Spatial Correlation Network Structure and Influencing Factors of Two-Stage Green Innovation Efficiency: Evidence from China

Abstract

With the continuous progress in global sustainable development, green innovation has become the primary driving force for the development of all countries and regions. China has implemented the strategy of constructing a cross-regional green innovation network. As the spatial correlation network structure of green innovation efficiency is complicated, it is necessary to study the change rules of the network structure to coordinate regional green and innovative development. In this paper, the Super-NSBM model is used to calculate the values of two-stage green innovation efficiency of China’s industrial enterprises from 2006 to 2019. Social network analysis is used to explore the rule of changes and causes of the spatial correlation network of two-stage green innovation efficiency. Our findings are as follows. Green innovation efficiency in the two stages presents the relationship of a non-adjacent complex network, and the network of green innovation and R&D efficiency is closely interconnected. Strong hierarchical correlation breaks down when searching for the best spatial configuration relationship. The transformation efficiency of the networked cooperation of green innovation achievements is stable. In the spatial correlation of green innovation and R&D efficiency, Guangdong, Shandong, Beijing, Jiangsu and Zhejiang are at the center of the network. In the spatial correlation of transformation efficiency of green innovation achievements, Shandong, Jiangsu, Guangdong, Henan and Hubei are in the center. The northern coastal areas fall within the scope of green innovation and R&D spillover has and have a close cooperation with the green innovation spillover plate in the southern coastal areas, making green innovation achievements spill over to the Chengdu-Chongqing region and northern region. The cooperation and connection of green innovation activities conform to the rule of geographical proximity. Environmental regulation and marketization are characterized by “hierarchy”, but the economic level is “non-hierarchical”. The government can implement relevant green innovation policies according to local characteristics. Our findings are of great significance to narrow regional green innovation gaps.

1. Introduction

With the increasing pressure of global economic development and the aggravation of environmental pollution, all countries have embarked on the road of sustainable development [1]. Countries and regions in the world are actively developing new technologies to reduce environmental pollution and achieve sustainable development [2]. China’s GDP is now the second largest in the world [3]. Rapid economic development imposes a huge impact on the environment [4]. The contradiction between ecological environment and economic development in China has become a key problem hindering sustainable development [5]. The development mode of green innovation has become an important force to boost economic development and solve environmental problems [6]. According to the data disclosed by the International Energy Agency, green technology innovation can reduce carbon dioxide emissions by about 60%. Therefore, green innovation plays a vital role in promoting sustainable development in China [7], becoming a new growth trend of economic development in various countries and regions [8]. China’s industrial enterprises are the leading force of green innovation. Green innovation efficiency is an effective index to measure the performance of green innovation activities. As a result, improving the green innovation efficiency of industrial enterprises is the key to improving the level of regional green innovation.

The Outlines on National Strategy for Innovation-Driven Development put forward the strategic goal of building a cross-regional innovation network. With the continuous improvement of information technology, transportation facilities, and regional integration policies, the cooperation bond of green innovation between regional industrial enterprises has been gradually formed. Yet there is still no efficient and orderly statement for this, and the government has failed to produce empirical evidence of formulating regional innovation resource allocation and division of the field for green innovation cooperation. For this reason, based on social network analysis, exploring the changing trend of spatial correlation network of regional green innovation efficiency, the role and status of each region, and the constraints on the formation of cooperation, and in order to narrow the differences in green innovation efficiency among regions, it is of far-reaching significance to establish long-term regional cooperation on green innovation and coordinate regional green innovation development.

At present, many scholars throw themselves into the study of green innovation efficiency, but there are still three limitations in the study of green innovation efficiency from the perspective of spatial pattern. In the measurement of green innovation efficiency, the most commonly used methods firstly, are stochastic frontier analysis and data envelopment analysis (DEA), such as the measurement (SBM) model based on relaxation [9]. But the single-stage DEA model measures green innovation efficiency as a “black box”, ignoring that innovation is a staged process. In this sense, scientific methods should be employed to measure green innovation efficiency in two stages. Secondly, based on the innovation value chain theory, green innovation activities can be divided into green innovation R&D activities and green innovation achievement transformation activities, both of which are heterogeneous and correlated. The spatial network structure formed of the two innovation activities should be analyzed separately. Finally, existing studies have confirmed the spatial difference of green innovation efficiency between the two stages, but its causes have not been thoroughly studied. The influencing factors of the formation of green innovation spatial correlation network have not been analyzed for the time being; nor have the factors restricting the formation of cooperation been resolved.

This paper makes the following contributions to the existing research. We adopted the Super-NSBM model to scientifically measure the green technology innovation efficiency in two stages. This method not only considered the subprocess network structure with intermediate flow from the first stage to the next, but also captured the dynamic change of green innovation efficiency of industrial enterprises. Then from the network analysis of two-stage green innovation efficiency of the spatial correlation network, we researched the status of all kinds of regions in the network, and formulated scientific and reasonable green innovation policies for different target areas. Finally, the influencing factors have an effect on the formation of a spatial correlation network of green innovation efficiency. Based on this, this paper discusses the constraints on the formation of a spatial correlation network of regional green innovation efficiency; and strengthens the stability of the cooperation relationship; and narrows the differences in green innovation among the regions.

This paper is structurally arranged as follows. 1. Introduction; 2. Literature Review; 3. Research Methods and Variable Selection; 4. Structural Characteristics Analysis of Spatial Correlation Network of Regional Green Innovation Efficiency. In this section, we first applied the Super-NSBM model to accurately measure the values of two-stage green innovation efficiency of industrial enterprises. The social network analysis was then employed to investigate changes in the spatial correlation network, explore network characteristics and the roles of the block model. 5. Analysis of Influencing Factors of Spatial Correlation Network of Regional Green Innovation Efficiency. Quadratic Assignment Program was employed to analyze the influencing factors of spatial correlation of two-stage green innovation efficiency. 6. Conclusions and Enlightenment: we drew relevant conclusions and put forward policy suggestions in this part.

2. Literature Review

Green Innovation Theory

Green innovation is a general term used for all kinds of technologies, processes or products that achieve clean production, improve environmental performance, and promote the comprehensive utilization of resources and energy [10]. Innovation sensitivity [11] is the existence and capability to create and implement an innovation process with existing resources. The index that measures innovation capability is innovation efficiency. The key to green innovation development is to lift the green innovation efficiency, so as to improve the quality of green innovation development. In the study of green innovation measurement, most studies regard green innovation activities as the single-stage green innovation efficiency, which was however divided into two stages by a few studies [12]. According to the innovation value chain [13], the process of green innovation includes the relationship between sub-stages. Green innovation activities can be divided into green innovation of R&D activities and transformation activities of green innovation achievement [14]. Moreover, the sub-stages of the green innovation process have mutual influence and a heterogeneous relationship.

To measure green innovation efficiency from the input-output perspective, it mainly includes stochastic frontier analysis (SFA) of the parametric method and data envelopment analysis (DEA) of the non-parametric method [15]. Charnes, an American operations research scientist, proposed a DEA model [16], although it has radial and angular problems. The SBM model constructed by Tone [17] has the characteristics of non-meridionality, non-angle and non-expected output, and the super-SBM model was constructed to solve the effective ranking problem. Then, in order to evaluate the efficiency of the overall decision-making unit and the sub-stage, based upon which Tone proposed the network DEA model [18].

Many scholars used different methods to measure green innovation efficiency, as shown in

Table 1. Measurement method of green innovation efficiency.

Research Methods	Authors	Research Objects
DEA	Luo et al. [19], 2019	Emerging industry of strategic importance
Network DEA	Chen et al. [20], 2021	High-tech industry
	Zhu et al. [14], 2021	Energy-intensive industry
SBM DEA	Fan et al. [21], 2021	City
	Liu et al. [22]., 2020	High-tech industry
	Zhao et al. [23], 2021	Province
	Zhang et al. [24], 2020	City
Super-SBM DEA	Li and Du. [25], 2021	City
	Li and Zeng [26], 2020	Intensive pollution industry
	Tang et al. [27], 2020	Industrial enterprise
	Zeng et al. [28], 2021	Yangtze River Delta Region
	Zhao et al. [29], 2020	Province

.

Scholars rarely consider the dynamic characteristics of green technology innovation efficiency currently. In order to avoid the problem that multiple effective decision-making units (DMU) cannot be ranked, a new ranking method for decision-making units was thus provided by considering the non-expected, non-angular and non-radial super-efficiency network SBM model [30].

In the study of regional green innovation efficiency, it has been confirmed that the level of green innovation in different provinces vary [31], and almost all spatial data have spatial correlation [32]. The change of green innovation efficiency in one region will affect the same in other regions [33], and the spillover effect will follow the law of decreasing distance [34]. However, scholars mostly used a spatial measurement method that cannot explore the spatial spillover effect of the green innovation network. Social network analysis is the primary method of studying the evolution of the spatial network relationship [35]. In the economic field, it is mainly applied to the correlation structure between regional industries and their influence on regional economic development. A spatial correlation network is characterized by stability and openness. In order to reveal the intrinsic law of green innovation activities, the spatial correlation network of green innovation will be divided into the spatial correlation network of green innovation and R&D efficiency and the spatial correlation network of achievement transformation efficiency of green innovation, with a view to exploring the difference of the regional cooperation connection in the process of realizing innovation value.

In the study of the influencing factors of the spatial network of green innovation efficiency, Boschma proposed the theory of multidimensional proximity innovation, after which a few scholars studied the impact of multidimensional proximity on innovation, such as geographical proximity and technological proximity [36,37]. In addition, there are other related factors that have not been further studied.

Based on the organization of the influencing factors of green innovation efficiency, the spatial differences of green innovation efficiency may be due to the regional difference, and differences in innovation factor input, economic development level, and pollution control level. This paper summarizes the regional influencing factors into the following three categories:

(1)

Resources: Human capital is the executor of green innovation activities, and the improvement of the human capital level is conducive to the perfection of innovation capability [38]. Investment in R&D funds underpins the innovation activities of enterprises, and full investment in R&D funds helps them to obtain more innovation resources as required [39]. Technology market maturity is a favorable guarantee for technology transfer, and technology flow is crucial for acquiring heterogeneous resources and absorbing innovative technologies [40]. Enterprise scale is the environment for innovation activities. The “Schumpeter Hypothesis” holds that the resource advantage and monopoly position of large-scale enterprises make them have a higher innovation input and risk resistance capability, which have a positive impact on R&D efficiency [41]. Foreign direct investment is an important channel for the rapid acquisition of innovative technology and management experience, which can promote green innovation [42].

(2)

Development: Enterprises in the industrial cluster are more innovative than those outside [43]. Regions with a high level of economic development have sufficient innovation resources, perfect institutions, and an active innovation environment, which will help improve innovation capacity. The road network density is an external link condition of innovation activities. The more convenient the traffic, the more conducive to the flow of innovative talents and products. The level of information contributes to the rapid dissemination of innovative information and the cooperation and exchange of innovative talents [44]. Market-oriented demand can carry forward the development of green innovation [45]. Geographically adjacent provinces share similar cultural atmospheres, policy environment, etc., which make it easy to further the communication of silent information and form innovative cooperation links with high reputation. The widening geographical distance acts against the dissemination of key technologies [37].

(3)

System: Environmental regulation can strictly limit the environmental pollution caused by enterprises in the production process and boost the development of green innovation [24].

In the block model analysis, innovation activities in each region can be divided into four innovation clusters, forming different innovation centers. Innovation clusters can improve the strong advantages of regional characteristics and improve the level of competition [46]. Therefore, it is necessary to analyze the characteristics of regional innovation agglomeration in the networks of green innovation R&D and the green innovation achievement transformation, so as to better formulate relevant policies according to the characteristics of regional agglomeration.

3. Research Methods and Variable Selection

3.1. Research Methods

3.1.1. Measurement of Green Innovation Efficiency

A two-stage super-efficiency network SBM model with non-radial, non-angular, non-desired output was adopted in this paper.

$$\rho \ast \mathrm{se}=\min \frac{{\displaystyle \sum _{k=1}^k{w}^k\left[1+\frac{1}{m_k}\left({\displaystyle \sum _{i=1}^{m_k}\frac{s_i^{k-}}{x_{i0}^k}}\right)\right]}}{{\displaystyle \sum _{k=1}^k{w}^k\left[1-\frac{1}{v_{1k}+v_{2k}}\left({\displaystyle \sum _{r=1}^{v_{1k}}\frac{s_r^{gk}}{y_{ro}^{gk}}+{\displaystyle \sum _{r=1}^{v_{2k}}\frac{s_r^{bk}}{y_{ro}^{bk}}}}\right)\right]}}$$

(1)

$$st.\left\{\begin{array}{cc}\hfill & \sum _{j=1,\ne 0}^n{x}_{ij}^k{\lambda }_j^k+s_i^{k-}={\theta }^k{x}_{io,}^{k}i=1,\dots ,m_k,k=1,\dots ,k\hfill \\ \hfill & \sum _{j=1,\ne 0}^n{y}_{ij}^{gk}{\mathsf{\lambda }}_j^k+s^{gk}={\mathsf{\phi }}^k{y}_{ro,}^{gk}r=1,\dots ,s_k,k=1,\dots ,k\hfill \\ \hfill & \sum _{j=1,\ne 0}^n{x}_{rj}^{bk}{\mathsf{\lambda }}_j^k-s^{bk}={\mathsf{\delta }}^k{y}_{ro,}^{bk}r=1,\dots ,s_k,k=1,\dots ,k\hfill \\ \hfill & \mathsf{\epsilon }\le 1-\frac{1}{v_{1k}+v_{2k}}\left(\sum _{r=1}^{v_{1k}}\frac{s_r^{gk}}{y_{ro}^{gk}}+\sum _{r=1}^{v_{2k}}\frac{s_r^{bk}}{y_{ro}^{bk}}\right)\hfill \\ \hfill & {}^{Z^{(k,h)}}{\mathsf{\lambda }}^h={}^{Z^{(k,h)}}{\mathsf{\lambda }}^{\mathrm{k}},\sum _{j=1,\ne 0}^{\mathrm{N}}{\mathsf{\lambda }}_j^k=\sum _{k=1}^K{w}^k=1\hfill \\ \hfill & {\mathsf{\lambda }}^k\ge 0,s^{k-}\ge 0,s^{gk}\ge 0,s^{bk}\ge 0,w^k\ge 0\hfill \end{array}\right.$$

(2)

In Formula (1), $m_k$ and $v_k$ represent the number of input and output at the stage K. In Formula (2), ${\phi }_k$ denotes the number of intermediate indicators; (k, h) represents the connection from stage K to stage H, x and Y represents the input and the output, respective; z denotes the intermediate output, ${\mathsf{\lambda }}_k$ means the model weight of stage K, ${\omega }_k$ is the weight of stage K. $s^{k-}$ refers to the slack variable of the input indicator, $s^{gk}$ and $s^{bk}$ represent the slack variables of the desirable output and the undesirable output, respectively.

3.1.2. Determination of Spatial Correlation Relationship of Regional Green Innovation Efficiency

Social network analysis is based on relational data, a gravity model and a Vector Autoregressive Granger causality test, which are used to determine the relationship [47]. The disadvantage of the VAR model is that it is too sensitive to the selection of lag order but is only suitable for data with a long timespan, not for cross-sectional data [48]. The gravity model is not only applicable to cross-sectional data, but also takes into account both economic and geographical distances. Therefore, this paper builds the spatial correlation matrix based on the modified gravity model. The calculation formulae of the spatial correlation strength of green innovation efficiency are as follows:

$$R_{ij}=K_{ij}\cdot \frac{\sqrt{R{P}_i\cdot T{E}_i}\cdot \sqrt{R{P}_j\cdot T{E}_j}}{D_{ij}^2}, K_{ij}=\frac{T{E}_i}{T{E}_i+T{E}_j}$$

(3)

$$R_{ij1}=K_{ij1}\cdot \frac{\sqrt{R{P}_i\cdot T{E}_{i1}}\cdot \sqrt{R{P}_j\cdot T{E}_{j1}}}{D_{ij}^2}, K_{ij1}=\frac{T{E}_{i1}}{T{E}_{i1}+T{E}_{j1}}$$

(4)

$$R_{ij2}=K_{ij2}\cdot \frac{\sqrt{R{P}_i\cdot T{E}_{i2}}\cdot \sqrt{R{P}_j\cdot T{E}_{j2}}}{D_{ij}^2}, K_{ij2}=\frac{T{E}_{i2}}{T{E}_{i2}+T{E}_{j2}}$$

(5)

$R_{ij}$, $R_{\mathrm{ij}1}$, $R_{ij2}$, represent industrial green innovation efficiency, industrial green innovation and R&D efficiency, correlation strength of achievements transformation efficiency of green innovation of provinces i and j, respectively. $K_{ij}$ serves as the gravitational constant; $R{P}_i$$R{P}_j$ represent the industrial R&D personnel of provinces i and j; $T{E}_i$, $T{E}_j$ represent the green innovation efficiency of provinces i and j, respectively. $T{E}_{i1}$, $T{E}_{j1}$ denote green innovation and R&D efficiency of provinces i and j, respectively. $T{E}_{i2}$, $T{E}_{j2}$ mean achievements transformation efficiency of green innovation of provinces i and j, respectively. $D_{ij}$ acts as the ij spherical distance between the capital cities of the two provinces. The method of average value binarization was used to process the strength and weakness of the matrix, a correlation matrix the average segmentation value of all elements in 2006, greater than or equal the value indicates as strong correlation, the assignment is 1, less than the value indicates as weak correlation, the assignment is zero, Construct the spatial binary correlation matrix of two-stage green innovation efficiency of provincial industry.

3.1.3. Social Network Analysis

Featuring globality, social network analysis is a method that mainly analyzes structure relations and decision relations of attribute data. Regional green innovation efficiency of a spatial correlation network is a collection of regional green innovative correlations. Upon discussion of a provincial network structure attribute, the role attributes of regional green innovation capability can be rationally divided to strengthen cooperation.

(1)

Overall network characteristics describe density, correlation, grade and efficiency of the network. Among others, network density reflects the degree of close cooperation between innovation subjects [49]; the greater the value, the closer the network connection. The network correlation reflects the reachability between innovation subjects, and the robustness of the spatial network [9]. Network level measures the asymmetric accessibility between innovation subjects; the greater the value, the tighter the network structure, and the more innovation subjects in the marginal position [50]. Network efficiency reflects the degree of redundancy; if the value is smaller, there will be more redundant lines [50].

(2)

Individual network characteristics reflect the centrality of innovation subjects, which consists of point centrality, intermediary centrality and proximity centrality [51]. The greater the centrality value of point degree is, the more central the region will be in the network. Among them, the in-degree and out-degree reflect the number of receiving and sending correlations, respectively. A higher out-degree reflects the direct impact on other provinces, and a higher in-degree means that resources are more accessible to this province [52]. Mediating centrality refers to the degree to which a province falls between other nodes. The greater the value, the greater its role as an intermediary bridge. The greater the value of proximity centrality, the higher the degree that the innovation subject is not controlled by other innovation subjects.

(3)

Block model determines the role and position of each block in the network by block clustering [53]. Provinces within the same block have similar functions, and green innovation spillovers exist both within and between blocks, which can be divided into four types: (i) net beneficial role, the plate that receives the number of external correlations is more than that of its spillover correlations; (ii) net spillover role, the plate that sends correlations to other plates is more than what it receives from other plates; (iii) role of isolated people, the internal members of the plate have a certain connection, but less contact with other external plates; (iv) role of broker, which has few internal membership relationships and is mainly concerned with accepting and issuing relationships to other sectors.

3.2. Index Selection

3.2.1. Two-Stage Green Innovation Efficiency Measurement Index

Input-output index selection of two-stage green innovation efficiency: In the stage of green innovation and R&D, the input index includes the input of R&D personnel, capital and energy. R&D personnel are the main performers of technological innovation, and the full-time equivalent index of R&D personnel can reflect the input of scientific and technological human resources [54]. Capital investment is a prerequisite for the realization of innovation activities in all regions [9]. In this paper, expenditures of R&D, new product development and non-R&D are included in the model [55]. Energy consumption is the basis of green technology innovation. The annual electricity consumption can effectively measure the amount of energy input [56]. Intermediate output indicators include the number of patent applications, the number of effective invention patents [57]. The number of patent applications and the number of effective invention patents are important indicators to measure technological innovation and output of enterprises. The number of new product development projects [55] measures the capability of industrial enterprises to convert R&D investments into developable technologies. The initial input generates the intermediate output produced in the R&D phase [58]. Subsequently, the intermediate output is input into the stage of innovation achievement transformation together with additional intermediate inputs to produce the final output [59]. There are three waste treatment investment funds for additional intermediate input. The input index of “three wastes” treatment is mainly through energy-saving and emission reduction measures such as the introduction and transformation of green equipment to reduce pollution emission. And the investment in “three wastes” treatment can be used as an index to measure green R&D investment [60].

In the achievement transformation stage of green innovation, the innovative products will be transformed into economic benefits [61]. The sales revenue of new products represents the final market value of technological innovation [27]. Some small inventions and process improvement can also effectively enhance the production efficiency and product quality of enterprises; hence, this paper introduces the main business income to measure the quality of enterprise innovation [62]. The unwanted output refers to the “by-product” of expected output, which directly or indirectly damages the pollutants generated in the innovation process. In this paper, the discharge of industrial wastewater, the production of industrial solid waste gas and the exhaustion of industrial waste gas were fitted into the comprehensive index of industrial environmental pollution by the entropy method [63]. Detailed index treatment is shown in

Table 2. Relevant indicators of green innovation efficiency of input-output selection.

Stages of Green Innovation Activity	Input-Output Factors	Variables	Measures
① Input of green innovation and R&D stage	Input of the R&D personal	Full time equivalent of R&D personnel	Sum of full-time equivalents of R&D project management and direct service personnel
	Input of investment	R & D investment	The R & D price index was deflated based on 2006 using the method of perpetual inventory for stock processing [64] to address depreciation and accumulation effects,
		New product development expenses	The processing method is the same as above
		Non-R & D expenditure	The expenditure for technology introduction, digestion and absorption, technical transformation, and purchase of domestic technology shall be handled in the same way as above
	Input of energy	Annual electricity consumption [56]	Use these indicator data directly
② Output of green innovation and R & D stage	Output of innovation	Patent applications	The number of patent applications submitted by the State Intellectual Property Office or its representative offices
		Number of valid invention patents	The State Intellectual Property Office examined and approved the number of granted patents
		New product development project	The number of new product development projects represents the ability of R & D investment translate into technology
③ Input of the transformation stage of green innovation achievements	➀ + ② + middle input	Investment funds for waste disposal	Including the introduction of green equipment, green technology transformation, etc., and the use of perpetual inventory method for stock treatment to solve the depreciation and accumulation effect.
④ Output of the transformation stage of green innovation achievements	Output of economy	Revenue from new product sales	The benefits of innovative products were obtained by deflating the producer price index
		Main business income	Technological innovation and transformation in the process of production and sales can improve production efficiency and quality, which can be obtained through the ex-factory price index of industrial products
	Output of environment pollution	Comprehensive index	The three non-expected outputs, including discharge of industrial waste water, production of industrial solid waste gas and exhaustion of industrial waste gas, were obtained by using the entropy method

. This article has carried out the stock processing to related indexes, indicating that the lag effect of relevant indicators has been taken into account, and the market orientation speed of industrial enterprises is fast, and the interval period between the two stages is not long; but lag period treatment has not been carried out in this paper.

3.2.2. QAP Model Setting and Variable Description

The dependent variables in this paper are relational data. In order to solve the problems of autocorrelation and multicollinearity, Quadratic Assignment Program was used to analyze the causes influencing the spatial correlation network of China’s two-stage green innovation efficiency. Accordingly, the following model was established:

$$GI/G{I}_1/G{I}_2=f(G,IC,ER,EC,T,R,S,HC,M,FDI,RN,I)$$

(6)

The explained variables, $GI$, $G{I}_1$, $G{I}_2$, represents the regional industrial efficiency of green innovation, green innovation and R & D efficiency, and the achievement transformation efficiency of green innovation of spatial correlation matrix, respectively. In terms of the explanatory variables, the resource: $HC$ is the difference of human capital, $R$ denotes the difference of R & D expenditure, $T$ refers to the difference of market maturity, $S$ means the difference of enterprises scale, $FDI$ represents the difference of foreign direct investment. The development class: $IC$ is the difference of industrial aggregation, $EC$ represents the difference of the economic development level, $RN$ denotes the difference of road network density, $I$ is the difference of informatization level, $M$ refers to the difference of marketization, $G$ represents geographical proximity. The system: $ER$ denotes the difference of environmental regulation. Specific index selection and treatment are shown in

Table 3. Variable indices of influencing factor of spatial correlation of industrial green innovation efficiency.

Influencing Factors	Measures
Geographic adjacency	If they are adjacent, provinces i and j are set as 1. If they are not adjacent, provinces i and j are set as 0
Industry clustering	$\mathrm{The} \mathrm{industrial} \mathrm{agglomeration} \mathrm{formula} \mathrm{is} G=\frac{H_{it}/H_t}{P_{it}/P_t}$$. \mathrm{Where} \mathrm{in}{H}_{it}$$\mathrm{represents} \mathrm{the} \mathrm{number} \mathrm{of} \mathrm{employees} \mathrm{in} \mathrm{industrial} \mathrm{enterprises} \mathrm{in} \mathrm{year} \mathrm{T} \mathrm{in} \mathrm{region} \mathrm{I}. H_t$$\mathrm{denotes} \mathrm{the} \mathrm{number} \mathrm{of} \mathrm{employees} \mathrm{in} \mathrm{industrial} \mathrm{enterprises} \mathrm{in} \mathrm{the} \mathrm{country} \mathrm{in} \mathrm{year} \mathrm{t}, P_{it}$$\mathrm{means} \mathrm{the} \mathrm{total} \mathrm{employment} \mathrm{in} \mathrm{year} \mathrm{t} \mathrm{in} \mathrm{region} \mathrm{I} P_i$ refers to the aggregate national employment in year t
Environmental regulation	Discharge of environmental pollutants/industrial output value denotes environmental regulation, measuring the difference of environmental regulation
Level of economic development	Regional differences in per capita gross regional product
Technology market maturity	Technical market turnover measures the differences in technical market
Level of R & D investment	Measuring the regional differences in R & D investment
Enterprise scale	The total output value of industrial enterprises/number of enterprises represents the size of enterprises, measuring the regional difference of enterprise size
Human capital	The faculty-student ratio in colleges and universities measures human capital, measuring regional differences in human capital
Level of marketization	Regional differences in marketization indices
Level of foreign direct investment	(Foreign capital + main business income of enterprises from Hong Kong, Macao and Taiwan)/total main business revenue represents foreign direct investment, measuring regional differences oi foreign direct investment
Convenience of transportation	The sum of railway density, highway density and inland waterway density
Level of informatization	Regional differences in integration index of informationization and industrialization

.

Cooperation links are influenced by geographical distance, scale of innovation, economic scale and other proximity factors [65].

(1)

Resources:

Human capital, regional differences in human capital levels. The difference in human capital is detrimental to the digestion and absorption of innovative technologies, thus hindering the cooperation and connection of green innovation among regions [66].

H1. 

Differences in human capital negatively affect green innovation cooperation.

Level of R & D investment. Enterprises with sufficient R & D funds can attract more innovation resources, which is conducive to the development of innovation activities. The difference of R & D funds among enterprises results in the failure of relevant innovation activities to be supported and the formation of cooperative relationships.

H2. 

R & D investment difference negatively affects green innovation cooperation.

Technology transfer. The dependence on geographical proximity will decrease as technology proximity reaches a certain level [67].

H3. 

Differences in technology transfer positively affect green innovation cooperation.

Enterprise scale. Large-scale enterprises are the inertia innovation mode, and small enterprises are the flexible innovation mode. The difference of innovative cooperation modes is unfavorable to the formation of cooperative relationship.

H4. 

Differences in enterprise scale negatively affect green innovation cooperation.

Foreign direct investment. Foreign direct investment that can quickly make use of advanced technology from abroad plays a leading role in innovation, driving the formation of cooperation links.

H5. 

Differences in foreign direct investment positively affect green innovation cooperation.

(2)

Development:

Industrial cluster. Enterprises in the industrial cluster are more innovative than those outside [68], and their differences propel the spillover benefits of cooperation and exchange between innovative subjects [69]. These make for the formation of cooperative relationships.

H6. 

Industrial agglomeration difference positively affects green innovation cooperation.

Level of economic development. Regions with high-level economic development share sufficient innovation resources, perfect institutions, and active innovation environment, forming innovative cooperation links with the demand for innovation in regions where the level of economic development is not that high [70].

H7. 

Differences in the level of economic development positively affect green innovation cooperation.

Road network density. The greater the difference in road network density, the more difficult it is to connect innovation activities between regions.

H8. 

Differences in road network density negatively affects green innovation cooperation.

Level of informatization. Regions with a large gap in the level of informatization hinder the diffusion of innovative technologies and fail to apply similar innovative technologies and production equipment at the same time to establish innovative cooperation [71].

H9. 

Differences in informatization negatively affects green innovation cooperation.

Level of marketization. If differences in the level of marketization are greater, the phenomenon of blockages to the flow of innovation and market failures will be more serious. This will hinder the cooperation and connection of green innovation.

H10. 

Marketization difference negatively affects green innovation cooperation.

Geographic adjacency. Geographically adjacent provinces share similar cultural atmosphere, policy environment, etc., making it easy to form innovative cooperation links.

H11. 

Geographical proximity positively affects green innovation partnerships.

(3)

System:

Environmental regulation. Enterprise innovation concepts, marketing management and other aspects vary between regions with strict environmental regulations and those without the same, which makes it difficult to form cooperation links. Institutional proximity makes technical cooperation more effective.

H12. 

Differences in environmental regulations negatively affect green innovation cooperation.

3.3. Data Sources

In this paper, China’s industrial enterprises from 30 provinces from 2006 to 2019 were sampled. The Tibet Autonomous Region, Hong Kong and Macao were excluded for lack of data. Data are from the China Statistical Yearbook, the China Industrial Economic Statistical Yearbook, the China Environmental Statistical Yearbook, the China Energy Statistical Yearbook, and the Evaluation Report on the Integrated Development Level of Industrialization and Informatization of China from 2007 to 2020. The regional marketization index compiled by Fan Gang was used as the marketization index.

4. Structural Characteristics Analysis of Spatial Correlation Network of Regional Green Innovation Efficiency

4.1. Spatial Distribution Pattern

MaxDEA software was used to calculate the values of two-stage green innovation efficiency of 30 provinces and cities in China. The results are shown in

Table 4. Green innovation efficiency of two stages in each region.

Regions	Green Innovation and R & D Efficiency						Transformation Efficiency of Green Innovation Achievements
	2006	2013	2017	2019	Mean	Rank	2006	2013	2017	2019	Mean	Rank
Beijing	1.12	2.89	2.89	2.42	2.51	1	0.96	0.61	0.68	0.67	0.67	14
Tianjin	0.71	0.74	0.69	1.01	0.83	6	1.00	1.44	0.56	0.79	1.01	2
Hebei	0.54	0.41	0.41	0.58	0.45	24	0.65	0.91	0.44	0.26	0.51	19
Shanxi	0.22	0.37	0.30	0.59	0.32	29	0.68	0.45	0.44	0.41	0.42	24
Inner Mongolia	0.39	0.27	0.31	0.52	0.29	30	0.79	1.02	0.41	0.68	0.74	11
Liaoning	0.29	0.45	0.36	0.64	0.42	27	0.58	0.77	0.29	0.45	0.52	18
Ji Lin	0.25	0.52	0.25	1.02	0.38	28	1.14	1.74	1.63	0.59	1.30	1
Heilongjiang	0.51	0.35	0.38	0.71	0.43	26	0.47	0.69	0.25	0.20	0.39	25
Shanghai	2.70	0.70	0.73	1.04	1.44	3	0.53	1.00	1.00	1.01	0.90	3
Jiangsu	0.66	0.73	0.53	0.69	0.71	11	0.85	0.94	1.24	0.46	0.90	4
Zhejiang	0.74	0.74	0.47	1.19	0.88	4	0.99	0.75	1.23	0.72	0.79	9
Anhui	0.52	0.90	0.83	1.01	0.86	5	0.51	0.62	0.67	0.59	0.54	17
Fujian	0.53	0.57	0.51	0.69	0.61	15	0.90	0.86	0.86	0.43	0.64	15
Jiangxi	0.43	0.50	1.06	1.00	0.59	18	0.86	1.19	0.99	0.66	0.85	6
Shandong	0.82	0.48	0.38	0.51	0.55	20	0.91	1.40	1.22	0.17	0.86	5
Henan	0.52	0.47	0.46	0.60	0.49	22	0.72	1.19	1.00	1.24	0.81	7
Hubei	0.62	0.52	0.43	0.62	0.59	17	0.50	1.01	1.07	1.38	0.71	12
Hunan	0.63	0.65	0.45	0.69	0.75	9	0.39	0.79	1.26	0.39	0.57	16
Guangdong	2.05	1.73	3.04	1.49	1.97	2	0.67	0.73	0.59	1.41	0.79	8
Guangxi	0.50	0.48	0.49	0.68	0.54	21	0.52	0.77	0.80	0.32	0.47	21
Hainan	0.25	1.04	0.75	0.87	0.82	7	1.43	0.37	0.29	0.19	0.69	13
Chongqing	1.29	0.67	0.56	0.54	0.77	8	0.25	0.82	1.23	0.86	0.77	10
Sichuan	0.86	0.73	0.65	0.76	0.72	10	0.28	0.62	0.67	0.48	0.42	23
Guizhou	0.66	0.63	0.77	1.00	0.69	12	0.26	0.25	0.22	0.27	0.21	30
Yunnan	0.51	0.66	0.84	0.87	0.65	13	0.40	0.36	0.07	0.22	0.33	27
Shaanxi	0.59	0.60	0.47	0.69	0.63	14	0.46	0.53	0.39	0.25	0.29	28
Gansu	0.48	0.48	0.47	0.57	0.46	23	0.42	0.57	0.32	0.25	0.36	26
Qinghai	0.80	0.27	0.57	0.88	0.45	25	0.53	0.48	0.33	1.07	0.47	22
Ningxia	0.82	0.48	0.69	1.01	0.61	16	0.26	0.51	0.21	0.24	0.26	29
Xinjiang	0.95	0.55	0.55	1.02	0.58	19	1.09	0.56	0.38	0.39	0.48	20
East of the mean	0.95	0.95	0.98	1.01	1.02	/	0.86	0.89	0.76	0.59	0.75	/
the middle of the mean	0.45	0.50	0.60	0.75	0.52	/	0.67	0.97	0.86	0.68	0.70	/
The western average	0.74	0.55	0.49	0.79	0.61	/	0.45	0.55	0.46	0.44	0.41	/

. The R & D efficiency of green innovation in the eastern, central and western regions of China is 1.017, 0.52 and 0.61, respectively. The R & D capacity of the eastern region is significantly higher than the central and western regions, which may be because the developed regions have a more favorable “hard” innovation environment [72]. The R & D efficiency of the western region is higher than that of the central region due to the establishment of a series of national key experimental bases [55]. It can be seen that paying attention to the “soft” innovation conditions within the region, such as innovation policy tools and management skills, can also improve green innovation capacity. This result is similar to those from the latest research that the R & D efficiency of green innovation in eastern and western regions is relatively higher than that in the central region [73]. The transformation efficiency of green innovation achievements in the eastern, central and western regions is 0.75, 0.70 and 0.41 respectively. Supported by the Yangtze River Delta Canal, the eastern coastal region forms a T-shaped diffusion pattern of green innovation achievements, and the eastern region strongly drives the transformation efficiency of green innovation achievements in the central region.

In this paper, UCINET6.0 software was used to draw the evolution chart of the spatial correlation network of green innovation efficiency in two stages of provinces in 2007 and 2019. The results are shown in Figure 1. Lines and arrow directions between nodes of 30 provinces represent spatial correlation and spillover direction. The spatial correlation evolution diagram of green innovation and R & D efficiency shows that Xinjiang has been an isolated province from 2007 to 2019. In 2007, eastern, central and western regions presented complex cooperative correlation. In 2019, Inner Mongolia, Shanxi, Jiangsu, Zhejiang, Anhui and Guangdong have established green innovation and R & D cooperative correlation with the Beijing-Tianjin-Hebei region. Liaoning has established cooperative relations with Shandong and Zhejiang. Chengdu and Chongqing have established good cooperative relations with Hunan, Guangdong, Guangxi, and Yunnan. Finally, Fujian, Jiangxi, Hunan, Hubei, and Henan have established more relations with other provinces, making the overall network structure more stable.

The evolution diagram of spatial correlation of transformation efficiency of green innovation achievement are shown in Figure 2. It shows that Inner Mongolia, Shaanxi, Ningxia, Gansu, Qinghai, Xinjiang and Hainan were isolated provinces in 2007. The three northeastern provinces and Chengdu-Chongqing region are only internal cooperative correlation, and the eastern region showed a simple spatial correlation. Xinjiang and Ningxia are isolated provinces in 2019. Beijing-Tianjin-Hebei region has also established cooperative relations with Henan, Hubei, Jiangsu, Zhejiang, Inner Mongolia and other regions. Fujian and Jiangxi in the Pearl River Delta Economic Belt have established cooperative relations with Jiangsu and Anhui in the Yangtze River Delta Economic Belt. Guangdong has established good cooperative relations with Hunan, Hubei and Chengdu-Chongqing

4.2. Characteristics of the Overall Network Structure

Changes in the characteristics of the overall network are shown in

Table 5. Characteristics of overall network spatial structure of two-stage green innovation efficiency.

	Green Innovation Efficiency				Green Innovation and R & D Efficiency				Transformation Efficiency of Green Innovation Achievements
	2007	2017	2018	2019	2007	2017	2018	2019	2007	2017	2018	2019
Network density	0.18	0.23	0.23	0.23	0.19	0.19	0.22	0.25	0.12	0.22	0.19	0.19
Network correlation	0.93	0.87	0.93	0.87	0.93	0.93	0.93	0.93	0.87	0.81	0.81	0.87
Network level	0.59	0.39	0.21	0.44	0.35	0.36	0.14	0.14	0.53	0.34	0.33	0.43
Network efficiency	0.78	0.74	0.75	0.74	0.80	0.80	0.77	0.75	0.80	0.73	0.78	0.78

. The network connection tightness of two-stage green innovation efficiency increases year by year. But there is still plenty of room for improvement. The network correlation degree remains unchanged, indicating that the network structure has strong robustness. The hierarchical relationship between green innovation efficiency and transformation efficiency of green innovation achievements decreases significantly before 2018, and the hierarchical cooperation relationship gradually increased in 2019, indicating that the cooperative relationship has gradually stabilized. The hierarchical relationship with strong R & D efficiency of green innovation already existed before 2017. After that, innovation subjects began freely to choose cooperative relationships to achieve an optimal space allocation, but they do not have mature and stable cooperative relationships. As the network efficiency decreases, the number of cooperative relationships needs to be controlled due to the increase in redundant links.

4.3. Characteristics of Individual Network Structure

The individual network structure is shown in

Table 6. Characteristics of individual network structure of two-stage green innovation efficiency in 2019.

Region	Green Innovation and R & D Efficiency					The Transform Efficiency of Green Innovation Achievements
	InDegree	OutDegree	Degreen	Betweenness	Closeness	InDegree	OutDegree	Degreen	Betweenness	Closeness
Beijing	7	14	48.28	27.58	39.73	4	7	24.14	11.85	25.44
Tianjin	8	10	34.48	18.57	35.80	7	8	31.03	74.02	26.36
Hebei	10	9	34.48	42.25	36.71	10	5	34.48	15.48	26.13
Shanxi	7	6	27.59	3.97	34.12	6	3	24.14	4.62	25.44
Inner Mongolia	4	1	13.79	0	29.89	2	3	13.79	0	23.77
Liaoning	4	2	17.24	104	34.12	2	1	6.89	46	21.97
Ji Lin	2	2	6.89	54	26.36	1	2	6.89	24	18.59
Heilongjiang	1	1	3.45	0	21.17	1	0	3.45	0	15.93
Shanghai	9	10	37.93	8.2	37.18	8	10	34.48	1.02	26.36
Jiangsu	14	15	51.72	31.65	39.19	13	12	48.28	51.67	28.15
Zhejiang	13	17	58.62	79.98	41.43	10	12	41.38	14.49	27.62
Anhui	13	13	48.28	19.93	38.67	9	11	37.93	3.28	26.61
Fujian	8	8	27.59	0.13	34.12	9	7	31.03	0.14	25.66
Jiangxi	9	10	34.48	1.06	36.25	9	9	31.03	1.23	25.66
Shandong	19	15	65.52	255.99	42.65	16	5	55.17	95.57	28.71
Henan	14	13	48.28	30.49	38.67	13	18	62.07	140.13	29.29
Hubei	12	11	41.38	12.38	37.66	9	16	55.17	24.31	28.71
Hunan	11	10	41.38	17.99	37.18	10	7	34.48	2.35	25.89
Guangdong	16	18	65.52	198.87	41.43	11	17	58.62	114.42	28.16
Guangxi	2	1	6.89	0	30.21	1	1	3.45	0	22.48
Hainan	1	1	3.45	0	29.89	1	0	3.45	0	22.48
Chongqing	6	4	20.69	5.48	33.33	5	9	31.03	41.43	26.13
Sichuan	4	5	17.24	19.27	34.12	4	2	17.24	0	25.22
Guizhou	4	6	20.69	6.29	31.52	2	1	6.89	0	22.66
Yunnan	2	2	6.89	0	30.21	1	0	3.45	0	22.48
Shaanxi	9	5	34.48	4.92	36.71	5	1	17.24	0	25.22
Gansu	2	1	6.89	0	30.85	1	1	6.89	0	23.02
Qinghai	1	2	6.89	0	30.85	0	2	6.89	0	23.02
Ningxia	1	1	3.45	0	30.53	0	0	0	0	0
Xinjiang	0	0	0	0	0	0	0	0	0	0

. The mean value of degrees is 26.9. Among others, Shandong, Guangdong, Henan, Jiangsu, and Hubei are provinces of higher degrees. Zhejiang, Anhui, Jiangxi, Hubei, and Hunan have strong capability of absorption and spillover of green innovation efficiency. Beijing, Guangdong, Chongqing, and Shandong have strong green innovation spillovers. Hebei, Shanxi and Shaanxi mainly rely on other provinces to obtain green innovation cooperation to promote self-development. In the spatial correlation of green innovation and R & D efficiency, Guangdong, Jiangsu, Zhejiang, Shandong, and Beijing are coastal provinces located in the network center. Beijing and Zhejiang have a strong spillover effect. Jiangsu and Guangdong fall within the scope of strong region of the green innovation R & D spillover and absorptive capacity. Shaanxi and Shandong are part of the cooperation absorption area of green innovation and R & D. Xinjiang is in the isolated position. In the spatial correlation of achievement transformation efficiency of green innovation, such coastal provinces as Shandong, Jiangsu and Guangdong, together with the central regions such as Henan and Hubei are located in the central position. Jiangsu, Zhejiang and Jiangxi have strong capabilities of absorption and spillover of green innovation achievement transformation Henan, Hubei and Guangdong are dominated by the cooperation relationship spillover of achievement transformation of green innovation. Shandong and Hebei mainly rely on the purchase of green innovation achievements to obtain the innovative commercial value, whereas Ningxia and Xinjiang are isolated.

The mean value of betweenness is 11.3. Only Jiangsu, Shandong, Henan, Guangdong, Hebei and Beijing have the capability to control the connections, resources and information among other nodes. In the spatial correlation of green innovation and R & D efficiency, the mean value of betweenness is 31.43, and the top five provinces are Guangdong, Shandong, Jilin, Zhejiang and Liaoning. In the spatial correlation of achievement transformation efficiency of green innovation, the mean value of betweenness is 22.2, and the top five provinces are Guangdong, Shandong, Jiangsu, Henan and Tianjin. It can be seen that each region plays an important role as a bridge in different places in the network. The most innovative provinces are more likely to hold influential positions in the network [74].

The mean value of closeness is 25.74. Shandong, Jiangsu, Henan and Guangdong can quickly correlate with other provinces. Xinjiang is in the marginal position. In the spatial correlation of green innovation and R & D efficiency, the mean value of closeness is 33, and Guangdong, Shandong, Beijing, Jiangsu and Zhejiang provinces have a high value of closeness. The eastern region cannot quickly form a R & D cooperation relationship with the central region, and Xinjiang is a marginal region. In the spatial correlation of achievement transformation efficiency of green innovation, the mean value of closeness is 23.2. The coastal areas of Shandong, Jiangsu and Guangdong and the central areas of Hubei and Henan can rapidly form cooperation relationships of achievement transformation of green innovation. Ningxia and Xinjiang are categorized as the marginal areas. Henan and Hubei can quickly form cooperative relationship with other regions, although they are not the rapidly developing regions. This is similar to Su [75] who has confirmed that Henan is in the center of China’s pollution control network. The government can make full use of the characteristics of each region to build a platform for cooperation and exchange of green innovation among provinces, thus enhancing the driving and demonstration role of the cooperation.

4.4. Block Model Analysis

This article used the UCINET software to analyze the CONCOR block with the maximum density of 2 and convergence criteria of 0.2. Furthermore, 30 provinces were divided into four parts, as shown in

Table 7. Spatial correlation between two-stage green innovation efficiency blocks in China in 2019.

Innovation Stages	Plates	Proviences	Number of Accepted Correlation		Number of Emitted Correlation		Expected Internal Relationship Ratio (%)	Actual Internal Relationship Ratio (%)	Type of Plate
			Internal Plate	External Plate	Internal Plate	External Plate
Stage of green innovation and R & D efficiency	First	Beijing, Tianjin, Hebei, Shanxi, Inner Mongolia, Liaoning, Gansu, Qinghai, Ningxia	20	24	20	26	27.6	43.48	Net overflow plate
	Second	Shanghai, Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, Shandong, Henan, Hunan, Hubei, Guangdong, Shaanxi	112	35	112	33	37.9	77.24	Net benefit plate
	Third	Heilongjiang, Jilin and Xinjiang	2	1	2	1	6.9	66.67	Isolated people plate
	Fourth	Yunnan, Guangxi, Hainan, Chongqing, Sichuan, Guizhou	9	10	9	10	17.24	47.37	Broker plate
Stage of green innovation achievement transformation	First	Beijing, Tianjin, Hebei, Shanxi, Inner Mongolia, Gansu, Qinghai	15	15	15	14	20.69	51.72	Broker plate
	Second	Heilongjiang, Jilin, Xinjiang, Liaoning, Ningxia	3	1	3	0	13.79	100	Isolated people plate
	Third	Shanghai, Jiangsu, Zhejiang, Guangdong, Anhui, Fujian, Jiangxi, Henan, Hunan, Hubei, Yunnan, Guangxi, Hainan, Chongqing, Shandong	86	15	86	33	31.03	72.27	Net overflow plate
	Fourth	Shaanxi, Sichuan, Guizhou	9	26	9	10	24.14	47.37	Net benefit plate

. In the spatial correlation network of green innovation and R & D efficiency, the first plate includes 9 provinces such as Beijing, Tianjin, Hebei and part of the northwest regions, failing within the scope of net overflow plate. The second sector includes 12 provinces such as Shanghai, Jiangsu, Hunan, Hubei and some regions, all of which can be categorized to the net benefit plate. The third plate includes Heilongjiang, Jilin and Xinjiang, belonging the isolated people plate. The fourth plate includes Yunnan, Guangxi and some southwestern regions which are 6 provinces, belonging to the broker plate. In the spatial correlation network of transformation efficiency of green innovation achievements, the first plate includes 7 provinces such as Beijing, Tianjin and Hebei, together with some northwestern regions, all of which have been categorized to the broker plate. 5 provinces including Heilongjiang, Jilin and other regions are part of the second plate, belonging the isolated plate. The third plate embraces 15 provinces including Shanghai, Jiangsu, Hunan, Hubei, and other regions, belonging to the net spillover plate. The fourth plate includes Shaanxi, Sichuan and Guizhou, which belong to the net benefit plate.

The density matrix and image matrix are shown in

Table 8. Spatial density matrix and image matrix of green innovation efficiency in China in 2019.

	Plates	Density Matrix				Image Matrix
		First Plate	Second Plate	Thrid Plate	Fourth Plate	First Plate	Second Plate	Thrid Plate	Fourth Plate
Green innovation and R & D efficiency	First	0.278	0.231	0.037	0	1	1	0	0
	Second	0.213	0.848	0	0.139	0	1	0	0
	Third	0.037	0	0.333	0	0	0	1	0
	Fourth	0	0.139	0	0.3	0	0	0	1
Transforming efficiency of green innovation achievements	First	0.357	0.029	0.10	0.107	1	0	0	0
	Second	0	0.15	0	0	0	0	0	0
	Third	0.186	0	0.956	0.25	1	0	1	1
	Fourth	0.036	0	0.10	0.161	0	0	0	0

. In the green innovation and R & D efficiency, the central and southern coastal provinces in the second plate have strong internal R & D cooperation links. Beijing-Tianjin-Hebei region and the northwest region transfer relevant innovation elements to the central and southern coastal provinces with strong “siphon effect”. Those northeastern provinces in the third plate and part of the southwest provinces in the fourth plate have strong internal R & D cooperation relationships. In the transformation efficiency of green innovation achievements, the internal relationship between the first and the third plates is very close, which divides the transformation channel of green innovation achievements into two major positions, namely, the northern coastal region, the northwest region, the southern coastal region, the central and southern region. Moreover, the third plate forms an overflow connection to the Chengdu-Chongqing region and the northern region.

5. Analysis of Influencing Factors of Spatial Correlation Network of Regional Green Innovation Efficiency

5.1. QAP Correlation Analysis

A QAP correlation analysis was employed to determine whether there was correlation between explanatory variables and explained variables. UCINET software was applied to 5000 randomly selected substitutions to obtain correlation analysis results, as shown in

Table 9. Two-stage regression analysis of green innovation efficiency.

	Indicators		Geographic Adjacent	Industry Clustering	Environmental Regulation	Economic Development	Technology Market	R & D Investment	Enterprise Scale	Human Capital	Marketization	FDI	Transportation	Informatization
Stage
Overall stage of green innovation		Normalization coefficient	0.31	not related	−0.18	0.28	not related	−0.02	not related	not related	−0.13	not related	−0.03	not related
		significant	0.0001	not related	0.03	0.005	not related	0.39	not related	not related	0.07	not related	0.38	not related
Stage of green innovation R & D		Normalization coefficient	0.39	not related	−0.15	0.24	not related	−0.0008	not related	not related	−0.06	not related	−0.07	not related
		significant	0.0001	not related	0.024	0.003	not related	0.49	not related	not related	0.23	not related	0.20	not related
Efficiency in transforming green innovation achievements		Normalization coefficient	0.33	not related	−0.14	0.26	not related	not related	not related	not related	−0.17	not related	0.003	not related
		significant	0.0001	not related	0.09	0.01	not related	not related	not related	not related	0.02	not related	0.49	not related

. The overall efficiency of industrial green innovation and R & D efficiency of green innovation are correlated with geographic proximity, environmental regulation, economic development level, R & D investment level, marketization level and road network density, respectively. The transformation efficiency of industrial green innovation achievements is correlated with geographical proximity, environmental regulation, economic development level, marketization level and road network density, respectively.

5.2. QAP Regression Analysis

In the regression of overall efficiency of industrial green innovation, the standardized regression coefficients of geographical proximity, environmental regulation difference and economic level difference are 0.31, −0.17, and 0.27, respectively, which are significant at the level of 5%. Hypothesis H11, H12, and H7 are true. The stronger the geographical proximity, the more it can promote tacit innovation knowledge exchange, and the more likely it is to form the spatial correlation of high-reputation innovation cooperation. This result is the same as that of Yang and Liu [76]. Geographical proximity is an important factor affecting China’s innovation, and its green cooperation is more easily affected. If the difference in economic level is greater, it will be easier for developed regions with abundant innovation resources to cooperate with those with low independent innovation capacity.

In the process of creating innovation value, enterprises in areas with strict environmental regulations pay attention to their impact on the environment, showing differences with those with lax environmental regulations in terms of innovation ideas and marketing management, which inhibit the spatial correlation of innovation cooperation. The standardized regression coefficient of the differences in marketization level is −0.129, which is significant at the level of 10%. Hypothesis H10 is true. The large difference in marketization levels will make it difficult for innovation resources to be fairly traded in the market and hinder the formation of the spatial correlation of green innovation. In the regression of R & D efficiency of industrial green innovation, the standardized regression coefficients of geographical proximity, environmental regulation difference, and economic level difference are 0.385, −0.15 and 0.24, respectively, all of which are significant at the level of 5%. Hypothesis H11, H12, and H7 are true. The differences of marketization level, R & D investment difference, and road network density difference are however not significant. R & D input can guarantee the launch of innovation R & D activities, and road network density can enhance the accessibility of innovation resources, although marketization can quickly meet the supply-demand connection of innovation factors. Innovation R & D is essential to support R & D capability, and the three have no significant impact on the spatial correlation of green innovation and R & D efficiency. In the regression of transformation efficiency of industrial green innovation achievements, the standardized regression coefficients of geographical proximity, marketization difference, and difference in economic level are 0.33, −0.168 and 0.26 respectively, which are all significant at the level of 5%. Hypothesis H11, H10, and H7 are true. If the geographic adjacency and marketization difference are smaller, and the economic level difference is greater, it will be more conducive to the cooperation relationship of spatial space to the transformation efficiency of green innovation achievements. Environmental regulation difference of standardized regression coefficients is −0.14 at the 10% significance level. Hypothesis H12 is true. If the difference in environmental regulation level is smaller, it will be more likely to form spatial correlation of industrial transformation efficiency of green innovation achievement. Institutional proximity can weaken the dependence of innovation networks on permanent geographical proximity.

6. Conclusions and Enlightenment

6.1. Main Conclusions

This paper employs social networks to analyze the spatial correlation characteristics of green innovation efficiency in China from 2007 to 2019 and also to explore the influencing factors. The main conclusions are as follows:

In the green innovation efficiency, the eastern region > the western region > the central region. In the transformation efficiency of green innovation achievements, the eastern region > the central region > the western region. The closeness of spatial correlation network of two-stage green innovation is not that high. The spatial correlation network of green innovation efficiency and transformation efficiency of green innovation achievement is not strong. This is possibly because China is currently experiencing a stage of slowing economic growth, surging energy consumption and worsening environmental pollution, thus causing the low network density [77]. Therefore, it is necessary to pay more attention to green innovation. The robustness level of transformation efficiency of networked cooperation of green innovation achievements is high, but the rank degree is low. Hierarchical cooperation is stable in 2019, but network efficiency is lower. The strong hierarchical structure relationship for green innovation of R & D efficiency is collapsing, in which case regions are free to seek the best partnership and needs to control the number of partnerships. From the analysis of individual network characteristics, in the stage of green innovation R & D, Shandong, Jiangsu, and Guangdong are in the center of the network. Beijing is the international exchange center of scientific and technological cooperation. Zhejiang is building a high-level industry innovation platform. It can quickly form R & D cooperation relations with other regions. Zhejiang, Liaoning and Jilin have strong intermediary bridge functions. In the transformation stage of green innovation achievements, Shandong, Jiangsu and Henan are in the center of the network. Guangdong has strong economic and financial support, as well as superior institutional environment for innovation, and Hubei has a transportation hub connecting the east to the west and the south to the north. These two regions can rapidly develop R & D cooperation. Guangdong and Tianjin are bridge provinces to integrate innovation cooperation to enhance the leading role of such regions to other regions.

From the Block Model Analysis, the green innovation and R & D overflow plate in the northern coast and northwest region put innovation resources into southeast coastal regions, central and southern regions with a strong “siphon effect”. Under the internal relationship of the plates, innovative research and development resources will be quickly transformed into green innovation achievements, thereby gaining the green innovation value. Moreover, the spillover of green innovation achievements to Chengdu-Chongqing region and the northern region is isolated.

In the stage of green innovation and R & D, the closer the geographical proximity, the smaller the difference in environmental regulation, and the greater the difference in economic level. Therefore, it is more conducive to the formation of the spatial correlation of green innovation and R & D efficiency. In the stage of transformation of green innovation achievements, the results consist of those arising from the stage of green innovation and R & D. The smaller difference in marketization level is advantageous to spatial cooperation relationship of the transformation efficiency of green innovation achievements. Green innovation activities follow the rule of geographic adjacency, hierarchical diffusion rules of environmental regulation, and marketization level. However, the economic level does not follow the rules of hierarchical diffusion. Different from the research results, Hansen [78] found that institutional proximity could not replace geographical proximity, which is mainly because long-distance cooperation to overcome institutional differences would be different due to the disparate research scope. In the global innovation network, the institutional gap is difficult to bridge, and the policies of different countries are also diverse. However, different provinces in the same country share the same national framework, and even the proximity of institutional innovation in remote areas facilitates the formation of cooperative networks.

6.2. Policy Implications

(1)

We can build a reasonable cooperation relationship of a two-stage green innovation network. The government should be able to stabilize appropriately the level of structural relationship of green innovation and R & D network. The government should issue relevant policies to limit the number of green innovation R & D partnerships and improve the quality of partnerships. The central region should establish control centers of green innovation of R & D, so that it can quickly form a stable R & D cooperation relationship with the eastern region, and effectively drive R & D efficiency in the central region. Meanwhile, the regional transformation efficiency network of green innovation needs to limit the number of cooperative arrangements and improve the network efficiency. The central control position of each region should be strengthened.

(2)

We should be fully aware of the functions and network roles of green innovation in China, and formulate different green and innovative development policies according to regional characteristics. For isolated areas, the government needs to implement preferential policies to promote innovational relationship with other areas. We should actively set up research and development institutions in the western and northeastern regions. Meanwhile, efforts should be made to provide them with sufficient policy support and propel the formation of innovative cooperative relationships with other regions. It is important to remove their isolation. The southeast coastal region should take the initiative to cooperate in both the R & D stage and the achievement transformation stage. Its “siphon effect” attracts a large number of innovation resources in the northern region, especially in the northwest region. The green innovation R & D capacity and spillover effect of the southern coastal provinces and cities should be strengthened. The northern region should strengthen the industrialization of green innovation, and complete the cooperation and contact with the centrally controlled regions. Ultimately, China can realize the comprehensive regional green innovation development by point to block, thus efficiently integrating the innovational elements.

(3)

To optimize the construction of cross-regional green innovation network, it is necessary to follow the principles of geographical proximity and convergence of environmental regulations to further the spatial correlation and connection of green innovation and R & D efficiency. The difference in economic development level is conducive to the flow of innovation resources and boost the cooperation and connection of green innovation capabilities between regions. In addition, a reasonable market mechanism should be established to narrow regional gap in marketization level, and strengthen the circulation of green innovative products in regional markets. By optimizing the transmission mechanism of regional spatial correlation, the smooth cooperation and efficient integration of innovative elements between regions can be pushed to effectively propel the cooperation and connection of regional green innovation, and narrow the regional gap in green technology innovation.

6.3. Limitations and Opportunities

First, this study takes provincial-level data as the unit of research, which can further narrow the scope of research, such as city- and industry-level evaluation of efficiency. It may be more convincing to study the green innovation efficiency network. Second, the spillover effect of green innovation efficiency can only be analyzed by a block model in social network analysis. Finally, we take China as the empirical research object, but we can introduce other countries and regions, such as OECD countries. Moreover, we can study the innovative cooperation links among countries on an international scale in our subsequent studies.