectory over time. Comparing mean values across regions, the Eastern region clearly ranks highest, followed by the Central region, with the Western region in third place, and the Northeastern region slightly behind the Western region.

At the provincial level, as shown in

Table 5. Financial virtual agglomeration index of Chinese provinces, 2011–2023.

Province	2011	2023	Province	2011	2023
Beijing	0.0445	0.9977	Sichuan	0.0057	0.1519
Shanghai	0.0241	0.6554	Guangxi	0.0048	0.1451
Guangdong	0.0161	0.2821	Anhui	0.0046	0.1951
Zhejiang	0.0159	0.1874	Shanxi	0.0043	0.1294
Fujian	0.0143	0.2649	Hebei	0.0042	0.1318
Tianjin	0.0116	0.2669	Heilongjiang	0.0041	0.1201
Jiangsu	0.0114	0.1837	Ningxia	0.0041	0.1489
Tibet	0.0100	0.1402	Inner Mongolia	0.0039	0.1431
Hainan	0.0100	0.7762	Jiangxi	0.0035	0.1468
Qinghai	0.0094	0.1129	Yunnan	0.0032	0.1399
Chongqing	0.0072	0.1997	Henan	0.0029	0.1061
Liaoning	0.0071	0.1566	Jilin	0.0028	0.1446
Shaanxi	0.0069	0.1842	Xinjiang	0.0017	0.1459
Hunan	0.0068	0.3525	Guizhou	0.0016	0.1956
Shandong	0.0061	0.2443	Gansu	0.0011	0.1367
Hubei	0.0059	0.1456

, the top five provinces in terms of the financial virtual agglomeration index in 2011 were Beijing, Shanghai, Guangdong, Zhejiang, and Fujian. By 2023, the top five provinces had shifted to Beijing, Hainan, Shanghai, Hunan, and Guangdong. A comparison between the two years shows that Beijing, Shanghai, and Guangdong maintained their leading positions consistently.

(2)

Convergence Characteristics of Financial Virtual Agglomeration

As shown in Figure 5, from 2011 to 2023, the levels of financial virtual agglomeration in China as a whole, as well as in the western and northeastern regions, exhibited signs of convergence. At the national level, a fluctuating convergence pattern was observed, with the coefficient of variation decreasing from 1.0044 in 2011 to 0.8612 in 2023. In the western region, the coefficient of variation declined from 0.5980 to 0.1688, and in the northeastern region, from 0.4664 to 0.1325, indicating a narrowing of relative disparities in financial virtual agglomeration within these regions.

In contrast, the eastern and central regions did not exhibit convergence. The coefficient of variation in the eastern region increased from 0.7290 in 2011 to 0.7481 in 2023, while in the central region it rose from 0.3151 to 0.5008, suggesting a widening of internal disparities in financial virtual agglomeration.

Economically, this phenomenon implies that even within relatively developed or rapidly growing regions, unequal access to financial virtual resources and development opportunities may lead to a “Matthew Effect” in the digital finance sector, thereby posing challenges to achieving balanced regional development.

4.2.2. Spatial Characteristics

(1)

Kernel Density Analysis

As illustrated in Figure 6, the kernel density estimation reveals the dynamic distribution pattern of financial virtual agglomeration levels across China.

First, in terms of distributional position, the kernel density curve exhibits an overall rightward shift, indicating a gradual upward trend in financial virtual agglomeration levels nationwide.

Second, regarding the peak characteristics, the main peak of the kernel density curve becomes lower and wider over time, implying an increase in the degree of dispersion within the sample. This suggests that the absolute disparities in financial virtual agglomeration levels among provinces have been widening.

Third, from the perspective of distributional extension, the curve displays a right-skewed tail, suggesting the existence of several provinces with significantly higher levels of financial virtual agglomeration compared with others.

Finally, in terms of the number of peaks, the kernel density curve evolves from a unimodal to a trimodal distribution between 2011 and 2023. The noticeable difference in height between the main and secondary peaks reflects the emergence of a clear regional differentiation pattern in financial virtual agglomeration across the country.

(2)

Spatial Correlation Analysis

As shown in

Table 6. Global Moran’s I of financial virtual agglomeration.

Year	Global Moran’s I	Z	p
2011	0.104	1.926	0.027
2012	0.107	2.093	0.018
2013	0.073	1.595	0.055
2014	0.033	1.164	0.122
2015	−0.016	0.386	0.350
2016	−0.031	0.066	0.474
2017	−0.042	−0.268	0.395
2018	−0.034	−0.023	0.491
2019	−0.034	−0.005	0.498
2020	−0.027	0.100	0.460
2021	−0.022	0.149	0.441
2022	−0.010	0.296	0.384
2023	−0.002	0.408	0.341

, the results of the Global Moran’s I indicate that from 2011 to 2023, the spatial distribution pattern of financial virtual agglomeration underwent a structural transformation—evolving from a significant spatially clustered pattern to a state of insignificant spatial correlation.

Specifically, this evolution can be divided into three stages:

Early stage (2011–2012): the Global Moran’s I was positive and statistically significant, suggesting a clear spatial clustering of financial virtual activities (such as early Internet finance and fintech). During this period, financial resources, innovative elements, and market demand were concentrated mainly in first-tier cities and a few core regions.

Transition stage (2013–2014): the Global Moran’s I remained positive but declined steadily, while the p-values became insignificant. This implies that the spatial clustering pattern began to loosen. Digital finance started to break through geographic constraints, and several provincial capitals and second-tier cities accelerated their digital financial development, exhibiting a catch-up effect with core regions.

Middle-to-late stage (2015–2023): the Global Moran’s I turned slightly negative, with very small absolute values and statistically insignificant p-values, indicating a fundamental shift from significant clustering to spatial independence. This reflects the network-based nature of financial virtual activities (e.g., mobile payments, online wealth management), which increasingly depend on internet connectivity rather than geographic proximity. Some remote areas, leveraging online access and local demand, developed specialized financial services, thereby weakening the “spatial stickiness” of traditional financial centers.

This transformation was driven by factors such as the nationwide expansion of digital financial platforms (for example, Ant Group, Tencent Finance) and inclusive financial policies aimed at narrowing regional financial disparities.

5. Evolutionary Characteristics of the Synergistic Integration of Financial Dual Agglomeration

To assess the level of coordination and integration between financial dual agglomeration, this study draws on Zhao et al. [40] and adopts the coupling coordination classification standards shown in

Table 7. Classification and criteria of coupling coordination.

Coupling Coordination Range	Coupling Coordination Level	Coupling Coordination Range	Coupling Coordination Level
(0.0–0.1)	Extremely Disordered (Extremely D)	[0.5–0.6)	Barely Coordinated (Barely C)
[0.1–0.2)	Severely Disordered (Severely D)	[0.6–0.7)	Primary Coordinated (Primary C)
[0.2–0.3)	Moderately Disordered (Moderately D)	[0.7–0.8)	Intermediate Coordination (Intermediate C)
[0.3–0.4)	Mildly Disordered (Mildly D)	[0.8–0.9)	Well-Coordinated (Well C)
[0.4–0.5)	Nearly Disordered (Nearly D)	[0.9–1.0)	Highly Coordinated (Highly C)

.

5.1. Evolutionary Characteristics of Financial Dual Agglomeration Coordination

5.1.1. National Level: Gradual Progress from Severely Disordered to Nearly Disordered

As shown in

Table 8. Coupling coordination levels of financial dual agglomeration in China, 2011–2023.

	National		Eastern Region		Central Region		Western Region		Northeastern Region
Year	Coupling Coordination Degree	Coupling Coordination Type	Coupling Coordination Degree	Coupling Coordination Type	Coupling Coordination Degree	Coupling Coordination Type	Coupling Coordination Degree	Coupling Coordination Type	Coupling Coordination Degree	Coupling Coordination Type
2011	0.1460	Severely D	0.2262	Moderately D	0.0879	Extremely D	0.1148	Severely D	0.1195	Severely D
2012	0.2079	Moderately D	0.2811	Moderately D	0.1511	Severely D	0.1792	Severely D	0.1926	Severely D
2013	0.2443	Moderately D	0.3173	Mildly D	0.1900	Severely D	0.2140	Moderately D	0.2305	Moderately D
2014	0.2652	Moderately D	0.3387	Mildly D	0.2143	Moderately D	0.2332	Moderately D	0.2498	Moderately D
2015	0.2889	Moderately D	0.3661	Mildly D	0.2370	Moderately D	0.2550	Moderately D	0.2715	Moderately D
2016	0.3095	Mildly D	0.3912	Mildly D	0.2595	Moderately D	0.2721	Moderately D	0.2865	Moderately D
2017	0.3353	Mildly D	0.4215	Nearly D	0.2828	Moderately D	0.2970	Moderately D	0.3066	Mildly D
2018	0.3560	Mildly D	0.4480	Nearly D	0.3043	Mildly D	0.3138	Mildly D	0.3212	Mildly D
2019	0.3749	Mildly D	0.4720	Nearly D	0.3258	Mildly D	0.3278	Mildly D	0.3376	Mildly D
2020	0.3947	Mildly D	0.4984	Nearly D	0.3455	Mildly D	0.3433	Mildly D	0.3534	Mildly D
2021	0.4421	Nearly D	0.5493	Barely C	0.3965	Mildly D	0.3869	Mildly D	0.3963	Mildly D
2022	0.4752	Nearly D	0.5889	Barely C	0.4206	Nearly D	0.4189	Nearly D	0.4308	Nearly D
2023	0.4914	Nearly D	0.6108	Primary C	0.4314	Nearly D	0.4336	Nearly D	0.4447	Nearly D

and Figure 7, from 2011 to 2023, the coupling coordination degree of national financial dual agglomeration increased from severely disordered (0.1460) in 2011 to nearly disordered (0.4914) in 2023. Overall, the evolution exhibits a phased progression: (1) 2011: severely disordered stage; (2) 2012–2015: moderately disordered stage; (3) 2016: entered mildly disordered stage; and (4) 2021: achieved a critical leap, surpassing the 0.4 threshold and entering the nearly disordered stage.

This development signifies that the systematic penetration of digital finance into traditional financial services is becoming evident, with initial integration of online and offline operations in sectors such as mobile payments and digital credit. It also reflects that the financial supply-side structural reform has made substantial strides in driving the digital transformation of traditional financial institutions. This evolution marks a new phase in the coordinated development between the geographical and virtual agglomerations of finance. Moreover, their interactive effects are progressively strengthening and shaping a new structure for the financial system.

5.1.2. Regional Level: Eastern Region Leading, Central, Western, and Northeastern Regions Following a Gradient

(1)

Eastern Region: Pioneering the Coordination Threshold and Entering the Primary Coordination Stage

The coupling coordination degree of financial dual agglomeration in the Eastern region increased from moderately disordered (0.2262) in 2011 to primary coordination (0.6108) in 2023, making it the only region among the four major economic zones to surpass the “coordination” threshold.

(2)

Central, Western, and Northeastern Regions: Continuous Improvement but Still in the Transition from Disordered to Coordinated

In the Central region, the coupling coordination degree increased from extremely disordered (0.0879) in 2011 to nearly disordered (0.4314) in 2023. In the Western region, it rose from severely disordered (0.1148) to nearly disordered (0.4336), and in the Northeastern region, from severely disordered (0.1195) to nearly disordered (0.4447). Although the level of financial dual agglomeration synergistic integration in these three regions has continuously improved, as of 2023, they remain in the “nearly disordered” stage, lagging two coordination levels behind the Eastern region.

The regional disparities in the level of synergistic integration of financial dual agglomeration reveal the spatially uneven pattern of China’s financial system. Benefiting from locational advantages, a solid economic foundation, a concentration of high-end talent, and preferential policy pilots, the Eastern region has achieved a relatively high degree of coordination and integration between financial geographical agglomeration (e.g., Shanghai as an international financial center, the Shenzhen Stock Exchange) and financial virtual agglomeration (e.g., digital finance innovation in Hangzhou, the fintech demonstration zone in Beijing). This builds a modern financial ecosystem in which the two forms of agglomeration develop synergistically. In contrast, the central, western, and northeastern regions, although continuously improvement in the synergistic integration of financial dual agglomeration, still lag in overall synergistic development. This is due to constraints such as delayed digital infrastructure and an underdeveloped financial ecology. This gradient disparity indicates that, in promoting nationwide financial coordinated development, regional heterogeneity must be acknowledged and differentiated strategies adopted.

5.2. Convergence Characteristics of Financial Dual Agglomeration Synergy Levels: Gradual Reduction in Intra-Regional Disparities

As shown in

Table 9. Coefficients of variation in financial dual agglomeration synergy levels in China’s four major economic regions.

Coefficients of Variation	National	Eastern Region	Central Region	Western Region	Northeastern Region
2011	0.5528	0.4256	0.2107	0.2709	0.2087
2012	0.3715	0.3407	0.1234	0.1707	0.1067
2013	0.3196	0.3090	0.1008	0.1482	0.0981
2014	0.3102	0.3243	0.0730	0.1251	0.0950
2015	0.3184	0.3535	0.0792	0.1163	0.0919
2016	0.3300	0.3834	0.0706	0.0976	0.0721
2017	0.3276	0.3892	0.0645	0.0810	0.0644
2018	0.3175	0.3701	0.0620	0.0827	0.0663
2019	0.3125	0.3600	0.0787	0.0833	0.0644
2020	0.3071	0.3450	0.0976	0.0839	0.0630
2021	0.2837	0.3211	0.1205	0.0759	0.0532
2022	0.2694	0.2975	0.1166	0.0771	0.0484
2023	0.2704	0.2956	0.1153	0.0756	0.0525

, the intra-regional disparities of financial dual agglomeration synergy levels exhibit a clear convergence pattern:

(1)

National level: The coefficient of variation for financial dual agglomeration synergy decreased from 0.5528 in 2011 to 0.2704 in 2023, representing an overall decline of approximately 51.09%.

This convergence in disparities reflects the progress made by less-developed regions in advancing the synergistic development of financial dual agglomeration. In essence, this progress is not merely a matter of scale expansion, but is reflected in pathways such as establishing digital financial platforms and cultivating FinTech ecosystems (as observed in Guizhou and Hainan). This have enabled these regions to catch up with regions traditionally advantaged in financial agglomeration. This trend indicates that the long-established hierarchical structure of financial agglomeration, which was historically shaped by geographical and historical endowments, is now evolving towards a more resilient and inclusive form.

(2)

Eastern region: The coefficient of variation fell from 0.4256 to 0.2956, showing a convergence trend. Nevertheless, its variation remains higher than that of the other three regions, reflecting relatively pronounced differences in the financial dual agglomeration synergy among provinces within the Eastern region.

The significant disparities in the level of synergistic integration of financial dual agglomeration among provinces within the Eastern region reveal that even in economically advanced regions, the coordination process between the two agglomerations remains uneven. As shown in

Table 10. Coordinated development level of financial dual agglomeration and driving types of provinces in 2023.

Province	Financial Geographic Agglomeration Index	Financial Virtual Agglomeration Index	Coupling Coordination Degree	Coupling Coordination Level	Financial Geographic Agglomeration Index/Financial Virtual Agglomeration Index	Driving Type
Beijing	0.9654	0.9977	0.9907	Highly C	0.9676	T
Tianjin	0.5252	0.2669	0.6119	Primary C	1.9678	S
Hebei	0.2008	0.1318	0.4033	Nearly D	1.5235	S
Shanxi	0.2643	0.1294	0.4300	Nearly D	2.0425	S
Inner Mongolia	0.2990	0.1431	0.4548	Nearly D	2.0894	S
Liaoning	0.2939	0.1566	0.4632	Nearly D	1.8768	S
Jilin	0.2897	0.1446	0.4524	Nearly D	2.0035	S
Heilongjiang	0.2553	0.1201	0.4185	Nearly D	2.1257	S
Shanghai	0.8204	0.6554	0.8563	Well C	1.2518	S
Jiangsu	0.3606	0.1837	0.5073	Barely C	1.9630	S
Zhejiang	0.3969	0.1874	0.5222	Barely C	2.1179	S
Anhui	0.1920	0.1951	0.4399	Nearly D	0.9841	T
Fujian	0.3346	0.2649	0.5456	Barely C	1.2631	S
Jiangxi	0.2108	0.1468	0.4194	Nearly D	1.4360	S
Shandong	0.2236	0.2443	0.4835	Nearly D	0.9153	T
Henan	0.1534	0.1061	0.3572	Mildly D	1.4458	S
Hubei	0.2321	0.1456	0.4287	Nearly D	1.5941	S
Hunan	0.1963	0.3525	0.5129	Barely C	0.5569	U
Guangdong	0.2967	0.2821	0.5379	Barely C	1.0518	T
Guangxi	0.1767	0.1451	0.4002	Nearly D	1.2178	S
Hainan	0.2295	0.7762	0.6497	Primary C	0.2957	U
Chongqing	0.3197	0.1997	0.5027	Barely C	1.6009	S
Sichuan	0.2419	0.1519	0.4378	Nearly D	1.5925	S
Guizhou	0.1575	0.1956	0.4190	Nearly D	0.8052	U
Yunnan	0.1453	0.1399	0.3776	Mildly D	1.0386	T
Shaanxi	0.2567	0.1842	0.4663	Nearly D	1.3936	S
Gansu	0.2316	0.1367	0.4219	Nearly D	1.6942	S
Qinghai	0.2585	0.1129	0.4133	Nearly D	2.2896	S
Ningxia	0.2497	0.1489	0.4391	Nearly D	1.6770	S
Xinjiang	0.2124	0.1459	0.4196	Nearly D	1.4558	S
Tibet	0.2935	0.1402	0.4504	Nearly D	2.0934	S

below, Beijing and Shanghai have reached a high integration level, while most other provinces are still in a preliminary or barely coordinated stage. This indicates that the synergistic integration of financial dual agglomeration not only depends on regional economic strength, but is also closely related to the pace of industrial upgrading and technological innovation capacity.

(3)

Central, Western, and Northeastern regions: The coefficients of variation in these regions all exhibit declining trends and remain relatively low in the long term (0.1153 in the Central region, 0.0756 in the Western region, and 0.0525 in the Northeastern region in 2023). This indicates that intra-regional disparities in financial dual agglomeration synergy are small; however, due to the overall lower level of synergy, these regions still display a “low-level equilibrium” pattern.

This “low-level equilibrium” indicates that the aforementioned regions have not yet established effective gradient-driven or endogenous growth momentum in the synergistic integration of financial dual agglomeration. Although regional financial centers such as Chongqing and Xi’an have emerged, their sphere of influence remains limited. And their capacity to integrate and stimulate financial resources in surrounding areas is still insufficient. Under such a structure, interregional competition and cooperation remain weak, constraining the efficiency of financial resource allocation.

Therefore, the central, western, and northeastern regions should focus on deviating from the current development pattern of “low-level equilibrium.” Moving forward, greater efforts should be made to leverage existing regional financial centers such as Chongqing and Xi’an, enhancing their pivotal role in both physical financial clusters and digital financial networks. Through coordinated policy support and market mechanisms, their cross-regional service and radiating capacity should be strengthened. On this basis, the spatial and functional integration of financial dual agglomerations should be advanced. This will gradually form a new structure characterized by core-city leadership and multi-level synergistic development and transit from low-level equilibrium to high-quality synergy.

5.3. Analysis of Provincial Financial Dual Agglomeration Synergy Levels and Driving Types in 2023

To gain a deeper understanding of the coordinated development patterns of financial geographic and virtual agglomerations across provinces, and to examine the relative influence of the two agglomeration types in the coordination process, this study follows the approach of Xu and Zhou [41]. Specifically, the provincial driving types are classified by comparing the financial geographic agglomeration index ${FG}_{it}$ with the financial virtual agglomeration index ${FV}_{it}$: if ${FG}_{it}/{FV}_{it}>1.1$, the province is categorized as geographically driven agglomeration (S); if, ${0.9\le FG}_{it}/{FV}_{it}\le 1.1$, the province is classified as synchronously driven by both geographic and virtual agglomeration (T); and if, ${FG}_{it}/{FV}_{it}<0.9$, the province is classified as virtually driven agglomeration (U).

As shown in Table 10, in 2023, the coordinated development level of financial dual agglomeration across China’s 31 provinces can be categorized into six tiers:

(1)

Highly coordinated: Beijing. The financial geographic agglomeration index and financial virtual agglomeration index of Beijing reached 0.9654 and 0.9977, respectively, reflecting its dual advantage as the national center for financial decision-making and digital financial innovation, where both agglomeration types form a highly efficient, mutually reinforcing cycle.

(2)

Well-coordinated: Shanghai. As an international financial center, Shanghai exhibits a high level of financial geographic agglomeration (0.8204) and financial virtual agglomeration (0.6554), achieving effective coordination between the two.

(3)

Primary coordinated: Tianjin and Hainan. Tianjin’s coordination is primarily driven by financial geographic agglomeration (0.5252), while Hainan relies on financial virtual agglomeration (0.7762), illustrating differentiated regional financial development pathways.

(4)

Barely coordinated: Jiangsu, Zhejiang, Fujian, Hunan, Guangdong, and Chongqing. Although these provinces exhibit some synergy between the two agglomeration types, the overall level remains relatively low.

(5)

Nearly disordered and mildly disordered: Henan and Yunnan are in a mildly disordered stage, while the remaining 19 provinces are classified as nearly disordered. This indicates that in most provinces, there exists a structural imbalance between the two agglomeration types, and the coordination mechanisms remain underdeveloped.

Regarding driving types, Table 10 shows three categories:

(1)

Geographically driven agglomeration (S): covering 23 provinces. This indicates that traditional physical financial institutions (example, banks, securities firms) remain the main driving force for financial development, whereas virtual agglomeration lags behind.

From an economic perspective, the financial systems of such provinces generally face the contradiction between reliance on traditional development pathways and slow digital transformation. Specifically, on the one hand, their financial structure has long been dominated by bank credit, with the indirect financing system and local industrial structure reinforcing each other. This constrains the responsiveness of financial resource allocation to economic digital transformation. On the other hand, due to constraints such as technology and talent, the expansion of digital financial application scenarios remains insufficient, leading to lagging development in virtual agglomeration. This contradiction ultimately results in a systemic mismatch between financial supply and the demands of the real economy. This is prominently reflected by the difficulty for key sectors such as small and micro-enterprises, agriculture, and rural areas to obtain commensurate inclusive financial and digital financial services.

(2)

Virtually driven agglomeration (U): Hainan, Guizhou, and Hunan. In these provinces, the financial virtual agglomeration index exceeds the geographic one, making digital finance the dominant force in regional financial development. This illustrates how late-developing regions can achieve “leapfrogging” through digital finance. The following section provides a detailed analysis using Hainan and Guizhou as examples.

The Hainan Path: Institutional Innovation Empowers Digital Finance Development.

This is reflected in the following aspects. First, institutional innovation promotes financial digital transformation. Hainan possesses pilot authorities in cross-border capital flows and financial openness, attracting projects such as international clearing houses and digital currency pilots, thereby advancing the digitization and internationalization of financial processes. Second, light-asset integration between industry and finance. Key sectors in Hainan—tourism, services, and high-tech industries—rely on virtual financial services such as online payments, supply chain finance, and digital insurance. Examples include the Sanya tourism points platform and the digitalization of medical insurance in Boao, both demonstrating the integration of financial virtual agglomeration with the needs of the real economy. The Hainan case shows that regions with a weak traditional financial foundation can deepen the integration of digital finance and industry through institutional innovation, bypassing the long-term accumulation phase of traditional financial institutions to construct a digital financial system.

The Guizhou Path: Data Factors Reshape Financial Locational Advantages.

This is reflected in the following. First, digital infrastructure attracts the agglomeration of financial back-office and technology institutions. Leveraging its climatic and energy advantages, Guizhou has established data centers, attracting data facilities from companies such as Apple, Huawei, and Tencent. This, in turn, has driven the clustering of fintech firms, data processing centers, and financial institution back-office departments, forming a financial virtual agglomeration characterized by “physical dispersion yet logical concentration.” Second, “Big Data + Finance” enables scenario innovation. Guizhou promotes the application of big data in areas such as credit reporting, risk control, and agricultural insurance. For instance, the “Guizhou Agricultural Credit Guarantee System” constructs farmer credit profiles based on big data, enabling the online and batch processing of agricultural loans, thereby alleviating the challenges of high costs and limited coverage in traditional agricultural finance. The Guizhou case demonstrates that regions distant from traditional financial centers can build competitiveness in regional financial development through digital infrastructure and data-driven approaches, achieving late-developer advancement.

Although the development paths of Hainan and Guizhou differ, they jointly demonstrate that digital finance can break geographical constraints and reshape regional financial development patterns through institutional empowerment and data-driven strategies. This provides practical references for other late-developing regions exploring new pathways for financial development.

(3)

Synchronously driven agglomeration (T): Beijing, Anhui, Shandong, Guangdong, and Yunnan. Beijing achieves “high-level coordination” due to both agglomeration indices being high, whereas Anhui, Shandong, and Yunnan display “low-level coordination” as both indices remain low.

“High-level coordination” refers to a state in which a region achieves high absolute levels in both financial geographic agglomeration and financial virtual agglomeration, while maintaining synchronized development. Its core characteristics include the capacity for cross-regional resource allocation, the authority to formulate financial rules, and a strong role in driving innovation within the national financial system. This stage signifies a systematic transition in regional financial functions, shifting from providing basic financial services to steering the direction of industry standards. Taking Beijing as an example, its financial geographic agglomeration index (0.9654) and financial virtual agglomeration index (0.9977), as shown in Table 10, are both at high levels. Their synergy drives its evolution from a traditional “financial service supply center” to a “rule-making and innovation-leading center,” securing a leadership position in the national financial reform and digitization process.

“Low-level coordination”, on the other hand, describes a state where a region exhibits low absolute levels in both financial geographic agglomeration and financial virtual agglomeration, yet still maintains synchronized development. At this stage, its functions are primarily confined to serving local economic needs. Financial geographic agglomeration mainly fulfills basic local functions such as financing and settlement, while financial virtual agglomeration manifests as the digital extension of local financial services, without yet developing cross-regional influence. Taking Anhui as an example, its financial geographic agglomeration index (0.1920) and financial virtual agglomeration index (0.1951) are both at low levels as shown in Table 10. Their synergistic development remains in a preliminary stage, primarily serving local economic activities and failing to establish cross-regional service functions.

6. Conclusions and Policy Recommendations

6.1. Conclusions

Based on provincial panel data from 2011 to 2023, this study analyzes the evolutionary characteristics of financial geographic agglomeration and financial virtual agglomeration, as well as their synergistic integration across China.

First, the evolutionary characteristics of financial geographic agglomeration of both the national level and the four major regions (eastern, central, western, and northeastern China) show a steady upward trend in financial geographic agglomeration. The regional order is eastern region highest, followed by the northeast, then the west, with the central region slightly lagging behind the west. The financial geographic agglomeration levels at both national and regional scales exhibit σ-convergence, indicating that the relative disparities among provinces are gradually narrowing. There exists a significant spatial positive correlation in provincial financial geographic agglomeration, forming a relatively stable spatial clustering pattern over time.

Second, the evolutionary characteristic of financial virtual agglomeration also demonstrates a rising trend nationwide and across all four regions, with the regional ranking being eastern > central > western > northeastern. The national, western, and northeastern regions exhibit convergence, meaning that the relative differences in financial virtual agglomeration within these regions are shrinking. In contrast, the eastern and central regions lack convergence, suggesting widening internal disparities in virtual financial development. Unlike financial geographic agglomeration, financial virtual agglomeration shows no significant spatial correlation, reflecting its dependence on digital technology and network connectivity rather than physical proximity.

Finally, the evolutionary characteristics of the synergistic integration between financial geographic and virtual agglomeration, the study found that the level of synergistic integration between financial geographic and virtual agglomeration has steadily improved nationwide and across all four major regions. The eastern region has taken the lead, entering the primary coordination stage, while the central, western, and northeastern regions remain at the edge of imbalance. The σ-convergence of synergistic integration indicates that the relative gaps among provinces are gradually narrowing, suggesting a tendency toward more balanced regional development. In 2023, the synergistic integration level across 31 provinces can be categorized into six tiers: (1) highly coordinated: Beijing; (2) well-coordinated: Shanghai; (3) primary coordinated: Tianjin, Hainan; (4) barely coordinated: Jiangsu, Zhejiang, Fujian, Hunan, Guangdong, Chongqing; (5) mildly disordered: Henan, Yunnan; and (6) nearly disordered: remaining 19 provinces. In terms of driving type, most provinces (23) are financial geographic agglomeration-driven; only Hunan, Hainan, and Guizhou are financial virtual agglomeration-driven. Beijing, Anhui, Shandong, Guangdong, and Yunnan represent synchronous development types, driven jointly by both geographic and virtual agglomeration forces.

6.2. Policy Recommendations

Based on the conclusions derived in this research, the following policy recommendations are proposed. First, improve the spatial distribution of finance to promote regional convergence. (1) Strengthen the radiating and driving role of core hubs. By leveraging institutional innovation and knowledge spillover effects from high-level financial agglomerations such as Beijing and Shanghai, efforts should be made to accelerate the establishment of cross-regional collaborative networks. This will facilitate the orderly diffusion of financial resources and innovation outcomes to surrounding and less-developed areas, thereby fully realizing their positive spatial externalities. (2) Enhance the cross-regional service functions of regional financial centers. Priority should be given to strengthening the radiating capacity of financial centers in central and western regions such as Chongqing and Xi’an, so as to address the “low-level equilibrium” dilemma in these areas. (3) Empower less-developed regions through digital finance to narrow absolute regional gaps. Practices in Hainan, Guizhou, and other regions demonstrate that digital finance can overcome traditional location constraints through institutional innovation or data empowerment. Mildly mismatched provinces such as Henan and Yunnan should learn from these experiences by actively developing digital finance and building virtual financial agglomeration platforms, thereby reducing developmental disparities with more developed provinces.

Second, curb regional divergence in financial virtual agglomeration and prevent the digital divide. It is essential to strengthen the development of digital infrastructure, with a focus on improving network coverage and accessibility of digital financial services in remote areas. This will help mitigate the widening relative disparities in financial virtual agglomeration between eastern and central regions.

Third, based on the research findings in Section 5.3, it is proposed to implement categorized development strategies tailored to the driving types of each province. (1) For provinces driven by financial geographical agglomeration (23 provinces), experiences from Zhejiang, where digital finance and the private economy are deeply integrated, can serve as a reference. Promoting the digital transformation of traditional financial institutions, increasing investment in fintech, and developing digital financial products that match local specialty industries are recommended to foster deeper integration between geographical and virtual agglomeration at the industrial level. (2) For provinces driven by financial virtual agglomeration (Hainan, Guizhou, Hunan), practices in Hainan and Guizhou show that financial virtual agglomeration can effectively serve the real economy, such as in rural revitalization and eco-tourism. It is advised that these provinces, while consolidating their advantages in digital finance, appropriately strengthen the development of physical financial networks to prevent risks associated with financial structural imbalances. (3) For provinces with synchronous financial geographical and virtual agglomeration (Beijing, Anhui, Shandong, Guangdong, Yunnan), these regions should leverage their comparative advantages of “dual agglomeration” based on their respective functional orientations. Among them, Beijing and Guangdong may focus on improving financial ecosystems, rules, and market development to support the implementation of national strategies. Anhui and Shandong should emphasize empowering and supporting the manufacturing sector through finance. Yunnan can dedicate efforts to promoting cross-border financial innovation along its borders. Such measures will optimize the allocation of regional financial resources and guide coordinated regional development.