Digital Finance and Advanced Manufacturing Industry Development in China: A Coupling Coordination Analysis

: The coordinated development of digital ﬁnance and the advanced manufacturing industry is vital for high-quality economic development. Based on the provincial data of China from 2012 to 2020, this study applied the coupling coordination degree model, σ convergence model and Dagum–Gini coefﬁcient decomposition method to analyze the coupling coordination level, convergence characteristics, spatial differences and sources of digital ﬁnancial and advanced manufacturing industry development in China. The results show that the coupling coordination level between the two has crossed from the run-in transition stage to the coordinated development stage and shows a rapid growing trend. The coupling coordination degree of the eastern region is the highest, followed by the central and western regions. It has an obvious convergence trend, and the overall difference is signiﬁcantly reduced. The intra-regional difference of coupling coordination degree in the western region is the largest, indicating the comparatively larger gap in the development of digital ﬁnance and the advanced manufacturing industry among western provinces. The inter-regional difference between the east–west regions is the largest and is the main source of overall differences, which proves the fact of unbalanced development between regions. It is suggested to adopt differentiated regional policies to promote the coordinated development of digital ﬁnance and the advanced manufacturing industry.


Introduction
High-quality economic development is an important strategy for China to shift from rapid growth in volume to structural adjustment. High-quality economic development emphasizes innovation, high-efficiency and sustainability in the economic development process [1]. Advanced manufacturing industry (AMI) was first defined by the US government in 1992 as industry with advanced manufacturing technology, and the connotation of advanced technology has been developed to incorporate more technologies such as internet technology, digital technology, artificial intelligence, etc. The AMI has now become the top choice for many countries to accelerate industrial upgrading and promote high-quality economic development [2]. Advanced manufacturing industry development (AMID) is based on innovation and needs substantial efforts in R&D. However, compared with developed countries, the development of AMI in China faces greater challenges in technology innovation and the tighter constraints of financing [3].
Digital finance, with the application of a variety of new technologies, such as artificial intelligence, big data and cloud computing, is a supplement to conventional finance and plays an important role in providing financial support for firms with lower capital cost and Sustainability 2023, 15, 1188 2 of 13 higher convenience [4]. The development of digital finance can effectively make up for the shortage of conventional finance, help to alleviate the financing difficulties and provide financial support for the innovation activities so as to increase the investment in innovation research [5]. Moreover, digital finance can also reduce the information asymmetry between the supply and demand of funds, reduce transaction costs and improve the efficiency of capital use [6]. So, the development of digital finance is conducive to guiding the flow of social capital to AMI and optimizing resource allocation. According to the Digital Financial Inclusion Index of Peking University [7], the mean and median of the digital financial inclusion index of 31 provinces in mainland China rose from 40.00 and 33.58 in 2011 to 341.22 and 334.82 in 2020, respectively. In the past ten years, China's digital inclusive finance realized leapfrog development, which provided a potential opportunity for AMID.
Given the background of rapid development of digital finance and increasing efforts to promote AMID in China, this study analyzed the coupling coordination degree and spatial characteristics between digital finance and AMID and traced the sources of spatial differences between the central, east and west regions of China. Based on the research results, this paper puts forward countermeasures and suggestions to promote the coordination degree of digital finance and AMID, so as to boost high-quality economic development.

Literature Review
High-quality economic development is essential for many developing countries who focus too much on volumes instead of quality in economic development. So, the influential factors for high-quality economic development have been widely discussed. Technological innovation, institutional reform, industrial upgrading and fintech development have significant effects on development effectiveness [1,8]. So, the coordinated development of digital finance and AMI is key for promoting high-quality economic development.
Digital finance has many similarities with Internet finance and fintech in concept, but, indeed, digital finance covers a wider range of applications from connotation to service mode. Digital finance refers to conventional financial institutions and Internet companies using digital technology to carry out financing, payment, investment and other new financial business models. Digital finance combines information technology such as big data and Internet with financial innovation, which has the advantages of low cost, fast speed and wide coverage. Digital finance can provide both inclusive and precise services to the real economy through digital technology at a lower capital cost and more convenient service, which meets the demand of high-quality economic development for financial services [7]. It can lower the threshold and cost of financial services and provide financial services to different economic entities more effectively [9]. As a new financial mode, the effect of digital finance has been widely discussed. Digital finance expands the availability of loans through peer-to-peer lending and crowdfunding [10] and eases the financing constraints on enterprises [11]. In other words, digital finance bridges the gap between loaners and loanees in conventional finance, reduces the difficulty of accessing financial services, improves financial inclusion and creates a more inclusive society [12,13]. The development of digital finance can also improve payment convenience and significantly increase residents' consumption, thus driving economic growth [14]. Moreover, digital finance can contribute to new energy firms' financial performance [4] and increase urban innovation significantly [1]. Based on previous studies, it can be concluded that digital finance can facilitate high-quality economic development by positively affecting economic efficiency and structure [8].
As the core competitiveness of future industries, scientific and technological innovation becomes the engine of industrial upgrading in developing countries, the AMI with high innovation ability has more advantages in profitability and production [15]. The AMI is a new form of manufacturing industry by constantly absorbing the latest scientific research achievements and applying them to the whole process of product research and development, design, improvement and production management. Technological innovation can also accelerate the replacement of the basic labor force, so as to realize industrial Sustainability 2023, 15, 1188 3 of 13 automization and intellectualization in the AMI [16]. Most enterprises in the AMI are high-tech firms which need substantial and continuous investment in R&D. Traditional ways of financing cannot meet the increasing fund demand of these firms and constrain their development, while digital finance can offer more financing services and funds to these firms. What is more, the development of the AMI can also provide technological support and more investment choices to digital finance. The development of the AMI may accelerate the revolution of digital and information technology, which may be applied into improving the infrastructure of digital finance [8].
Both digital finance and the AMI are hot research topics. In previous literatures, extensive discussion was conducted on the connotation and related effects of digital finance and AMID and analyzed the impact of digital finance on technology innovation and the development of the real economy. It has been widely accepted that the development of digital finance can optimize the capital allocation and provide financial support to firms in the AMI with higher efficiency and lower cost. Since the AMI is a high technology and efficient industry, investment in the AMI can yield higher returns with lower risk, which contributes to the sustainable development of digital finance. So, there may be a mutually reinforcing relationship between digital finance and AMID, which means coordinated development of digital finance and the AMI is important for high-quality economic development. This research tries to evaluate the coupling coordination degree of digital finance and AMID in different regions of China, so as to clarify the relationship between the development of finance and the real economy and promote high-quality economic development in China. The main research contents are as follows: (1) Use coupling coordination degree model to measure the coupling coordination degree of digital finance and AMID in different provinces and regions in China.
(2) Use σ convergence model to analyze the convergence characteristics of the coupling coordination degree between digital finance and AMID in the eastern, central and western regions of China. (3) Measure the overall difference, intra-regional difference and inter-regional difference of coupling coordination degree of digital finance and AMID from the spatial perspective. Dagum-Gini coefficient and its decomposition method are applied to analyze the source and contribution rate of coupling coordination degree difference and explore the characteristics of intra-regional and inter-regional imbalance. It can provide an important reference for precise policies to achieve sustainable and coordinated development of economy.

Coupling Coordination Degree Model
To construct the coupling model of digital finance and AMID, the efficacy function of both should be determined first. Set DF i (i =1, 2, . . . , m) as the ith order parameter of digital finance and AI j (j = 1, 2, . . . , n) as the jth order parameter of AMID. α i and β i are the upper and lower limit value of the order parameter of the digital financial stability critical point, and α j and β j are the upper and lower limit of the order parameter of the stable critical point of AMID. Standardized coefficients of d f i and ai j are efficacy contribution value of DF i and AI j and d f i , ai j ∈ [0, 1]. When the efficacy coefficient is 0, the efficacy contribution value of this index is the lowest, and when the efficacy coefficient is 1, the efficacy contribution value of this index is the highest. When DF i and AI j has a positive effect, the calculation formulas of efficiency coefficients are d f i = (DF i − β i )/(α i − β i ) and ai j = AI j − β j / α j − β j , respectively. When DF i and AI j has a negative effect, the calculation formulas of efficiency coefficients are d f i = (β i − DF i )/(α i − β i ) and AI j = β j − AI j / α j − β j , respectively.
Set U d f . and U ai as the integrated order parameters of the two subsystems, λ i and λ j as the corresponding weight of each order parameter, then U d f = λ i d f i (i = 1, 2, . . . , m), U ai = λ j ai j (j = 1, 2, . . . , n). The coupling degree of the composite system is C, and it is defined as Equation (1) in reference to previous studies. Since the coupling degree cannot fully reflect the overall efficacy of the two subsystems, it is necessary to further construct a comprehensive development model as Equation (2), in which a and b are undetermined parameters representing the weight of digital finance and advanced manufacturing industry innovative development, respectively. Based on previous literature, this study sets a = b = 0.5. Coupling coordination model, which can fully reflect the overall coordination degree and effect of two subsystems, assuming Y for digital financial and coupling coordination degree of AMID, its value can be calculated by Equation (3).
Based on the research results of Hong et al. (2021) [17], the coupling coordination degree is divided into the following nine periods and three stages (see Table 1).
High-level coordinated development

The σ Convergence Model
In order to investigate the development and evolution trend of the coupling coordination degree between digital finance and AMID in different provinces and regions of China (The study takes the regional division by the National Bureau of Statistics in 2017 for reference and divides the country into three regions: eastern, central and western. The eastern region includes 11 provinces: Beijing, Tianjin, Liaoning, Shandong, Jiangsu, Shanghai, Zhejiang, Fujian, Hebei, Guangdong and Hainan. The central region includes eight provinces: Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan and Shanxi. The western region includes 12 provinces: Guangxi, Shaanxi, Gansu, Qinghai, Inner Mongolia, Xinjiang, Tibet, Sichuan, Guizhou, Yunnan, Ningxia and Chongqing), this study applied σ convergence model to analyze evolution characteristics of the coupling coordination degree of the different provinces and regions based on the method developed by Barro and Sala-i-Martin (1992) [18] and Sala-i-Martin (1996) [19].
In Equation (4), i is provincial subscript, j is regional subscript, n j is the number of provinces in region j, y ji is the coupling coordination degree of digital finance and AMID of province i in region j, y j is the mean value of coupling coordination degree between digital finance and AMID of all provinces in region j.

Dagum-Gini Coefficient and Decomposition Method
Dagum-Gini coefficient has obvious advantages in analyzing the spatial difference characteristics. This study uses the Gini coefficient proposed by Dagum (1997) [20] and its decomposition method to analyze the spatial differences and sources of the coupling coordination degree of digital finance and AMID in China. The overall Gini coefficient is calculated in Equation (5) as follows: In Equation (5), i, r are provincial subscript, n is the number of provinces, j, h are regional subscript, k is the total number of regions; in this study, k = 3, and the three regions include: eastern region, central region and western region; y is the mean value of coupling coordination degree between digital finance and AMID in all provinces. y ji and y hr are the coupling coordination degree of digital finance and AMID of province i in region j and province r in region h, respectively.
When the overall Gini coefficient G is decomposed by region, the first step is ranking the mean value of coupling coordination degree between digital finance and AMID in eastern, central and western regions, then decomposing the overall Gini coefficient (G) into three parts: intra-regional difference (G w ), net inter-regional difference (G nb ), and contribution of inter-regional hypervariable density to the overall Gini coefficient (G t ). For details, see Equations (6)- (8).
In Equation (6), p j = n j /n, s j = n j y j /ny, j = 1, 2, 3, G jj represents the Gini coefficient in region j (see Equation (9)). In Equations (7) and (8), G jh represents the Gini coefficient between region j and h (see Equation (10)), p h = n h /n, s h = n h y h /ny, h = 1, 2, 3, D jh represents the relative influence of coupling coordination degree between region j and h, D jh = d jh − p jh / d jh + p jh , d jh is the difference of coupling coordination between regions j and h, and represents the mathematical expectation of the sum of all the samples of y ji − y hr > 0 (see Equation (11)), p jh is the hypervariable first order matrix between region j and h and represents the mathematical expectation of the sum of all the samples of y hr − y ji > 0 (see Equation (12)); in Equations (11) and (12), F j and F h represent the cumulative distribution function of the coupling coordination degree between digital finance and AMID in region j and region h, respectively.

Description of Variables, Data Sources and Processing
The "Peking University Digital Financial Inclusion Index" is jointly released by Peking University Digital Finance Research Center and Ant Financial Services Research Institute [1,4] and widely recognized and authoritative. So, this study chooses it to evaluate  [21] and other scholars, this study constructs the evaluation index system of AMID from 2012 to 2020. Since the evaluation indexes of "Peking University Digital Financial Inclusion Index" are all relative quantity indexes, relative quantity indexes are also selected in the evaluation indexes of AMID.
The full-time equivalent of R&D personnel/total population and R&D project expenditure /GDP in high-tech industries were selected as the evaluation indexes of the innovation input dimension of the advanced manufacturing industry. The new product sales revenue of high-tech industries /GDP and the number of patent applications/total population are selected as indicators of the dimension of innovation output of the advanced manufacturing industry (see Table 2). The number of patent applications/total population (55.57%) ai4 Firstly, the efficacy function method is used to conduct non-dimensional treatment of the data, and the specific calculation is shown in Equation (13). Then, the weights of each index and dimension are determined by AHP (see Table 2). Finally, the innovative development level of the advanced manufacturing industry in 30 provinces and cities (Tibet Autonomous Region is not included because of data missing) and east, central and west regions is comprehensively evaluated. The above index data are from the China Science and Technology database of EPS database.

The Coupling Coordination Degree Digital Finance and AMID
The results of coupling coordination degree and convergence of digital finance and AMID in provinces and regions of China are shown in Table 3. The coupling coordination degree of digital finance and AMID in China increased from 0.596 in 2012 to 0.883 in 2020 with an increase of 0.287 and jumped from the late run-in transition stage to the high-level coordinated development stage, indicating the integration of digital finance and AMID was improved significantly. From the perspective of a development trend, the coupling coordination degree of digital finance and AMID in all regions showed an upward trend. From the spatial perspective, the mean value of coupling coordination degree in the eastern region was always higher than the national average level. From 2012 to 2020, only Hebei in 2012 was in the late stage of run-in transition, while the others were all in the coordination stage. In 2012, four provinces were in the stage of low-level coordinated development, and six provinces were in the stage of medium-level coordinated development. From 2013 to 2017, eleven provinces were in the stage of medium-level coordinated development, while the others were in the stage of high-level coordinated development. From 2018 to 2020, all provinces were in a stage of high-level coordinated development.
The mean value of coupling coordination degree in the western regions was lower than that of central regions, and both were lower than the national average level. For the central region, six provinces in the central region were in the late stage of run-in transition, and the other two provinces were in the stage of low-level coordinated development in in 2013, there were ten provinces in the coordinated development stage (six at low-level coordination, four at medium-level coordination); in 2014, there were nine provinces in the coordinated development stage (two at low-level coordination, six at mediumlevel coordination and one at high-level coordination). From 2015 to 2020, all provinces were in the coordinated development stage (three at low-level coordination, twenty-eight at medium-level coordination and thirty-four at high-level coordination). Overall, the coupling coordination between degree of digital finance and advanced manufacturing industry innovative development in eastern China was significantly higher than that in central and western China.

Convergence of Coupling Coordination Degree Digital Finance and AMID
While the coupling coordination degree between digital finance and AMID presents a rapid growth trend, there is still a great difference between various provinces (see Figure 1). In 2012, the coupling coordination degree of digital finance and AMID of Guangdong was highest and was 3.3 times than that of Xinjiang (0.227), which was the lowest. The eastern region (0.684) was 1.35 times than that of the western region (0.508) (see Table 3). In 2020, the ratio reduced to 1.39 and 1.1, respectively, indicating that the differences of coupling coordination degree among provinces and regions are gradually narrowing down. The convergence coefficient of σ can be used to analyze the difference of the coupling coordination degree of digital finance and AMID in each province from the overall average level. If the convergence coefficient σ decreases, it can be concluded that the coupling coordination degree of digital finance and AMID has a convergence trend, indicating that the gap between provinces or regions is gradually narrowing down. Convergence coefficients σ of provincial and regional coupling coordination degree of digital financial and AMID are calculated by Equation (4), and results are shown in Figure 1.
2015 to 2020, all provinces were in the coordinated development stage (three at low-level coordination, twenty-eight at medium-level coordination and thirty-four at high-level coordination). Overall, the coupling coordination between degree of digital finance and advanced manufacturing industry innovative development in eastern China was significantly higher than that in central and western China.

Convergence of Coupling Coordination Degree Digital Finance and AMID
While the coupling coordination degree between digital finance and AMID presents a rapid growth trend, there is still a great difference between various provinces (see Figure 1). In 2012, the coupling coordination degree of digital finance and AMID of Guangdong was highest and was 3.3 times than that of Xinjiang (0.227), which was the lowest. The eastern region (0.684) was 1.35 times than that of the western region (0.508) (see Table 3). In 2020, the ratio reduced to 1.39 and 1.1, respectively, indicating that the differences of coupling coordination degree among provinces and regions are gradually narrowing down. The convergence coefficient of σ can be used to analyze the difference of the coupling coordination degree of digital finance and AMID in each province from the overall average level. If the convergence coefficient σ decreases, it can be concluded that the coupling coordination degree of digital finance and AMID has a convergence trend, indicating that the gap between provinces or regions is gradually narrowing down. Convergence coefficients σ of provincial and regional coupling coordination degree of digital financial and AMID are calculated by Equation (4), and results are shown in Figure 1.  From the provincial aspect, σ convergence coefficient was significantly decreased from 0.246 in 2012 to 0.072 in 2020, except for a slight rebound in 2014, indicating that the gap of coupling coordination degree between provinces in China is shrinking. From the regional aspect, convergence coefficient σ of the eastern region was the lowest, and σ of central ranked secondly, while σ of the west was highest. What is more, σ convergence coefficients of the eastern, central and western regions were all declining year by year, from 0.156, 0.202, 0.336 in 2012 to 0.046, 0.050, 0.081 in 2020, respectively. It indicates that the difference of the coupling coordination degree between digital finance and AMID in the eastern region is always lower than that in the western region, and the difference of the regional coupling coordination degree is reducing. In order to further explore the changing rules of the coupling coordination degree between digital finance and AMID, Dagum-Gini coefficient is used to analyze the spatial differences and sources.

Spatial Differences in Coupling Coordination Degree of Digital Finance and AMID
The overall Gini coefficient (G), intra-regional Gini coefficient (G w ) and inter-regional Gini coefficient (G nb ) of the coupling coordination degree between digital finance and AMID were calculated by Equations (5)- (7), and results are shown in Table 4. The overall Gini coefficient of coupling coordination showed a downward trend of volatility, from 0.098 in 2012 to 0.039 in 2020, with a decrease of 0.059. It proves that the differences in overall coupling coordination degree of digital financial and AMID is narrowing, which is consistent with the results of σ convergence model. The intra-regional differences of the coupling coordination degree of digital finance and AMID in the east, middle and west also showed a decreasing trend of volatility (see Figure 2). From 2012 to 2020, the mean value of intra-regional differences in the western region was the highest (0.052), followed by that of the eastern region (0.030) and central region (0.022), while the standard deviation was the highest in the western region (0.029), followed by the eastern region (0.006) and central region (0.003). By comparison, the intra-regional difference of coupling coordination degree in the western region was the largest, and its fluctuation was more violent, while the intra-regional differences in the eastern region was the smallest, and the fluctuation was moderate. In terms of decreasing amplitude, the provincial difference in the western region showed a rapid decreasing trend, from 0.127 in 2012 to 0.038 in 2020, with an average annual changing rate of 0.73%. The changes of intra-regional differences in the eastern and central regions were relatively gentle and decreased from 0.046 and 0.022 in 2012 to 0.029 and 0.021 in 2020, respectively.  Moreover, the inter-regional differences of coupling coordination degree among the eastern, central and western regions were also decreasing(see Figure 3). From 2012 to 2020, the mean value of inter-regional Gini coefficient was the highest in the east-west region (0.073), followed by central-west region (0.047) and the lowest in east-central region (0.044). The standard deviation of inter-regional Gini coefficient was highest in east-west (0.039), followed by central-west (0.019) and lowest in east-central (0.013).The inter-regional Gini coefficient between east-west regions was high, while the inter-regional Gini coefficients between central-west regions and east-central regions were low. The inter-regional Gini coefficient between east-west regions decreased from 0.152 in 2012 to 0.055 in 2020, the inter-regional Gini coefficient between central-west regions decreased from 0.095 in 2012 to 0.038 in 2020 and the inter-regional Gini coefficient between east-central regions decreased from 0.079 in 2012 to 0.033 in 2020. It demonstrates that the regional differences of the coupling coordination degree of digital finance and AMID have gradually narrowed, and the difference between the east-west regions is significantly higher than those between the central-west regions and the east-central region. The differences between the central-west region and the east-central region are similar, and the changing trend is also consistent. Moreover, the inter-regional differences of coupling coordination degree among the eastern, central and western regions were also decreasing(see Figure 3). From 2012 to 2020, the mean value of inter-regional Gini coefficient was the highest in the east-west region (0.073), followed by central-west region (0.047) and the lowest in east-central region (0.044). The standard deviation of inter-regional Gini coefficient was highest in east-west (0.039), followed by central-west (0.019) and lowest in east-central (0.013).The inter-regional Gini coefficient between east-west regions was high, while the inter-regional Gini coefficients between central-west regions and east-central regions were low. The inter-regional Gini coefficient between east-west regions decreased from 0.152 in 2012 to 0.055 in 2020, the inter-regional Gini coefficient between central-west regions decreased from 0.095 in 2012 to 0.038 in 2020 and the inter-regional Gini coefficient between east-central regions decreased from 0.079 in 2012 to 0.033 in 2020. It demonstrates that the regional differences of the coupling coordination degree of digital finance and AMID have gradually narrowed, and the difference between the east-west regions is significantly higher than those between the central-west regions and the east-central region. The differences between the central-west region and the east-central region are similar, and the changing trend is also consistent.
low. The inter-regional Gini coefficient between east-west regions decreased from 0.152 in 2012 to 0.055 in 2020, the inter-regional Gini coefficient between central-west regions decreased from 0.095 in 2012 to 0.038 in 2020 and the inter-regional Gini coefficient between east-central regions decreased from 0.079 in 2012 to 0.033 in 2020. It demonstrates that the regional differences of the coupling coordination degree of digital finance and AMID have gradually narrowed, and the difference between the east-west regions is significantly higher than those between the central-west regions and the east-central region. The differences between the central-west region and the east-central region are similar, and the changing trend is also consistent.

Sources of Spatial Differences in Coupling Coordination Degree of Digital Finance and AMID
The contribution rates of spatial differences in coupling coordination degree of digital finance and AMID are the ratio of , and to , respectively, and the results are shown in Table 5.

Sources of Spatial Differences in Coupling Coordination Degree of Digital Finance and AMID
The contribution rates of spatial differences in coupling coordination degree of digital finance and AMID are the ratio of G w , G nb and G t to G, respectively, and the results are shown in Table 5. Generally speaking, the difference of coupling coordination degree between digital finance and AMID mainly came from inter-regional differences, then intra-regional differences, and the contribution rate of super-variable density was lowest(see Figure 4). The mean value of intra-regional difference, inter-regional difference and contribution rate of hypervariable densities were 24.90%, 63.30% and 11.80%, respectively, and the standard deviations were 0.011, 0.050 and 0.040, respectively. Moreover, the change curves of the three variables did not cross over during the same period, showing obvious hierarchical structure. By analyzing the development trend of the sources of differences, it can be found that the fluctuation of the three sources of differences is relatively gentle, the contribution rate of intra-regional the differences and the hypervariable density shows an increasing trend, and the contribution rate of inter-regional differences shows a decreasing trend. Specifically, the contribution rate of intra-regional differences increased from 23.87% in 2012 to 26.54% in 2020, the contribution rate of hypervariable density increased from 5.79% in 2012 to 15.24% in 2020, and the contribution rate of inter-regional differences decreased from 70.33% in 2012 to 58.23% in 2020. It indicates that the difference of the coupling coordination degree between digital finance and AMID is mainly due to inter-regional differences. sity shows an increasing trend, and the contribution rate of inter-regional differences shows a decreasing trend. Specifically, the contribution rate of intra-regional differences increased from 23.87% in 2012 to 26.54% in 2020, the contribution rate of hypervariable density increased from 5.79% in 2012 to 15.24% in 2020, and the contribution rate of inter-regional differences decreased from 70.33% in 2012 to 58.23% in 2020. It indicates that the difference of the coupling coordination degree between digital finance and AMID is mainly due to inter-regional differences.

Discussion
The relevant studies focus on the development of digital finance and its macro and micro impact, but there are few studies discussing the relationship between digital finance AMI and high-quality development. The development of digital finance and the AMI relies on a good economic foundation and contributes to the economic development in return. This can be proved by the obvious increasing trend of the coupling coordination degree of digital finance and AMID in China from 2012 to 2020. To be more specific, the coupling coordination degree of digital finance and AMID in the eastern region is highest and intra-regional difference is lowest, while the situation in the western region is the opposite. The geographical advantages, population density, infrastructure construction and many other favorable conditions in the eastern region provide good foundation for the development of digital finance and the AMI. The high coupling coordination degree can partially prove the mutually reinforcing relationship between digital finance and AMID. The high innovation and quick development of east regions also prove that the coordinated development between digital finance and AMID is beneficial for economic development. The western regions lag behind eastern and central regions in the development of both digital finance and the AMI due to the weak economic foundation, and the low coupling coordination degree in western regions implies that there is still a big gap between east and west. This finding is in accordance with Li et al. (2022), whose study revealed that the heterogeneous impact of digital finance on urban innovation is reflected in cities with different levels of commercial attractiveness [6]. The main sources of overall differences of coupling coordination degree are inter-regional differences, which further prove that the lagging development of west may hinder the high-quality development of China. Zhou et al. (2022) also proved that the low innovation output rate and unmatched infrastructure construction had a negative effect on high-quality economic development [1]. The results of coupling coordination degree and spatial difference of digital finance and AMID have strong policy implications that promoting coordinated development of digital finance and the AMI in western regions can be a solution to low economic growth.

Conclusions
Based on the data of 30 provinces in China from 2012 to 2020, this study applied the coupling coordination degree model, σ convergence model and Dagum-Gini coefficient decomposition method to analyze the coupling coordination degree, convergence characteristics, spatial differences and sources of differences between digital finance and AMID. It is found that the coupling coordination degree of digital finance and AMID in China shows a trend of rapid development, rising to a high-level coordinated development stage. The coupling coordination degree in the eastern region is the highest followed by central and the western regions, which means high-quality development is closely related to high coupling coordination degrees of digital finance and AMID. Both the overall and the regional coupling coordination degrees of digital finance and AMID show σ convergence trend, indicating the differences of coupling coordination degree among regions are narrowing down. The intra-regional difference in the western region is the largest while the intra-regional difference in the eastern region is the smallest, evidencing the comparatively larger gap in the development of digital finance and the AMI among western provinces. The inter-regional difference between east-west regions is the largest, which is the primary source of overall differences, demonstrating the unbalanced development between east and west.
Based on the fact that there are significant differences in coupling coordination degrees in different regions, it is necessary to implement differentiated and dynamic industrial development strategies according to the reality of different regions. The eastern region should continue to play the leading role in exploring new financial service models and encouraging innovative activities in the AMI. While the central and western regions need more financial support from the government to accelerate the construction of digital infrastructure and promote the innovation and development level of the AMI. Moreover, cross-regional exchanges and cooperation should also be strengthened. The government should provide policy incentives to encourage eastern regions bringing advanced technology and modern information resources to the central and western regions and make full use of advantageous regional sources to promote the coordinated development of digital finance and the AMI in central and western regions.
There are some limitations for this study. First, the indicators to evaluate the development level of AMI in this study are simple and insufficient. Second, the study only discusses the coupling and coordination interaction between digital finance and AMID but does not give empirical evidence for the reasons and factors of the inter-reginal and intra-regional differences. So, in a future study, more indicators such as the degree of digitization and informatization need to be incorporated to evaluate the development level of the AMI, and quantitative analysis of factors that may influence the coupling coordination level between digital finance and AMID is needed to provide a theoretical basis for improving the regional economic development policies.