Entropy method.

The entropy method is an objective empowerment method that is frequently employed in the comprehensive evaluation of multiple indicators. This method determines the weights of indicators by calculating the information entropy of each indicator. The larger the entropy value, the smaller the amount of information of the indicator is, and the smaller the impact on the comprehensive evaluation. Conversely, the smaller the entropy value, the larger the amount of information of the indicator is, and the larger the impact on the comprehensive evaluation [26].

The fundamental steps of the entropy method are as follows:

1) Constructing the raw data matrix

It is hypothesized that there are m evaluation objects and n evaluation indicators. The raw data moments are therefore as follows:

(1)

Where: x_ij denotes the value of the i object on the j indicator.

2) Data standardization

Positive indicator:

(2)

Negative indicator:

(3)

Where:

xij is the value of indicator j;

is the minimum value for indicator j;

is the maximum value for indicator j;

p_ij and represent standardized values for positive and negative indicators, respectively.

3) Calculate the entropy value of each indicator

Calculate the weight of the i sample under the j indicator:

(4)

Calculate the information entropy of this indicator:

(5)

Where: is a normalization factor that ensures that the entropy value is between 0 and 1.

4) Calculate the entropy weights

Calculation of the coefficient of variation for the indicator:

(6)

Where:

d_j is the coefficient of variation for the j indicator.

Calculate the weight of the j indicator:

(7)

5) Calculate the composite score

(8)

Where:

S_i is the composite score for the i evaluator.

Dagum Gini coefficient.

The Dagum Gini coefficient is an improvement on the traditional Gini coefficient proposed by Camilo Dagum and is primarily used to measure income or wealth inequality [27]. Compared to the traditional Gini coefficient, the Dagum Gini coefficient is able to provide a more nuanced picture of imbalances in the distribution of income or wealth, especially inequality between groups and inequality within groups.

1) Improvement of the Dagum Gini coefficient

The Dagum Gini coefficient can be expressed as:

(9)

Where:

Gw: Within-group inequality;

Gb: Between-group inequality;

Gt: Transvariation inequality.

2) Calculation of the Dagum Gini coefficient It is assumed that a dataset contains q income groups, with n_k individuals in each group, and an income level of x_ik:

(10)

Where:

(11)

Subsequent to this initial decomposition, Dagum puts forward a series of equations that govern inequality Within-group, inequality Between-group, and inequality Transvariation.

Within-group inequality:

(12)

Where:

p_k is the income share of group

G_k is the Gini coefficient for the group.

Between-group inequality:

(13)

Where:

denotes the mean income of group k;

denotes the mean income of group h;

μ denotes the mean income of all samples.

Transvariation inequality:

(14)

Where:

Tkh is the Transvariation Overlap Index.

The Dagum Gini coefficient is a statistical tool that can accurately identify disparities in the development of e-commerce among different geographical regions. By constructing an e-commerce development index system, quantifying the overall development level of e-commerce in each region using the entropy value method, and calculating the Dagum Gini coefficient, we are able to examine and analyze the spatial variations among the four primary regions: East, Central, West, and Northeast. This analysis also encompasses the dynamic evolution of these regions over time [28].

Moran’s I.

Moran’s Index (Moran’s I) is a pivotal indicator employed in spatial statistics to ascertain the presence of autocorrelation—that is, the existence of a correlation between the values in one region and its neighboring regions. This index enables the assessment of the extent to which a variable exhibits spatial aggregation, in addition to unveiling spatial patterns such as agglomeration and dispersion. In this paper, the Moran index is used to assess the presence of spatial autocorrelation between e-commerce development levels across different regions [29,30]. This analysis aims to unveil inter-regional variability and identify agglomeration trends.

(1) Global Moran’s I

The Global Moran’s I is a statistical indicator that is employed to measure the spatial autocorrelation of data within the entire study area. It assists in determining whether a phenomenon (e.g., the level of e-commerce development) is distributed in a random manner, is clustered, or is discretely distributed. The Global Moran’s I is calculated as follows:

(15)

Where:

n is the number of regions, that is to say, the sample size;

xi is the observed value for region i (e.g., e-commerce development index);

xj is the observed value for region j;

is the arithmetic mean of all regional observations;

wij is the element of the spatial weight matrix, which represents the spatial relationship between regions a and b. This study employs an adjacency matrix for its analysis.

S0 is defined as the total of all elements contained within the spatial weight matrix,

The presence of i > 0 indicates positive spatial autocorrelation, signifying that the e-commerce development levels of neighboring regions exhibit similarity and a clustering effect. Conversely, if i < 0 is present, it denotes negative spatial autocorrelation, indicating a substantial difference in the e-commerce development levels of neighboring regions. e-commerce development level of neighboring regions, which manifests itself as a spatial dispersion; and if , it means a spatial random distribution, which indicates that there is no obvious tendency of clustering or dispersing of the e-commerce development level of neighboring regions.

The Global Moran’s I can be utilized to assess the agglomeration of different provinces or regions in China in terms of e-commerce development. This approach enables the determination of whether e-commerce has formed a centralized or homogeneous distribution in specific regions or groups of regions.

(2) Local Moran’s I

The Local Moran’s I is a statistical tool that is primarily employed to discern the local spatial autocorrelation present within each region. This index facilitates the identification of distinct autocorrelation patterns within a specific region, thereby enabling the differentiation of various types of spatial relationships. The formula employed to calculate the localized Moran Index is as follows:

(16)

Where: is defined as the variance of all observations.

The local Moran’s index, in contrast to the global Moran’s index, is employed to discern particular spatial patterns. For instance, the High-High (HH, Hot Spot) configuration signifies regions of high values that are encircled by regions of high values, thereby engendering a clustering effect. Similarly, the Low-Low (LL, Cold Spot) configuration denotes regions of low values that are encircled by regions of low values, resulting in a clustering effect. The third type is the High-Low (HL) configuration, in which high-value regions are surrounded by low-value regions, manifesting as isolated high-value points. The fourth type is the Low-High (LH) configuration, in which low-value regions are surrounded by high-value regions, manifesting as isolated low-value points.

Convergence model.

The convergence model is derived from economic growth theory, which is mainly based on the neoclassical growth model and endogenous growth theory [31,32]. The basic idea is that under certain economic environment and policy conditions, the economic development levels of different regions or countries will gradually tend to equalize over time, i.e., the economic gap may show a tendency to narrow, thus achieving a certain degree of convergence. Convergence analysis generally includes σ-convergence and β-convergence.

(1) σ-convergence

σ-convergence refers to whether the dispersion of an economic variable (e.g. e-commerce development index, etc.) across regions or countries is decreasing over time. The standard deviation (SD) or coefficient of variation (CV) is usually used as a measure. If the standard deviation or coefficient of variation shows a decreasing trend, it indicates that the economic development levels of different regions are converging and there is σ-convergence.

The following steps are involved in the σ-convergence analysis:

1) Calculating the mean value

(17)

Where:

N denotes the total number of regions or countries in the sample.

2) Calculating the standard deviation

(18)

Where:

Xi,t is the economic variable (e.g., the e-commerce development index) for the i region or country at time t;

is the mean value for all regions at time t.

3) Calculating the coefficient of variation

(19)

Convergence is indicated by a decrease in standard deviation or coefficient of variation over time. Conversely, an increase or maintenance of standard deviation or coefficient of variation indicates absence of convergence, and the possibility of divergence exists.

(2) β-convergence

β-convergence is a statistical measure of economic development that quantifies the rate of growth and convergence of regions with different levels of economic development. In essence, the analysis of β-convergence examines the dynamic adjustment process of the development level between regions. The presence of β-convergence in a region is indicated by a negative correlation between its economic growth rate and its initial development level. That is, if a region with a lower initial development level exhibits a faster growth rate, then the presence of β-convergence can be deduced. The assumption of β-convergence postulates that, under specific conditions, regions with lower development levels can attain faster growth rates and eventually attain a stable, long-term equilibrium state. The aforementioned concept of β-convergence is primarily classified into two distinct categories: absolute β-convergence and conditional β-convergence.

1) Absolute β-convergence

The absolute β-convergence is predicated on the assumption that all regions possess an identical long-run equilibrium level, with growth rates being contingent solely on initial levels. In the event that a region commences at a lower level but exhibits accelerated growth, it possesses the capacity to ultimately converge with other regions. The regression model is as follows:

(20)

Where:

Xi,0 denotes the economic variables (e.g., e-commerce development index, GDP per capita, etc.) in the initial year(0) for the i region;

Xi,T denotes the economic variables of the i region in the termination year(T);

is used to denote the average annual growth rate over a period of years;

is defined as the logarithm of the economic variable in the initial year;

α and β represent regression coefficients, is designated as the error term.

In the event that the parameter β is found to be less than zero and is deemed to be statistically significant—that is to say, growth rates are observed to be higher in areas where initial levels are lower—then it can be concluded that there is absolute β convergence. Conversely, if β is found to be greater than zero or is not deemed to be statistically significant, then it can be concluded that there is no convergence and there may even be a divergence trend.

2) Conditional β-convergence

The conditional β-convergence enables disparate regions to possess disparate long-run equilibrium levels (e.g., due to discrepancies in policy, industry structure, infrastructure, etc.). Subsequent to controlling for these factors, if β remains significantly negative, it signifies that under analogous development conditions, regions with less advanced economies continue to exhibit faster growth. The regression model is as follows:

(21)

Where:

Zi,k is a control variable that may affect growth. Consistent with previous studies, this paper selected four control variables: per capita regional GDP(ln_gdp), local fiscal expenditure on transportation(ln_finance), the year-end urban population share by region(ln_county), and the average number of enrolled students at all levels of education per 100,000 population(ln_edu).

If β < 0 and statistically significant, it suggests that, after controlling for other factors, economic development still exhibits a convergence trend, indicating the presence of conditional β-convergence. Conversely, if β 0 or is not statistically significant, it implies that regions with lower development levels have not achieved faster growth.

The degree of e-commerce development exhibits significant variations across different regions (e.g., eastern coastal regions versus central and western regions) due to various factors, including Internet penetration, consumer purchasing power, and logistics systems. The convergence model offers a means to analyze the temporal dynamics of these variations, determining whether they are converging or maintaining their distinct characteristics. By examining the data on e-commerce sales and the number of users in each province, it is possible to assess the regional disparity of e-commerce on a national scale.

Descriptive statistics.

As illustrated in Table 2, the development patterns of the 31 provinces, municipalities, and autonomous regions in mainland China have undergone dynamic shifts between 2013 and 2023 in the relevant fields. The disparities between regions have been progressively diminishing, thereby enhancing the overall balance of development. Nevertheless, the characteristics of data distribution in different years exhibit variability. The disparities in development speed and level among regions persist, influenced by a multitude of factors. However, the distribution of data exhibits variability from year to year. A multitude of factors contribute to the heterogeneity in the pace and level of development among different regions. Despite these variations, there has been an observed shift towards a more balanced and coordinated approach in the overall development trajectory.

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Table 2. Descriptive statistics of entropy method results.

https://doi.org/10.1371/journal.pone.0330066.t002

Spatial distribution characteristics of China’s overall e-commerce development level.

This paper proposes a methodology for assessing the overall e-commerce development level of Chinese provinces (with the exception of Hong Kong, Macao, and Taiwan) from 2013 to 2023. The proposed methodology utilizes an entropy value method to quantify the development level, as illustrated in Fig 3.

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Fig 3. Spatial distribution characteristics of overall E-commerce Development in China.

(A) Spatial distribution of overall e-commerce development in China, 2013; (B) Spatial distribution of overall e-commerce development in China, 2018; (C) Spatial distribution of overall e-commerce development in China, 2023. Maps are derived from a free and open-source website: https://cloudcenter.tianditu.gov.cn/dataSource).

https://doi.org/10.1371/journal.pone.0330066.g003

As illustrated in (A), the regions that exhibited higher levels of e-commerce development in 2013 were predominantly located in the eastern coastal areas, particularly Shanghai, Jiangsu, Zhejiang, and Guangdong. The darker color of these regions indicates that their e-commerce development level is between 0.456601 and 0.778000. In contrast, the central and western regions demonstrate a comparatively lower level of e-commerce development, as evidenced by the lighter color of their regions, which are concentrated between 0.000000 and 0.047700. This observation suggests that in 2013, there was a discernible regional disparity in the advancement of e-commerce in China, with the eastern region at the forefront and the central and western regions exhibiting a comparatively lagging position.

In 2018 (B), the level of e-commerce development in the eastern coastal regions exhibited a persistent high trend, accompanied by an increase in the depth of color, suggesting a further escalation in the e-commerce development index within these regions. Notably, certain regions have attained an interval of 0.409201 - 0.689800, indicating a significant advancement in their e-commerce development. A similar trend is observed in the central and western regions, where a gradual intensification of color indicates an increase in e-commerce development, particularly in the central regions such as Henan and Hubei, where the development has been particularly robust, reaching the interval of 0.046501 - 0.077500. These findings suggest that from 2013 to 2018, e-commerce development in China experienced a substantial nationwide expansion, with the central and western regions rapidly approaching the levels of the eastern regions.

In 2023 (C), the eastern coastal region maintains its lead in e-commerce development, though the intensity of the color remains relatively unchanged, suggesting that the region has entered a period of relative stability in its development. Concurrently, the e-commerce landscape in the central and western regions has shown signs of advancement, as evidenced by an intensification of the color in these regions, particularly in western areas such as Sichuan and Chongqing, where there has been a substantial surge in e-commerce activity, reaching levels between 0.060601 and 0.078800.Overall, during the period spanning from 2013 to 2023, China’s e-commerce development has exhibited notable growth, with a gradual convergence between regions. However, the eastern region continues to maintain a competitive edge.

From 2013 to 2023, China witnessed a substantial surge in its e-commerce development across the nation. The eastern coastal region has historically led the nation in e-commerce development; however, the central and western regions have also shown notable progress, narrowing the gap with the eastern region over the past decade. This indicates that China has achieved substantial progress in e-commerce development and that the imbalance between regions is progressively diminishing.

Global Moran’s I.

As demonstrated in Table 5, the global Moran’s I of China’s overall e-commerce development level from 2013 to 2023 has passed the significance test, indicating spatial autocorrelation. The results of the global Moran’s I demonstrate that the e-commerce development level of each province is not randomly distributed, but exhibits clear spatial clustering characteristics. Consequently, further examination of the distribution pattern and characteristics of spatial clustering of e-commerce development level in China is warranted, utilizing the local Moran’s I.

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Table 5. Overall Development Level of E-Commerce Global Moran’s I from 2013-2023.

https://doi.org/10.1371/journal.pone.0330066.t005

Local Moran’s I.

An analysis of China’s e-commerce development reveals notable geographic disparities and evolving trends between 2013 and 2023, as illustrated in Fig 4. In general, regions exhibiting higher levels of e-commerce development are predominantly situated in the eastern coastal areas, exhibiting a decline in development from coastal regions towards inland areas.

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Fig 4. The Lisa cluster map of China’s overall e-commerce development level.

(D shows the LISA cluster map of China’s overall e-commerce development level in 2013; E shows the LISA cluster map of China’s overall e-commerce development level in 2018; and F shows the LISA cluster map of China’s overall e-commerce development level in 2023, with the maps taken from a free and open source website: https://cloudcenter.tianditu.gov.cn/dataSource).

https://doi.org/10.1371/journal.pone.0330066.g004

As illustrated by the Lisa cluster map, in the three-year period under consideration, regions exhibiting high levels of e-commerce development are predominantly located in the eastern coastal region, including Beijing, Shanghai, and Guangdong. These regions are distinguished by their economic development, advanced infrastructure, and high Internet penetration rates, which collectively create a conducive environment for the proliferation of e-commerce. Conversely, the central and western regions exhibited comparatively lower levels of e-commerce development. A notable disparity in the levels of e-commerce development was observed between 2013 and 2018. In 2013, the eastern coastal region dominated, while in 2018, e-commerce development had penetrated the central and western regions, though the eastern coastal region maintained its dominance. By 2023, e-commerce development had further advanced into the central and western regions, with some inland regions also experiencing an increase in their development levels.

A close overall look at China’s e-commerce development shows a trend of gradual diffusion from the east coast to the central and western regions. While the eastern coastal region continues to dominate, the central and western regions are rapidly gaining ground. This observed geographical differentiation and evolutionary trend in can be attributed to a complex interplay of various interconnected factors. Firstly, policy support, encompassing targeted regional development strategies, fiscal incentives, and regulatory frameworks, has played a pivotal role in shaping uneven growth trajectories and fostering specific e-commerce hubs or lagging regions over time. Secondly, infrastructure development, particularly advancements in digital connectivity and logistics infrastructure, directly determines the physical and digital accessibility of e-commerce services, thereby creating significant spatial disparities. Furthermore, the varying rates of Internet penetration, reflecting not only access but also affordability and digital literacy, critically influence the size and engagement level of the online consumer base across different regions. Lastly, dynamic changes in consumer attitudes and purchasing habits, driven by increasing trust in online platforms, a preference for convenience, and evolving digital literacy, have collectively fueled the overall evolutionary trajectory of e-commerce adoption and its spatial diffusion, leading to a nuanced landscape of development.

σ-convergence.

The coefficient of variation (CV) method was employed to assess the σ-convergence of e-commerce development levels across the country, as well as within the eastern, central, western, and northeastern regions ( as shown in Fig 5), it is evident that a pronounced σ-convergence trend is observed nationwide. The eastern region exhibits stability, devoid of any discernible convergence or divergence. The central region experiences an initial widening of disparities, followed by a subsequent convergence. The western region demonstrates erratic fluctuations in internal disparities. The northeastern region displays convergence during the initial period, subsequently accompanied by a widening of variance in the subsequent period. The coefficient of variation for the entire country attained its maximum value in 2013, approaching 1.2, and subsequently exhibited an annual decline, approaching 1 by 2023. This declining trend signifies a nationwide σ-convergence phenomenon, indicating a gradual narrowing of the disparities among regions. The coefficient of variation in the eastern region exhibited relative stability during the period 2013-2023, fluctuating within the range of 0.7 to 0.8. This finding suggests that the variations observed among the regions within the eastern region do not exhibit a discernible trend during the specified period. Additionally, it indicates an absence of significant σ-convergence or divergence phenomena.

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Fig 5. Coefficient of variation of the level of e-commerce development in China.

https://doi.org/10.1371/journal.pone.0330066.g005

The coefficient of variation for the central region demonstrates an increasing trend that subsequently transitions into a decreasing trend over the observed period from 2013 to 2023.The coefficient of variation exhibits a gradual increase from 2013 to 2017, with a rise from approximately 0.2 to nearly 0.4.Following 2017, a decline is initiated, leading to a value close to 0.3 by 2023. This trend signifies that the central region initially experienced an expansion in internal variation during the initial period, subsequently exhibiting a degree of convergence in the subsequent period. The coefficient of variation in the western region exhibited a decreasing trend, followed by an increasing trend, and then a subsequent decreasing trend during the period from 2013 to 2023. The coefficient of variation demonstrated a decline from approximately 0.4 to approximately 0.3 during the years 2013 to 2015, an increase to approximately 0.5 in the period from 2015 to 2019, and a subsequent gradual decrease after 2019. This intricate trend suggests that the variation within the western region is more unstable, with no discernible σ-convergence or divergence trend. The coefficient of variation in the Northeast region exhibited a decreasing trend, followed by an increasing trend, during the period 2013-2023. The coefficient of variation decreased from approximately 0.4 to approximately 0.3 in the 2013-2019 period, and subsequently increased to approximately 0.4 after 2019. This trend suggests that the Northeast region experienced a degree of σ-convergence in the early period, followed by a widening of internal differences in the later period. The internal variation subsequently widened.

Absolute β-convergence analysis.

As illustrated in Table 6, the spatial error model indicates the presence of significant spatial autocorrelation, as evidenced by both Moran’s I and the Lagrange multiplier test. However, the robustness test (Robust Lagrange multiplier) suggests that this correlation may not be substantial. In the spatial lag model, the Lagrange multiplier test indicates the presence of significant spatial autocorrelation; however, the robustness test (Robust Lagrange multiplier) suggests that this correlation may not be significant. Consequently, the OLS model was selected.

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Table 6. Results of the Lagrange test.

https://doi.org/10.1371/journal.pone.0330066.t006

As illustrated in Table 7, the OLS model run for the absolute β-convergence analysis of China’s e-commerce development level indicates that the coefficient of 1_score (initial e-commerce development level) is −0.0176644, the standard error is 0.0062189, the t-value is −2.84, and the P-value is 0.005. The findings indicate that for each unit increase in the initial e-commerce development level, the subsequent e-commerce development speed will decrease by 0.0176644 units. The p-value is less than 0.05, indicating that the coefficient is statistically significant. The initial level of development exerts a significant negative influence on the subsequent speed of development, indicating that there is an absolute β-convergence of the level of e-commerce development in China. Concurrently, the data also indicate that the regions that initiated later have faster e-commerce development and are rapidly catching up with the pioneers.

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Table 7. Results of the OLS.

https://doi.org/10.1371/journal.pone.0330066.t007

Conditional β-convergence analysis.

As illustrated in Table 8, the results of the Lagrange test for the level of e-commerce development in China and the explanatory variables indicate that, in the spatial error model, Moran’s I, Lagrange multiplier, and Robust Lagrange multiplier tests all demonstrate significant spatial autocorrelation. In the spatial lag model, both Lagrange multiplier and Robust Lagrange multiplier tests exhibited significant spatial autocorrelation.

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Table 8. Results of the Lagrange test.

https://doi.org/10.1371/journal.pone.0330066.t008

Given the observed significant spatial autocorrelation in the test results, this study employs the Spatial Durbin Model (SDM). To ascertain whether the SDM would degenerate, a Wald Test for SAR was conducted, yielding a p-value of 0.0498. This result indicates that the SDM does not degenerate. Furthermore, Likelihood Ratio (LR) tests were performed to compare the SDM with the Spatial Autoregressive Model (SAR) and the Spatial Error Model (SEM), At the 10% significance level, the results demonstrate a superior goodness-of-fit for the SDM. Consequently, the SDM is preferentially selected for this analysis.

The results of the SDM model run, as presented in Table 9, reveal a direct effect characterized by a significant positive relationship between economic development and e-commerce development. The regression coefficient (ln_gdp) of 0.0710209 and a P-value of 0.010 indicate statistical significance, suggesting that economic development in a region has a substantial positive influence on its e-commerce development. This indicates that as a region’s economic development level increases, the level of e-commerce development in the region also tends to rise. The ln_county coefficient is 0.0699656, and the P-value is 0.089, indicating that it is close to being significant at the 10% level. This suggests that the county’s economic development has a positive impact on e-commerce development in the region. In the spatial spillover effect, the ln_finance coefficient is −0.0177471, with a P-value of 0.089, which is close to significant at the 10% level of significance, indicating that the level of financial development in neighboring regions exerts a negative impact on the level of e-commerce development in this region. The ln_county coefficient is 0.20. 90297, with a P-value of 0.006, which is significant, indicating that the neighboring regions’ level of county economic development has a significant positive impact on the level of e-commerce development in this region, i.e., the more developed the county economy in the neighboring regions, the higher the level of e-commerce development in this region, and there is a significant spatial spillover effect.

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Table 9. Results of the SDM model.

https://doi.org/10.1371/journal.pone.0330066.t009

The preceding analysis demonstrates a significant positive correlation between regional economic development and e-commerce development, indicating economic development as a crucial driver. Notably, a spatial spillover effect of county-level economic development exists, whereby neighboring regions’ economic prosperity exerts a significant positive influence on local e-commerce development. This suggests that interregional economic integration, facilitated by e-commerce, fosters interconnected growth through mechanisms such as logistics integration, supply chain optimization, and consumer market expansion.

This phenomenon can be attributed to: (1) the direct impact of local economic development on e-commerce adoption, driven by increased income, enhanced consumer demand, and robust infrastructure; (2) the market integration effect, where e-commerce dismantles geographical barriers, promoting cross-regional economic interactions. Specifically, regional economic growth stimulates contiguous consumption and production, while improved logistics and supply chains, developed in one region, positively impact neighboring areas through network interconnections. Furthermore, successful e-commerce strategies in adjacent counties serve as models for emulation, while competitive pressures incentivize accelerated local e-commerce development.