Research on the coordination characteristics and interaction between the innovation-driven development and green development of the Yangtze River Economic Belt in China

Both innovation-driven development and green development are important ways to achieve regional sustainable development. This study considers the innovation-driven development and green development evaluation systems of 130 cities in the Yangtze River Economic Belt. The entropy TOPSIS method is used to measure the innovation-driven development index and the green development index of 130 cities in the Yangtze River Economic Belt. Then, a coupling coordination evaluation model and a spatiotemporal heterogeneity analysis model are constructed to discuss the coupling coordination index of regional innovation-driven development and green development in the Yangtze River Economic Belt and to determine its temporal and spatial distribution characteristics. Finally, we choose a spatial panel regression model to explore the relationship between the innovation-driven development index and the green development index of the Yangtze River Economic Belt. The research results show that there is a significant difference between the innovation-driven development index and the green development index of the 130 cities in the Yangtze River Economic Belt in terms of the temporal and spatial distribution. The level of innovation-driven development lags behind the level of green development on the whole, and the two fail to form a good spatial matching degree. The coordination index of the two has an imbalanced distribution feature, and there is a significant direct or indirect relationship between the two structural indicators in a mathematical sense. This study improves the academic community’s understanding of the interaction between innovation-driven development and green development, provides scientifically based support for green development, and offers guidance for the implementation of innovation capabilities.


Introduction
Innovation-driven development is an important development method for the global economy in the twenty-first century. It promotes the transformation and development of the economy from a focus on resource agglomeration and environmental pollution to a focus on resource-saving and environmentally friendly production (Yang and Huang 2019). Innovation-driven development leads to the transformation from the traditional economy, which relies on resource input to promote economic growth, to an economy that relies on scientific and technological changes, and labour productivity increases to promote the two-way improvement of the economy in terms of quantity and quality. Most innovationdriven studies focus on innovation-driven economic development methods, paths, and effects (Alheet and Hamdan 2020;Chen et al. 2016a;De Marchi 2012;Li et al. 2020;Mensah et al. 2018;Ranta et al. 2020;Redding 2002;Rogerson 2018), and it helps us to have a deep understanding of the formation mechanism and action mode of innovation drive, but they rarely consider innovation-driven impact factors. The analysis of the relationship among the impact factors on innovation is conducive to further improving the regional innovation level and optimizing innovation-driven performance (Yang and Yan 2019).
Green development is an important approach to regional sustainable development and the main means to solve problems linked to economic development, resources, and the environment in the twenty-first century (Zhao et al. 2010). While promoting the further improvement of the regional economy, green development needs to consider the sustainable use of resources and the improvement of the environmental protection quality. The current academic research on green development mainly focuses on the evaluation of the level of green development, the action mechanism, and implementation approaches to environmental factors (Chen et al. 2016aHe et al. 2019;Li and Wu 2017;Ma et al. 2019;Wang et al. 2018Wang et al. , 2019bYang and Huang 2019;Yuan et al. 2020), and it helps us to understand the economic form of green development and the influence mode of ecological environment, while the research on the relationship between green development and the driving factors of green development is relatively insufficient. This paper studies the interaction between green development and innovation from the perspective of innovation-driven development and aims to promote a virtuous cycle of innovation-driven and green economic development to provide a new impetus for regional green development.
Innovation-driven development is one of the important driving forces of regional green economic development. The improvement in the green development level feeds back to the supply of innovation-driven factors, and there is an interactive relationship between the two factors under spatiotemporal constraints (Feng and Chen 2018). Both innovationdriven development and green development are composed of complex elements, and the synergistic mechanism between them is reflected in the interaction between elements and in the interaction between elements and the whole system. However, the existing literature studies on innovation-driven development and green development are limited to the general relationship between innovation-driven development and green development (Chen et al. 2016b), and it lacks a local understanding. Only by deeply analysing the local and overall relationship between innovation-driven indicators and the green development index can we implement a specific path that supports the synergetic relationship between innovation-driven development and green development.
Green development and innovation-driven development are both important ways to achieve sustainable economic development. Through a literature review, we found that previous literature did not study the interaction between green development and innovation-driven development, and this paper will supplement this gap. By comprehensively measuring the innovation-driven development index and green development index in the case of the Yangtze River Economic Belt, this article uses a coupling coordination model to explore the coordinated development of the two spatiotemporal patterns and finally analyses the spatial mechanism of the innovation-driven development index and the green development index through a spatial panel model. This effort provides a basic reference for the innovation-driven model and the green development model of regional sustainable development and promotes the further expansion of the research paradigm of regional sustainable development.

Innovation-driven development
Innovation-driven development relies on the social and economic benefits brought by scientific and technological innovation to realize an intensive growth mode, and the core aim is to improve the productivity of production factors by using technological change (Alheet and Hamdan 2020;Laužikas and Dailydaitė 2014). In the twenty-first century, innovation is the primary driving force for world economic development, the strategic support for building a modern economic system, and the only way to achieve high-quality development (Cao et al. 2019). The academic research on innovation-driven development has a long history. The research focus has been extended from the initial productivity improvement that drives economic development to recent changes in production methods and production technologies that have brought economic growth, resource conservation, environmental protection, and other multidimensional benefits, and the connotations of innovation-driven development have been constantly enriched (De Marchi 2012;Mensah et al. 2018). Second, in terms of evaluating the innovationdriven index, the education level or productivity level has been taken as the core index of the innovation-driven index in the last century. Recently, outcome assessment indicators, such as innovation performance, have been added, and the evaluation system has gradually tended to focus on comprehensiveness, integrity, and fairness (Fei et al. 2020;Zhang and Li 2020).

Green development
Green development is currently the best form of social and economic development, and it reflects the harmonious symbiosis between human society and the natural environment . From ancient times to the present, the survival and development of human beings have been closely related to the natural environment, and human production and lifestyles have led to profound changes in the natural environment. The focus on green development in academic studies started with the industrial revolution. With the rapid development of industry, the Earth's environment has been constantly deteriorating, and the living space of human beings is threatened. Therefore, the concept of green development has attracted the attention of all humankind (Song et al. 2016). Green development is a harmonious mode of development between humans and the land. Its core significance is to realize the unity between human social development and environmental protection. Scholars have studied the course of green development from the reduction of the discharge of industrial wastewater, waste gas, and waste residue to the transformation of production methods (Burnett et al. 2013), and studies of the connotation and extension of green development are gradually expanding from the main focus on industrial production to the integrated development of production, life, and ecology (Craig 2020;He et al. 2019;Yuan et al. 2020). Currently, scholars consider how to achieve a high-quality green development mode and what social, economic, and ecological benefits are generated by green development (Li and Wu 2017;Wang and Shao 2019).

Relationship between innovation-driven development and green development
In addition to facing the shortcomings of traditional development, green development requires innovative development methods to achieve the integration and unity between socioeconomic development and ecological environmental protection (Meirun et al. 2021). Innovation-driven development is a technological means to realize the transformation of the development mode. Scholars have studied the relationship between innovation and green development from the perspective of diversified innovations. At the beginning, productivity can be improved to reduce the emission of environmental pollutants, and in this period, the relationship between industrial production and environmental pollution is the main focus of attention ). In the middle stage of industrialization, the level of productivity is greatly improved, and the research on innovation-driven development and green development focuses on the role of the improvement in science and technology and the treatment rate of environmental pollution (Shao et al. 2016;Yuan and Xiang 2018;Zhang et al. 2018). In the later stages of industrialization, human material levels are mainly satisfied. The restoration of the ecological environment has become a new pursuit for humans' quality of life, and innovation is mainly applied in the field of ecological environment restoration (Chen et al. 2016c;Li et al. 2019;Sotarauta and Suvinen 2019) and environmental economic creation (del Rio Gonzalez 2004). The environmental economy is generated by innovative technologies and is an economic growth with environmental friendliness.

Current deficiencies and improvements
Innovation-driven development, green development, and their interaction have not received sufficient attention in the following aspects. (1) Studies on innovation-driven development have focused too much on the analysis of the drivers of results, such as which innovation-driven measures are adopted and which development achievements are obtained, and have placed little emphasis on the influence of various factors on innovation and the interaction between innovation and achievements. This paper intends to elaborate on the relationship between innovation drive and innovation achievement from the three aspects of green life, green ecology, and green production. (2) Although they focus on the social, economic, and ecological benefits of green development, previous studies have neglected the dynamic mechanism of maintaining green development. The sustainable and stable driving force of green development is the power source for realizing the sustainable development of humankind. This paper aims to explore the relationship between green development and the driving forces from three aspects, namely innovation input, innovation performance, and innovation potential.
(3) Academic studies on the relationship between innovation-driven development and green development have devoted more attention to the overall connection than to the mechanism of action between the two structures. However, the composition structure is the basis for analysing the mechanism of action between innovation-driven development and green development, and it is the focal point for implementing the optimization path. Therefore, this paper explores the contribution of details to overall progress by analysing the components of innovation-driven development and green development.

Analytical framework
The above literature review shows that there is a significant direct or indirect relationship between innovation-driven development and green development at different stages of economic development, but this mechanism has not been addressed in previous studies. We established a complete set of evaluation processes, as shown in Fig. 1. The evaluation is divided into three parts. The first part is the comprehensive evaluation (blue arrow). Through the construction of an evaluation index system, the innovation-driven development index and green development index are comprehensively evaluated at the functional and structural levels. The second part is the coordination evaluation (red arrow). The coupling coordination model is used to explore the coordination relationship between innovation-driven development and coordinated development, and the spatial agglomeration and anomalous distribution characteristics of the coupling coordination index are analysed based on a spatial-temporal heterogeneity model. The third part is impact assessment (yellow arrow). In this part, the dimension of the interaction between innovation-driven and green development is reduced to the level of specific indicators, and the positive and negative properties and the strength of the impact factors of innovation-driven development and green development are explored. Finally, on the basis of the above three research conclusions, the paper proposes policy suggestions to promote regional innovation-driven development and green development.

Study area and dataset
Located in southern China, the Yangtze River Economic Belt covers 11 provinces and cities (Shanghai, Jiangsu, Zhejiang, Anhui, Jiangxi, Hubei, Hunan, Chongqing, Sichuan, Yunnan, and Guizhou) from east to west (Fig. 2a). The 11 provinces and cities include 130 cities, such as Shanghai, Nanjing, Wuhan, and Chongqing ( Fig. 2b), which cover an area of approximately 2.05 million km 2 and represent more than 40% of China's population and GDP. The Yangtze River Economic Belt is a giant river basin economic belt with the largest population, the largest industrial scale, and the most complete urban system in the world.
The statistical data used in this analysis come from the 2004, 2011, and 2018 China City Statistical Yearbooks (http:// www. stats. gov. cn/ tjsj/), the National Economic and Social Development Statistical Bulletin, and the Statistical Yearbook of the 11 provinces and cities along the Yangtze River Economic Belt; the administrative division map of the Yangtze River Economic Belt was downloaded and drawn from the standard map service system website of the Ministry of Natural Resources of China (http:// bzdt. ch. mnr. gov. cn/) for a spatial analysis.

Evaluation index system
Following the principles of representativeness, comparability, hierarchy, and operability and referring not only to the relevant literature (Chan and Lee 2019a;Latif et al. 2017aLatif et al. , 2018Latif et al. , 2017bLatif et al. , 2017cLiu et al. 2020;Sun et al. 2018;Wang et al. 2018Wang et al. , 2019b but also to the overall consideration of common international indicators and China's actual situation (see Table 1 for the specific sources), combined with expert opinions, an innovation-driven development and green development evaluation system for the Yangtze River Economic Belt was established. The green development index provides a comprehensive evaluation at the three levels of green production, green life, and green ecology. Production, life, and ecology include all the behavioural characteristics relevant to regional socioeconomic development and the natural environment. The green behaviour reflected by these three factors can essentially represent the level of regional green development. Innovation-driven development refers to the innovation input, innovation performance, and potential of the three dimensions, represents the characteristics of innovation activity based on inputs, and emphasizes innovation as the driving force of the social and economic development of the whole process.

Comprehensive index evaluation
We consider the difference in the weights between the innovation-driven development and green development evaluation indexes and the comparative advantage of the model (Latif et al. 2017a(Latif et al. , 2018(Latif et al. , 2017b(Latif et al. , 2017c. Delphi, AHP, and TOPSIS are usually used as comprehensive evaluation methods. The Delphi method overemphasizes the subjective opinions of experts, and it is difficult to determine the differences between the evaluation indicators (Chan and Lee 2019b;Perveen et al. 2017). The AHP method is used to calculate the weight, but the construction of a judgement matrix of evaluation indicators is not easy (Latif et al. 2017a(Latif et al. , 2018(Latif et al. , 2017b(Latif et al. , 2017cYang and Huang 2019;Freeman et al 2015;Wang et al 2018;Kim et al. 2021;Maceika et al. 2021). The TOP-SIS method effectively solves these two problems. Therefore, TOPSIS is used as the analysis method of this paper. This method uses the technique of approaching the ideal solution to determine the order of the evaluation objects (Koulinas et al. 2021;Sultana et al. 2015). The calculation steps are as follows: 1) Assume that there are m evaluation objects and each object has n evaluation indexes. Based on this, the judgement matrix is constructed as Eq. (1): 2) Standardize the judgement matrix: The positive index and negative index are shown as follows: 4) Determine the weight of index j:

5) Calculate the weighted matrix:
(5)  (Dutta et al. 2014) 6) Determine the optimal solution S + j and worst solution S − j : 7) Calculate the Euclidean distance between the optimal solution and the worst solution of each scheme: 8) Calculate the comprehensive evaluation index: In the formula, when the value of C i is larger, the evaluation object is better.

Coordinated development evaluation
The coupling coordination model in physics is used for reference (Wang et al. 2019a) to establish the coupling coordination evaluation model of innovation-driven development and green development in the Yangtze River Economic Belt, and the calculation formula is as follows: where OU is the coupling degree between innovation-driven development and green development, which is between [0 − 1] , IDA is the innovation-driven composite index, and GDL is the green development composite index. When the value of OU is greater, the interaction between innovationdriven development and green development is stronger; otherwise, the interaction is weaker.
The coupling degree indicates the degree of correlation between the systems but cannot represent the ranking relationship. The coordination degree model (Wang et al. 2019a) is adopted to evaluate the level of coordination between innovation-driven development and green development. The calculation formula is as follows: In the formula, XE is the degree of system coordination and OU is the degree of system coupling. The value of XE ranges from [0-1], and ZHZ is the weighted average of the innovation-driven index and the green development index. When the value of XE is larger, the degree of coordination between innovation-driven development and green development is higher, and vice versa.

Analysis of the influencing factors
The traditional panel econometric model ignores the effect of spatial parameters on the regression results. This article combines the spatial panel regression model  and provides regression results that are more consistent with reality by including the relationship between the spatial units of the Yangtze River Economic Belt in the econometric model. The spatial lag model, spatial error model, and spatial Durbin model are adopted to reflect the spatial interaction relationship between the impact factors on the innovation-driven capacity and the green development level of the Yangtze River Economic Belt. The model can be set as where GGAQ it is the innovation-driven index or green development index, i and j represent different regions of the Yangtze River Economic Belt, W ij is the spatial matrix of N × N , X it is the dependent variable, is the spatial error regression coefficient, is the spatial regression coefficient of the dependent variable, is the regression coefficient vector of the explanatory variable, is the spatial regression coefficient of the independent variable, and i is the random error term. When ≠ 0 and = 0 , Eq. (12) is transformed into a spatial lag model: When ≠ 0 and = 0 , Eq. 2.13 is transformed into a spatial error model: When = 0 , ≠ 0 , and ≠ 0 , Eq. 2.13 is transformed into a spatial Durbin model: The three models are suitable for analysis of the influencing factors of different mathematical fractals, and the most suitable influencing factor regression model for this study can be determined only after a correlation coefficient test is performed.

Empirical findings
Provincial change characteristics Figure 3 shows the distribution of the green production index, green life index, green ecological index, innovation input index, innovation performance index, and innovation potential index, which are components of the green development index and innovation-driven development index, in the 11 provinces and cities along the Yangtze River Economic Belt in 2003, 2010, and 2017. The green production index, green living index, and innovation performance index show a trend of balanced development, and the gap between the 11 provinces and cities gradually narrows over time. The green ecological index, innovation input index, and innovation potential index exhibited little change, and the spatial distribution characteristics presented a stable and unbalanced distribution. Figure 4 shows that the 11 provinces and cities in the Yangtze River Economic Belt have great differences in their innovation-driven indexes, and the spatial pattern is relatively stable over time. The differences between the green development index and comprehensive development index in the provinces and cities gradually narrow over time and present a more balanced distribution trend.
The coupling relationship and coordination relationship between the innovation-driven index and green development index in the 11 provinces and cities along the Yangtze River Economic Belt have a high matching degree (Fig. 5); they are all at a high level, and the differences between these indexes in the provinces and cities are small.

Urban change characteristics
Cities with a high index value tend to form high-value planar areas, while cities with a low index tend to form lowvalue agglomeration areas. As shown in Fig. 6, the spatial distribution of the innovation-driven index of 130 cities in the Yangtze River Economic Belt in 2003, 2010, and 2017 shows significant differences. The high-value areas of the innovation-driven index are distributed in a point-like form, and the low-value area gradually expands.
Compared with the innovation-driven index, the green development index in the Yangtze River Economic Belt has a strong high-value agglomeration feature in terms of the temporal and spatial distribution. As shown in Fig. 7, the high-value area of the green development index gradually expands from east to west, while the low-value area gradually shrinks. Figure 8 shows the spatial distribution characteristics of the coordination index of innovation-driven development and green development. The high values of the coordination index are distributed in central cities, such as provincial capitals, while the low-value areas show an overall expanding trend.

Spatial heterogeneity analysis
To solve the problem of regional integration development and balanced distribution, it is important to use spatial heterogeneity analysis as a tool to determine the abnormal value of a spatial distribution. As shown in Table 2, the global autocorrelation indexes of the innovation-driven development index, green development index, and coordinated development index of the Yangtze River Economic Belt in 2003, 2010, and 2017 are all positive, which indicates that these indexes have positive clustering characteristics in terms of their spatial distribution and they all pass the significance test at the 5% level, which suggests that the results of the spatial heterogeneity analysis are credible.
As shown in Fig. 9, the clusters with a high innovationdriven development index are distributed in the eastern cities. The low-high cluster city is Chuzhou compared with nearby Nanjing. The high-low clusters include Wuhan, the capital city of Hubei Province, and Chengdu, the capital city of Sichuan Province. The surrounding areas of the lowlow clusters are all nonsignificant areas, which are evenly distributed in the central and western regions of the Yangtze River Economic Belt.
The spatial heterogeneity distribution of the green development index is similar to the innovation-driven development index. As shown in Fig. 10, many high-high clusters are distributed around Shanghai. Only Chengdu, Sichuan Province, remains in the high-low cluster. The low-low clusters are still distributed in the middle and western regions of the Yangtze River Economic Belt.  The spatial distribution characteristics of the coordinated development index are significantly different from those of the green development index and innovationdriven development index, and the outliers are mostly distributed in a point-shaped form (Fig. 11). The high-high cluster is still dominated by Shanghai and its surrounding areas. The high-low clusters are the provincial capitals of the central and western provinces of the Yangtze River Economic Belt, and the low-low clusters are distributed around them. The low-high clusters are distributed around the high-high clusters.

Influencing mechanism analysis
The above analysis shows that the coupling index and the coordination index of innovation-driven development and green development of the Yangtze River Economic Belt have the characteristics of spatial heterogeneity, which indicates that different characteristic variables have different influences on the two types of development and their influence presents spatial variation. Therefore, a spatial panel regression model is used to discuss the interaction between the structures of innovation-driven development and green development in the Yangtze River Economic Belt. To control the interaction and random disturbance in the multivariable regression process, variable constraint processing is carried out; that is, the interference variables are locked in the regression process to prevent the result deviation. Tables 3  and 4 show that the SDM has a higher R 2 than the SLM and SEM and that the SDM passes the Hausman test at the 1% confidence level and rejects the random effect. Therefore, we focus only on the regression results of the fixed-effect SDM in Tables 3 and 4.

The innovation-driven impact on green development
The results in Table 3 show that the proportion of R&D investment in GDP (KB), the number of R&D personnel per ten thousand people (KR), the education expenditure per ten thousand yuan of GDP (JZ), and the number of education practitioners per ten thousand people (EP) all have a significant positive impact on the regional green development index. Two indicators, namely, the proportion of R&D investment in GDP and the number of R&D personnel per ten thousand people, have an intermediary effect on the region but no significant effect on the green development of neighbouring areas. The education expenditure per ten thousand GDP and the number of educated employees per ten thousand GDP have not only positively affected the level of green development in this region but also are positively correlated with neighbouring regions. Table 4 shows that there is a significant interaction between the innovation-driven development index and the gross value of industrial wastewater emissions per ten thousand yuan of industrial output (FS), the hazard-free treatment rate of waste (WL), the number of days with good air quality (YK), and the ratio of surface water at or better than that of class III (GP). The two indicators of wastewater emissions per ten thousand yuan of industrial output and the hazard-free treatment rate of waste have direct effects only on the regional innovation-driven development index, with high correlation coefficients. Wastewater emissions per ten thousand yuan of industrial output is negatively related with the regional innovation-driven development index, and the hazard-free treatment rate of domestic waste is positively related. There is a significant positive correlation between the two indicators of the proportion of days with good air quality in the entire year and the proportion of surface water at least or better than type III and the innovation-driven development index of the region and adjacent regions. Other relevant research results Liu et al. 2020;Wu and Zhang 2021) are similar to this paper, which indicates that there is indeed a spillover effect between cities in the Yangtze River Economic Belt.

The spatial distribution of the innovation-driven development and green development coordination indexes
This study shows that the spatial distribution of the innovation-driven development and green development coordination indexes in the Yangtze River Economic Belt presents an unbalanced trend and that the differences between cities and regions are gradually increasing, especially between central cities (provincial capitals, municipalities directly under the central government, etc.) and surrounding cities. An increase or decrease in the coordination index reflects an increase or decrease in the cooperation coefficient between innovation-driven development and green development. From the perspective of classification, from 2003 to 2017, the high-value area of the green development index of the Yangtze River Economic Belt shows an expanding trend from east to the centre, while the highvalue area of the innovation-driven development index shows a shrinking trend from the centre to the east. Such spatial distribution characteristics are related to the Chinese administrative system's characteristics. Innovation depends on the investment of science, education funds, and personnel. Compared with central cities, general cities in the western region have limited science and education resources, which are not closely connected to innovationdriven development. The lack of coordination between education and innovation-driven development leads to the lack of both sustainability and the self-generation of regional green development. Therefore, it is important measure to improve the level of sustainable development to solve the problem of the source of innovation funds for ordinary cities.

Spatial heterogeneity of the innovation-driven development and green development coordination indexes
Spatial heterogeneity across regions is a key issue for the coordination between the innovation-driven development and green development of the Yangtze River Economic Belt. According to the above research conclusions, there is significant spatial heterogeneity across regions of the Yangtze River Economic Belt in terms of the innovationdriven development index, green development index, and coordinated development index from 2003 to 2017. Lowlow clusters indicate that the development index values of a region and its surrounding regions are significantly low; such areas are mainly distributed in the central and western Table 3 Panel model regression results of the green development impact factors Note: *, **, and *** indicate significance levels of 10%, 5%, and 1%, respectively Effect regions of the Yangtze River Economic Belt. Compared with the downstream areas, these areas have a low economic development level, a poor innovation atmosphere, and limited green development, and they therefore form an agglomeration area with low-low clusters. High-high clusters refer to the areas with high development indexes of their own and in the surrounding areas within the Yangtze River Economic Belt. Such areas are concentrated in the eastern region with a high level of economic development, high investment in innovation resources, and an interactive and cooperative mechanism between innovation and green development. The coordination index of low-high clusters is significantly lower than that of surrounding areas. Policy mechanisms, such as resource investment, process management, and efficiency improvement, should be developed to quickly improve the unfavourable positions of these areas and facilitate the spatial expansion and extension of high-value areas. The coordination index of high-low clusters is significantly higher than that of the surrounding areas. How to link related resources and drive the coordinated development of surrounding areas is the core of improving the overall level of low-low clusters.

Interaction mechanism between innovation-driven development and green development
The analysis of the impact mechanism is a key step in promoting innovation-driven development and green development. In the interaction between innovation-driven development and green development in the Yangtze River Economic Belt, there are many-to-one and one-to-many relationships between the two impact modes. To improve the level of green development in low-high clusters, it is necessary to increase the proportion of R&D investment in GDP and increase the number of R&D personnel per ten thousand people, as both of these indicators have a significant positive impact on the improvement in the level of green development in the region. To improve the green development level of low-low clusters, it is necessary to increase the education expenditure per ten thousand GDP and increase the number of education employees per ten thousand people. Both of these measures not only improve the green development level of a particular region but also have a significant impact on the green development level of neighbouring regions, and they are thus suitable for contiguous low-low clusters.
The influencing mechanism of the innovation-driven development index is also improved by differentiation according to the subregional types mentioned above. For continuous innovation in the low index areas of low-low clusters, the application of two-way indicators has direct and indirect effects, which enhance the overall level of innovation in these clusters. The model results show that indexes such as the proportion of days with good air quality and the ratio of surface water at or better than level III can be effectively improved. For the development of low-high clusters, the indexes with significant effects in individual regions but not in neighbouring regions should be selected. The model results emphasize the importance of the two indexes of industrial wastewater discharge per ten thousand yuan of the industrial output value and the harmless disposal rate of domestic waste. Reducing the industrial wastewater discharge per ten thousand yuan of the industrial output value and increasing the harmless treatment rate of domestic waste can effectively improve the innovation-driven development index of low-high clusters.

Strengths and limitations
This study has several advantages. First, the Yangtze River Economic Belt, which is a pilot area of innovation-driven development and green development in China, is taken as a case study of the coordinated relationship between innovation-driven development and green development. This study is representative and can be used as a reference for the development of other regions. Second, by constructing an evaluation index system, we evaluate the innovation-driven development index and green development index in different dimensions, which can comprehensively represent the actual level of evaluation targets. Third, by decomposing the overall and local relationships between innovation-driven development and green development, we can find specific indicators with spatial heterogeneity to support the implementation of countermeasures and suggestions.
Our study has some limitations. First, the study scale of spatial distribution is at the provincial level and the city level, and some characteristic conclusions are drawn. However, some indicators, such as the domestic sewage treatment rate, household garbage harmless treatment rate, and per capita park green area, can be refined to more microscopic research scales, such as the county level and township level, and more detailed research conclusions can be drawn to overcome the spatial limitations of this study. Second, the index data from the China Statistical Yearbook, such as the per capita park green area, green coverage rate of built-up areas, science and technology expenditure per ten thousand GDP, and education expenditure per ten thousand GDP, are counted only in municipal districts, and the integrity of the research data needs to be further strengthened. Third, due to the limitations of city data, we did not select green R&D, energy R&D, and other indicators that are closer to green development (Gu et al. 2019) and chose the overall data of R&D as a substitute. Fourth, in the chapter on the influencing mechanism, we analyse the action mechanism of specific indicators on the overall development, including the differentiation analysis of both an individual region and adjacent regions. However, some indicators also have differences in the action cycle or even lag effects, which are not extended to the action cycle because of the model's limitations. All the above four points need to be addressed in follow-up studies.

Conclusion
In this paper, the entropy weight TOPSIS method and the coupling coordination model were used to evaluate the coupling coordination relationship between innovation-driven development and green development in the Yangtze River Economic Belt, and the influencing mechanism between the two was explored from the perspective of spatial panel data. In general, the coordination index of innovation-driven development and green development in the 11 provinces and cities of the Yangtze River Economic Belt has a distribution pattern of high in the east and low in the west. The eastern coastal region of the Yangtze River Economic Belt, as the frontier for the land acquisition of foreign enterprises, presents a strong coordination between innovation-driven development and green development. The improvement in innovation ability can support advancement toward the goal of green development, and green development can optimize the development environment and promote further improvement in innovation ability. The central and western regions of the Yangtze River Economic Belt are located inland, and their innovation-driven development and green development indexes are both low, which indicates that these regions have not formed a well-coordinated relationship. Local influencing factors have significantly heterogeneous effects on the overall development space. This study fills the gap in the literature regarding the interaction mechanism between innovation-driven development and green development in the academic world, and the proposed evaluation index system has a certain universality and significance. It will help other regions understand their innovation-driven capacity and green development level in economic development, compensate for their weak points in development, promote their comparative advantages, and achieve a higher level of sustainable development.