Regional Differences and Spatial-Temporal Evolution Characteristics of Digital Economy Development in China

Abstract

The digital economy, as an emerging productive force, has become a critical catalyst for economic sustainable progress. This study examines the regional disparities and origins of the digital economy, as well as its spatial and temporal growth patterns, which are essential for bridging the financial gap among regions and promoting synchronized economic progress. We developed a multidimensional index system to evaluate the level of digital economic development across 30 Chinese provinces, encompassing aspects such as the Internet’s evolution, digital infrastructure, capacity for digital innovation, and the application of digital technologies. The regional imbalances and origins of the digital economy were scrutinized using Dagum Gini coefficient decomposition. Furthermore, the study investigated the spatiotemporal dynamics of digital economy progression in China, employing methods like kernel density estimation, migration models of the gravity center, and an analysis via the standard deviation ellipse. The results reveal the following: (1) Digital economic development is more advanced in Eastern China compared to the western regions, with variations primarily driven by inter-regional differences. (2) The absolute gap in national digital economic development levels is widening, and relative disparities within the eastern region are increasing. Significant polarization is observed in the development of the digital economy across the central and western regions, while disparities in the northeastern region are comparatively minimal. (3) The center of gravity for China’s digital economy has overall shifted southward; the standard deviation ellipse has extended both northward and southward and become more oblate; and the dispersion within China’s digital economy has intensified.

1. Introduction

As a novel economic paradigm, the digital economy has emerged as the foundational driving force for China’s sustainable development. Digital technology fosters digital capabilities for sustainable development by constructing cyberspace infrastructures. In 2023, the scale of China’s digital economy was projected to reach 53.9 trillion CNY, accounting for 42.8% of its GDP. The contribution rate of digital economy growth to GDP growth is as high as 66.45%. Industrial digitalization and digital industrialization serve as critical pathways through which the digital economy exerts its influence. Digital transformation within enterprises and governments drives innovation [1] and supports sustainable development [2]. Employees’ digital competencies significantly enhance corporate performance [3]. Furthermore, digital industrialization elevates the value of data elements and facilitates the formation of digital industrial clusters.

As the digital economy continuously evolves, significant disparities in digital resource endowment exist between provinces and regions in China, including differences in digital technology and infrastructure construction. These disparities contribute to a digital divide and a digital Matthew effect, in which the inequality and agglomeration of the digital economy have gradually become more apparent. This situation poses social and environmental challenges, making the expansion of the digital economy and its regional differences critical areas of focus.

The main contributions of this paper are introducing a more scientifically robust indicator system for gauging digital economic development levels, inspired by the techno-economic paradigm and definitions of the digital economy; outlining some detailed indicators reflecting the current innovation level of the digital economy; and innovatively adding the application of digital technologies by the government. Employing the Dagum Gini coefficient decomposition method, this paper conducts a thorough analysis of the geographical differences and driving factors behind the levels of digital economy in China’s eastern, central, western, and northeastern regions. Additionally, the dynamic evolution of digital economic development levels is visually depicted, and the key factors influencing the evolution of each region are analyzed using the ArcGIS geographic information system, supplemented by methods such as kernel density estimation, the center of gravity migration model, and the standard deviation ellipse. This approach is highly significant in advancing the digital economy in each area tailored to specific circumstances and provides a powerful reference for the formulation of national and local policies related to the digital economy.

This study aims to construct a new evaluation index for the digital economy, which is expected to comprehensively reflect the spatial-temporal aspects of its development in recent years. Based on this, the study investigates regional development disparities and their underlying causes, thereby providing targeted policy recommendations. This not only enriches the existing research in the field of the digital economy but also offers data support for promoting its sustained and stable growth. Furthermore, it facilitates the coordinated development of regional industries and the economy, contributing significantly to the sustainable development of the national economy.

2. Literature Review

The research on the digital economy mainly includes the following aspects: firstly, the concept of and measurement research on the digital economy [4,5]; secondly, research on enterprise digital transformation, including the path and impact of enterprise digital transformation [6,7]; and thirdly, research on the digital economy and high-quality development, including the digital economy and high-quality economic development [8], the digital economy and high-quality green growth [9], and the digital economy and high-quality industrial development [10].

The measurement of the digital economy’s development level has garnered considerable attention from scholars, who have approached it from various perspectives and methodologies. Currently, four main methods are utilized: (1) the national economic accounting method, which defines the scope of digital economic accounting, identifies digital economic products and corresponding industries, and calculates indicators such as the digital economic added value and total output [11]; (2) the value-added measurement algorithm, which estimates the added value of capital stock across industries, constructs a measurement system that includes industrial digitization and digital industrialization, and employs a growth accounting framework model to evaluate the digital economy [12,13]; (3) the satellite account method, which separates digital-economy-related indicators from the input–output table based on the classification of the digital economy industry, thereby reconstructing the digital economy satellite account [14]; and (4) the indicator system method, which develops relevant indicators to assess the state of the digital economy and synthesizes an indicator to represent its development level using statistical techniques [3,4,5,6,9,15,16,17].

In terms of examining the spatial-temporal evolution of the digital economy, studies have been conducted from both temporal and spatial perspectives. Temporally, research by Chen et al. indicated that China’s digital economy remains largely stable [18], while Pan et al. asserted that the advancement of the Internet economy is consistent with its progress [19]. The evolution of the digital economy is seen as promoting overall economic progress [18] and enhancing sustainable development [20]. However, some studies have shown that in certain provinces, such as Jiangsu, Liaoning, Hainan, Gansu, Heilongjiang, and Qinghai, digital economy development levels are fluctuating or declining [21]. From a spatial perspective, China’s digital economy development level exhibits a stepped distribution [22], progressively diminishing from east to west [23]. Several scholars have analyzed the geographical agglomeration pattern of China’s digital economy using the Moran index [24,25], and previous research has explored the geographical disparities in China’s digital economy, employing the Terre index [26] or the Gini coefficient [27]. There are also studies that focus on regional differences within specific areas, such as the Yangtze River Economic Belt, Beijing–Tianjin–Hebei, and Guangdong–Hong Kong–Macao [26,28,29]. However, existing studies still require refinement: firstly, the disparities in the extent and sources of digital economy development across sub-regions are not adequately explored, and the development countermeasures provided are not sufficiently targeted; secondly, there is a lack of an intuitive portrayal of the spatial-temporal evolution of the digital economy development level, making it challenging to ascertain the current status and predict future trends of digital economy development in each region and the country as a whole. Although extensive research has been conducted on the digital economy both domestically and internationally, the rapid pace of its development underscores the importance of clarifying its trends. Firstly, this paper endeavors to establish a scientific and comprehensive evaluation index system, employing objective measurement methodologies to assess the digital economy levels across various provinces in China. Secondly, the Dagum Gini coefficient is utilized to analyze and dissect the disparities in the digital economy nationwide, as well as within four major regions categorized based on geographical and economic factors. Furthermore, an in-depth exploration of the dynamic development of the digital economy in both the nation and these four regions is conducted using the three-dimensional kernel density method. Lastly, the spatial and temporal evolution of the national digital economy is analyzed through the lens of the center of gravity shift and standard deviation ellipse.

3. Data Processing and Research Methods

3.1. Indicator Selection and Data Description

Numerous scholars have developed various index systems to assess the digital economy’s progress level from different perspectives. Xue et al. developed an index system based on the digital basic environment, digital industrialization, and industrial digitization [30]. Chen et al. added the dimension of digital investment to the bases of digital foundation and digital industry scale [18].

The concept of “technology-economy” is foundational to the digital economy [31], emphasizing the dominance of technology [32]. The Internet is fundamental to digital economy development, and the breadth of Internet usage significantly reflects the digital economy level. The roles of digital technology depend on digital infrastructures, in which robust digital infrastructure construction can reduce information transportation costs and enhance the effectiveness of knowledge flow. Digital technology updates and iterates rapidly, and the key to maintaining the long-term vitality of digital technology lies in the capacity for digital innovation. The extent of digital technology application is a crucial factor for value creation. The degree of digital technology utilization by governments, businesses, and the public, as builders, service providers, and users of digital infrastructure, as well as formulators and change agents of organizations and systems, significantly impacts the value created by the digital economy. An indicator system to assess the digital economy level is established based on existing research findings, encompassing four dimensions: Internet development [33,34,35], digital infrastructure [21,36], digital innovation capacity [21], and digital technology application [21,33,34], with the individual indicators delineated in

Table 1. Indicator system of the digital economy development level.

First-Level Indicator	Second-Level Indicator	Third-Level Indicator
Internet evolution	Internet user	Internet broadband access users
		Internet broadband access port
	Network construction	Number of domain names
		IPv4 ratio
Digital infrastructure	Digital infrastructure	Capacity of mobile telephone exchange
		Long-distance optical cable line length
	Digital popularity level	Mobile phone penetration rate
Digital innovation capacity	Digital innovation investment	Full-time equivalent R&D personnel of industrial enterprises above designated size
		R&D funds for industrial enterprises above designated size
	Digital innovation outputs	The number of inventions related to the digital economy applied for in the year
		The number of inventions related to the digital economy authorized in the year
		Revenue from software operations
		Revenue from software products
Digital technology application	The application of digital technology by the public	Computers per 100 population
	The application of digital technology by the enterprise	Number of websites owned by 100 enterprises
		Percentage of companies with e-commerce activities
	The application of digital technology by the government	Attention to digital technology applications in government

. Among them, “the application of digital technology by the government” and “the number of patent applications and authorizations related to the digital economy” are new indicators.

The sample data are sourced from the China Statistical Yearbook, provincial statistical yearbooks, the China Science and Technology Statistical Yearbook, and provincial government work reports. In addition, the degree of governmental digital technology application is assessed by analyzing the attention given to governmental digital technology applications and the number of terminals in public libraries’ electronic reading rooms. The attention to governmental digital technology applications is determined by extracting 121 keywords related to digital technology and digital applications from the governmental work reports of each province using Python 2019.3.1. These keywords include “Big Data”, “5G”, “Cloud Computing”, “Industrial Internet”, “artificial intelligence (AI)”, “Mobile Internet of Things”, “Smart Agriculture”, “E-Commerce”, “blockchain”, “government affairs platform”, etc. The frequency of their occurrence is determined. All 121 keywords can be found in Appendix A 

Table A1. The keywords related to digital technology and digital applications.

Index 1	Index 2	Keyword
Digital technology	Big data	Big data; Data mining; Data warehouse; Heterogeneous data; Augmented reality; Mixed reality; Virtual reality; Digital twin
	Cloud computing	Cloud computing; Flow computing; Graph calculation; Memory computing; Secure multi-party computation; Brain-; spired computing; Green computing; Cognitive computing; Fusion architecture; Billion-level concurrency; Eb-level storage; Internet of Things; Cyber-physical system; Cloud platform; Quantum computing
	Blockchain	Blockchain; Digital currency; Distributed computing; Differential privacy technology; Smart contract
	Artificial intelligence	Artificial intelligence; Machine learning; Mining algorithm; Intelligent algorithm; Robot; Expert System; Virtual reality; Intelligent technology; Computer vision; Business intelligence; Decision support system; Decision support system; Intelligent robot; Intelligent data analysis
	Communication technology	Network security; 4G; 5G; 6G; Communication; 5G network; Satellite
	Internet of Things	Internet of Things; Radio frequency identification; RFID; Infrared sensor; Positioning system; Laser scanner; Intelligent sensing; Navigation system; Mobile Internet of Things
Digital application	Industry	Industrial Internet; Intelligent manufacturing; Digital supply chain; Intelligent supply chain; Driverless car; Smart home; Intelligent production equipment; Industrial digitalization; Smart wearable; Intelligent transportation
	Agriculture	Digital agriculture; Smart agriculture; Agricultural big data; Agricultural big data platform; No one tills; Unmanned agriculture
	Service industry	Platform Internet; smart medical care; Smart elderly care; Unmanned bank; E-commerce; Mobile payment; Online entertainment; Mobile Internet; Internet-based medical care; E-commerce; Third-party payment; NFC payment; Intelligent energy; B2B; B2C; C2B; O2O; Internet connection; Intelligent medical care; Intelligent customer service; Smart home; Autonomous driving; Intelligent investment advisor; Intelligent cultural tourism; Intelligent environmental protection; Smart grid; Unmanned retail; Online finance; Digital finance; Financial technology; Quantitative finance; Open banking; Intelligent warehousing; Unmanned retail; Digital RMB; Digital economy; Information industry
	Digital Government	Digital government; Smart city; Smart village; Government affairs platform; Rural big data cloud platform; Data center; Intelligent computing center; Digital service system; Government affairs service platform; Government affairs application system

. The adoption of digital financial applications is gauged using the Digital Inclusive Finance Index created by the Digital Finance Research Center at Peking University [37]. The study sample covers 30 provinces, excluding Tibet due to data unavailability, and spans from 2013 to 2022. According to factors such as geographical location, natural conditions, and economic level, the whole country is divided into four major regions: east, central, west, and northeast. The division results are shown in Appendix A 

Table A2. The provinces included in each region.

Region	Province
The East	Beijing, Tianjin, Hebei, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Hainan
The Central	Shanxi, Anhui, Jiangxi, Henan, Hubei, Hunan
The West	Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang
The Northeast	Heilongjiang, Jilin, Liaoning

.

3.2. Calculation Method

3.2.1. Entropy Weight TOPSIS Method

The entropy weight method allocates weights to various indicators impartially, minimizing subjective bias and the issue of data overlap [38]. TOPSIS is a widely used method that leverages raw data to evaluate the digital economy levels across provinces [39]. Firstly, the data are standardized to eliminate dimensional differences; secondly, weights are assigned to the indicators; and finally, the weighted value of the digital economy is obtained. The entropy weight TOPSIS calculation proceeds as follows:

(1) Assume there are m items to evaluate, each with n indicators. Construct the evaluation matrix X by Equation (1).

$$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}& x_{m2}& \dots & x_{mn}\end{array}\right]$$

(1)

(2) Standardize the data.

$$x_{ij}^{’}=\{\begin{array}{c}{\displaystyle \frac{x_{ij}-x_{min}}{x_{max}-x_{min}}};\mathrm{The} j \mathrm{column} \mathrm{is} \mathrm{positive} \mathrm{indicators}\\ {\displaystyle \frac{x_{max}-x_{ij}}{x_{max}-x_{min}}};\mathrm{The} j \mathrm{column} \mathrm{is} \mathrm{positive} \mathrm{indicators}\end{array} i=1, 2, \dots , m;j=1, 2, \dots , n$$

(2)

In Equation (2), $x_{ij}$ represents the value in the ith row and jth column, indicating the jth indicator for the ith item. $x_{max}$ and $x_{min}$ are the maximum and minimum values in the jth column, respectively.

(3) Calculate the characteristic weight $p_{ij}$ by Equation (3).

$$p_{ij}={\displaystyle \frac{x_{ij}^{’}}{{{\displaystyle \sum }}_{i=1}^n{x}_{ij}^{’}}}$$

(3)

(4) Determine the information entropy ($e_j$) for each indicator, where $p_{ij}\ln p_{ij}$ = 0 is taken when $p_{ij}$ is equal to 0. A lower entropy value indicates more variability in the index, warranting a higher weight by Equation (4).

$$e_j=-{\displaystyle \frac{1}{\ln n}}{\displaystyle \sum }_{i=1}^n{p}_{ij}\ln p_{ij}$$

(4)

(5) Assign weights to each indicator by Equation (5).

$$W_j={\displaystyle \frac{1-e_j}{{{\displaystyle \sum }}_{j=1}^m\left(1-e_j\right)}}$$

(5)

(6) Formulate the digital economy level weighting matrix by Equation (6).

$$Z_{ij}=x_{ij}^{’}\times W_j$$

(6)

(7) Establish the optimal solution vectors by Equations (7) and (8).

$$z_j^{*+}=\left(z_1^{+},z_2^{+},\dots ,z_n^{+}\right)$$

(7)

$$z_j^{*-}=\left(z_1^{-},z_2^{-},\dots ,z_n^{-}\right)$$

(8)

where $z_i=w_j\times x_{ij}^{\text{’}}$, $z_i^{+}=\max \left(z_i\right)$, and $z_i^{-}=\min \left(z_i\right)$.

(8) Compute the ideal solution and the comprehensive score by Equations (9)–(11).

Calculate the Euclidean distances $D_i^{+}$ and $D_i^{-}$ as well as the overall score $C_i$ of the digital economy level of the ith province.

$$D_i^{+}=\sqrt{{\displaystyle \sum }_{j=1}^m{\left(Z_{ij}-Z_j^{*+}\right)}^2}$$

(9)

$$D_i^{-}=\sqrt{{\displaystyle \sum }_{j=1}^m{\left(Z_{ij}-Z_j^{*-}\right)}^2}$$

(10)

$$C_i={\displaystyle \frac{D_i^{-}}{D_i^{+}+D_i^{-}}}$$

(11)

where the greater the $C_i$ value, the higher the development level of the digital economy in province i.

3.2.2. Dagum Gini Coefficient and Its Decomposition

The Dagum Gini coefficient is utilized to analyze geographical disparities and their origins [40]. This coefficient offers a detailed examination of the distribution within sub-samples and mitigates issues of cross-overlap among samples, distinguishing it from traditional measures such as the Gini coefficient, coefficient of variation, and Theil index, thus providing greater scientific precision for analyzing spatial differences.

First, calculate the Dagum Gini coefficient, and then decompose it into intra-regional coefficients, inter-regional coefficients, and the intensity of transvariation. The intra-regional coefficients reflect the differences within each region, the inter-regional coefficients reflect the differences among regions, and the intensity of transvariation reflects the degree of cross-overlap among regions.

(1) Calculate the comprehensive Dagum Gini coefficient (G), which is defined by Equation (12):

$$G={\displaystyle \frac{1}{2n^2{\mu }_n}}{\displaystyle \sum }_{i=1}^k{\displaystyle \sum }_{j=1}^k{\displaystyle \sum }_{h=1}^{n_i}{\displaystyle \sum }_{r=1}^{n_j}\left|y_{n,ih}-y_{n,jr}\right|$$

(12)

where k is the serial number of regions. $y_{n,ih}$ ($y_{n,jr}$) represents the digital economy development level for province h (r) within area i (j) during year n; ${\mu }_n$ denotes the average digital economy development level in year n; and $n_i$ ($n_j$) indicates the number of provinces within area i (j).

(2) Calculate the intra-regional differences, inter-regional differences, and the intensity of transvariation.

The comprehensive Dagum Gini coefficient (G) (Equation (13) below) is broken down into intra-regional differences ($G_{n,w}$) (Equations (14) and (15) below), inter-regional differences ($G_{n,nb}$) (Equations (16) and (17) below), and the intensity of transvariation ($G_{n,t}$) (Equation (18) below).

$$G=G_{n,w}+G_{n,nb}+G_{n,t}$$

(13)

$$G_{n,ii}={\displaystyle \frac{1}{2n_i^2{\mu }_{n,i}}}{\displaystyle \sum }_{h=1}^{n_i}{\displaystyle \sum }_{r=1}^{n_j}\left|y_{n,ih}-y_{n,ir}\right|$$

(14)

$$G_{n,w}={\displaystyle \sum }_{i=1}^k{p}_i{s}_i{G}_{n,ii}$$

(15)

$$G_{n,ij}={\displaystyle \frac{1}{n_i{n}_j({\mu }_{n,i}+{\mu }_{n,j})}}{\displaystyle \sum }_{h=1}^{n_i}{\displaystyle \sum }_{r=1}^{n_j}\left|y_{n,ih}-y_{n,jr}\right|$$

(16)

$$G_{n,nb}={\displaystyle \sum }_{i=2}^k{\displaystyle \sum }_{j=1}^{i-1}\left(p_j{s}_i+p_i{s}_j\right)G_{n,ij}{D}_{n,ij}$$

(17)

$$G_{n,t}={\displaystyle \sum }_{i=2}^k{\displaystyle \sum }_{j=1}^{i-1}\left(p_j{s}_i+p_i{s}_j\right)G_{n,ij}(1-D_{n,ij})$$

(18)

where $p_i=n_i/n$, $s_i=p_i{\mu }_i/\mu$ and $D_{n,ij}=\left(d_{n,ij}-p_{n,ij}\right)/\left(d_{n,ij}+p_{n,ij}\right)$. $d_{n,ij}$ represents the difference in digital economy development levels between the ith area and the jth area in the year n. $d_{n,ij}$ is represented by Equation (19). $p_{n,ij}$ represents the initial instance of transvariation, as described in Equation (20).

$$d_{ij}={{\displaystyle \int }}_0^{\infty }{{\displaystyle \int }}_0^y\left(y-x\right)f_j\left(x\right)dx{f}_i\left(y\right)dy$$

(19)

$$d{p}_{ij}={{\displaystyle \int }}_0^{\infty }{{\displaystyle \int }}_0^y\left(y-x\right)f_i\left(x\right)dx{f}_j\left(y\right)dy$$

(20)

3.2.3. Three-Dimensional Kernel Density Estimation

The core of kernel density analysis is converting spatial data points into continuous density surfaces through a sliding window (i.e., kernel function). Continuous density curves are a powerful tool to examine a spatial disequilibrium and to identify the dynamic evolution features of the digital economy growth level [41]. The horizontal position of the kernel density curve in a specific year represents the digital economy level, while the height of the curve’s peak reflects the extent of integration within that interval, with a higher peak indicating a greater data density. The number of peaks on the curve indicates the level of polarization in the sample data. The curve’s distribution ductility, or the degree of trailing, shows the largest disparity in digital economy levels across different provinces within the region. The longer the trailing, the greater the disparity within the region. Three-dimensional kernel density maps allow for a vertical comparison of the kernel density curves from different years to track the dynamic evolution of the digital economy development level and a horizontal comparison to discern variations in digital economy levels.

Suppose (z,q) is a two-dimensional random variable. F(z,q) is a joint kernel density estimator of variable (z,q). The kernel density is calculated by Equation (21).

$$f\left(z,q\right)={\displaystyle \frac{1}{n{h}_z{h}_q}}{\displaystyle \sum }_{i=1}^n{K}_z\left({\displaystyle \frac{z-z_i}{h_z}}\right)K_q\left({\displaystyle \frac{q-q_i}{h_q}}\right)$$

(21)

where $K_z(·)$ and $K_q(·)$ denote the kernel density functions, $z_i$ and $q_i$signify the digital economy development levels, z and q represent the mean values, n is the number of provinces in the region, and $h_z$ and $h_q$refer to the window widths. In reference to other studies, the kernel function is usually chosen as a Gaussian kernel function for estimation, which is computed by Equation (22).

$$K\left(x\right)={\displaystyle \frac{1}{\sqrt{2\pi }}}\exp \left(-{\displaystyle \frac{x^2}{2}}\right)$$

(22)

3.2.4. Center of Gravity Migration Model

The center of gravity migration model calculates the center of gravity coordinates and migration distance for each time point based on geographical location and weight and combines Arcgis to draw the migration trajectory. It analyzes the movement characteristics of the digital economy’s center of gravity, providing an intuitive law of spatial agglomeration displacement.

(1)

Calculate the coordinates of the center of gravity, which are determined by Equation (23) [42]:

$$\overline{X}={\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^n{C}_i{X}_i}{{{\displaystyle \sum }}_{i=1}^n{C}_i}},\overline{Y}={\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^n{C}_i{Y}_i}{{{\displaystyle \sum }}_{i=1}^n{C}_i}}$$

(23)

where ($X_i$, $Y_i$) are the latitude and longitude coordinates of the center of gravity of province i, $C_i$ is the digital economy development level of province i, n is the number of provinces, and ($\overline{X}$, $\overline{Y}$) are the latitude and longitude coordinates of the center of gravity of the digital economy.

(2)

Calculate the distance of the center of gravity migration using Equation (24):

$$D_{s-t}=R\sqrt{{\left(X_s-X_t\right)}^2+{\left(Y_s-Y_t\right)}^2}$$

(24)

where $D_{s-t}$ is the distance of the center of gravity migration from year t to year s, R is the conversion coefficient, that is, the coefficient of conversion of Earth surface coordinate units into plane distances, which is taken as a constant of 111.111 km [43], and ($X_s$, $Y_s$) are the coordinates of the center of gravity of the digital economy in the year s, while those in the year t are ($X_t$, $Y_t$).

3.2.5. Standard Deviation Ellipse Model

The standard deviation ellipse is a spatial statistical method that illustrates the geospatial deviation of point elements in various directions [44]. First, calculate the azimuth of the standard deviation ellipse using the center of gravity coordinates and then calculate the major and minor axes. The fundamental components of the standard deviation ellipse, including the centroid, the standard deviation of the major and minor axes, and the azimuthal angle, reveal the centrality, distribution, directionality, and spatial pattern of point elements, offering a more intuitive demonstration of the dynamic process of geospatial evolution.

(1)

Calculate the direction of the ellipse using Equation (25).

$$\tan \theta ={\displaystyle \frac{\left({{\displaystyle \sum }}_{i=1}^n{C}_i^2{\overline{x}}_i^2-{{\displaystyle \sum }}_{i=1}^n{C}_i^2{\overline{y}}_i^2\right)+\sqrt{{\left({{\displaystyle \sum }}_{i=1}^n{C}_i^2{\overline{x}}_i^2-{{\displaystyle \sum }}_{i=1}^n{\overline{y}}_i^2\right)}^2+4{{\displaystyle \sum }}_{i=1}^n{C}_i^2{\overline{x}}_i^2{\overline{y}}_i^2}}{2{{\displaystyle \sum }}_{i=1}^n{C}_i^2\overline{x_i}\overline{y_i}}}$$

(25)

(2)

Calculate the standard deviation.

The standard deviation of the X-axis is calculated using Equation (26).

$${\sigma }_x=\sqrt{{\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^n{\left(C_i\overline{x_i} cos\theta -C_i\overline{y_i} sin\theta \right)}^2}{{{\displaystyle \sum }}_{i=1}^n{C}_i^2}}}$$

(26)

The standard deviation of the Y-axis is calculated using Equation (27).

$${\sigma }_y=\sqrt{{\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^n{\left(C_i\overline{x_i} sin\theta -C_i\overline{y_i} cos\theta \right)}^2}{{{\displaystyle \sum }}_{i=1}^n{C}_i^2}}}$$

(27)

where $\theta$ is the azimuth of the ellipse, representing the angle of rotation in a clockwise direction from the north to the principal axis of the ellipse. $\overline{x_i}$ and $\overline{y_i}$ represent the deviation of the study object’s spatial coordinates from the average center.

4. Results and Discussion

4.1. Digital Economy Development Level in China

The study employed the equidistance discontinuity method of ArcGIS 10.8 software to analyze the spatial distribution attributes of the digital economy across different provinces in China. Figure 1 shows the spatial distribution attributes of the digital economy in China. In Figure 1, the digital economy level is divided into five levels, which are obtained according to the maximum digital economy level of all provinces in 10 years, to ensure that the change of digital economy is more directly reflected under the same standard. The results in Figure 1a show that in 2013, China’s digital economy exhibited regional disparities, with higher concentrations in the east and lower in the west. Beijing and Guangdong emerged as leaders in the digital economy, with Shandong, Jiangsu, and Zhejiang following as the second tier, and the remaining provinces comprising the third tier. In Figure 1b, the digital economy level in Jiangsu rapidly improved, propelling it into the top tier, and coastal regions demonstrated a strong developmental momentum, enhancing the vibrancy of neighboring areas. Shanghai and Fujian ascended to the second tier in 2016. In Figure 1c, the digital economy in eastern provinces continued to expand, dominating the top tier, with a noticeable ripple effect, leading the central provinces to rise to the second tier in 2019. In Figure 1d, the central and eastern regions continue to grow, and Shandong enters the first tier of the digital economy in 2022, while Anhui and Hunan are in the second tier.

A comprehensive comparison of Figure 1a–d reveals a substantial disparity in China’s digital economy development level, consistent with the findings of previous scholars [45], showing a clear east-to-west gradient with a clear advantage in the southeast coastal region, and a strong development momentum in the central region in the later stages of research.

Figure 2 shows the value and growth percentage of the digital economy development level of each province and the national average for 2013 and 2022. The image shows a significant disparity in the level of digital economy development. In 2013, the digital economy levels in Beijing, Guangdong, Jiangsu, Liaoning, Shandong, Shanghai, Sichuan, and Zhejiang surpassed the national average; by 2022, all except Liaoning maintained this status. The analysis reveals that Beijing, Guangdong, Jiangsu, Shandong, Shanghai, Sichuan, and Zhejiang have consistently led the country’s digital economy, while Liaoning has fallen behind due to industrial path dependence and other factors. It experienced a 34.30% increase in the level of digital economy during the research period, the lowest growth rate in the country. Except for Hainan, Hebei, Liaoning, Inner Mongolia, Shandong, Shanxi, and Yunnan, the growth rates of all other provinces exceeded 100%. Due to the growth percentage and the base value, the disparity in digital economy levels among provinces widened by 2022, exemplifying the polarization phenomenon of “the strong get stronger and the weak get weaker”. Similarly, Hou et al. noted significant fluctuations and gaps in China’s digital economy level [46], while Yu et al. identified a “four-polarization” pattern centered around Beijing–Tianjin–Hebei, the Pearl River Delta, Chengdu–Chongqing, and the Yangtze River Delta, with provincial capitals leading a pattern of “small agglomeration, large dispersion” [47], which aligns with the findings of this study.

4.2. Analysis of Regional Differences in the Digital Economy Development Level

4.2.1. Overall Regional Differences and Sources of the Digital Economy Development Level

Utilizing the Dagum Gini coefficient decomposition method, this paper elucidates the factors contributing to regional disparities within the digital economy. This analysis quantifies the variations and underlying causes of the digital economy across China from 2013 to 2022 (

Table 2. Dagum Gini coefficient decomposition and contribution rate of digital economy levels in China.

Year	Overall	Contribution Rate (%)
		Intra-Regional (${\mathit{G}}_{\mathit{n},\mathit{w}}$)	Inter-Regional (${\mathit{G}}_{\mathit{n},\mathit{n}\mathit{b}}$)	Intensity of Transvariation (${\mathit{G}}_{\mathit{n},\mathit{t}}$)
2013	0.378	21.670	68.615	9.715
2014	0.361	21.380	69.147	9.473
2015	0.350	21.307	69.295	9.398
2016	0.354	21.189	69.885	8.926
2017	0.359	20.834	69.916	9.250
2018	0.355	21.576	68.820	9.605
2019	0.354	22.072	68.594	9.334
2020	0.356	22.782	67.507	9.711
2021	0.365	22.357	68.468	9.175
2022	0.378	22.200	68.571	9.228

). This approach offers a more precise and scientific method for examining spatial variations compared to traditional metrics such as the standard Gini coefficient, coefficient of variation, and Theil’s index, as it fully accounts for the distribution of subsamples and the overlap among samples. The Gini coefficient exhibits a declining trend from 2013 to 2015, fluctuates from 2015 to 2019, and increases from 2019 to 2022. Comparing the overall Gini coefficient of the digital economy between 2013 and 2022, it is evident that significant regional disparities persist, with the overall Gini coefficient ranging between 0.35 and 0.38, which is within a relatively reasonable range. The inequality in the digital economy stems from inter-regional variations, showing a trend of growth–decline–growth, with the hypervariable density contributing the least, while intra-regional disparities account for the remainder. This echoes the findings of Luo and Zhou [45], who state that regional differences dominate in their study.

4.2.2. Decomposition of Regional Differences in the Digital Economy Development Level

Figure 3 illustrates the intra-regional variations of the Gini coefficient and the digital economy level throughout China’s four major regions from 2013 to 2022. The complete data for Figure 3 and Figure 4 are provided in Appendix A,

Table A3. Dagum Gini coefficient decomposition of digital economy levels in China’s four major regions.

Year	Intra-Regional Differences				Inter-Regional Differences
	East	Central	West	Northeast	East–Central	East–West	East–Northeast	Central–West	Central–Northeast	West–Northeast
2013	0.327	0.231	0.103	0.208	0.430	0.416	0.537	0.200	0.288	0.248
2014	0.311	0.222	0.110	0.187	0.417	0.400	0.516	0.192	0.269	0.237
2015	0.303	0.109	0.207	0.179	0.385	0.416	0.503	0.184	0.236	0.248
2016	0.296	0.099	0.168	0.197	0.397	0.478	0.503	0.176	0.225	0.199
2017	0.294	0.087	0.152	0.203	0.410	0.491	0.513	0.165	0.224	0.192
2018	0.311	0.093	0.110	0.193	0.393	0.494	0.504	0.182	0.231	0.166
2019	0.312	0.081	0.216	0.117	0.377	0.495	0.503	0.236	0.212	0.179
2020	0.333	0.073	0.211	0.120	0.373	0.498	0.493	0.241	0.201	0.176
2021	0.336	0.074	0.201	0.119	0.394	0.511	0.515	0.232	0.204	0.169
2022	0.337	0.090	0.215	0.134	0.399	0.529	0.524	0.254	0.215	0.185

. The chart illustrates that the intra-regional disparity within the digital economy level of Eastern China was most pronounced from 2013 to 2022. The intra-regional disparity within the digital economy level of the central region had been shrinking, becoming the region with the smallest internal difference among the four regions by 2015. The intra-regional disparity in the digital economy level in the northeast region demonstrated a fluctuation pattern of “decrease-increase-decrease-increase”, with an overarching downward trend, suggesting a narrowing of intra-regional deviations in digital economy levels. The intra-regional disparity in the western area demonstrated a variable increase, exceeding that of the central and northeastern areas in 2019, and ranking second only to the eastern region.

From 2013 to 2022, Figure 4 delineates the variations in the inter-regional Gini coefficient and the developmental trajectory of the digital economy across China’s four principal regions. The diagram shows that the disparity between the east and northeast regions is most pronounced, with the east–west gap following closely. The analysis of the evolutionary pattern indicates a decreasing trend in inter-regional disparities across the east–northeast, east–central, central–northeast, and west–northeast relationships, while disparities between the east–west and central–west relationships are widening. This pattern highlights that the digital economy in the western region lags behind the eastern and central regions, with this gap widening over time. The digital infrastructure and Internet infrastructure of the eastern region is significantly better than that of the western region, and the return on capital generated by expanding digital investment is higher than that of the western region. In the evaluation index system of the digital economy, the regional gap between software operations and the software product income index is the largest. The eastern region has a leading level of digital technology innovation and a huge market capacity, and the digital economy plays an effective market role, enabling the eastern region to obtain more revenue from digital products and services, resulting in a widening difference between the east and the west.

Compared with the conclusions drawn by Luo and Zhou [45], who utilized the Gini coefficients at the beginning and end of their study period to determine that intra- and inter-regional disparities had decreased, this paper provides a more intuitive and reliable analysis of disparity changes through line graphs. The narrowing intra-regional disparities observed in the northeast and central regions can be attributed to regional economic integration policies. In contrast, intra-regional disparities within the western region have fluctuated and increased due to policies advocating “the wealthy first driving the less wealthy”, whereas disparities within the eastern region have shown a slight increase. Inter-regional disparities indicate that the digital economy level in the eastern region remains significantly higher than in other regions, and widening gaps between regions may further exacerbate the digital divide.

4.3. Characteristics of the Spatial and Temporal Evolution of the Digital Economy Development Level

4.3.1. Kernel Density Estimation

The dynamic evolution tendency of the digital economy level across the entire country is examined using kernel density estimation. The results for China’s four major regions are presented in Figure 5.

In Figure 5a, the distribution centers for the nation exhibited no notable movement. The main peak was lower, reflecting a broadening in the dispersion of the digital economy at the national level and an increase in the absolute differences, which is influenced by resource endowments, location advantages, and industrial structures. From the standpoint of distribution extensibility, the national three-dimensional kernel density curve exhibits a pronounced right tail, indicating that the digital economy levels of some provinces are significantly higher than others. From the perspective of the number of wave peaks, the national kernel density curve initially shows a primary peak and several side peaks, indicating a gradient effect in the national digital economy level. After 2017, it transitions to a single peak, indicating a weakening trend of multipolarity.

In Figure 5b, the distribution centers for the eastern region exhibited no notable movement. The reduction in and narrowing of the main peak suggest a growth in the disparity within the digital economy across the provinces. The overall level of digital economy in each province is relatively high, but the differences are large, and the efficiency of resource utilization is different, and there is a “siphon effect” leading to the widening of the gap. The emergence of a right tail suggests a widening disparity among provinces; Beijing, Shanghai, and Guangdong have obvious advantages. It maintains a single peak, and bipolarity does not occur.

In Figure 5c, the distribution center of the central region shifted rightward, signifying an enhancement in the digital economy development level within the region. The central provinces have actively advanced digital transformation, fostering advanced digital industrial clusters of several trillion CNY and unleashing the potential of the digital economy. The main peak in the central region initially decreased and then rose, indicating a temporary widening followed by a narrowing of disparities among the provinces. Provinces with a robust digital economy, such as Hubei and Henan, have taken the lead in developing core industries of the digital economy, thereby contributing to the widening of regional disparities. These provinces have also fostered close linkages and coordinated development, leveraging knowledge spillover effects and radiation to promote the growth of surrounding areas, ultimately helping to narrow these disparities. A left tail in the central region’s curve indicates that some provinces significantly lag behind their counterparts and the wave peak transitions from a single peak to dual peaks, demonstrating the beginning of polarization in the digital economy level. Hubei and Henan provinces in the region have spearheaded the development of digital industries, exhibiting a pronounced digital agglomeration effect that has contributed to the emergence of regional polarization.

In Figure 5d, the distribution centers for the western region exhibited no notable movement. The lowering of the main peak denotes an increase in the variance among provincial digital economy levels. Chongqing and Guizhou have made great efforts to develop digital industries and have developed certain advantages. A pronounced right tail indicates that some provinces have higher digital economy levels than others, and double peaks indicate a persistent polarization phenomenon. Sichuan in the region has set up a series of national-level data centers and digital industrial clusters, fostering the rapid expansion of its digital economy.

In Figure 5e, the northeastern region’s center shifted leftward, indicating a decline in its digital economy development level. The digital transformation of traditional industries in the northeast provinces faces significant challenges due to having a relatively industrial structure, an over-reliance on heavy industries, and the slower development of the information technology sector. The rising and narrowing of the main peak indicate a growing concentration of the digital economy, with a gradual reduction in absolute differences among provinces. This trend is closely tied to the region’s reliance on established industrial paths and similar economic bases. The northeastern region shows no obvious trailing, indicating that the differences in digital economy levels among the three northeastern provinces are relatively minor, reflecting the synergistic development within the region. The presence of double peaks both at the initial and final stages of the study suggests a re-emergence of polarization after its initial disappearance. This region has experienced significant fluctuations, primarily due to the intricate nature of the transition from traditional heavy industries.

The kernel density analysis results indicate that China’s digital economy level still varies significantly, with developmental tendencies differing across regions. The digital economy level is relatively high in the eastern area, showing no signs of polarization, but the differences among provinces within the area are progressively widening. This is mentioned in the research study by Zhou and Chen [48], who think that the Beijing–Tianjin–Hebei and coastal regions, with their developed information technology industries, tend to siphon resources from neighboring provinces. The disparities among provinces in the central area and the western area are gradually increasing, leading to polarization. As Zhou and Chen highlighted in their research, central provinces, including Hubei and Hunan, have effectively harnessed technology and resources transferred from the eastern regions, significantly enhancing their digital economies [48]. The study further indicates that Sichuan’s digital economy is prominent within the western region [25]. The digital economy in the northeast area has not shown significant improvement, and regional disparities remain relatively limited. As noted by Tian et al. [49], their research highlights that the digital transformation of resource-based industries, which dominate the region, has been slow. Additionally, insufficient government investments in science and technology have contributed to the delayed development of the digital economy in this area.

4.3.2. Center of Gravity Migration

Table 3. Coordinates of the center of gravity of China’s digital economy from 2013 to 2022.

Year	Gravity Coordinates of the Digital Economy Center	Year	Gravity Coordinates of the Digital Economy Center
2013	(114.518° E, 33.243° N)	2018	(114.238° E, 32.569° N)
2014	(114.441° E, 33.193° N)	2019	(114.167° E, 32.512° N)
2015	(114.370° E, 33.036° N)	2020	(114.199° E, 32.652° N)
2016	(114.298° E, 32.721° N)	2021	(114.263° E, 32.643° N)
2017	(114.349° E, 32.608° N)	2022	(114.374° E, 32.701° N)

displays the coordinates of the digital economy’s center of gravity from 2013 to 2022, and Figure 6 depicts its migration path. The data reveal that the center of gravity was consistently located in Henan province, specifically between the latitudes of 32.512° N and 33.243° N. Over the decade, the center of gravity shifted southward, traveling a total distance of 129.757 km.

From 2013 to 2016, the center of gravity moved southwestward from Shangcai County to Runan County in Henan Province. It then shifted southeastward to Zhengyang County from 2016 to 2017, followed by a southwesterly movement to Zhushan County over the next two years. From 2019 to 2023, it migrated northeastward back to Zhengyang County.

The study indicates that the gravitational center of the digital economy has shifted southward. Wu et al. also pointed out in their research that, due to the accelerated construction of the digital economy in the Yangtze River Delta and the Sichuan–Chongqing region and the establishment of the National Big Data Comprehensive Experimental Zone in Guiyang, the center of gravity of the digital economy has shifted southwestward [50]. This shift is also closely associated with the regional industrial layout; the north has a significant proportion of traditional industries in which digital transformation proves challenging, while the south enjoys a boom in emerging industries and widespread e-commerce penetration. The southward shift of the digital economy’s center of gravity alleviates the population and environmental pressure in the northern regions and promotes the economy in the southwestern regions, but it is not conducive to the digital transformation of industries in the northeastern regions.

4.3.3. Standard Deviation Ellipse

Figure 7 illustrates the standard deviation ellipse of China’s digital economy using ArcGIS 10.8 software in 2013 and 2022.

Table 4. Elliptical parameters of standard deviation of China’s digital economy.

Year	Semi-Axis	Long Semi-Axis	Azimuth	Area of an Ellipse
2013	824,125.291	1,060,090.767	14.627	2,744,492,046,963.689
2022	820,866.862	1,025,000.913	12.783	2,643,158,103,411.756

shows the elliptical parameters of the standard deviation of China’s digital economy. The ellipse predominantly covers the eastern and central regions, with an orientation that is roughly north–south. From 2013 to 2022, the area of the ellipse decreased, and its orientation shifted slightly southeastward, with the specific characteristics detailed in Table 3. Changes in the standard deviation ellipse parameters reveal that the short semi-axis narrowed from 824,125.291 to 820,866.862, indicating an increase in the centripetal force within the digital economy. The long semi-axis was reduced from 106,090.767 to 1025,000.914, and the ratio of the short to long semi-axis increased from 0.777 to 0.801, suggesting a decrease in the ellipse’s flattening rate and a convergence towards a more orthorhombic shape, reflecting an increase in the dispersion of China’s digital economy. The azimuthal alteration of the ellipse indicates a counterclockwise rotation of 1.844° from 2013 to 2022, highlighting a more pronounced north–south orientation in the overarching structure of the digital economy.

From the perspective of ellipse shape and parameter variations, the distribution pattern of the digital economy is predominantly oriented along the north–south axis, though dispersion has increased, indicating a spillover effect. The southwest region should leverage its advantages, such as abundant land resources and low-temperature climate conditions, to accelerate its development under regional strategies such as “East Data West Computing”, the Western Development Initiative, and the promotion of digital industry growth in central China. Such measures would help optimize the allocation of digital resources, promote digital industry development, create employment opportunities, and maintain social stability.

5. Conclusions

Utilizing the definition of the digital economy and the “technology-economy” paradigm, the study developed an indicator system to assess the level of digital economic development across 30 provinces. It then examined regional disparities and determinants of digital economic development and analyzed the spatial evolution of the digital economy. The main findings are as follows: (1) There is a marked disparity in China’s digital economy, described as “high in the east and low in the west”, with increasing provincial polarization. The coastal areas have obvious advantages in the digital economy. Beijing, Guangdong, Jiangsu, Shandong, Shanghai, Sichuan, and Zhejiang have consistently led the country’s digital economy.

(2) The spatial disparities in the digital economy are primarily due to inter-regional factors, with the most significant intra-regional discrepancy in the eastern area and the most pronounced inter-regional disparity in the east–northeast. Although disparities in digital economy levels across provinces nationwide have increased, the trend toward multipolarization has weakened. Regionally, disparities among eastern provinces have widened without evident polarization. The digital economy in central China has notably improved, accompanied by emerging polarization. Significant disparities and persistent polarization characterize the digital economy in the western region. In Northeast China, the level of digital economic development shows a declining trend, with polarization observed at both the beginning and end of the research period.

(3) The overall migration path of the center of gravity of China’s digital economy is southward, and the spatial distribution pattern of the digital economy is southward and northward, with a trend of dispersion, which is specifically manifested by the standard deviation ellipse decreasing in area, reorienting southeastward, and becoming more elliptically rounded.

6. Practical Implications

This research has significant practical significance for promoting the sustainable development of China’s digital economy. National and local governments can make scientific decisions based on this.

(1) Strengthen cross-regional collaborative cooperation by leveraging the fluidity of data resources and the spillover effects of knowledge and technology. Gradually relocate the digital industries from the eastern regions to the central and western regions to effectively narrow the “digital divide”. Improve digital infrastructure, increase investment in information technology research, and deepen the application of digital technologies. It is vital to accelerate the development of national high-voltage power grids, expedite the rollout of 5G, establish big data centers, and boost computing power. Accelerate the layout of digital industries and facilitate the digital transformation of traditional industries.

(2) Develop the digital economy in accordance with local conditions. In the eastern region, leveraging existing digital infrastructure and economic foundations, schools and enterprises should jointly cultivate high-level multidisciplinary talent, accelerate the innovation and commercialization of digital technologies, and actively facilitate the transfer of talent and technologies to other regions, thereby maximizing knowledge spillover effects and stimulating leapfrog development in other regions. The central region should actively establish computing centers, provide policy support to attract leading Internet enterprises, and foster the formation of digital industry clusters, thus creating a favorable digital ecosystem. The western region needs to enhance digital infrastructure development, improve transportation accessibility, increase policy support, and accelerate the establishment of ‘East Digital and West Computing’ to drive the relocation of related industries and optimize the industrial layout. The northeast should promote digital transformation in enterprises, establish industrial Internet platforms, and advance the integration of digital finance, AI, and smart logistics into traditional industries.

Enterprise managers can also make the following decisions to promote the sustainable development of enterprises:

(1) Develop cross-regional cooperation. Enterprises can exchange information with businesses nationwide through Internet platforms, which not only enhances transaction efficiency and reduces the costs associated with information collection but also expands the industrial chain and strengthens their capacity to mitigate risks.

(2) Improve the digital literacy of enterprises. Increase investment and cooperation in digital technology research and development with universities and research institutes and cultivate digital talent, which is crucial for the continual renewal and iteration of digital technologies.

7. Limitations of the Study and Future Research

This paper acknowledges certain limitations, such as the need to expand the geographical scope of the study to include cities or counties and to consider different urban agglomerations when classifying regions. In the future, extending the sample period will be crucial to more precisely delineate temporal patterns in digital economy development and to explore specific factors influencing its progression, thereby aiding the development of strategic initiatives.