Dynamic Evolution of High-Quality Economic Development Levels: Regional Differences and Distribution in West China

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Introduction
The 19th CPC National Congress pointed out that China's economic development has stepped into a new period, where the focus of economic development should be on quality rather than speed, and that China's economy is moving toward high-quality development.Encouraging HQED in the new era is an inevitable trend in China.The western region holds a crucial strategic position, but because of the constraints imposed by objective natural conditions, humanistic backgrounds, and other factors, it has lagged behind in development as a whole, being the "weak spot" of China's economic and social development.There is an urgent need to strengthen the HQED of the region.The Guiding Opinions of the CPC Central Committee and the State Council on Promoting the Formation of a New Pattern in the Large-scale Development of China's Western Regions also pointed out that the unbalanced and inadequate development of West China remains a pressing issue.Given that consolidating poverty eradication is still an arduous task and that there is a large gap in development compared with the eastern region, it is necessary to study the issue of western HQED.Therefore, this paper focuses on West China from the perspective of studying the HQED of the western region in recent years and hopes to summarize the development problems, advantages, disadvantages, and development trends of this western region and provides corresponding development suggestions according to the development characteristics of each region.The main problems solved in this paper are as follows: What is the level of HQED in West China?Is there a large difference in the HQED of West China?If so, where do these differences come from?What is the trend of HQED in West China?How can we raise the level of HQED in West China to a higher level?The research of this paper is helpful to provinces in the western region such that they can examine their own development, and the suggestions put forward in this paper are of great significance for the scientific promotion of the high-quality development level of the western economy.This paper consists of seven parts.The first part reviews the research on the quality of development and the impact of economic policies.The second part constructs an evaluation index system for HQED in the western region by referring to the existing research and expounds on the indexes contained in each sub-dimension.The third part briefly describes the study area and study methods of the article.The fourth part analyzes the result of the high-quality development of the western economy.The fifth part analyzes the regional differences, dynamic evolution process, and development trend of HQED in the western region.The sixth part discusses problems that exist in the economic development of the western region according to the research results and then provides corresponding suggestions according to these problems, and it analyzes the limitations of the article and future research trends.The seventh part summarizes the conclusion of the whole paper.

Literature Review
Some scholars have begun to study economic growth and economic development in the last century, but at first, scholars were more concerned about the speed of economic growth, and the selected measurement indicators were also very singular [1].Kamaev (1977) was the first to define the "quality of economic growth", stating that "quality of economic growth" is a complex concept that includes the rate of economic development, the quality of the goods produced, and the efficiency of the material means of production.Scholars then discussed the concept of the "quality of economic development".Xu Xuemin argued that the improvement of production efficiency is equivalent to an increase in the quality of the economy; i.e., it is the ability to produce more output for a given input [2].Other scholars believe that the quality of economic development should include the regulation of economic risk and allocations of social resources (Thomas 2001) [3], the social order and health of the people (Barro RJ 2002) [4], the urban ecosystem and social welfare (Fabio Sabatini 2008) [5], and the economic growth and living standards of people (Boyle, D.; Simms, 2009) [6].It can be seen that the early scholars' research identified the limitations of a single indicator in measurement but failed to establish a complete system to study the "quality of economic development".
In later years, scholars tried to set up a complete system to define and study the "quality of economic development".The system constructed by Liu Shucheng (2007) [7] showed that the "quality of economic development" includes "the stability of the economic development, the sustainability of the development model, the harmony of the development structure, and the harmony of the development interests".The system built by Qian Xiaojing and Hui Kang (2009) [8] contains five points, that is, "the structure of development, the stability of development, the distribution of benefits and outcomes of development, the use of development resources, and the environmental costs of development".Meng Xia (2011) [9] pointed out that the quality of economic growth is driven by the five factors of "balance, inclusiveness, sustainability, innovation, and stability".It is obvious that, at this stage, the research on the "quality of economic development" began to start from the perspective of the system, but scholars did not have a unified view of how to select the system.
Since the United Nations put forward 17 sustainable development indicators [10] in 2015 and China proposed "HQED" and its five new visions for development [11], the system of research on the quality of China's economic development has gradually shown signs of unification; i.e., most scholars have begun to define and evaluate the quality of economic development according to their own understandings of the "new visions for development" and the current economic development in China.At the same time, there has been a shift in the measurement of the quality of economic development from a single indicator, total factor productivity [12], to a composite indicator encompassing social governance, quality of life, employment, education, and national life expectancy [13][14][15][16].With the new visions for development gaining popularity, innovation, coordination, green development, opening up, and sharing have been the main components of the measurement indicators of HQED in China [17].Yang et al. (2021) evaluated HQED in China from the perspective of economic structure, economic efficiency, and ecological environment and explored the relationship between green finance, fintech, and HQED [18].Pan et al. (2021) constructed an indicator system to measure the HQED index of 301 counties and explored its spatial pattern in the five dimensions of economic development, innovation efficiency, environmental impact, ecological services, and livelihood [19].Liu Yaxue, Tian Chengshi, and Cheng Liyan constructed a comprehensive indicator system to measure HQED based on the five development visions and analyzed the measurements of 99 countries [20].Kong et al. (2021) constructed a quality index system for economic growth, including efficiency, stability, and sustainability [21].Li et al. (2021) established a multi-indicator system to calculate HQED, including five dimensions and 24 detailed indicators that fully correspond to the five visions for development [14].Guo et al. (2023) constructed a municipal indicator-evaluating system for HQED in five dimensions of industrial structure, inclusive total factor productivity, technological innovation, ecological environment, and living standards of residents [22].Li Fanglin and Li Mingdi (2021) built an evaluation system including economic operation, social development, and ecological sustainability to calculate the HQED of 41 cities in the Yangtze River Delta and found there are significant differences between cities [16].Guan et al. (2023) constructed an indicator system to measure HQED in the Yellow River Delta in terms of innovation, coordination, green development, opening up, and sharing and analyzed its distributional and spatiotemporal evolution characteristics [23].Yin Peiwei, Xie Pan, and Lei Hongzhen (2023) [24] constructed an indicator system to measure the HQED of nine national central cities based pm the three dimensions of quality change, efficiency change, and power change on the supply side of economic operation and found that the composite index of the HQED of national central cities showed an increase during the past 17 years but a gradient decline from east to west.Chao Xiaojing, Lian Yuanmei, and Shen Lu (2023) [25] constructed an index system based on the three-dimensional framework of "conditions-process-results" to measure the HQED level of 282 cities at the prefecture level and above in China over the past 18 years and found that the HQED of these cities went up steadily, with a narrowing gap between the three dimensions.Li Yan (2023) [26], by incorporating the government's governance effectiveness into the study of HQED, measured the HQED of 30 provinces in China using the entropy weight method and found an increase in the HQED index of China and the eastern, central, and western regions every year.Chen Zixi (2022) [27] built a measurement indicator system based on the "new visions for development" and evaluated the dynamic evolution and spatial convergence of the HQED of urban agglomerations in the three dimensions of time, region, and space, finding that it is significantly polarized and that there is an obvious gradient of high in the east and low in the west with a narrowing gap.Liu Yan (2023) [28] constructed a regional HQED measurement system based on the new visions for development and analyzed the spatial-temporal evolution and regional differences of HQED in Hunan Province using the entropy method and spatial analysis tools on a multi-scale, finding that HQED in Hunan goes up on the whole, but there is a large gap between the four regional plates in the province.
In addition, scholars have also begun to pay attention to the impact of economic policies on HQED, and most of these studies have focused on the three sub-dimensions of green development, innovation development, and openness development.In terms of greenrelated policies, some scholars have said that environmental supervision (Yin Xingmin et al., 2023) [29], environmental regulation (Wang Jun and Zhang Guixiang 2022) [30], green finance, and energy development (Wang Rong and Wang Fayuan 2022) [31] have a significant positive impact on HQED, while directive-based environmental regulation significantly hinders the improvement of the quality of economic development (Yin Xingmin 2023) [29].Some scholars believe that green finance (Gao Jing et al., 2023) [32] and environmental supervision (Chen Lingming et al., 2020) [33] can promote HQED by changing industrial structure, and environmental regulation (Yu Zhuoxi et al., 2023) [34] inhibits HQED by influencing fiscal decentralization.In addition, Liu Yun et al. (2021) [35] indicate that environmental regulations have a significant impact on HQED in the central and eastern regions, while this impact is not significant in the western regions.Lin Tao et al. (2022) [36] believe that there is a U-shaped relationship between environmental regulation intensity and HQED, and the correlation between environmental regulations and HQED is affected by the level of green technology innovation.AlKhars Mohammed et al., 2020 [37], however, suggest that GCC countries should be cautious in implementing energy conservation policies because the relationship between energy consumption and economic growth here mainly supports the growth and feedback hypothesis.Lu Weixue et al. (2023) [38] found that the combination of environmental regulation and control policies has obvious synergistic effects on HQED.Related to innovation policy, Qi Peipei et al. (2023) [39] found that data factors play an important driving role in high-quality economic growth and have a greater impact on coordinated development, green development, and innovative development, while the impact on open development is not obvious.Ding Chenhui et al. (2022) [40] suggest that, although the digital economy can promote HQED, its role is diminishing.What is surprising is the research on the opening-up policy.Jahanger A. (2021) [41] said that the comprehensive quality of FDI did not have a significant impact on the high-quality development of China's economy.Luo Haiyan and Qu Xiaoe (2023) [42] also indicate that China's export trade has a positive impact on the opening-up and coordination subsystem of HQED only when the regional absorption capacity is higher than the threshold.It can be seen that the most direct and obvious impact on HQED is policies related to green development, which is worthy of reference in the subsequent provision of policy suggestions in this paper.
In summary, the current research on HQED in China has established a highly accepted method and paradigm.That is, this research has built an indicator system to measure HQED based on its own innovation points and the new development visions and then analyzes the differences and development trends between regions within the scope of the study using analytical methods and pointed out problems in existing development, providing corresponding recommendations for future development.A wide range of studies on HQED in China are already available at scales including the state, urban agglomerations, provinces, central cities, and other regions, but there is still little attention paid to the western region.Given the importance of its strategic location, studying its HQED is a vital task in the context of the continuous promotion of the strategy of large-scale development in West China.Based on relevant research and according to the new visions for development, this paper constructs an indicator system for evaluating western HQED to measure its development level with analysis and puts forward reasonable suggestions to address the existing problems.

Construction of the Indicator System
According to the Guiding Opinions of the CPC Central Committee and the State Council on Promoting the Formation of a New Pattern in the Large-Scale Development of China's Western Regions and based on the relevant research and the data availability, this paper constructs an indicator system for measuring the level of western HQED consisting of 49 indicators in the dimensions of innovation support capacity, coordination support capacity, opening up support capacity, green support capacity, and sharing support capacity, as shown in Table 1.The dimensions of innovation support capacity are innovation input, innovation investment, and innovation contribution.The first dimension consists of four measures: R&D investment intensity, R&D personnel investment, the proportion of science and technology expenditure to fiscal expenditure, and the number of national higher-education institutions per million population.The second dimension includes three measures: the number of patent grants for inventions per 10,000 citizens, the proportion of technology market turnover, and the proportion of output value of high-tech industries to industrial output value above the designated size.The third dimension includes two measures: high-tech income generation and the total factor productivity growth rate.
The dimensions of coordination support capacity are urban-rural development coordination, industrial structure coordination, and energy coordination.The first dimension includes three measures: the urban-rural per capita income ratio, urban-rural consumption level comparison, and the urban-rural Theil index.The second dimension includes two measures: the advanced industrial structure index per unit and the industrial structure rationalization index.The third dimension includes three measures: energy consumption elasticity coefficient, electricity consumption elasticity coefficient, and energy self-sufficiency.
The dimensions of green support capacity are resource-saving, pollution control, environmental protection, and environmental governance capacity.The first dimension includes two measures: energy consumption per CNY 10,000 of GDP and water consumption per CNY 10,000 of GDP.The second dimension includes three measures: wastewater emissions per unit of GDP, exhaust emissions per unit of GDP, and solid waste emissions per unit of GDP.The third dimension includes four measures: forest coverage, wetland retention rate, coverage of nature reserves, and greening coverage of built-up areas.The fourth dimension includes two measures: the proportion of pollution control investment to GDP and the number of environmental protection persons per 10,000 citizens.
The dimension of opening up support capacity includes the five measures of trade dependence, foreign investment, domestic tourism revenue, international tourism revenue, and domestic trade dependence, which represent the levels of foreign trade openness, foreign investment, tourism openness, and domestic trade dependence.
The dimension of sharing support capacity includes the 14 measures of transportation facilities, communication facilities, environmental protection facilities, water conservancy facilities, energy facilities, education, culture and sports, healthcare, social security, social governance, housing security, Engel coefficient, per capita disposable income, and GI, which represent the levels of facility sharing, resource sharing, security sharing, and welfare sharing.

Study Area
The western region is of great strategic value in China's economic development.The study in this paper is on a total of 11 regions, that is, Chongqing Municipality, Sichuan Province, Guizhou Province, Yunnan Province, Gansu Province, Shaanxi Province, Qinghai Province, Guangxi Zhuang Autonomous Region, Inner Mongolia Autonomous Region, Xinjiang Uygur Autonomous Region, and Ningxia Hui Autonomous Region.

(1) Entropy
The entropy method is one of the objective methods of determining weights, and it is highly respected by the majority of scholars given its simple operation and mature theory.The current entropy method is mainly used for modeling two-dimensional data, and it does not work well for panel data (three-dimensional data).Therefore, we have improved the method so that it can better fit the panel data formats, detailed below: Suppose there are N provinces (N = 1, 2,. .., n), the time is T (T = 1, 2,. .., t), and the indicator is K (K = 1, 2,. .., k).The procedure for the panel format is as follows.
Step 1: Standardize Because there are different dimensions between different variables, and different units will lead to a large difference in absolute values between variables, resulting in a large difference in weighted results, eliminating the impact of dimension is essential.Therefore, it is necessary to standardize the indicators.We introduced the maximin method in this paper.
Standardization of positive indicators: Standardization of negative indicators: where y ij is the j-th indicator of the i-th unit that has been dimensionlessly normalized, and x ij is the original value of the j-th indicator of the i-th unit.In addition, to ensure that all the values make sense in the use of the entropy method later, here, we add 0.001 to the standardized variables.
Since panel data have both object and time properties, the standardization of one alone will inevitably lead to ignoring the other.For this reason, we need to consider the two points when standardizing.We record Z nk as the standard matrix for both province and indicator properties.Z tk as the standard matrix for both time and indicator properties.The standardization is calculated as in the equation above.Thus, the final standardized value is Step 2: Feature weights Step 3: Determine the information entropy value, e, and the information utility value, d, of the indicator.The information entropy value of the j-th indicator is The information utility value is Step 4: Calculate weights For the evaluation indicator weights, a larger value of information utility indicates that the indicator is more important and more significant to the evaluation.Finally, the weight of the j-th indicator is as follows: Step 5: Calculate the combined value of the five sub-dimensions: The final HQED score is based on the five sub-dimension scores with sub-dimension weights.

Dagum GI and Decomposition
This paper analyzes the differences and sources of western HQED based on the GI proposed by Dagum (1997) [43].For research convenience, this paper divides the 11 regions in West China into three groups for analysis based on geographic location and economic status (GDP per capita) as follows: GI includes intra-regional difference, inter-regional difference, and intensity of transvariation.This paper determines their calculations as follows according to the relevant research: where G is the overall GI, G jj is the intra-regional GI, G jh is the inter-regional GI, k is the number of groups, n is the number of all provinces, Y is the average HQED of all regions, n j is the number of provinces in group j, and y ji is the level of HQED of the region i in group j.The ratio of the intra-regional GI to the overall GI is the intra-regional contribution, G w ; the ratio of the inter-regional GI is the inter-regional contribution, G nb ; and the rest is the transvariation intensity contribution, G t , with the three in the relationship of G = G w + G nb + G t .

Kernel Density Estimation
Kernel density estimation is a nonparametric test method used to estimate the unknown density function.In this paper, we introduced kernel density estimation to analyze the distributional dynamics and the evolution of western HQED.Let the probability function of the composite index, X, of the HQED of an urban agglomeration be f (x); its expression is as follows: where N is the number of observations, X i is the independent and identically distributed observation, x denotes the mean of the observations, and h is the bandwidth.The size of the bandwidth determines the accuracy of the kernel function.A smaller value indicates a higher accuracy, and vice versa.

Markov Chain
Traditional Markov chain is a mathematical model to study natural processes proposed by Russian mathematician A.A. Markov in 1906.The model has the advantages of randomness, stability, and no aftereffect, and is used by geographers and economists to describe the evolution process of natural geographical phenomena and the empirical study of the socioeconomic phenomenon of "club convergence".Its mathematical definition is For sequence state . . ., X t−2 , X t−1 , X t , X t+1 . .., if That is, the conditional probability of the state at time X t+1 depends only on state X t at the previous moment; then, this sequence of states is called a Markov chain.In this paper, the economic high-quality development level of each spatial unit from 2000 to 2020 is divided into four grades, high, medium-high, medium-low, and low, and then, a 4 × 4 matrix reflecting the probability of the transfer of the economic high-quality development level from one grade to another is constructed to record the probability distribution so as to describe the whole process of the spatial and temporal transfer of the regional economic development level.Its expression is as follows: where M ij is a 4 × 4 rank transfer probability matrix, and n ij is the sum of the number of all spatial units in which the level of HQED changes from grade i in period t to grade j in period t + 1. n i is the sum of the number of all spatial units with a level i of HQED throughout the study period.

Analysis of the Comprehensive Results for HQED by Region
Figure 2 shows the trend of comprehensive results for western HQED.The results of the measurement allow us to conclude that the regions with the highest levels of HQED were Qinghai from 2000 to 2009 and Chongqing from 2011 to 2020, while the rest of the regions were at a low level in two gradients.Chongqing and Qinghai had annual average scores of 0.101 and 0.100, respectively, and were in the first echelon out of the 11 regions, followed by Shaanxi (0.093), Xinjiang Uygur Autonomous Region (0.091), Sichuan (0.087), Inner Mongolia Autonomous Region (0.087), and Ningxia Hui Autonomous Region (0.080) in the second echelon, with annual average scores in a range of 0.080~0.099;the rest of the regions, that is, Guangxi Zhuang Autonomous Region (0.074), Yunnan (0.069), Gansu (0.068), and Guizhou (0.063), were in the third echelon with annual average scores less than 0.080.
In addition, the HQED of all 11 regions as a whole showed an upward trend over the 21-year period.Sichuan had the largest increase, with its score rising from 0.0295 in 2000 to 0.1441 in 2020, up by 389.23%;Qinghai had the smallest increase with its score rising

Analysis of the Comprehensive Results for HQED by Region
Figure 2 shows the trend of comprehensive results for western HQED.The results of the measurement allow us to conclude that the regions with the highest levels of HQED were Qinghai from 2000 to 2009 and Chongqing from 2011 to 2020, while the rest of the regions were at a low level in two gradients.Chongqing and Qinghai had annual average scores of 0.101 and 0.100, respectively, and were in the first echelon out of the 11 regions, followed by Shaanxi (0.093), Xinjiang Uygur Autonomous Region (0.091), Sichuan (0.087), Inner Mongolia Autonomous Region (0.087), and Ningxia Hui Autonomous Region (0.080) in the second echelon, with annual average scores in a range of 0.080~0.099;the rest of the regions, that is, Guangxi Zhuang Autonomous Region (0.074), Yunnan (0.069), Gansu (0.068), and Guizhou (0.063), were in the third echelon with annual average scores less than 0.080.In addition, the HQED of all 11 regions as a whole showed an upward trend over the 21-year period.Sichuan had the largest increase, with its score rising from 0.0295 in 2000 to 0.1441 in 2020, up by 389.23%;Qinghai had the smallest increase with its score rising from 0.0591 in 2000 to 0.1357 in 2020, up by 129.72%; and the rest of the regions saw varying degrees of increase in their HQED.
Figure 3 shows the rankings of GDP per capita and the HQED index in 2020 divided by region.A comparison of HQED in 2020 shows that Chongqing ranked first in terms of economic strength and comprehensive score, with a high level of economic development.Guizhou, Gansu, Shaanxi, and Xinjiang Uygur Autonomous Region had economic strength consistent with the comprehensive score in ranking, while Sichuan, Yunnan, Guangxi Zhuang Autonomous Region, Inner Mongolia Autonomous Region, and Ningxia Hui Autonomous Region saw some difference between economic strength and comprehensive score rankings, indicating that HQED was in agreement with the economic development in each region.However, there was a difference in four places between Qinghai's economic strength ranking and its comprehensive score ranking, suggesting a possible structural mismatch between the indicators representing the economic development in Qinghai and those used for measuring HQED.

Analysis of the Sub-Dimension Results for HQED by Region
Table 3 shows the annual average sub-dimension index of HQED in 11 regions from 2000 to 2020.The analysis in Table 3 shows that, in the innovation dimension, Chongqing and Shaanxi were ahead of other regions on average, with 0.0966 and 0.0911, respectively, followed by Sichuan with an average of 0.0749, and the rest of the regions had an average of 0.060 or less, suggesting a high correlation between the innovation index and economic strength of a province.The coordinated development index of the 11 regions was relatively balanced, with the highest score in the Inner Mongolia Autonomous Region (0.0595) and the lowest in Gansu (0.0356).The green development index was high on the whole, above 0.06 for all 11 regions, suggesting remarkable achievements made in West China in environmental protection, with the highest score in Chongqing (0.0937) and the lowest in Guizhou (0.0614).Open development scored the lowest among the five dimensions, with the highest score in Chongqing (0.0513) and the lowest in Xinjiang Uygur Autonomous Region at only 0.0184.The shared development index scored the highest among the five dimensions, with the highest in Qinghai at up to 0.1655 and the lowest in Guizhou at 0.0828; 8 of the 11 regions scored above 0.1, indicating that western development has achieved remarkable results and that people's living and sharing levels there have seen improvement.

Analysis of Regional Differences
There are great differences in the HQED between provinces in the western region, and analyzing the main sources of these differences is helpful in solving the problem at the root.Understanding the difference in HQED in the western region can effectively

Analysis of the Sub-Dimension Results for HQED by Region
Table 3 shows the annual average sub-dimension index of HQED in 11 regions from 2000 to 2020.The analysis in Table 3 shows that, in the innovation dimension, Chongqing and Shaanxi were ahead of other regions on average, with 0.0966 and 0.0911, respectively, followed by Sichuan with an average of 0.0749, and the rest of the regions had an average of 0.060 or less, suggesting a high correlation between the innovation index and economic strength of a province.The coordinated development index of the 11 regions was relatively balanced, with the highest score in the Inner Mongolia Autonomous Region (0.0595) and the lowest in Gansu (0.0356).The green development index was high on the whole, above 0.06 for all 11 regions, suggesting remarkable achievements made in West China in environmental protection, with the highest score in Chongqing (0.0937) and the lowest in Guizhou (0.0614).Open development scored the lowest among the five dimensions, with the highest score in Chongqing (0.0513) and the lowest in Xinjiang Uygur Autonomous Region at only 0.0184.The shared development index scored the highest among the five dimensions, with the highest in Qinghai at up to 0.1655 and the lowest in Guizhou at 0.0828; 8 of the 11 regions scored above 0.1, indicating that western development has achieved remarkable results and that people's living and sharing levels there have seen improvement.

Analysis of Regional Differences
There are great differences in the HQED between provinces in the western region, and analyzing the main sources of these differences is helpful in solving the problem at the root.Understanding the difference in HQED in the western region can effectively prevent the phenomenon of regional development polarization, and only in the true sense of HQED.In this paper, provinces in the western region were grouped according to Table 4, the Dagum Gini coefficient decomposition method was used to analyze the main sources of regional differences and provide a reference for the formulation of policies to reduce regional differences.(1) Analysis of overall differences.The results of the measured decomposition of GI for western HQED using the approach described above are shown in Table 5.Table 5 shows that the average of the overall GI in western HQED from 2000 to 2020 was 0.3199, in a trend of first rising and then declining as a whole.The GI fluctuated from 2000 to 2012, rising to 0.4180 and then declining to 0.2050 by 2020, indicating that the western regions initially developed in a way that widened regional disparities, followed by higher regional coordination with the policy regulation in development.(2) Analysis of intra-regional differences.The average intra-regional differences for the three groups investigated from 2000 to 2020 were 0.0574, 0.2582, and 0.2544, all at a low level, because the grouping based on the economic development (as above) reduced the intra-group differences to a certain extent.In addition, intra-group differences were minimized in the first group and close to each other in the second and third groups.
(3) Analysis of inter-regional differences.The average inter-regional differences between Group 1 and Group 2; Group 1 and Group 3; and Group 2 and Group 3 from 2000 to 2020 were 0.4195, 0.4650, and 0.2761, respectively, suggesting that there were large differences in HQED between Groups 1 and 2 and Groups 1 and 3, while the regional differences between Groups 2 and 3 were small, conforming to the objective economic development level of all regions.Moreover, during the study period, the differences in HQED between Groups 1 and 2 and between Groups 1 and 3 showed a tendency to increase and then decrease, except for the inter-regional differences between Groups 2 and 3, which did not change much, suggesting that Groups 2 and 3 took the lead in integrating into the regional development strategy of western development and experienced rapid development and that Group 1 was led to join the regional development strategy later on.
(4) Difference contribution analysis.Table 5 provides the sources of overall differences in western HQED and Figure 4 shows the contribution rate of regional differences in HQED in western China.We found that inter-regional differences contributed the most, with an annual average of 73.82% over the study period, followed by intra-regional differences with 15.77%, while the intensity of transvariation had the smallest contribution at 10.41.It is obvious that most of the differences between different groups came from inter-regional differences.Therefore, to reduce inter-regional differences and promote high-quality and balanced economic development, addressing inter-regional differences should be the focus.
(3) Analysis of inter-regional differences.The average inter-regional differences between Group 1 and Group 2; Group 1 and Group 3; and Group 2 and Group 3 from 2000 to 2020 were 0.4195, 0.4650, and 0.2761, respectively, suggesting that there were large differences in HQED between Groups 1 and 2 and Groups 1 and 3, while the regional differences between Groups 2 and 3 were small, conforming to the objective economic development level of all regions.Moreover, during the study period, the differences in HQED between Groups 1 and 2 and between Groups 1 and 3 showed a tendency to increase and then decrease, except for the inter-regional differences between Groups 2 and 3, which did not change much, suggesting that Groups 2 and 3 took the lead in integrating into the regional development strategy of western development and experienced rapid development and that Group 1 was led to join the regional development strategy later on.
(4) Difference contribution analysis.Table 5 provides the sources of overall differences in western HQED and Figure 4 shows the contribution rate of regional differences in HQED in western China.We found that inter-regional differences contributed the most, with an annual average of 73.82% over the study period, followed by intra-regional differences with 15.77%, while the intensity of transvariation had the smallest contribution at 10.41.It is obvious that most of the differences between different groups came from inter-regional differences.Therefore, to reduce inter-regional differences and promote high-quality and balanced economic development, addressing inter-regional differences should be the focus.

Analysis of the Dynamics and Evolution of the Spatial Distribution of Western HQED
Figure 5 shows the dynamic evolution of the composite index of western HQED from 2000 to 2020.The distribution of the 11 western regions showed a rightward move during the study period.The height of the main peak of the distribution curve first rose sharply and then fell sharply and went up later with slow fluctuations, with the peak in the vicinity of the interval (0.05, 0.1), indicating that the 11 regions enjoyed steady growth in HQED during the 21-year period, and the distribution of their HQED composite indexes experienced a process of centralization-dispersion-centralization.There are almost no side peaks in the graph except for one main peak, suggesting that the western region had balanced HQED with no polarization.Short and wide tails on both sides indicate that the HQED of urban agglomerations had no or few extreme values and tended to converge at an interval.To sum up, western HQED has improved significantly, and its spatial distribution has gradually been equalized.

Analysis of the Dynamics and Evolution of the Spatial Distribution of Western HQED
Figure 5 shows the dynamic evolution of the composite index of western HQED from 2000 to 2020.The distribution of the 11 western regions showed a rightward move during the study period.The height of the main peak of the distribution curve first rose sharply and then fell sharply and went up later with slow fluctuations, with the peak in the vicinity of the interval (0.05, 0.1), indicating that the 11 regions enjoyed steady growth in HQED during the 21-year period, and the distribution of their HQED composite indexes experienced a process of centralization-dispersion-centralization.There are almost no side peaks in the graph except for one main peak, suggesting that the western region had balanced HQED with no polarization.Short and wide tails on both sides indicate that the HQED of urban agglomerations had no or few extreme values and tended to converge at an interval.To sum up, western HQED has improved significantly, and its spatial distribution has gradually been equalized.

Markov Chain
The traditional Markov chain, proposed by A.A. Markov in 1906, is a mathematical model used to study natural processes.Since the model has the advantages of randomness, stability, and no aftereffect, it has been used by geographers and economists in empirical studies describing the evolutionary process of natural geographic phenomena and the socioeconomic phenomenon of "club convergence".According to the viewpoint of spatial economics, geographic and economic phenomena in a region in a period of time have no aftereffect property, so a Markov chain works wonders for studying the pattern of change in regional economic differences and exploring the path of spatial and temporal shifts in regional economic development and their probability of shifts [17].Therefore, we introduced the traditional Markov chain in this paper to analyze the internal trend characteristics of western HQED [7,16,18,19]; employed the quartile method to classify the index of the HQED of 11 regions into low, medium-low, medium-high, and high levels in the study period; and calculated the probability transfer matrix, as shown in Table 6.The results in Table 6 show that the probability of the transfer matrix on the diagonal is greater than the non-diagonal probability, meaning that the regions at the low level, medium-low level, medium-high level, and high level have a tendency to maintain their own development.It is obvious that western HQED remained steady and showed "club convergence".In addition, the probability of convergence between the low and high levels was significantly higher than between the medium-low and medium-high levels, suggesting that there was a certain degree of "Matthew Effect" in the HQED of West China.Furthermore, there was a probability of migration from the medium-low level and the medium-high level to a higher or lower level in West China, but more likely to a higher level, indicating an upward trend in HQED in the western regions and a sound development condition known as the "backbone force".No probability of "leapfrogging" migration at any level indicates a steady rate of western HQED.

Markov Chain
The traditional Markov chain, proposed by A.A. Markov in 1906, is a mathematical model used to study natural processes.Since the model has the advantages of randomness, stability, and no aftereffect, it has been used by geographers and economists in empirical studies describing the evolutionary process of natural geographic phenomena and the socioeconomic phenomenon of "club convergence".According to the viewpoint of spatial economics, geographic and economic phenomena in a region in a period of time have no aftereffect property, so a Markov chain works wonders for studying the pattern of change in regional economic differences and exploring the path of spatial and temporal shifts in regional economic development and their probability of shifts [17].Therefore, we introduced the traditional Markov chain in this paper to analyze the internal trend characteristics of western HQED [7,16,18,19]; employed the quartile method to classify the index of the HQED of 11 regions into low, medium-low, medium-high, and high levels in the study period; and calculated the probability transfer matrix, as shown in Table 6.The results in Table 6 show that the probability of the transfer matrix on the diagonal is greater than the non-diagonal probability, meaning that the regions at the low level, medium-low level, medium-high level, and high level have a tendency to maintain their own development.It is obvious that western HQED remained steady and showed "club convergence".In addition, the probability of convergence between the low and high levels was significantly higher than between the medium-low and medium-high levels, suggesting that there was a certain degree of "Matthew Effect" in the HQED of West China.Furthermore, there was a probability of migration from the medium-low level and the medium-high level to a higher or lower level in West China, but more likely to a higher level, indicating an upward trend in HQED in the western regions and a sound development condition known as the "backbone force".No probability of "leapfrogging" migration at any level indicates a steady rate of western HQED.

Exploration of the Path of Sustained Western HQED
The research of this paper finds that the level of HQED in the western region is increasing year by year, but there are large differences between regions, there is an obvious "club convergence" phenomenon, and the dynamic evolution of spatial distribution tends to be stable, which means that the pattern of HQED in the western region under the influence of the market has basically formed, and the existing development problems need more precise policy guidance.Moreover, Long Ying and Wang Fei, 2023, also pointed out that the HQED in the western region has some problems: "the overall level is lower than that in the eastern region [44], the differences among sub-dimensions are large, and the levels of various regions are uneven".Therefore, based on the results of this study, this paper discusses the problems and feasible paths for the sustainable promotion of western HQED according to its actual development conditions.
Green development is a necessary condition, an important symbol for achieving HQED, and a distinctive base of HQED, so it is indispensable in promoting green development in West China.The green development of West China grew fast during the study period, but it was lower than the comprehensive level for most of the time, indicating that green development has not fully played its role as a "base".That is to say, the develop-thewest strategy has effectively bridged the gap in the amount of economic growth between regions and promoted an increase in the value-added of the enterprises in West China, but it has also led to an increase in environmental pollution (Ma Qianqian, Chen Shiyi 2023) [45].Therefore, to promote green development in West China, firstly, it should be made clear that an economic growth model that depletes the quality of the environment is not an option, and secondly, policy tools are essential for formulating appropriate development plans for the western regions in accordance with the local conditions in order to reduce the pollution caused by industry by strengthening environmental regulations, improving the level of urbanization, and promoting the upgrading of the industrial structure.
The development of the innovation dimension is in the middle of the five dimensions, and innovative development requires the support of a large amount of capital and advanced technology.Chi Shuxian and Zhou Xiaochang (2023) [46] argued that western development will effectively bring down the tax rate in West China, thus attracting enterprises and capital.Therefore, encouraging the settlement of advanced enterprises in the west is crucial for its innovative development.
The coordinated development of West China was at a low level during the study period, and there was a large gap in economic development across different regions.Large differences in economic strength, resource endowment, demographic conditions, human customs, and high transportation costs increased inter-regional barriers and impeded the process of coordinated regional development.
West China is landlocked and lacks opportunities for foreign trade compared with the eastern coastal areas, and there is an obvious gap between Northwest and Southwest China, with the northwest lagging behind significantly (Fang Xingming et al., 2023) [47].Promoting the open development of the western region requires, based on the location conditions, giving full play to the role of the "Belt and Road" policy in order to actively explore the international market along the border.
Shared development in West China is at a high level, but in the new pattern of western development, it has the new mission of promoting common prosperity.Therefore, shared development should not only include the connotations and characteristics of sharing and the joint construction and common prosperity of the western development results but also involve the implementation of the government's rural revitalization strategy and the construction of the "Belt and Road".

Recommendations for Promoting Western HQED
This paper puts forward the following recommendations based on the above discussion of high-quality economic development in West China: First, the government should make full use of policy tools to formulate appropriate development plans for all regions to gradually reduce industry in the Qilian Mountains, the Yellow River, the Yangtze River origin, the Liupan Mountain ecological zone, and other key ecological reserves, as well as other areas with weak environmental carrying capacity, supplemented by the development of the service industry and tourism; pool industries in Chengdu, Xi'an, Chongqing, and other densely populated provinces and municipalities with a better industrial base; promote technological progress and reforms relying on the industrial cluster effect and a higher intensity of environmental regulations; and guide the upgrading of the industrial structure with technological advances to reduce the emission of pollutants and sustainably promote the green development of the economy in West China.
Second, the government should take the lead in creating a favorable external environment for enterprises and attract enterprises in the eastern region with the cost advantages of production factors in West China so that enterprises drive the transfer of capital and technology and promote innovative development.
Third, the government should accelerate the synergistic development of the western regions.Given the low level of the coordination dimension of HQED and the large interregional differences, the western regions should establish more convenient communication bridges, continuously reduce market barriers, and engage in closer political and economic dialogs; they should give full play to the driving role of the cities of Chongqing, Xi'an, and Chengdu, and actively establish a development network to promote synergistic development and raise the synergy index of HQED.
Fourth, the government should support Xinjiang to be the "fifth growth pole" of economic development in West China (Fang Xingming et al., 2023) [47]; help it explore the international market; deepen economic exchanges with neighboring countries; and become involved in the national "Belt and Road" policy to drive the opening up of the rest of the regions through the nationalization of Xinjiang, thus providing an opportunity to open up their HQED and contribute western strength to the domestic and international double cycle in order to increase the open development in the west.
Fifth, the government should strengthen the construction and maintenance of infrastructure for the sharing economy; implement and promote the strategy of rural revitalization, address employment and living problems in rural areas; raise the income of residents; and improve the level of economic sharing in West China with the goal of common prosperity.

Limitations of the Method and Research Prospects
This paper establishes a large index system to measure the level of HQED in the western region.Although the entropy weight method can provide an objective result, it still has limitations.For example, the entropy weight method cannot consider the correlation between indicators; it assumes that indicators are independent of each other.Secondly, the entropy weight method is a method with a strong dependence on data samples, and the changes in indicators and data may have a great impact on the results, so it needs high data integrity.
The research of this paper found that the level of HQED in the western region is increasing year by year, but there is a "club convergence" phenomenon, and inter-regional differences are the main source of development differences.Therefore, future research needs to pay more attention to the theme of "how to narrow the inter-regional differences in the western region".At the same time, the HQED of the eastern, central, and western regions has been revealed.By comparing the development of the three major sectors, studying how to connect the western region with the eastern and central regions may become the main direction of future research.

Conclusions
Based on the "new visions for development", the Guiding Opinions of the CPC Central Committee, and the State Council on Promoting the Formation of a New Pattern in the Large-Scale Development of China's Western Regions, this paper constructed an index system for evaluating western HQED consisting of 49 indexes and introduced the entropy weight method to measure the composite index of HQED in 11 regions in the west (except for Tibet) in the period of 2000-2020, as well as the indexes of sub-dimensions.It then analyzed the sources of differences in HQED between the regions in the west using the Dagum GI decomposition method, and finally, it studied the spatial distribution and dynamic evolution of western HQED using the kernel density estimation method and deduced the trend of HQED using a Markov chain.The results are set out below: First, the western region saw an increase in HQED every year from 2000 to 2020, indicating its economic development was in good condition.However, there was a large gap between the 11 regions, which can be divided into three echelons, with Chongqing and Qinghai in the first echelon; Shaanxi, Xinjiang Uygur Autonomous Region, Sichuan, Inner Mongolia Autonomous Region, and Ningxia Hui Autonomous Region in the second echelon; and Guangxi Zhuang Autonomous Region, Yunnan, Gansu, and Guizhou in the third echelon.The composite index of HQED across the regions showed an overall increasing trend during the 21-year period.By dimension, the green and sharing dimensions in West China developed faster, and there was obvious polarization in recent years; the scores of the innovation and coordination dimensions showed a fluctuating rise, while the opening-up dimension scored the lowest and showed a declining trend overall due to the effect of its geographic location.
Second, the overall GI in West China increased first and then fluctuated downward, indicating that the western regions began to take into account inter-regional harmonization while developing their economies.In terms of intra-regional differences, the three groups had small values, with the intra-group differences in the first group significantly smaller than those in the second and third groups; in terms of inter-regional differences, the differences between the first group and the other two groups were large and showed a tendency to increase and then decrease, while the differences between the second and third groups were small and showed no significant change in the study period, indicating more similar economic characteristics between the latter two groups.In terms of difference contribution, inter-regional differences were the main source, accounting for more than 70%.
Third, according to the dynamic distribution of kernel density estimation, the 11 regions in West China showed a rightward move during the study period, with the height of the main peak going down first and then up, suggesting that the HQED of the 11 regions grew steadily during the 21-year period and that they went through a process of centralizationdispersion-centralization in distribution.There were no side peaks in the distribution graph, with very few extreme values at both ends and overall convergence at an interval, and the spatial distribution of western HQED was gradually equalized.
Fourth, western HQED showed "club convergence" and the "Matthew Effect" in a steady state, and it was more likely to shift upward than downward, indicating that western HQED was still on the fast track.
Based on the conclusions and discussions in this paper, we put forward the following suggestions for western HQED: It is imperative to first determine the importance of green development in western HQED and to tailor the development of industry to local conditions under environmental regulatory policies; second, we should attract enterprises from the eastern areas with the factor cost advantages; third, we should remove the barriers between different regions and build a western development network; fourth, we should help Xinjiang to open up international markets; fifth, we should develop the sharing economy with a view to achieving common prosperity.

Results for Western HQED 4 . 1 .Figure 1 23 Figure 1 .
Figure 1 demonstrates a chart showing the evolution of the time trend of the composite dimension and sub-dimension of the index of western HQED from 2000 to 2020.The data in Table 2 reveal that the index of western HQED went up in the past 21 years, indicating the remarkable implementation results of the develop-the-west strategy with some achievements made in economic construction.Out of the five sub-dimensions, both the green and sharing indexes experienced the largest growth, up by 451.08% and 281.81%, respectively, suggesting that the develop-the-west strategy has largely enhanced the level of living and sharing of residents in West China, while also making significant contributions to its environmental protection.The five sub-dimensions are shared, green, innovative, coordinated, and open development in descending order according to the development results.Shared development and green development are in the first echelon, with averages of 1.2956 and 0.8923, respectively, over the 20-year period, indicating that the western region did not pursue economic development at the cost of destroying the environment but instead took a resource-sharing and environmentally friendly path of economic development.Limited by technology, talents, and other factors, innovative development and coordinated development made only slow progress, ranking in the second echelon with averages of 0.6579 and 0.5488, respectively.The level of open development is the lowest among the five dimensions of western HQED, which is closely related to the geographic location of the western region.Open development was at the lowest level among the five dimensions of western HQED, closely related to its geographic location.Land 2023, 12, x FOR PEER REVIEW 12 of 23

Figure 1 .
Figure 1.Trend of comprehensive and sub-dimension results for western HQED from 2000 to 2020.

Figure 2 .Figure 2 .
Figure 2. Trend of comprehensive results for HQED by region from 2000 to 2020.

Figure 2 .Figure 3 .
Figure 2. Trend of comprehensive results for HQED by region from 2000 to 2020.

Figure 3 .
Figure 3. Comprehensive results and ranking of HQED by region in selected years.

Figure 3 .
Figure 3. Comprehensive results and ranking of HQED by region in selected years.

Figure 4 .
Figure 4. Regional difference contribution rate of HQED in West China from 2000 to 2020.

Figure 4 .
Figure 4. Regional difference contribution rate of HQED in West China from 2000 to 2020.

Figure 5 .
Figure 5. Dynamics of the distribution of the composite index of western HQED.

Figure 5 .
Figure 5. Dynamics of the distribution of the composite index of western HQED.

Table 1 .
Measurement indicator system for western HQED.

Table 2 .
Comprehensive and sub-dimension results for western HQED from 2000 to 2020.

Table 3 .
Average sub-dimension index of western HQED from 2000 to 2020.

Table 3 .
Average sub-dimension index of western HQED from 2000 to 2020.

Table 4 .
Grouping of regions in West China.

Table 5 .
Regional differences and contribution to western HQED.