Introduction

China’s economic development has made a qualitative leap over the past few decades, and policy support for such achievements is indispensable. One far-reaching policy was the policy of reform and opening up, with eastern China as the pivot (Lu et al., 2019). Against this policy context, the eastern region has achieved progress, but the western region has failed to realize the expected economic growth, resulting in a worsening east–west divergence (Lin & Chen, 2004). In particular, long-standing inequalities in economic development have triggered negative consequences for other aspects of society and need to be addressed.

Financial development, which is closely associated with economic development, has also undergone a sharp east–west polarization. The primary reason for this is that the industrial structure of the western region is predominantly agricultural, which makes it difficult to access support from financial institutions. Accordingly, inclusive finance has emerged as a new approach to extend the availability of financial services to fulfill the needs of all regions and individuals. Nevertheless, it is essential to recognize that ATMs have limitations in overcoming geographical constraints.

Considering this, the incorporation of inclusive finance with the Internet and big data has contributed to the expansion of digital financial inclusion. Digital financial inclusion emphasizes expanding the reach and penetration of financial services to meet the needs of regions and populations that suffer from financial exclusion. Digital financial inclusion has not only further broadened the coverage of financial services, but financial services such as online banking and lending have also offered additional financing channels for remote western areas facing borrowing challenges (Ding et al., 2022). As a result, digital financial inclusion represented by Alipay began to blossom in China. By 2022, Alipay users covered nearly 91% of the population. Although Alipay has reached most of the population, the east–west inequality in digital financial inclusion has been exacerbated, as 39% of the population (1.5 times more than in the West) gather in the developed eastern regions, coupled with advanced infrastructure and technology.

In summary, an in-depth investigation of the dynamics of the East–West gap in terms of economic development and digital financial inclusion would be more informative in mitigating inequality. Additionally, given the enormous impact of COVID-19 on all aspects of society in 2020, it is critical to include 2020 in the research framework. Therefore, this study focuses on 31 provinces from 2011 to 2020 and applies ESTDA (Exploratory Space–Time Data Analysis) (Le Gallo & Ertur, 2003; Ye & Rey, 2013; Ye & Carroll, 2011) to answer the following research questions: How have East–West disparities in economic development and digital financial inclusion changed over time and space? Which regions should be targeted? What has been the influence of the epidemic on the variations in the East–West gap?

The contributions of this study are as follows. First, in contrast to the unitary perspective in previous research, this study sheds light on changes in East–West inequality from a combined spatial-temporal perspective. Furthermore, this research provides practical information for identifying focal regions for policy implementation. Last, this study compensates for the lack of relevant literature by delving into the key components of digital financial inclusion.

This paper also includes the following sections. In “Literature review” section, we outline the relevant literature. The data and methods are explained in “Data” and “Methodology” sections. The empirical analysis results are further reported in “Empirical results” section. Finally, “Conclusion” section summarizes the paper’s conclusions and future work.

Literature review

Regarding the economic geography theory, unequal geographical development is an essential branch that includes theories of spatial aggregation and geographical dispersion under capitalism (Gallup et al., 1999; Harvey, 2005). First, the theory of spatial aggregation emphasizes that the concentration of capital in different regions leads to unequal development. Capital tends to concentrate in regions with better infrastructure and industrial foundations, and these developed regions attract more capital to invest, widening the gap with regions that do not receive capital favor. Furthermore, the theory of spatial dispersion highlights that the geographical mobility of capital results in unequal development (Das, 2017). Developed regions where capital is centralized also face the challenge of higher business costs. Therefore, to maximize profits, capital begins to relocate some low-end industrial chains to regions with cheaper labor while maintaining the technological industries with core competitiveness in developed regions (Kim, 2008). Moreover, the Solow growth model underscores that technology is the key to continuous economic growth and contributes to the persistence of divergence between countries (Solow, 1956). Consequently, more entrenched inequalities have emerged between regions. In the case of China, the aggregation of capital in the eastern region at the early stage of the reform and opening-up process and the spatial dispersal of capital after the eastern region became well-developed have produced far-reaching effects on the persistent east–west inequality in China (Fan, 1997).

A considerable body of literature has discussed China’s east–west division. Chai (1996) proved that the reform and opening-up policy, implemented with the east regions as the center, resulted in a long-term east–west disparity. Specifically, Fan and Sun (2008) discovered that the east–west divergence gradually worsened between the 1980s and the 1990s. Provincial investigations found a continuous deterioration of the east–west gap between 1978 and 2007 (Li & Wei, 2010). He et al. (2017a) further extended the period to 2010 and proved the arisen east–west divergence. Moreover, county-level research also revealed a persistent east–west inequality from 1997 to 2010 (He et al., 2017b). In addition, Zhang and Zou (2012) clarified that the potential cause of the continuous east–west gap was the polarization between the high-income clusters in the east and low-income clusters in the west. However, Wang et al. (2022) conducted research from 2001 to 2020 and found a declining trend in east–west inequality. Given the shock of COVID-19, city-level studies from 2013 to 2020 indicated that it led to worsening inequality (Wan et al., 2023). Based on the same research scale, Shen et al. (2021) examined quarterly data from 2019 to 2020 and verified the widening inter-regional gap after the pandemic.

Moreover, numerous studies have investigated the impact of digital financial inclusion on economic development. Ahmad et al. (2021) conducted provincial exploration and found that digital financial inclusion could facilitate economic growth by improving human capital. Similarly, Liu et al. (2021) further validated that digital financial inclusion can contribute to economic growth through the promotion of SMEs. Regarding the regional heterogeneity of digital financial inclusion, Li et al. (2022) clarified the spatially varied impacts of digital financial inclusion, which is more favorable to Western provinces. Li et al. (2023) also proved that the development of digital fintech is essential to improve the economic performance of rural regions in the West. However, Xi and Wang (2023) and Ding et al. (2021) argued that digital financial inclusion is more effective for enhancing the quality of economic development in the eastern provinces.

Despite the informative insights discussed in the literature, the limitations of these studies warrant further consideration. First, previous research on the east–west gap primarily starts from a single perspective, which will be complemented by this study through integrated spatio-temporal exploration. Furthermore, there has been limited in-depth spatial investigation of the components of digital financial inclusion. Considering this, we will delve into the sub-indicators of digital financial inclusion. Last, from the standpoint of policy application, relatively few studies have been conducted to locate key regions for policy implementation. Therefore, this study will fill the research gap by applying ESTDA to identify focal areas.

Data

Given the severe lack of data for the western area at other regional scales, this study undertakes a spatial-temporal exploration of 31 provincesFootnote 1 from 2011 to 2020 to achieve data completeness and maximize coverage in all regions. GDP data is obtained from the Statistical Yearbook.Footnote 2 With the intention of comprehensively measuring the developmental extent of digital financial inclusion, we cite the digital financial inclusion index published by Peking University (Guo et al., 2020). The distinctive feature of this index is the multi-dimensional metric that contains not only three macro components: breadth of coverage, depth of usage, and digitalization level but also incorporates about 33 sub-indicators into the macro dimensions.Footnote 3 The composite index is derived by applying the AHP(Analytic Hierarchy Process) method to define the weight of each macro element. Each macro aspect is explored in the following section to achieve a thorough investigation of digital financial inclusion. Indeed, besides digital financial inclusion, we also consider the importance of traditional finance, which is evaluated by loan-deposits rates.Footnote 4 The provincial boundary vector data are acquired from GADM (Global Administrative Areas, 2022). Table 1 shows summary statistics for variables after the logarithm.

Table 1 Descriptive statistics
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Methodology

In accordance with the core objective of this study, ESTDA is applied to investigate space–time variations of East–West inequality in economic development and digital financial inclusion. Marked divergence from the ESDA, the ESTDA exhibits the capability to dynamically capture variations between regions and relationships between variables. The ESTDA consists of the following steps: global investigation, local exploration, and spatio-temporal examination. At the outset, a global investigation is carried out by testing the existence of clustering using Moran’s I. Next, LISA is conducted to locate the significant clusters. Moreover, expanding on the above spatial investigation, the temporal dimension has been incorporated by directional LISA to clarify the co-movement of regions across time. It is vital to note that endogeneity issues can interfere with identifying relationships between variables in the context of multivariate spatial examinations. As a result, this study conducts individual explorations of variables, and the regional overlap revealed in the comparative analysis can also sufficiently reflect the relationship between variables. This study further applies a local neighbor match test to specify the statistical significance of regional overlaps to obtain more convincing results. Figure 1 outlines the methodological workflow, and an extensive description is provided in the following subsection.

Fig. 1
figure 1

Flowchart of methods

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Weight matrix selection

Appropriate spatial weights are crucial in spatial exploration. In China, there is an island called Hainan province. The neighbors assigned to this island based on the fixed distance or K-nearest neighbor weight matrix may not be reasonable. Considering that Hainan used to be affiliated with Guangdong, the Queen contiguity weight matrix is adopted to connect Hainan and Guangdong while ensuring that other regions are unaffected. It is worth stressing that after comparing the fixed distance and K-nearest neighbor weight matrix, the z-value of Moran’s I for the Queen continuity weight matrix is statistically the highest (Anselin, 1995), which further supports the choice of the weight matrix (Fig. 2).Footnote 5

Fig. 2
figure 2

Connectivity map of Queen contiguity weight matrix

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Global Moran’s I

Global Moran’s I is commonly used to measure the sign of clustering (Moran, 1948). The equation of global Moran’s I is as follows:

$$\begin{aligned} I=\frac{\sum _a \sum _b W_{a b} z_a \cdot z_b / \sum _a \sum _b W_{a b}}{\sum _a z_b^2 / N} \end{aligned}$$
(1)

where \(z_a=x_a-\bar{x}\), \(z_a\) represents the deviation from the mean of x in the region a. \(W_{a b}\) is the row-standardized weight to clarify the spatial connections between a given region and its neighbors. N is the number of regions. The range of Moran’s I is from -1 to 1, and a positive and significant Moran’s I value indicates the presence of a sign of clustering, suggesting that the values of x in the region a are similar to those in its neighboring areas. Conversely, a negative and significant Moran’s I value represents a sign of alternating, indicating that the values of x in the region and its neighboring regions have a checkerboard pattern distribution, indicating dissimilarity.

Anselin (2019) further proposed the Moran scatter plot to reflect the relationship between standardized \(x_a\) and its spatial lag and show the regions’ distribution in four quadrants. High–High and Low–Low quadrants show the similarity of local areas with surrounding regions, but the high–low and low–high quadrants show dissimilarity.

Local Moran

Although Moran’s I scatter plot can provide insight into the spatial distribution of regions, it cannot precisely indicate the geographical location and significance of each point on the plot. Therefore, LISA is developed by Anselin (1995) to identify the core areas. The expression of LISA is as follows :

$$\begin{aligned} I_a=\frac{\sum _b W_{a b} z_a z_b}{\sum _a z_a^2} \end{aligned}$$
(2)

The calculation for each region involves multiplying the value at its location by the weighted sum of the values at neighboring locations. Like global Moran’s I, local Moran also consists of four quadrants. High–high clusters consist of high-level local areas with surrounding areas, and low–low clusters are the opposite, which shows the similarity between the local area and neighboring regions. In addition, the spatial outliers include the High–Low and Low–High groups. The high–low group is made up of regions with high levels and surrounding regions with low levels, and the Low–High group is the opposite.

Directional LISA

Building on LISA, Rey et al. (2011) introduced a temporal dimension to measure the dynamic movement between regions and surrounding areas over time. The specific equation is as follows:

$$\begin{aligned} L_{a, t}=\frac{z_{a, t} \sum _b W_{ab} z_{b, t}}{\sum _a z_{a, t}^2} \end{aligned}$$
(3)

The spatial weight \(W_{ab}\) is also utilized to capture the neighboring structure. \(z_{a, t}\) is the deviation of the variable from the temporal mean at time t. Like LISA, directional LISA also includes four quadrants with different meanings. The High–High quadrant denotes that region a and its neighboring areas’ development level has improved together. In contrast, the quadrant of Low–Low indicates that both have deteriorated together. The regions in the second quadrant (Low–High) and fourth quadrant (high–low) of the directional LISA reflect spatial heterogeneity because their local development movement direction is opposite to the neighbors. The standardized directional Moran scatter plot is applied to present the dynamic changes of the variable between a region and its neighboring regions through visualization. Unlike the point representation of regions in the Moran scatter plot, each arrow in the standardized directional Moran scatter plot represents a region’s movement vector from the initial year to the final year (Sastré Gutiérrez & Rey, 2013).

However, we need to confirm whether the comovement of a region and its neighbors is spatially random. Although Murray et al. (2012) recommended the use of computational permutation due to the potential issue of lower variance of lag and dependence of movement vectors, Rey et al. (2011) employed a conditional permutation method to assess spatial randomness. The expression used for this purpose is given below:

$$\begin{aligned} \begin{aligned}&H_0: h_{i, t+k}=h_{i p, t+k} \\&H_1: h_{i, t+k} \ne h_{i p, t+k} \end{aligned} \end{aligned}$$
(4)

The statistical significance of the difference between the observed number of movement vectors (\(h_{i, t+k}\)) distributed in each quadrant and the number based on spatial randomization (\(h_{i p, t+k}\)) is evaluated using pseudo-p-values.

Local neighbor match test

Anselin and Li (2020) proposed a local neighbor match test to examine the significant overlap of the regions and better understand the relationship between different variables in both the attribute and geographical space. This approach compares the k-nearest neighbors of a region in the attribute space with its actual geographical neighbors to evaluate the degree of overlap. The equation to determine the significance of an overlapped area is as follows:

$$\begin{aligned} P = \frac{C(k,o){\cdot } C(N-k,k-o)}{C(N,k)} \end{aligned}$$
(5)

The test’s formula includes variables such as N, representing the number of observations minus one. k is the number of nearest neighbors. o represents the number of neighbors in common, and C is the combinatorial operator.

Empirical results

Basic regional distribution

Prior to undertaking more in-depth spatial investigations, the box map in Fig. 3 shows the spatial distribution of variables across time. Economic development exhibits a continuous dichotomy between the eastern and western clusters, and this pattern is also reflected in digital financial inclusion. However, no distinct regional division is observed in traditional finance, and the distribution over time is relatively random, which merits further exploration. As crucial components of digital financial inclusion, coverage and usage also present a similar east–west divergence as the composite index. In contrast, the regional distribution of digitization tends to fluctuate erratically over time. Considering the varying patterns of the different variables, it is worth conducting a more thorough spatial exploration to statistically clarify the significance of the east–west disparity.

Fig. 3
figure 3

Spatial distribution of variables

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Spatial dependence and regional inequality

Figures 4, 5, and 6 show the spatial autocorrelation of each variable over time, respectively. First, the regional similarity in economic development revealed a yearly decline, and inequality, as measured by \(\sigma\) convergence, has gradually deteriorated since 2014. More notably, after the epidemic, the spatial similarity between regions suffered the most severe decline in a decade, probably due to the lockdown policy (Chen et al., 2020), and inequality experienced explosive growth. Given that spatial similarity moves inversely with inequality, enhancing inter-regional spatial dependence warrants consideration when alleviating inequality in economic development.

In addition, digital financial inclusion has exhibited progressive spatial similarity over the years, with no disturbance from the epidemic. Among the components of digital financial inclusion, both usage and coverage have significant spatial dependence for all years, whereas digitization has insignificant spatial autocorrelation in some years. However, traditional finance lacks spatial dependence. The above results derive from the fact that the scope of digital financial services is not limited by geographical boundaries but depends on Internet coverage (Ozili, 2018). By contrast, traditional financial institutions are entirely governed by local central banks, resulting in regional independence. Consequently, capitalizing on the stable and growing spatial similarity of digital financial inclusion to lessen inequalities in economic development is also a viable approach.

Fig. 4
figure 4

Comparison of spatial dependence and regional inequalities in economic development

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Fig. 5
figure 5

Spatial dependence of digital financial inclusion and traditional finance

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Fig. 6
figure 6

Spatial dependence of digital financial inclusion components

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LISA

Considering that economic development, digital financial inclusion, and its key elements (coverage and usage) exhibit significant and robust spatial autocorrelation, LISA is applied to investigate the regional clustering of these four variables. First, economic development presents an east–west polarization with the high–high group in the east and the low–low group in the west, as shown in Fig. 7. Unsurprisingly, the high–high cluster is dominated by Jiangsu, Zhejiang, and Shanghai, which are some of China’s most developed regions. In contrast, the low–low group consisted of the least developing areas. More prominently, the east–west division reveals no indications of improvement during this period. Even after the COVID-19 pandemic, more regions have attained a position in the high–high group. One plausible reason for this is that the epidemic contributed to the economic recession in Jiangsu, Zhejiang, and Shanghai. Concretely, these three regions have often collaborated intensively, and the interventions of epidemics and lockdown policies have resulted in disruptions and even the termination of economic cooperation, which is partially supported by the declining spatial autocorrelation noted in the previous section. As a result, even though these regions still occupied a position in the high-level groups, the relative gap with neighbors narrowed under the strain of the epidemic.

Fig. 7
figure 7

LISA map of GDP

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In terms of digital financial inclusion, Fig. 8 displays a similar east–west divergence. Jiangsu, Zhejiang, and Shanghai are still fixated on the high–high cluster, whereas the low–low group encompasses most of the western and northeastern regions. Due to the fact that Jiangsu, Zhejiang, and Shanghai have persistently occupied the first echelon of technological and financial innovation, digital financial inclusion is also ahead of other regions amidst such a conducive environment. Notably, Anhui and Jiangxi have uplifted to the high–high group after the epidemic. Apart from the geographical advantage in the vicinity of Zhejiang, the widespread application of health QR codes expanded people’s acceptance of digital products during the pandemic (Xiao, 2020), further promoting the profound use of digital financial apps such as Alipay. In stark contrast, all northeastern provinces descended into the low–low group after the epidemic. Delving into the potential factors, the failure of industrial upgrading and rapid population exodus caused the sluggish economic performance and technological development of the northeast region (Hou et al., 2019; Ma et al., 2020), and the pandemic further expedited this decline. Unsurprisingly, the development of digital financial inclusion in the Northeast has stagnated.

Fig. 8
figure 8

LISA map of digital financial inclusion

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To embark on a more comprehensive analysis, we also investigate the two primary components of the digital financial inclusion index. First, similar to the aggregated index, the coverage also exhibits an east–west disparity. It is also noteworthy that the number of regions in both the high and low sub-clusters increased in 2019 and 2020 compared with 2011 and 2015. To explain this better, we should direct attention to the coverage index itself, which centers on measuring the number of accounts of Alipay users. Among the potential factors that affect the number of users, infrastructure construction deserves attention. Specifically, Internet coverage is still limited in the western regions with low population density (Liu et al., 2021). Infrastructure construction is generally characterized by a long duration, while the epidemic has resulted in delays, thus indirectly leading to the persistence or even exacerbation of east–west inequality in coverage (Fig. 9).

Fig. 9
figure 9

LISA map of coverage

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Although the role of the user base cannot be underestimated, the penetration depth of digital financial services warrants further exploration. In terms of usage, the eastern high–high cluster includes Jiangsu, Zhejiang, Shanghai, and the adjacent areas, whereas the western low–low group covers more northwestern regions (Fig. 10). Assessing the constituent members of the high–high and low–low groups, the situation of east–west disparity remained stalemated from 2011 to 2020, even though Anhui disappeared from the high–high group after the epidemic. The probable explanations are as follows: For high-level areas, rapid economic growth stimulates more demand for financial services, and the supply side has satisfied growing needs through sustained innovation to expand the diversity of financial services. Ultimately, the continued deepening of digital financial services has been realized. Nevertheless, for the western regions, the demand-supply cycle cannot be developed with insufficient demand and retarded infrastructure. The essential reason for the deficient demand is that, except for weak economic growth, the information asymmetry issue is particularly acute, with individuals having inadequate knowledge of usage and access to online financial products (Peng et al., 2022).

In accordance with the above results, it is worth highlighting a distinct regional overlap between regions belonging to the high–high and low–low subgroups regarding economic development, digital financial inclusion, and even its components. Therefore, economic development is not only spatially linked to digital financial inclusion but is also associated with its constituent elements.

Fig. 10
figure 10

LISA map of usage

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Directional LISA

In the above LISA section, we carried out a spatial examination of individual years, which underestimated temporal exploration. Accordingly, the directional LISA approach is applied to investigate missing temporal variations across regions in the following section.

Regarding economic development, the directional LISA results in Fig. 11 diverge from the rigid east–west inequality shown in the LISA maps. From 2011 to 2019, most western regions were concentrated in the high–high quadrant, which implies improved economic performance in these regions. Meanwhile, most eastern regions were clustered in the low–low quadrant, indicating a relative recession in economic growth. Given this opposite moving direction, it further underscores that the east–west disparity does not persist but instead shifts to improve over time. However, the epidemic reversed this progression, with more western regions transferred to the low–low quadrant and eastern areas relocated to the high–high quadrant. The economy’s vulnerability is higher in the West, where the shock of the epidemic has led to regression. Conversely, eastern economies have a relatively more risk-resistant capability (Duan et al., 2021) and experience less regression than the West, thus exacerbating the east–west disparity.

Fig. 11
figure 11

Standardized directional Moran scatter plot of GDP

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Digital financial inclusion also presents a regional distribution similar to that of economic development from 2011 to 2019, as depicted in Fig. 12. The east–west division is not a lasting antagonism, and improvements in western provinces have eased the situation. The progressive improvement of digital financial inclusion in the West embodies the following aspects. First, it is inextricably linked to support from the Go-West and Silk Road programs (Szczudlik-Tatar et al., 2013). With the facilitation of these projects, infrastructure has been systematically strengthened in favor of digital financial inclusion. Moreover, for the western region, where agriculture still occupies a major role, microfinance provided by digital financial inclusion has become increasingly desirable, as it effectively alleviates the borrowing pressures confronted by farmers (Wang & He, 2020). Notably, the onset of the epidemic disrupted the regional distribution, with regional differentiation within the east–west group distinctly greater than the polarization between east and west. Several western areas with better risk tolerance remained in the high–high zone, whereas others shifted to the low–high zone. Along with a similar situation in the east, improvements in the east–west gap in digital financial inclusion have stalled.

Fig. 12
figure 12

Standardized directional Moran scatter plot of digital financial inclusion

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Finally, regarding the components of digital financial inclusion, the east–west inequalities between 2011 and 2019 improved but performed disparately in the post-epidemic period (Fig. 13). It merits attention that coverage has primarily preserved the pre-epidemic situation, although the magnitude of the improvement has been moderated. In parallel with the previous discussion, the epidemic contributed to delays in the construction and refinement of the Internet, thereby confining the extent of coverage.

Conversely, for usage, eastern areas transitioned to high–high, while the west dropped to low–low quadrant, indicating deteriorated east–west inequality. The epidemic interrupted economic activities and resulted in a severe contraction in investment demand. Coupled with the inherently low demand for social investment in the western region, demand for financial services has inevitably declined. The eastern region’s economic base and financial markets are more developed and stable than those in the west, consequently widening the gap (Fig. 14).

Fig. 13
figure 13

Standardized directional Moran scatter plot of coverage

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The above results also suggest the following crucial insights: Consistent with previous findings, spatio-temporal exploration also confirmed the regional overlap, underscoring the connection between economic development and digital financial inclusion. More importantly, although we discussed the stagnation or deterioration of the east–west split during the epidemic for digital financial inclusion and its components, the volatility was less intense than that for economic development, indicating a superior risk resistance of digital financial inclusion. Furthermore, the inability of traditional financial institutions to provide offline financial services during the pandemic highlights the value of digital financial inclusion. As a result, it is worthwhile for policymakers to consider digital financial inclusion as an entry instrument to alleviate depreciating east–west inequality in the post-COVID period.

Additionally, Table 2 presents the regional distribution under the assumption of spatial randomization. This study centers around two aspects: the significance and number of regions per quadrant. In light of economic development, the significance of the first quadrant further statistically supports the advancement of economic performance in the West before the epidemic and validates the relative progression of economic growth in the eastern regions after the pandemic. Simultaneously, the second and fourth quadrants were also significant, indicating the presence of spatial heterogeneity. However, by comparing the number of regions distributed in each quadrant, the first quadrant has allocated even more areas than the sum of the second and fourth quadrants. Thus, considering the above situation, spatial homogeneity is more dominant than spatial heterogeneity, favoring policy implementation. To be more specific, spatial homogeneity emphasizes the consistency of regional co-movement direction (Rey, 2004), so under such a premise, executing regional cooperation policies will strengthen regional convergence, which in turn contributes to narrowing the east–west gap.

Fig. 14
figure 14

Standardized directional Moran scatter plot of usage

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Similarly, from 2011 to 2019, both the overall index and usage reveal a significant first quadrant, further supporting the findings of the western region’s improvement in digital financial inclusion, as discussed in the previous section. After the outbreak, most quadrants were insignificant, implicitly affirming the tiny fluctuations reflected in the axes of the standardized Moran plot and the conclusion that digital financial inclusion has better stability. In addition, the first quadrant of these two indicators has a greater regional share than the other quadrants, further signifying dominant spatial homogeneity. Nevertheless, coverage was significant only in the fourth quadrant before the pandemic. Although it has two significant quadrants after the epidemic, in conjunction with previously identified slight variations in the directional LISA plot, there is no credible evidence to assert the improvement in the east–west divergence of coverage.

Considering the similar spatial homogeneity discussed between digital financial inclusion and economic development in this section, policymakers should seize the opportunity to capitalize on the spatial homogeneity of digital financial inclusion to mitigate east–west inequality in economic development. More precisely, as the east–west gap in coverage is still stalemated, while the east–west disparity of usage reveals a significant improvement, policies should centralize to expand usage intensiveness to fulfill the better function of digital financial inclusion.

Table 2 Significance table of regional distribution
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Local neighbor match test

Based on the above discussions, regional duplications between digital financial inclusion and economic development occur frequently. Accordingly, this section examines regional coincidence and locates focal areas using the probability of overlap in the attribute and geographical spaces of the six nearest neighbors of each region through the local neighbor match test.

Fig. 15
figure 15

Local neighbor test of digital financial inclusion VS GDP

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Fig. 16
figure 16

Local neighbor test of coverage VS GDP

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Fig. 17
figure 17

Local neighbor test of usage VS GDP

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First, when investigating only digital inclusion and economic development, Figure 15 presents that most core areas with three or fourFootnote 6 identical neighbors in the attribute and geographical spaces also commonly appear in either the high or low subgroups of LISA and directional LISA. In addition, although the number and location of the core regions fluctuated over time, the clusters formed by the core regions with their neighbors remained relatively robust. Similarly, statistically significant regional overlaps exist between coverage, usage, and economic development. More remarkably, most of the western and northwestern regions are core regions. Therefore, for these regions, policies related to enhancing digital financial inclusion deserve government consideration as they can also attain the additional goal of easing inequality in economic development and maximizing policy outcomes (Figs. 16, 17).

Conclusion

Based on provincial data from 2011 to 2020 in China, this study not only specifies the temporal and spatial variations of the east–west gap in economic development and digital financial inclusion, but also investigates the connection between digital financial inclusion and its elements with economic development through ESTDA. The main conclusions are as follows:

First, inequality in economic development is inversely related to spatial similarity, with rising inequality being accompanied by declining regional similarity. This finding highlights that, as governments embark on addressing inequality issues, they may consider artificially boosting spatial dependence by increasing the intensity of regional cooperation. In addition, digital financial inclusion and its components (coverage and usage) have spatial similarities distinct from spatially independent traditional finance, and this regional dependence is growing and unaffected by epidemics. Accordingly, digital financial inclusion is potentially valuable and could be leveraged to alleviate the inequalities in economic development exacerbated by the pandemic.

Second, based solely on the local spatial perspective, economic development, digital financial inclusion, and its components all form a high–high cluster in the east and a low–low cluster in the west, and there is a distinct regional overlap within the subgroups. For policymakers, the location of these clusters and their members will contribute to a more precise orientation toward policy implementation, thus enhancing their effectiveness. Moreover, both coverage and usage as vital components of digital financial inclusion have distinct connections with economic development, which points to a more concrete direction for leveraging digital financial inclusion.

Third, spatio-temporal exploration indicates that both economic development and digital financial inclusion exhibit similar spatial homogeneity from 2011 to 2019, and that improvements in the West mitigate the east–west disparity. However, the outbreak of the epidemic has exacerbated the east–west gap in economic development, as the western region is more vulnerable to risk. Conversely, digital financial inclusion is less disrupted by the epidemic, especially in the usage dimension. Thus, the stability of digital financial inclusion once again highlights its value and further confirms that policies centered on deepening usage warrant consideration.

Fourth, there is significant regional overlap between digital financial inclusion and its components with economic development, and the coverage of regional overlap is predominantly concentrated in the high–high and low–low clusters. More importantly, regional overlaps provide crucial information for identifying core areas in which a single policy can realize the dual benefits of simultaneously advancing digital financial inclusion and economic development. In summary, ESTDA offers more insights into regional clustering, the detection of core regions, and even the relationships between variables, which in turn provides essential ideas for policy design.

Despite the above discussion, some significant limitations of this study must be considered. First, digital financial inclusion remains under-measured. The digital financial inclusion index data employed in this study are mainly derived from Alipay and lack measurements of commercial banks’ online financial services. Therefore, encapsulating more relevant indicators in the measurement system is a future research priority.

In addition, the selection of the regional scope is crucial for spatial analysis. However, as mentioned, conducting research at other administrative levels is challenging because of the severely missing values of GDP data in western China. With the application of satellite data in economics, measuring economic development by incorporating remotely sensed data to achieve a wider range of exploration is another direction for future research.