Regional Differences and Spatial-Temporal Evolution Characteristics of Digital Economy Development in the Yangtze River Economic Belt

Abstract

Digital economy has emerged as one of the primary driving forces for economic globalization. However, assessing digital economy development in a robust and scientific manner remains a great challenge. This paper proposes an evaluation system with measurement errors correction to accurately research the regional differences in and the spatial-temporal evolution characteristics of digital economy development in the Yangtze River Economic Belt (YEB), combining the entropy method, the Dagum–Gini coefficient, an $\sigma$ convergence model and grey correlation analysis. The results present that the digital economy development index in the YEB rose from 2012 to 2021, with the greatest weight being social livelihood benefits. Meanwhile, there were noticeable regional differences in digital economy development in the YEB; in particular, the middle reaches showed obvious convergence. The grey correlation degree between the influence factors and the digital economy development ranged from 0.5286 to 0.9144, demonstrating a robust positive correlation. The theoretical framework of this paper integrates economic development models with advanced statistical analysis techniques, providing a robust analytical perspective for examining the complexities of digital economy evolution. The insights offer a blueprint for policymakers seeking to foster a robust and equitable digital economy, underscoring the potential of data-driven policy formulations in navigating the intricate landscape of economic globalization.

1. Introduction

Digital economy is not only the key driving force for promoting the high-quality development of global economy, but also a strategic choice to seize new opportunities in the technological revolution and industrial transformation. Since Tapscott proposed the academic elaboration of “digital economy” in 1996, digital economy has attracted wide attention due to its high innovation, strong penetration and wide coverage [1]. In recent decades, many international organizations and scholars also have undertaken extensive research on the definition and measurement of digital economy [2,3,4,5,6]. Noteworthily, the 14th Five-Year Plan for the Development of Digital Economy in China emphasizes that the digital economy is a new economic form that integrates fairness and efficiency more closely [7,8]. The sustainable development of digital economy is constantly being improved through the promotion of real economic growth [9], the enhancement of market factors and natural resources’ production and utilization efficiency [10,11] and leadership in scientific and technological innovation [12,13]. Compared with the traditional physical economy, the digital economy shows broad application prospects and huge growth potential, which is significant for achieving the sustainable development goals and enhancing the comprehensive competitiveness of the country.

How to comprehensively measure the digital economy development has become one of the key issues in the contemporary statistical field [14]. The data envelopment analysis [15,16,17,18], principal component analysis [19,20,21] and entropy value method [22,23,24,25] have been employed to measure digital economy development in recent years. However, the concept of digital economy is very wide-ranging, and even encompasses various connotations of the boundary of the field from different perspectives. At present, we still lack standard criteria for the selection of indicators to assess digital economy development; additionally, the measurement data are often limited in a specific year or without timeliness [26,27,28,29]. Some research sometimes overlooks the realities of the situation and fails to consider the impact of measurement errors caused by excessive information noise and poor data quality, which will result in a certain bias and inaccuracy during the evaluation [30,31,32,33,34].

The digital economy plays a significant role in enhancing, advancing and fostering the sustainability development of the economic system, and having a profound effect on the global economic landscape [35,36]. Nowadays, China has emerged as a leading player in the global digital economy, showing remarkable development and positioning itself among the fastest-growing nations worldwide. In particular, the YEB covers 11 cities across China’s eastern, central and western regions, and serves as a crucial strategic belt for facilitating the economy’s development [37,38]. Relying on its advantageous geographical location and abundant natural resources, the YEB has experienced rapid development and achieved an advanced level of technological innovation ability. According to the Industrial Development Report, the economic output of the YEB has reached 53.02 trillion yuan by 2021, accounting for 46.14% of the Chinese GDP as a whole. The development of the digital economy in the YEB presents a thriving scene. It is reported that the key aspects of this period encompass the continuous growth of the digital economy, ongoing improvements to network infrastructure, and the seamless integration of digital industries during [39]. However, there are still numerous issues of imbalanced and uncoordinated development among the different reaches along the YEB, which will result in various social and economic development risks [40]. Hence, a comprehensive and objective evaluation of the digital economy’s development in the YEB is significant to promote regional cooperation and formulate sustainable economy improvement strategies.

Digital economy is a hot issue in the field of economy. In recent years, there have been numerous studies focusing on the economic effects brought about by the development of the digital economy, exploring the impact of the digital economy on the development of the green economy, the enhancement of enterprise productivity and the high-quality development of the urban economy. For example, Dai et al. proposed a comprehensive development index, shedding light on its influence on the trajectory of regional green innovation in the realm of digital economy [41]. Zhang et al. demonstrated the substantial influence of the digital economy in improving industrial eco-efficiency within the urban agglomeration of the Yangtze River Delta [42]. Furthermore, Shang et al. conducted an in-depth analysis of the spatial-temporal evolution and elucidated the underlying mechanisms driving the digital economy’s contribution to promoting high-quality economic development [43]. Notedly, there is also a growing interest in examining the measurement and spatial distribution of the digital economy development index. Xian et al. established a measurement framework for China’s core digital economy industries, providing a systematic observation and analysis of their current state and development trends [44]. Meanwhile, Wang et al. have undertaken an investigation into the measurement methodologies and spatial-temporal dynamics of China’s digital economy, revealing issues related to inadequacy and disparity in its progress [45].

It should be pointed out that these studies on the digital economy have been enlightening, but there are several shortcomings. On the one hand, the issue of measurement error in assessing the digital economy has not been adequately addressed yet, which limits an accurate assessment of its development. On the other hand, while the development of the digital economy within the YEB has been analyzed, it often fails to pay sufficient attention to the spatial and temporal characteristics of its development and lacks an in-depth exploration of inter-regional differences and influencing factors.

The marginal contributions of this paper are as follows: (a) A novel evaluation model is designed to address the prevalent challenge of measurement errors in assessing the digital economy. This pioneering model enables a more precise and nuanced analysis of digital economy development. Applied for the first time, this model facilitates a systematic exploration of the spatial-temporal evolution of the digital economy within the YEB, unveiling insights previously obscured by measurement inaccuracies. (b) This paper conducts a comprehensive analysis of digital economy development within the YEB, examining disparities and origins among different regions. Additionally, the study establishes a robust research paradigm for relevant economic development evaluation systems. These contributions are significant for promoting regional cooperation in the digital economy and fostering high-quality economic development.

2. Data Processing and Research Methods

2.1. Indicators Selection and Data Description

The digital economy development greatly promotes the innovation of novel Internet information technology, and significantly expedites the transformation of traditional industries [46]. In particular, digital infrastructure has become one of the main engines of the national economy [47]. Additionally, the digital economy also plays an essential role in creating international cooperation, attracting financial support and improving social livelihood. After consulting the digital economy report proposed by authoritative institutions and summarizing the measurement methods of other scholars on digital economy development, it was found that the benefits brought by the digital economy at the economic and social levels are intricately linked to its level of advancement [48,49].

The YEB, spanning across China’s eastern, central and western regions, constitutes an inland river economic belt with numerous advantages and immense potential. The YEB covers eleven cities with different resources and economic conditions, namely Shanghai, Jiangsu, Zhejiang, Anhui, Jiangxi, Hubei, Hunan, Chongqing, Sichuan, Guizhou and Yunnan. Based on its geographical location, the YEB can be divided into the following three parts: the upper (Chongqing, Sichuan, Guizhou and Yunnan), middle (Hubei, Hunan, Jiangxi and Anhui) and lower reaches (Shanghai, Jiangsu and Zhejiang). Clarifying the development status of the digital economy in these cities can not only help build an economic network with complementary advantages but also could enhance the potential for intercity synergies. Here, the data regarding digital economy development in the YEB cover a period from 2012 to 2021, during which significant policy developments and technological advancements in the digital economy took place. The selection of this period also aligns with the elevation of the YEB to a major national development strategy following the 18th National Congress of the Communist Party of China in 2012.

The digital economy development of the YEB is systematically measured using the following dimensions: digital infrastructure, development of digital economic innovation, international cooperation and social livelihood benefits, as shown in

Table 1. Digital economy evaluation index system.

First-Level Dimension	Weight *	Second-Level Dimension	Weight *
Digital infrastructure	0.300	Infrastructure	0.208
		Operational level	0.092
Development of digital economic innovation	0.198	Input	0.104
		Output	0.094
International cooperation	0.170	International cooperation	0.170
Social livelihood benefits	0.332	Digital life	0.114
		Digital agriculture	0.093
		Digital education	0.125

* The weights are obtained based on the calculation method presented in Section 2.2.2.

. The detailed explanations of indicators are listed in Table S1 in the Supporting Information (SI). All data are from the China Statistical Yearbook and the China High Count Industry Statistical Yearbook.

2.2. Calculation Method

2.2.1. Measurement Errors and Factor Scoring Method

Accurately measuring the true value of the predictor variable ($x_{it}$) in the practical conditions remains a difficult task. Actually, the observed value is often taken as a substitute for $x_{it}$ and named as the substitution variable ($w_{it}$). Assuming that the error between $w_{it}$ and $x_{it}$ is denoted as $u_{it}$, then a panel data series with measurement errors can be expressed as follows:

$$w_{it}=x_{it}+u_{it}, i=1,2,\cdots ,N; t=1,2,\cdots ,T$$

(1)

where N and T are taken as the number of cities in the YEB and the time of the study period, respectively. Here, $u_{it}$ follows an independent homogeneous distribution with a mean of 0 and a variance of ${\sigma }_u^2$. Namely, $E(u_{it})=0$, $Var(u_{it},u_{js})=\left\{\begin{array}{l}{\sigma }_u^2, i=j; t=s\\ 0, others\end{array}\right.$, where ${\sigma }_u^2$ is the standard deviation.

Notedly, when there is a measurement error, $u_{it}$, it becomes challenging to ensure the unbiasedness of the parameter estimation for $x_{it}$. The advantage of the factor score method is that it only assumes a normal distribution for the regression error, the measurement error and the instrumental variable error, without making any other assumptions about the variances of different error distributions. This overcomes the need to assume that the variances of the measurement error and instrumental variable error are equal or equally proportional. Here, the factor scoring method can be taken to eliminate the influence of measurement errors in the variables by the following steps:

1.

Expressing the variables as a matrix as below:

$$w_i=x_i+u_i$$

(2)

where $x_{it}$ is a p-dimensional vector defined as the explanatory variables.

2.

Estimating ${\widehat{X}}_i$: Based on Formula (1), work variables $Z_i$ are introduced to fulfill the requirement as follows:

$$Z_i={\nu }_{0i}+{\nu }_{1i}{X}_i+{\delta }_i$$

(3)

By merging Equation (2) with Equation (3), we obtain:

$$\left(\begin{array}{l}{W}_i\\ Z_i\end{array}\right)=\left(\begin{array}{c}0\\ V_{0i}\end{array}\right)+\left(\begin{array}{c}1\\ V_{1i}\end{array}\right)X_i+\left(\begin{array}{l}{u}_i\\ {\delta }_i\end{array}\right)$$

(4)

Assuming $\mathrm{var}(u_i)=\mathrm{var}({\delta }_i)={\psi }_i^2$ and $\mathrm{var}(X_i)={\gamma }_i^2$, we will obtain:

$$\mathrm{cov}\left(\begin{array}{c}{W}_i\\ Z_i\end{array}\right)={\Sigma }_i={\gamma }_i^2{\Lambda }_i{\Lambda }_i^{\text{'}}+{\Psi }_i$$

(5)

where ${\Lambda }_i=\left(\begin{array}{c}1\\ v_{1i}\end{array}\right)$, ${\Psi }_i=\left(\begin{array}{cc}{\psi }_i^2& 0\\ 0& {\psi }_i^2\end{array}\right)$ and $S_i=\left(\begin{array}{cc}{s}_{i11}& s_{i12}\\ s_{i21}& s_{i22}\end{array}\right)$ represent the variance of the data set $\left(\begin{array}{c}{W}_i\\ Z_i\end{array}\right)$ based on observed values.

Subsequently, we take the moment estimation method to solve the following equations and obtain the estimates of $v_{1i}$ and ${\gamma }_i^2$:

$$\left\{\begin{array}{l}{s}_{i11}={\gamma }_i^2+{\psi }_i^2\\ s_{i12}=v_{1i}{\gamma }_i^2\\ s_{i22}=v_{1i}^2{\gamma }_i^2+{\psi }_i^2\end{array}\right.$$

(6)

The solution of Equation (6) can be expressed as follows:

$$\left\{\begin{array}{l}{\widehat{v}}_{1i}=\frac{(s_{i22}-s_{i11})+\sqrt{{\left(s_{i22}-s_{i11}\right)}^2+4s_{i12}^2}}{2s_{i12}}\\ {\widehat{\gamma }}_i^2=\frac{s_{i12}}{{\widehat{v}}_{1i}}\end{array}\right.$$

(7)

Then, the factor score $x_{it}$ can be expressed as follows:

$$X_i=A_i\left(\begin{array}{c}{W}_i\\ Z_i-{\widehat{v}}_{0i}\end{array}\right)$$

(8)

where $A_i={\gamma }_i^2{\Lambda }_i^{\text{'}}{\Sigma }_i^{-1}$.

3.

Based on the expectation to estimate $v_{0i}$, the following can be obtained:

$$E(Z_i)=v_{1i}E(X_i)+v_{0i}=v_{1i}E(W_i)+v_{0i}$$

(9)

where the ${\widehat{v}}_{0i}$ can be expressed as ${\widehat{v}}_{0i}={\overline{Z}}_i-{\widehat{v}}_{i1}\overline{w}$. Meanwhile, $A_i$ is obtained by the estimates of ${\gamma }_i$, ${\Lambda }_i$, ${\Sigma }_i$ and $v_{0i}$, then combined with Equation (8) to obtain the estimate of ${\widehat{X}}_i$.

2.2.2. Entropy Method

The entropy method is taken to assess the comprehensive index of digital economy development in the YEB, as it effectively addresses subjective human factors and offers a straightforward calculation process. Also, this approach determines indicator weights based on their variability, ensuring a more objective evaluation. The entropy method is chosen to assess the composite index of digital economy development in the YEB mainly due to its objectivity in weight determination and computational efficiency. The entropy method, which objectively determines the weights through the variability of each indicator, is suitable for dealing with the multidimensional dataset in our study and is able to comprehensively capture the complexity of the digital economy. This weight allocation mechanism based on data variability enhances the science and reliability of the assessment and provides a solid foundation for quantitative analysis of the YEB digital economy. The specific calculation process is as follows:

• Standardize the raw data in order to eliminate inconsistencies in index dimensions;
• The weight of the j indicator in the i region is computed as follows: $y_{ij}=\frac{x_{ij}^{\text{'}}}{{\displaystyle {\sum }_{i=1}^n{x}_{ij}^{\text{'}}}}$;
• Calculate the information entropy of j metric as follows: $e_j=-K{\displaystyle \sum _{i=}^n{y}_{ij}\ln y_{ij}},K=\frac{1}{\ln \left(n\right)}$;
• Obtain the weight $w_j$ for the j indicator as follows: $w_j=\frac{1-e_j}{{\displaystyle {\sum }_{j=1}^m\left(1-e_j\right)}}$;
• The comprehensive score of the digital economy S can therefore be defined as follows:

$$S={\displaystyle \sum _{j=1}^m\left(100\times y_{ij}\times w_j\right)}$$

(10)

2.2.3. Dagum–Gini Coefficient

The Dagum–Gini coefficient (G) is one of the commonly used indexes to measure the disparity of a variable. The advantages of the Dagum–Gini coefficient method lie in its ability to capture differences between different regions or groups and to reflect the overall level and distribution of digital economic development. Compared to other methods, the Dagum–Gini coefficient has higher sensitivity and accuracy in reflecting the unevenness of the distribution of variables. Here, the difference of digital economy development level is decomposed into intra-regional ($G_w$), inter-regional ($G_b$) and super-variable density contributions ($G_t$). The cities along the YEB are categorized into upper, middle and lower reaches. The G can be calculated as follows:

$$G={\displaystyle \sum _{j=1}^k{\displaystyle \sum _{h=1}^k{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_h}\left|y_{ji}-y_{hr}\right|/(2n^2\overline{y})}}}}$$

(11)

where k is the number of regions divided; n is the total number of provinces and cities; $n_j\left(n_h\right)$ denotes the number of provinces in the $j\left(h\right)$ region; $n_j\left(n_h\right)$ is the internal digital economy index in the $j\left(h\right)$ region; and $y_{ji}\left(y_{hr}\right)$ is the average of digital economy development indicators across the cities.

Before the decomposition of G, the average value of digital economy indicators in each region is arranged in order from small to large, as follows:

$${\overline{y}}_1\le {\overline{y}}_2\le \cdots \le {\overline{y}}_j\le \cdots \le {\overline{y}}_k$$

(12)

$$G_{jj}=\frac{{\displaystyle {\sum }_{i=1}^{n_j}{\displaystyle {\sum }_{r=1}^{n_j}\left|y_{ji}-y_{jr}\right|/\left(2{\overline{y}}_j\right)}}}{n_j^2}$$

(13)

$$G_{jh}=\frac{{\displaystyle {\sum }_{i=1}^{n_j}{\displaystyle {\sum }_{r=1}^{n_j}\left|y_{ji}-y_{hr}\right|}}}{n_j{n}_h\left({\overline{y}}_j+{\overline{y}}_h\right)}$$

(14)

where $G_{jj}$ and $G_{jh}$ represent the calculated G of the j reach and the inter-region between j and h; $y-j$ and $y-h$ represent the mean value of digital economy indicators in the j region and the h region; and $n_j$ and $n_h$ denote the number of provinces in the j region and the h region, respectively.

Then, the G, $G_w$, $G_b$ and $G_t$ can be expressed as follows:

$$G=G_w+G_b+G_t$$

(15)

$$G_w={\displaystyle \sum _{j=1}^{\mathrm{k}}{G}_{jj}{p}_j}{s}_j$$

(16)

$$G_b={\displaystyle \sum _{j=2}^k{\displaystyle \sum _{h=1}^{j-1}{G}_{jh}(p_j{s}_h+p_h{s}_j)}}{D}_{jh}$$

(17)

$$G_t={\displaystyle \sum _{j=2}^k{\displaystyle \sum _{h=1}^{j-1}{G}_{jh}(p_j{s}_h+p_h{s}_j)\left(1-D_{jh}\right)}}$$

(18)

where $p_i=n_j/n,s_i=\left(n_j{\overline{y}}_i\right)/\left(n\overline{y}\right)$, ${\displaystyle \sum p_j}={\displaystyle \sum s_j}={\displaystyle {\sum }_{j=1}^k{\displaystyle {\sum }_{h=1}^k{p}_j{s}_j}}=1$. $D_{jh}$ is the relative impact of the first interregional digital economy development indicator, calculated by the following formula.

Here, $d_{jh}$ and $p_{jh}$ represent the mathematical expectation of the sum of sample values of all $y_{ji}>y_{hr}$ or $y_{ji}<y_{hr}$ in the j and h reaches, respectively. The specific calculation formulas of $d_{jh}$ and $p_{jh}$ are below:

$$d_{jh}={\displaystyle {\int }_0^{\infty }d{F}_j\left(y\right)}{\displaystyle {\int }_0^y\left(y-x\right)d{F}_h\left(x\right)}$$

(19)

$$p_{jh}={\displaystyle {\int }_0^{\infty }d{F}_h\left(y\right)}{\displaystyle {\int }_0^y\left(y-x\right)d{F}_j\left(x\right)}$$

(20)

where $F_j$ and $F_h$ represent the cumulative distribution function in the j and h reaches, respectively.

2.2.4. σ Convergence Model

The σ convergence model is chosen for its ability to effectively capture the temporal dynamics of disparities, offering insights into whether the gaps between different regions or groups are narrowing overall or widening over time. The divergence of digital economy indicators from the average tends to decrease over time, which is referred to as σ convergence. This paper intends to determine whether the development level of the digital economy along the YEB exhibits a trend of “balanced convergence” within itself or a “catch-up effect” compared to the other researches. Here, the variation coefficient method is used to measure the convergence in equalizing the indicators of digital economy development level, as follows:

$${\sigma }_t=\frac{\sqrt{\frac{1}{n}{{\displaystyle {\sum }_{i=1}^n\left(y_{it}-\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{y}_{it}}\right)}}^2}}{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{y}_{it}}}$$

(21)

where $y_{it}$ represents the score of the digital economy development level of i province. If ${\sigma }_t$ decreases over time, it shows that the disparity between digital economy indicators of cities is narrowing and tends to converge. Conversely, there is a divergence trend.

2.2.5. Grey Correlation Analysis

The grey correlation analysis often is taken to qualify the correlation between different factors based on their development changes. Similar trends indicate high correlation, while opposite trends suggest low correlation. The calculation process is as follows:

1.

Determining the reference sequences $Y$ and multiple comparison sequences $X_i$ for the grey correlation analysis;

2.

Dimensionless processing, as follows:

$$x_i\left(k\right)=\frac{{x_i}^{\text{'}}\left(k\right)}{x_i\left(1\right)}$$

(22)

3.

Calculating the absolute values for reference and comparison sequences at each moment, as follows:

$${\Delta }_i\left(k\right)=\left|y\left(k\right)-x_i\left(k\right)\right|\left(k=1,2,\cdots ,m; i=1,2,\cdots ,n\right)$$

(23)

4.

Obtaining the grey correlation coefficient ${\xi }_i\left(k\right)$ of $Y$ and $X_i$ for index $K$, as follows:

$${\xi }_i\left(k\right)=\frac{{\min }_i{\min }_k{\Delta }_i\left(k\right)+\rho {\max }_i{\max }_k{\Delta }_i\left(k\right)}{{\Delta }_i\left(k\right)+\rho {\max }_i{\max }_k{\Delta }_i\left(k\right)}$$

(24)

5.

Calculating the grey correlation degree $r_i$, as follows:

$$r_i=\frac{1}{N}{\displaystyle \sum _{k=1}^n{\xi }_i\left(k\right)}$$

(25)

3. Results and Analysis

3.1. Overall Status of Digital Economy Development Level in the Yangtze River Economic Belt

The weight of digital economy development indexes in the YEB from 2012 to 2021 were calculated by the entropy method, as depicted in Table 1. It was observed that the social and livelihood benefits carried the highest weight (0.332) in the first-level indicators, followed by digital infrastructure (0.300). External cooperation (0.198) and innovative development (0.170) held relatively lower weights. In terms of the second-level indicators, infrastructure, opening up and cooperation level accounted for a significant weightage, exceeding 17%. Conversely, operational level, innovation, development output and digital agriculture had comparatively smaller weights, at approximately 9%.

In order to provide a more intuitive description of the yearly development situation, the comprehensive index and sub-index for digital economy development in the YEB from 2012 to 2021 were calculated, as shown in Table S2 in SI. It is clear that the comprehensive index showed a steady upward trend, increasing from 15.97 in 2012 to 25.03 in 2021. Notably, the average growth rate from 2016 to 2018 exceeded 5%, which can be attributed to the rapid expansion of openness and cooperation levels. In April 2016, the Outline of the Development Plan for the YEB was officially released, thereby elucidating its development objectives and directions. This significant milestone signified that the development had embarked upon a new phase. From the perspective of sub-indicators, the level of infrastructure and operation of digital infrastructure, and the output of development of digital economy innovation continued to increase during the research period. Overall, the digital economy in the YEB was stable, suggesting a pervasive trend of comprehensive and outstanding advancement.

3.2. Regional Status of Digital Economy Development Level in the Yangtze River Economic Belt

The measured results of the digital economy development index for each section of the YEB are presented in Figure 1. It is clear that the digital economy development across the different reaches exhibited obvious disparities. Specifically, the digital economy development index in the lower reaches significantly surpassed that of the middle and upper reaches. In contrast, the digital economy in the upper reaches exhibited a relatively low level with a sluggish growth rate. The digital economy development index in the middle reaches was higher than that of the upper reaches, but lower than that of the lower reaches. Combining Figure 1 with Table S2, it can be speculated that the imbalanced growth of the digital economy was intricately linked to the economic, scientific and financial spheres.

It is noteworthy that the publication of the Outline of the YEB Development Plan in 2016 provided a clear development trajectory. In the subsequent year, the digital economy was included in the national government report for the first time, signifying the digital economy development of YEB had entered a new stage. Hence, the temporal evolution characteristics of digital economy development for the cities along the YEB were analyzed by selecting 2015 and 2018 as the intermediate time observation points. The city–time maps of the digital economy development index in 2012, 2015, 2018 and 2021 are shown in Figure 2. The legend segmentation method was carefully chosen to effectively represent the range of the calculated values, with the minimum value set at 5 and the maximum value at 50.

There were obvious variations in the temporal progression of the digital economy development index among these cities. To be specific, the digital economy development index of economically advanced cities like Jiangsu, Zhejiang and Shanghai exhibited a relatively high level and consistently increased year after year. Hubei, Hunan and Sichuan showed a positive upward trend in digital economy development. In particular, Sichuan had a higher growth rate, averaging an annual increase of 9.45%, which was attributed to the accelerated development of the “Internet Plus” initiative [50].

Subsequently, the effect of the first-level indicators on the digital economy development of the cities was further analyzed, and the results are shown in Figure 3. It can be observed from Figure 3a that Shanghai and Zhejiang maintained a significant leading position in terms of digital infrastructure. Meanwhile, Sichuan made great progress in the digital foundation sphere, and its development index was expected to surpass that of Zhejiang in the next few years. In terms of the development of digital economic innovation, most cities in the YEB achieved steady growth. Especially in Shanghai, Zhejiang, Jiangsu and Hubei, the remarkable improvement effect can be seen, as presented in Figure 3b. Note that the innovative development index of Guizhou in 2012 was extremely high, which was closely related to the “Several Opinions of The State Council on Further Promoting the Sound and Rapid Economic and Social Development of Guizhou” issued that year. However, its later development momentum was insufficient and it even became a regressive situation. From the perspective of international cooperation, the cites in the lower reaches had always been in the leading position. Hunan had shown potential in promoting trade, attracting investment and promoting cooperation in recent years, despite its low starting position. In addition, due to the outbreak of the novel coronavirus pneumonia, the index of opening to the outside world for many cities in 2018 was better than that in 2021. Figure 3c indicates that lower YEB cities like Shanghai and Jiangsu led in international cooperation. This could be attributed to their strategic geographic locations, well-established port facilities and historical ties to international trade, which were further amplified by digital advancements. Notably, inland cities like Sichuan and Chongqing also advanced in international cooperation despite initial geographic disadvantages, leveraging digital technologies to overcome barriers and actively seeking international partnerships. Overall, the trend toward increased openness and cooperation among YEB cities suggests potential for further collaboration and knowledge exchange to foster a more interconnected and competitive digital economy in the region. Figure 3d presents the fact that Jiangsu maintained a high level in the social livelihood benefits. Notedly, in 2012, the index of social and livelihood benefits for Hunan was at a high level. However, as a result of the recalibration of social policies, the transformation in economic structure and the inequitable allocation of resources, it regrettably failed to sustain its initial momentum for development and exhibited a discernible decline.

Through the above analysis, it can be observed that Jiangsu, Zhejiang and Shanghai all presented significant advantages in several key indicators. However, other cities still exhibited a substantial gap in the overall level, due to the influence of regional economic structure, policy guidance and resource allocation.

3.3. Regional Differences and Sources

The upper, middle and lower reaches of YEB exhibited relatively independent development, with limited connectivity and significant disparities in terms of regional development conditions, public services and living standards [51]. Conducting a thorough assessment of digital economy development would maximize advantages and establish a new framework for regional collaboration and growth.

From the overall and inter-regional perspectives, the differences in digital economy development were analyzed comprehensively. The G was calculated for the YEB and the corresponding reaches; the results are shown in Figure 4a. It was found that the average value of G for the YEB was 0.300, lower than the “alarm value” in golden division law (0.382), indicating reasonable regional differences in the digital economy development. During the observation period, the overall G showed a fluctuating pattern. Between 2013 and 2018, the overall G initially increased, reaching its peak, and then rapidly decreased. Note that the increase from 2018 to 2019 was only 0.66%, implying that the overall difference was significantly reduced. From the perspective of the reaches, the digital economy development of the upper, middle and lower reaches was relatively stable, and the highest/lowest difference value of G was less than 0.1. Further, the average G in the lower reaches (0.178) was higher than that in the middle (0.131) and upper reaches (0.166), indicating significant disparities in digital economy development in the lower reaches. Notedly, the G of the upper reaches gradually increased and surpassed that of lower reaches in 2018. In contrast, the G of middle reaches as a whole remained at a low level.

To clarify the origins of differences in the digital economy development across the reaches, the overall differences were distinguished into three components: intra-regional variances ($G_w$), inter-regional discrepancies ($G_b$) and the contribution of super-variable density ($G_t$). The calculated results are depicted in Figure 4b. It can be seen that the average annual contribution rates of $G_w$, $G_b$ and $G_t$ were 19.2%, 71.5% and 9.3%, respectively. The contribution of $G_b$ was always dominant, with an average of about 71%. The contribution of $G_t$ was relatively low, with a slight upward trend between 8% and 11%. This suggests that regional differences had a small impact on the overall G. This is closely linked to the inherent economic development imbalance in YEB.

3.4. Convergence Analysis

Subsequently, the σ convergence model was employed to quantitatively analyze the convergence characteristics of the digital economy development, as plotted in Figure 5. It is clear that the convergence coefficient of digital economy remained stable, fluctuating between 0.15 and 0.18, without clear convergence or divergence characteristics. The convergence in the upper, middle and lower reaches exhibited distinct characteristics. Specifically, from 2012 to 2017, obvious convergence characteristics could be seen in the upper reaches; this pattern shifted towards divergence after 2017. In the middle reaches, although noticeable fluctuations in the convergence appeared during the study period, the digital economy’s development exhibited clear convergence characteristics with the lowest point in 2019. The lower reaches demonstrated an increasing trend of the convergence coefficient, but its value still remained relatively low compared to the other reaches. In addition, the time variable was treated with regression to ensure its robustness. The results show that the estimated coefficients of time in the upper and lower reaches were positive at a level of 5%, which further confirms that the indicators of the digital economy development in these reaches did not meet the convergence criteria.

3.5. Influencing Factors Analysis

The influencing factors of digital economy in the YEB were studied using grey correlation analysis. The advantage of grey correlation analysis lies in the representativeness of the data, as it only requires a minimal amount of indicator data to sufficiently construct a model and analyze the degree of correlation between explanatory variables.

Economic foundation, digital infrastructure, technological innovation, human capital investment, capital investment and government support were taken as the explanatory variables, the results in Table S2 were taken as the explained variables, as listed in

Table 2. Influencing factors of the digital economy development.

Explanatory Variable	Specific Indicator	Units
Economic foundation	Per capita regional gross domestic product	CNY/person
	Proportion of tertiary industry output to regional gross domestic product	%
Digital infrastructure	Number of broadband internet access ports	million units
	Length of optical cable routes	kilometers
	Capacity of mobile switching stations	million households
	Number of computers per hundred households	million units
Technological innovation	Number of patent applications in IT field 1	pieces
	Transaction volume in technology market	100 million CNY
Human capital investment	Total real human capital	billion CNY
	Number of graduates from regular higher education institutions	10 thousand people
	Number of employees in IT industries 1	people
Capital investment	Fixed assets investment in IT services industry 1	100 million CNY
	Scientific research and technical services investment	100 million CNY
Government support	General budget expenditure of local finance	100 million CNY

¹ “IT” refers to “information technology”; “IT services industry” refers to “information transmission, software and information technology services industry”.

. Economic foundation encapsulated the underlying economic strength that can support digital initiatives. Digital infrastructure was identified as a critical component, given its indispensable role in facilitating the connectivity and expansive reach of the digital economy. Moreover, technological innovation was recognized as embodying the vibrancy and dynamism inherent in the digital sector. It is a key driver of growth within the digital economy, propelling advancements and competitive edge. The inclusion of government support in the analysis was particularly pertinent, as it sheds light on the influence of governmental policies and initiatives on the trajectory of the digital economy. This selection of variables offered a holistic perspective on the digital economy, encompassing both supply-side elements such as technological innovation and human capital investment, as well as demand-side factors like capital investment. All the data were taken from the China Statistical Yearbook, the China High-tech Industry Statistical Yearbook and the China Human Capital Index Report Database.

The results of the correlation degree of influencing factors are presented in

Table 3. Ranking of the influencing factors.

Rank	Explanatory Variable	Specific Indicator	Correlation
1	Capital investment	Scientific research and technical services investment	0.9909
2	Digital infrastructure	Capacity of mobile switching stations	0.9843
3	Digital infrastructure	Length of optical cable routes	0.9837
4	Government support	General budget expenditure of local finance	0.8767
5	Capital investment	Fixed assets investment in IT services industry	0.8379
6	Digital infrastructure	Number of broadband internet access ports	0.8336
7	Technological innovation	Number of patent applications in information technology field	0.7877
8	Human capital investment	Total real human capital	0.7549
9	Technological innovation	Transaction volume in technology market	0.7206
10	Human capital investment	Number of employees in IT industries	0.6930
11	Digital infrastructure	Number of computers per hundred households	0.6057
12	Economic foundation	Proportion of tertiary industry output to regional gross domestic product	0.5756
13	Human capital investment	Number of graduates from regular higher education institutions	0.5470
14	Economic foundation	Per capita regional gross domestic product	0.4815

. The grey correlation degree between each factor and the digital economy development ranged from 0.4815 to 0.9909, indicating a strong positive correlation. The average value of correlation degree for capital investment, digital infrastructure and government support was more than 0.8, but economic foundation exerted a limited influence on the digital economy development.

(a)

Tier 1: capital investment and digital infrastructure. Capital investment showed the highest correlation with digital economy development compared to the other factors. The digital infrastructure was also a key factor, with the capacity of mobile switching stations and the length of optical cable routes ranking second and third in correlation, respectively.

(b)

Tier 2: government support. Government support was ranked at fourth with a correlation of 0.8767, which greatly influenced the digital economy development in the YEB.

(c)

Tier 3: technological innovation. It can be seen that the correlation between the two indicators (the number of patent applications in the field of information technology and the technology market turnover) and the digital economy development was more than 0.7.

(d)

Tier 4: human capital investment and economic foundation. These two factors had a low rank and a correlation degree of 0.5 to 0.7, suggesting that talent input and economic basis are crucial for promoting digital economy development in the YEB. It is worth mentioning that the relatively low correlation index might suggest that these factors, although contributing to the digital economy, had a limited impact or required more time to manifest their effects.

All the above analysis revealed that it is crucial to employ a comprehensive approach from multiple aspects for enhancing digital economy development in the YEB. The correlation degree of per capita regional gross domestic product was the lowest, reaching 0.4815, which confirmed the accuracy of the selected influencing factors in this paper.

4. Discussion

The digital economy constitutes a pivotal driving force that is reshaping the global competitive landscape. This research aims to gain insights into the development and influencing factors of the digital economy in the YEB and provide feasible suggestions for promoting high-quality and regionally integrated digital economy development. Here, the reliability and novelty of this study are evaluated, and the limitations of this study compared with the existing literature are pointed out.

First, it was found that the overall trend of digital economy development in the YEB continued to rise, which is consistent with the results in previous studies [52]. Lu et al. [53] reported that the digital economy in various regions of China was growing, providing a strong impetus for economic growth and innovation. Wang [54] and Zheng et al. [55] calculated the digital economy index of the YEB using the entropy weight method and pointed out that the digital economy’s development gradually weakened from east to west, which was consistent with the results of this study. On this basis, our research highlighted the key role of social livelihood benefits in the development of the digital economy. In addition, capital investment and digital infrastructure were also considered to be the key factors affecting the digital economy development [56,57].

Although the overall trend of digital economy development in YEB remains positive, a noticeable regional imbalance still exists in the middle and lower reaches, which underscores the necessity for government intervention through tailored policy support strategies to foster equitable growth across diverse regions within the digital economy landscape. This is in line with the views of Wu et al., who emphasized that the uneven development of the digital economy may be affected by regional resource allocation and policy support [58]. Furthermore, our study also yielded findings that diverged from those of previous research [59], which may have attributed to the variations in data samples or calculation methods.

By incorporating results from both domestic and international research on digital economy development, this study enriched our understanding on the measurement techniques and influential factors thereof. Meanwhile, there remain certain constraints in this study that necessitate further enhancement, such as considering the influence of additional factors on the advancement of the digital economy or broadening the research scope to a greater extent [60,61,62,63].

In light of the current findings and their implications, we acknowledge the need for further research to address the limitations of this study and to expand upon its contributions. Future work should aim to incorporate a wider array of socio-economic indicators, in order to capture the multidimensional nature of digital economy development. Additionally, longitudinal studies with extended timeframes could provide a more in-depth understanding of the long-term trends and impacts of digital economy policies. It is also recommended that subsequent research explore the impact of the digital economy on a broader geographic scope, possibly at the global level, in order to contextualize regional findings within a larger economic framework. By taking these steps forward, future studies can build upon the robust theoretical and empirical foundation established herein, contributing to a more comprehensive and nuanced understanding of the role played by digital economy in economic globalization.

5. Conclusions and Recommendations

This paper innovatively proposed a measurement error-corrected evaluation model of digital economy development with four dimensions; namely, digital infrastructure, innovation and development of the digital economy, level of openness and cooperation with the outside world, and social benefits and people’s livelihood. Firstly, the entropy method was utilized to measure the development level of the digital economy across the 11 provinces of the YEB from 2012 to 2021. Subsequently, the regional differences and spatial-temporal evolution characteristics of the digital economy’s development along YEB were systematically studied based on the Dagum–Gini coefficient and the $\sigma$ convergence model. In addition, the degrees of influence of multiple explanatory variables was analyzed using grey correlation analysis. The main conclusions were as follows:

(a)

It was found that the development of digital economy in YEB was relatively stable, and the overall trend continued to rise during the research period, but there was an obvious development imbalance between the different reaches. Specifically, the digital economy development in the lower reaches significantly surpassed that in the middle and upper reaches. Although increasing growth rates were observed in other reaches over the years, substantial disparities still persisted.

(b)

The overall G of the digital economy index, as calculated along the YEB, exhibited a discernible pattern of initial ascent followed by subsequent descent. Although there were variations in the level of digital economy development among the regions, it still fell within a reasonable range. In addition, the variation trend of the Dagum–Gini coefficient was different in each of the reaches. To be specific, the differences among cities in the lower reaches were more significant, while the development of digital economy in the middle reaches was relatively well-balanced. It should be pointed out that the main source of the difference in digital economy development in the YEB was the variation among the reaches, followed by differences within the reaches and super-variable density, which were closely related to the inherent imbalances in regional economic development.

(c)

The overall convergence characteristics of the YEB were not significant. The middle reaches showed clear convergence characteristics, with its convergence coefficient reaching the lowest point in 2019. The upper and lower reaches did not meet the rule of the σ convergence model. Although the regional disparities among different cities in the lower reaches are presently negligible, they are progressively expanding.

(d)

The grey correlation analysis revealed that capital input and digital infrastructure were the fundamental factors influencing the digital economy’s development. Government support, especially through the allocation of funds in local finance, consistently served as a catalyst for digital economy development. Meanwhile, technological innovation, talent input and economic foundation played a vital role in promoting the high-quality development of the digital economy.

Finally, the development of the digital economy in the YEB could further enhance the need for human capital. This aspect has been widely demonstrated as a crucial factor contributing to modern economic growth [64,65].

This paper provides empirical support for promoting the development of digital economy in the YEB. Based on the above results, it is recommended that the following steps should be taken to further promote the premium and stable development of digital economy in YEB:

• Accelerate economic transformation and establish a strong investment link for digital infrastructure;
• Realize resource linkage and sharing, and facilitate the balanced development of the digital economy in all cities along the YEB;
• Formulate differentiated policies to support strategies and enhance inter-regional cooperation;
• Improve the digital infrastructure and establish a holistic, top-notch and enduring ecosystem for the digital economy.