China is a traditional agricultural country, agricultural technology is constantly improving, agricultural green and sustainable development is becoming increasingly important, and agricultural ecologization has attracted attention at state level (Huang et al., 2021). The government of China has emphasized agricultural ecological and environmental protection in the No. 1 document of the central government for several consecutive years. Therefore, based on the perspective of win-win economic benefits and environmental benefits, improving agricultural eco-efficiency (AEE) is critical for realizing sustainable agricultural development in China (Sun et al., 2017). Moreover, new policy incentives to ensure the sustainability of agriculture and ecosystem services will be crucial for meeting food demands (Tilman et al., 2002). This indicates that an improved understanding of agroecological sustainability can help to better address food security issues (Wu et al., 2022a). Furthermore, high-quality development has become a new requirement for China’s social and economic development (Wang et al., 2022). Thus, as a key indicator of high-quality agricultural development, related research on AEE is vital (Xing et al., 2018). The concept of eco-efficiency was first described by Schaltegger and Sturm in 1990 (Schaltegger and Sturm, 1990). The core of eco-efficiency lies in the introduction of economic and ecological dimensions in the context of production evaluation (Wang, 2011), and this emphasizes the unity of economic and environmental benefits such as maximizing output while minimizing resource consumption and environmental pressure (Yin et al., 2012). AEE is an important indicator of the level of sustainable agricultural development. It can be quantitatively analyzed and evaluated to allow for the effective utilization of agricultural production resources and efficient and sustainable development of agriculture. The first law of geography states that everything is related to everything else and that near things are more related than distant things (Tobler, 1970; Zhu et al., 2018). Likewise, space is highly consequential in environmental and resource economic analyses (Anselin, 2001). Therefore, this study not only considers the regional differences in AEE, but also the spatial correlation of AEE between regions. Furthermore, this study divides the time interval into sub-periods based on the FYP. Consequently, this study aids to better understand the dynamic changes in AEE and the structural changes in AEE driving factors, taking into account interregional differences and spatial linkages. Thus, AEE can be evaluated more scientifically and rationally, and appropriate countermeasures can be developed to promote sustainable development of agriculture.

AEE has always been an important area of research for numerous scholars both in China and abroad. The current research hotspots on AEE focus on two levels. The first is the measurement and spatial-temporal characteristic analysis of AEE. Currently, the common methods used for AEE evaluation include the stochastic frontier method and data envelopment analysis (DEA) method (Nie and Yu, 2017). DEA is a method for evaluating the relative efficiency of decision-making units and was proposed by Charnes, Cooper, and Rhodes in 1978 (Charnes et al., 1978). DEA has become the most commonly used method for evaluating AEE (Huang et al., 2018). In 2001, Tone (2002) constructed a DEA-SBM (DEA-Slack Based Measure) model that solved the problem of traditional models and gradually became the mainstream model for measuring eco-efficiency. Coluccia et al. (2020) determined that Italy had a relatively good AEE; however, there was still room for progress. Hou and Yao (2018) observed that the overall AEE in China existed at a relatively low level and exhibited a large potential for improvement, presenting higher levels in the eastern and western parts, but lower levels in the central part. Specifically, the overall level of AEE was low in Sichuan Province, China (Xiong and Xu, 2019). The average AEE exhibited a fluctuating growth trend with phase characteristics in Jilin Province, China (Guo et al., 2022). The overall trend of AEE in the Yangtze River Basin has increased annually (Hu et al., 2022). The development of AEE presented a spatial agglomeration in Anhui Province, China (Wu et al., 2022b). Although these studies have explored AEE at both spatial and temporal scales, most of them are limited to the spatial relations of adjacent regions, and the dynamic evolution process of the green development of AEE among the regions has not been fully elucidated. There are large differences in economic development, resource consumption level, and degree of environmental pollution among the different regions in China, and there is an interactive relationship between resource flow and interaction among different regions. Therefore, this study constructed an inter-provincial AEE spatial association network in China to explore the spatial flow of AEE among different regions and promote their sustainable and coordinated development. In addition, considering the influence of national policies and government macro-control on AEE in the previous single time scale, the time span of this study was divided according to the FYP.

The second hotspot involves analyzing the factors influencing AEE. Measuring the driving factors of AEE provides policymakers with important information for developing policies focused on sustainable management and the efficient use of natural resources in the agricultural sector (Carauta et al., 2022). Research on the factors of AEE has been conducted at the micro, meso, and macro scales in recent years (Maxime et al., 2006; Zhang and Qian, 2010). Owing to differences in agricultural development levels in various countries and regions, AEE is affected by different factors (Grovermann et al., 2019). At the national level, meso-scale studies, such as those conducted in Italy, on the sustainability of agricultural ecology can be provided by more ecological and friendly management of land use (Coluccia, et al., 2020). The agricultural sectors of some member states of the European Union (i.e., Austria, French, Germany, Portugal) have inefficient AEE because they use too much fertilizer (Rybaczewska-Blazejowska and Gierulski, 2018). Micro-scale studies have been conducted in the southern region of Portugal, and the use of organic fertilizers can reduce pollution and thus improve agricultural eco-efficiency (Maia et al., 2016). It can be concluded that most meso-scale studies on AEE focus on the measurement and decomposition of the driving factors of regional differences in AEE under a variety of methodological frameworks. Micro-scale studies generally focus on specific differences leading to regional AEE differences and propose corresponding suggestions and measures. Although China’s research on AEE started relatively late, it has achieved relatively rich research results. At present, there are various methods to explore the influence of AEE. Examples include the Tobit model (He et al., 2021); and the geographic detector model (Shu et al., 2022). In particular, it is necessary to pay attention to the key indicators for improving AEE (Wang, et al., 2022). Moreover, different indicators have different effects on AEE in different regions. At the regional level, the development of urbanization can promote the improvement of AEE in China’s main grain-producing areas (Shang et al., 2020). AEE increased with greater crop diversity in Northeast China, but the effects were reversed elsewhere (Zeng et al., 2020). Water resource, pesticide, and labor inputs are significant controlling factors affecting the spatial differentiation of AEE in eastern, central, and western China (Liao et al., 2021). Agricultural mechanization and government regulation have positive effects on agricultural eco-efficiency in the Yangtze River Economic Belt (Cao and Zeng, 2019). Thus, most of the discussions on the influencing factors of AEE in the existing research are limited to the regional internal, without considering that owing to the mobility of inter-regional resource elements, the development of AEE in the region is not only affected by the internal factors of the region, but also by other regions. A multidimensional proximity framework is mainly used to discuss the influencing factors in the flow process of resource elements, which is defined as a ‘class’ or ‘group’ of characteristics common to different network subjects (Boschma, 2005). Presently, proximity analysis is used in many areas. Examples include innovation and inter-city scientific collaboration (Caragliu and Nijkamp, 2016). However, few studies have used multidimensional proximity in analyses related to AEE. Thus, it is essential to construct a multidimensional proximity framework to analyze the factors influencing the formation of the AEE network. Therefore, geographical, economic, technological, institutional, and cognitive proximities were introduced to construct a multidimensional proximity network to analyze its influence on the inter-provincial AEE spatial relation network.

In view of this, the FYP in China was used to divide the time interval into sub-time segments in this study. This is useful for advancing the understanding of the influence of national macro-control on AEE. The aim of this study was to evaluate the AEE of different provincial regions in China using a spatial correlation network and explore the driving factors of AEE in various provincial regions based on a multidimensional proximity framework. These efforts will help provide a scientific basis for increasing AEE and decreasing regional differences in agricultural development. They can also assist with the formulation of localized policies that coordinate agricultural growth with the development of resources and environmental protection.

The Super-SBM (Super-Slack Based Measure) model was selected to calculate the AEE values of 31 provincial regions in China from 1997 to 2019. Data do not include Hong Kong, Macao and Taiwan of China due to incomplete data

Suppose there are H DMUs (Decision Making unit), each DMU exhibits M types of investment, R₁ types of expected outputs, R₂ types of unexpected outputs, the AEE_i is agricultural eco-efficiency values, and the Super-SBM model can be expressed as (Tone,2002):

where $ {w}_{i}^{-} $, w^d, and w^u represent the amounts of slack in investment, expected outputs, and unexpected outputs, respectively. λ represent the weight vector. x_i, y^d, and y^u represent the vectors of investment, expected outputs, and unexpected outputs, respectively. x₀, y_s0, y_q0 represent the vectors of investment, expected outputs, and unexpected outputs of every DMU, respectively. i denotes the investment type. j stands for the DMU.

According to the requirements of sustainable agricultural development in China and the actual situation, the purpose of AEE is to achieve maximum output with the smallest input. In reference to existing research (Liao et al., 2021), in this study, a set of AEE index systems that selects eight types of input indices for agricultural production. Additionally, the total output value of agriculture represents the expected output index of agricultural production, agricultural carbon emissions are used as the poor output index of agricultural production in the agricultural production stage, and the agricultural carbon emission estimation method uses the carbon emission index multiplied by the corresponding coefficient (Li et al., 2016). The AEE index system in China is presented in Table 1.

The gravity model first proposed by Stewart (1948) and more recently employed by Ullman (1958) for spatial correlation was not only more suitable for aggregate data but was also better able to comprehensively consider economic development, distance, population, and other factors when describing the relationships between two regions. This model can also use cross-sectional data to reflect the evolutionary trends in the spatial correlation network (Liu et al., 2015). Therefore, we applied the gravity model and introduced the AEE values measured using the Super-SBM model. The gravity coefficient K is modified by using the proportion of the AEE value of a region to the sum of the AEE values of the two associated regions. Concurrently, the distance between the two associated regions is represented in terms of geographical distance (the longitude and latitude distance of the geometric center of gravity of each region) and time cost distance (railway mileage between cities divided by average speed per hour). In this manner, an AEE spatial correlation network was constructed.

The improved gravity model is as follows:

where P_ij was the gravity between regions i and j；POPU_i，POPU_j, AEE_i, AEE_j, GDP_i, and GDP_j are the total urban population, the level of AEE, and the gross regional product of regions i and j, respectively; K_ij is the contribution rate of region i to the AEE connection between regions i and j; D_ij is the distance between regions $ i $ and $ j $.

According to Eq. (5), the gravity matrix of the AEE correlation intensity can be obtained. The average value of each gravity matrix row was used as the critical value. It was set to 1 if the value was greater than the critical value and indicated that there was a AEE relationship between the row and column regions, and it was set to 0 if the value was less than the critical value and indicated that there was no AEE association between the row and column regions (Liu et al., 2015).

Social network analysis is a method used to describe the relationship between ‘individual’ and ‘whole’ in the network, as well as the structural characteristics of the network. To more clearly reveal the structural characteristics of the inter-provincial AEE-related network in China, the parameters network density and connectedness (Freeman et al., 1979) were chosen as the measure of the overall network structure. The characteristics of an individual network primarily focus on the status and role of each member in the network through centrality, including degree centrality, betweenness centrality, and closeness centrality (Freeman, et al., 1979). Block model analysis is a method used to analyze the location characteristics of network nodes (White et al., 1976). In reference to the definition and classification standards of existing studies (Li et al., 2014), this study divides the blocks in China’s AEE network into four types: net spillover block, net benefit block, broker block, and bidirectional spillover block. In the net spillover block, the number of sending relations in the block is far greater than the number of receiving relations, and the number of sending relations in the net benefit block is far less than the number of receiving relations. The broker block, in which the number of sending relations is greater than that of the receiving relations, acts as an intermediary and bridge in the network. In the bidirectional spillover block, the number of relations sent to others is not significantly different from those that are received (White, et al., 1976).

In this study, the correlation network of AEE is used as the dependent variable, that represents the binary relationship between regions, and the independent variable must also be measured as a binary relationship (Yu and Yan, 2017). When regions possess similar attributes, interaction and learning become easier (Boschma, 2005). This study constructed a multidimensional proximity framework based on geographical, economic, technological, institutional, and cognitive proximities for research purposes and analysis.

(1) Geographic proximity represents the spatial distance of each node within the cooperative network. In this study, the spherical distance between the two provincial capitals was chosen to measure the degree of geographical proximity between regions (Wei and Yu-sung, 2013).

(2) Economic proximity represents the differences in economic development levels between regions. This study measures the degree of proximity of the economic development level to the gross local product of a region. Its calculation is:

where e_i and e_j represent the GDP values of i and j, respectively, and E_ij is the economic proximity between regions i and j.

(3) Technology proximity represents the relevance and similarity of different subjects in terms of cognitive basis and technological structure. In this study, the Jaffee index was used to measure the degree of technological proximity (Jaffe, 1986), and is calculated as:

where k represents the number of people employed in different industries, k = (1,…, m). Industry classification adopts the National Economy Industry Classification of China (GB/T 4754−2017) (Li et al., 2021). Therefore, m = 3. F_ki and F_kj represent the number of employees in industry k in regions i and j, respectively, and T_ij is the technology proximity between regions i and j.

(4) Institutional proximity represents the similarity between different subjects that are constrained to certain rules (Xia et al., 2017). It is calculated as:

where w_i and w_j represent the total expenditure of agriculture, forestry, and water affairs in regions i and j, respectively; v_i and v_j represent the total expenditure of local finance of region i and j, respectively, and I_ij is the institutional proximity between regions i and j.

(5) Cognitive proximity indicates the similarity degree of subjects in regard to the knowledge base, technological structure, cultural customs, and other aspects and describes the similarity of human capital between provincial regions. In this study, the average years of education were used to measure the degree of cognitive proximity between regions (Barro and Lee, 2001). Its calculation equation is:

where edu_i and edu_j are the average years of education in regions i and j, respectively; u_i is the proportion of the population educated to university level in region i; u_i is the proportion of the population educated to senior high school level; j_i is the proportion of the population educated to junior middle school level; p_i is the proportion of the population educated to the primary school level. Therefore, C_ij is the cognitive proximity between regions i and j.

Our data sources include 31 provincial regions in China (excluding Hong Kong, Macao, and Taiwan) for the network nodes, the time span of 1997−2019, AEE level measurement indicators involved, and gravity model variables that included data derived from the corresponding years from the National Bureau of Statistics (2019a, 2019b), and the annual provincial data from the National Bureau of Statistics data website (https://data.stats.gov.cn/).

The Super-SBM model was used to measure the AEE values of 31 provincial regions in China from 1997 to 2019. Based on the National Geographic Subdivision (Cheng et al., 2019) (Fig. 1), the ecological level of the region is represented by the mean AEE of the provincial regions within the region that the FYP was selected as the basis of the research period division. The results are presented in Fig. 2.

Figure 1.  Geographical information about the seven regions in China

Figure 2.  Agricultural eco-efficiency (AEE) in different regions of China from 1997 to 2019. FYP stands for Five-Year-Plan; Data do not include Hong Kong, Macao and Taiwan of China due to incomplete data

It was shown that the national AEE had increased from 1.1937 in 1997 to 1.2024 in 2019. It illustrated that AEE is strengthening in general, but its change process is volatile. More specifically, during the period from the 9th FYP to the 10th FYP, the average value of AEE in South China decreased significantly from 1.5821 to 1.2522, and that in Northwest China decreased significantly from 1.4530 to 1.3495, after which they all maintain the trend of steady increase. In the 11th FYP to 13th FYP period, all regions show a more stable growth trend. And the average value of AEE in North China increased significantly from 1.0996 in the 12th FYP period to 1.2450 in the 13th FYP period. The results indicated that the AEE values fluctuate and improve nationally as well as regionally, driven by a series of agricultural development measures and national incentives.

From 1997 to 2019, the AEE value exhibited a phasic feature in accordance with a national economic plan in time and space. During the 9th FYP period, South China, such as Guangdong, has a more developed economic level, has a greater development location advantage, and the growth rate of AEE is faster. Guangxi has a vast territory, superior natural water and heat conditions, great potential for comprehensive agricultural development, and broad prospects for economic development. During the 10th FYP period, South China and Northwest China showed a significant downward trend, while all other regions maintained a stable development trend. The 10th FYP period is an important foundation period for Guangdong to adapt to the new situation of joining the World Trade Organization. Therefore, the AEE value of this period shows a decreasing trend. During the 11th and 12th FYP periods, agricultural development also entered the post-agricultural tax period, with obvious progress in agricultural modernization and a significant increase in comprehensive agricultural production capacity, and thus the AEE was again improved. During the 13th FYP period, agricultural energy-saving and emission reduction measures were further strengthened. There are large regional differences in the efficiency of agricultural production. North China shows a significant growth trend. Clearly, national policy incentives have become an important driver of AEE development (Barro and Lee, 2001). In particular, the implementation of market mechanisms for agricultural products, the abolition of agricultural taxes, and the increase in agricultural subsidies have all led to continuous changes in AEE in time and space (Wagan et al., 2018).

To further reveal the spatial and temporal patterns of AEE evolution, ArcGIS software was used to determine the spatial distribution trends of inter-provincial AEE in China, as shown in Fig. 3. Using the due east direction as the X-axis, the due north direction as the Y-axis, and the vertical direction as the Z-axis, the vertical lines in space represented the AEE values and provincial locations of each provincial region, and the two trend lines were fitted lines of points in space that projected toward the X-Z and Y-Z planes, respectively. If the two trend lines are parallel to the X-Y plane, there is no spatial divergence characteristic of AEE. Here, the trend lines were obviously inclined or curved, thus indicating that there is a certain spatial divergence characteristic.

Figure 3.  China’s agricultural eco-efficiency (AEE) spatial trend of China in 1997−2019. Notes: X refers to an easterly direction, Y refers to a northerly direction, Z refers tothe vertical direction. The black lines represent the AEE values, the green and blue curves represent the trend of AEE values in X-Z and Y-Z planes, respectively. FYP stands for Five-Year-Plan. Data do not include Hong Kong, Macao and Taiwan

The results revealed that the spatial distribution pattern of AEE in China was high in the west and low in the east, high in the south and low in the north. From the perspective of periods, the ‘U’ shaped trend from east to west in the 9th FYP period is not obvious, and the curve is relatively smooth. From the 10th FYP to the 13th FYP period, the ‘U’ shaped trend from east to west gradually becomes obvious, while the trend from south to north gradually disappears, thus highlighting the trend of high in the south and low in the north. The analysis further confirms that the AEE of China exhibits certain spatial differentiation characteristics, and the development of different provincial regions is not balanced.

According to the gravitational value of the inter-provincial AEE in China can be obtained. The spatial correlation network of AEE in China from 1997 to 2019 can be obtained as shown in Fig. 4.

Figure 4.  Spatial correlation network for China’s agricultural eco-efficiency (AEE) in 1997−2019. FYP stands for Five-Year-Plan. Data do not include Hong Kong, Macao and Taiwan

Specifically, from 1997 to 2019 the spatial association of inter-provincial AEE in China has become increasingly close. During the period of the 9th FYP and the 11th FYP period, Tibet possessed no spatial connection with other provincial regions, and it did not exhibit spatial connection with other provincial regions until the 12th FYP period. Xinjiang also developed from only one connection during the 9th FYP period to multiple connections during the 13th FYP period. Moreover, the provincial regions possessing larger gravitational values of AEE are concentrated in Northeast and East China, particularly between Hebei, Beijing, Tianjin, Jiangsu, Anhui, Shanghai, Zhejiang, and Hunan. The gravitational values for AEE among these provincial regions all presented as large values and maintained a steady growth trend during the period of the 9th FYP to the 13th FYP. The Northeast China region possesses superior hydrothermal conditions and a larger scale of agricultural production and irrigation. Additionally, agricultural production is more sensitive to climate, policy, and economy, and the AEE values fluctuate more. The economic development of East China is more rapid, and the process of agricultural modernization is accelerated. Thus, the progress of AEE is faster. In summary, the spatial correlation network of AEE in China exhibits the spatial distribution characteristics of dense in the east and sparse in the west.

This study investigated the overall structural characteristics of the spatial network of AEE in China from spatial correlation intensity and connectedness.

From the perspective of spatial association strength (Fig. 5a), the changing trend of network density and network relationship is highly consistent. During the 10th FYP period, there was a large upward trend. During the 11th FYP and 12th FYP, a stable and declining trend of fluctuation was observed. The government still attached great importance to the issues of agriculture, rural areas and farmers. In 2006, the agricultural tax was completely canceled, and agricultural development entered the post-agricultural tax period. During the 13th FYP period, there was an upward trend. During this period, the guiding role of the government was reflected in guiding the behaviors of market subjects. Additionally, the Ministry of Agriculture of China issued ‘the 13th FYP Development Plan for the Development of National Agricultural Mechanization’ that played a positive role in further strengthening the AEE. Specifically, both government macro-control and policy incentives contributed to the formation and development of inter-provincial AEE spatial correlation networks in China.

Figure 5.  Spatial correlation network of China’s agricultural eco-efficiency (AEE) based on intensity (a) and connectedness (b) respectively in 1997−2019. FYP stands for Five-Year-Plan. Data do not include Hong Kong, Macao and Taiwan

From the perspective of spatial network connectedness, the AEE network showed a close relationship between agricultural ecological development among provincial regions in China with obvious spatial correlation and spillover effects. The network hierarchy fluctuated from 0.3483 in 1997 to 0.1269 in 2019 (Fig. 5b). During the 10th FYP period, the network hierarchy dropped significantly, and this corresponded to a sharp increase in network density as shown in Fig. 5a. The network density of the AEE network of China increased, the hierarchical structure decreased, and it was easier to establish more connections between provincial regions. The network hierarchical structure maintained a basically stable level during the 11th FYP and 12th FYP, and during this period, the network efficiency exhibited a fluctuating downward trend, thus indicating that the inter-provincial AEE network correlation possessed an upward trend. During the period of the 13th FYP, the spatial connection of AEE was closer and more stable. This demonstrates that the overall regulation of the government and the implementation of relevant agricultural policies have played a positive role in promoting the formation of the spatial correlation network in China.

(1) Degree centrality

Fig. 6a reveals that from 1997 to 2019, Henan, Shandong, Jiangsu, Hubei, Guangdong, and Hunan were all at the center of the AEE correlation network and possessed high node centrality. Moreover, most of these provincial regions are located in Central, East and South China. In Central China, due to the flat regional topography, good soil and water conditions, and sufficient labor force, the level of agricultural production and the process of agricultural modernization were synchronized. Based on the marked changes in agroclimatic resources and socio-economic environment, the growth rate of AEE in South China was more rapid. With the economic development in the eastern part of China, the process of agricultural modernization is accelerated, and the growth of AEE is faster. This is all consistent with the conclusion of the above analysis of the changing trend of AEE in each region. Further analyses were carried out to calculate the net indegree values (indegree values minus outdegree values) of each provincial region (Table 2).

Figure 6.  Spatial correlation network of China’s agricultural eco-efficiency (AEE) based on centrality. a. Degree centrality; b. Betweenness centrality; c. Closeness centrality. FYP stands for Five-Year-Plan. Data do not include Hong Kong, Macao and Taiwan. The larger the circle of the node in the network is, the darker the color is, indicating the greater the centrality value of the node in the network. The thicker the lines between nodes are, the more important the nodes are in the network

From the direction of correlation (Table 2), the provincial region with a positive net indegree values were mostly located in the northern, southern, and eastern China such as Hebei, Guangdong, Jiangsu, Shandong, and Henan, thus indicating that these provincial regions possess a strong absorption capacity for AEE development, a high level of economic development, superior natural conditions, and a strong position in the development of agricultural modernization and agricultural mechanization processes. The level of eco-efficiency of these regions is relatively high, and a stronger absorption capacity further helps the regions themselves to improve and develop ecologically. Most of the provincial regions possessing a negative net indegree values were located in the southwest and northwest regions such as Sichuan, Guizhou, Yunnan, Heilongjiang, Jilin, and Liaoning. The economic development of the central and western regions and the northeast region was relatively backward despite the observation that they possessed more land resources and better water and heat conditions. Additionally, the development of agricultural mechanization and agricultural modernization level was relatively backward however, they could easily establish connections with more regions, and this helped to improve the eco-efficiency level of the region. A stronger radiation capacity result in more obvious AEE advantages.

(2) Betweenness centrality

Betweenness centrality reflects the ability of each provincial region to control agricultural ecological resources. Provincial regions possessing higher betweenness centrality also exhibit a higher level of eco-efficiency, thus indicating that nodal provincial regions can benefit from their ‘throat’ status in the critical path of network resource flow. As presented in Fig. 6b, the betweenness centrality in each provincial region varied significantly during the five periods. During the 9th FYP period, the provincial regions that played a pivotal role in the spatial network of AEE included Henan, Hubei, Shandong, Guangdong, Hunan, and Sichuan, and these were located in different regions such as East China, South China, Southwest China, and Central China, thus indicating that these provincial regions played an important role in different regions. From the 10th FYP to the 13th FYP, the release and implementation of agricultural policies and the unified macro-control of the government ensured that new provincial regions such as Shaanxi and Liaoning were added as central provincial regions to control the flow of agro-ecological resources, and the gap between the betweenness centrality values of provincial regions gradually narrowed, thus indicating that more regions were involved in the flow and transmission of agricultural resources in the spatial correlation network of AEE. This indicated that the degree of networking of AEE correlation networks in China was increasing and that the structure of the correlation networks changed from monocentric to polycentric.

(3) Closeness centrality

Closeness centrality in relation to the center can allow researchers to judge the degree of difficulty in generating the spatial correlation of AEE among provincial regions, as shown in Fig. 6c. Provincial regions possessing higher closeness centrality were located at the center of the AEE correlation network and played the role of central actors in the overall network. Specifically, these provincial regions can connect with other provincial regions more quickly. For example, Zhejiang, Fujian, Guangdong, Guangxi, Sichuan, Hainan, and other provincial regions were distributed in the southwestern, southern and eastern China where there are abundant amounts of water and heat, superior natural conditions, rich land resources, and higher levels of economic development, and this is consistent with the above analysis of degree centrality and betweenness centrality. However, the provincial regions possessing lower closeness centrality were characterized as marginal actors in the association network.

Provincial regions within the same block possess similar functions, and there are spillovers of AEE both within and between blocks. Table 3 illustrates the relationships within and between blocks in the spatial association network of AEE and also the role and function of each block in each period. According to the previous calculation results, for five periods the density of the spatial association network of AEE were 0.313, 0.313, 0.322, 0.314, and 0.315, respectively, and the number of network relations were 291, 291, 299, 292, and 293, respectively. This indicates that there are obvious spatial correlations and spillover effects among the various blocks in the correlation network.

The spatial AEE of each period was divided into four blocks, and the relevant features within and between blocks were analyzed (Fig. 7).

Figure 7.  Transmission relationship among the four blocks of agricultural eco-efficiency (AEE) correlation network in 1997−2019. FYP stands for Five-Year-Plan. Data don not include Hong Kong, Macao and Taiwan

During the 9th FYP period, block Ⅰ belongs to the broker block. The members of this block were predominantly distributed in North and Northeast China. The number of relationships that block Ⅱ received from ther blocks was significantly higher than the number of relationships that it spilled out. The spillover effect of block members was relatively limited, and thus the block was characterized as a net benefit block. Most members of this block are distributed in East China. Block Ⅲ not only received the spillover from other blocks but also has exerted spillover effect on other blocks. The spillover relation-ship to other blocks was greater, and based on this, the block was characterized as a bidirectional spillover block. The members of this block are predominantly distributed in the northwestern region. Block Ⅳ exhibits more spillover relation to other blocks and less spillover relation to receiving other blocks, and the actual internal relation proportion for this block was the smallest. The net spillover effect within the block is obvious, thus indicating that the block is a net spillover block. The members of this block were predominantly distributed in Central China, Southwest China, and South China. During the 10th FYP period, the net spillover block and bidirectional overflow block changed roles, while the remaining blocks remained unchanged. Specifically, as the blocks change, the roles of the provincial regions they include also change. During the 11th FYP period, the bidirectional spillover and broker blocks exchanged roles. During the 13th FYP, significant changes occurred among the blocks. The roles of the net spillover block and the bidirectional spillover block changed, the net benefit block expanded, and the number of provincial regions this block contained increased. The broker block was smaller and contained fewer provincial regions. During the 13th FYP, block Ⅰ was distributed in Northeast China and North China. The advantage of land resources in Northeast China was obvious, and the level of agricultural modernization in North China developed rapidly. Agricultural element resources were concentrated in the interior of the block, and this contributed to the development of green agriculture.

Further analysis of the inter-block relationships and the spillover effects of AEE identified the density matrix and the image matrix of the spatial correlation network of AEE (Table 4). From the image matrix, we can visualize the correlation relationship and transmission mechanism that exist between the blocks of the inter-provincial AEE correlation network, and we can draw the spillover effect map from these data (Fig. 7) using different colors to indicate different blocks on the map, and using the same color to indicate the same block in different periods. Thus, we can more clearly express the evolutionary process of each block.

All the elements on the diagonal of the image matrix were 1, thus indicating that there was a significant correlation between the AEE in each block and that the club clustering effect was produced. Specifically, from the 9th FYP to the 13th FYP period, each block exhibits its own internal correlation. During the 9th FYP period, block Ⅰ exerted a spillover effect to block Ⅱ, block Ⅲ exerted a spillover effect on block Ⅱ and block Ⅳ, and block Ⅳ also exerted spillover effects on block Ⅱ. Based on this, it was clear that block Ⅱ could be characterized as the net benefit in the correlation network. The correlation between the blocks in the 10th FYP was consistent with that in the Ninth FYP. During the 11th FYP, based on the previous network correlation relationship, the spillover effect of block Ⅳ to block Ⅱ was increased. This was the period when the agricultural tax was abolished and macro-regulation to promote agricultural development was actively promoted, and based on this, the inter-provincial correlation also increased significantly. During the 13th FYP, the correlation between the blocks was closer. Block Ⅲ built an overflow relationship with block Ⅰ and block Ⅱ through the transmission function of block Ⅳ. Therefore, block Ⅳ played an intermediary role in the correlation network. Overall, during the development of inter-provincial AEE spatial association patterns in China, the association and spillover effects within and among each block were increasing, and its internal club clustering effect was obvious, where each block possessed its own advantages and assumed its own role in the association network. This highlighted the linkage of the common development effect.

The correlations between the independent variables from 1997 to 2019 were analyzed in this study, and the results are presented in Table 5.

The results revealed that there is a significant positive correlation between economic, institutional, and technological proximities during the period from the 9th FYP to the 13th FYP. Technological proximity exhibited a significant positive correlation with institutional proximity, thus indicating that the technological level of regional development is increasingly matched with the financial resources provided by the government. Technological proximity possessed an increasingly significant positive correlation with cognitive proximity, thus suggesting that similarity in education levels is likely to hinder the development of similar technologies between provincial regions. Geographic proximity exhibited a significant positive correlation with institutional proximity, thus suggesting that geographic proximity leads to similarity in the orientation of the government toward resource provision. Geographic proximity possessed a significant negative correlation with cognitive proximity, thus suggesting that increased geographic distance leads to variability in education levels.

The multidimensional proximity matrix and the spatial association matrix of inter-provincial AEE in China for the above five periods were randomly replaced 2000 times, and the regression results for the three periods are presented in Table 6. The regression results revealed that from the 9th FYP period to the 13th FYP period, the geographic proximity of the regression coefficient was significantly negative, thus indicating that geographic distance on the provincial agricultural eco-efficiency weakens the effects of contact strength and that the provincial regions were more likely to exhibit stronger spatial correlations with areas closer to them in regard to AEE green development. The regression coefficient of economic proximity was significantly positive, and this indicates that provincial regions possessing higher economic level development and larger development scales are more likely to establish spatial linkages of AEE with each other. The regression coefficient of technological proximity changes from negative to positive, and this indicates that during the development process, different provincial regions develop and utilize different agricultural technologies according to local natural resources and land conditions, thus suggesting that the process of developing technologies for different types of agriculture may be very different. Thus, provincial regions that develop similar agricultural technologies exchange and learn from each other, and this strengthens the spatial correlation of their AEE. The regression coefficient of institutional proximity was significantly positive in the 13th FYP period after the abolition of agricultural tax and the enactment of macroeconomic regulation by the national government, and policy incentives, thus indicating that the green development and exchange of AEE between the two provincial regions was strengthened based on the knowledge that provincial regions implementing similar policies tend to learn from each other. The regression coefficients of cognitive proximity were not significant in all five periods, thus indicating that the similarity of cognitive levels between provincial regions does not influence and affect the spatial association of green development of AEE. Therefore, it was suggested that the combination of geographic, economic, technological, and institutional proximities contributed to the formation and development of inter-provincial AEE correlation network in China.

This paper has explored the spatio-temporal evolution of the AEE. Although relevant researches have been carried out (Yuan and Zhou, 2021), there are still some innovations made in our study. Firstly, this study introduced the improved gravity model to construct a spatial association network of inter-provincial AEE in China, which differs from the nonlinear Granger causality teat approach by Zheng and Huang (2021). Second, this study also provides a new perspective on the analysis of the spatio-temporal evolutionary characteristics of AEE spatial association networks based on existing research Zheng and Huang (2021) with dividing the research period into five periods according to the FYP, and can provide more comprehensive and specific targeted suggestions for agricultural policy formulation (Deng and Gibson, 2019). With the increasing improvement of China’s agricultural market system, the spatial cross-regional flow and interoperability of agricultural production factors tend to be obvious (Wu, 2010). Therefore, provincial AEE depends on both local agricultural mechanization level, agricultural financial input, industrialization level, planting structure, and the influences from other provincial regions. Thus, this study investigated and analyzed the specific factors affecting the formation of AEE network from a new perspective of multidimensional proximity, and then the AEE value could be increased through cross-regional correlation relation-ships. Regional innovation spatial correlations are closely related to proximity, which is defined as common ‘class’ or ‘group’ characteristics in different network subjects. Multidimensional proximity is mostly applied to studies on import/export trade (He and Yu, 2022), urban innovation (Zhou et al., 2021), and population mobility (Zhuo et al., 2021). At present, few studies have examined the specific factors influencing the formation of AEE networks from a multidimensional proximity perspective, so this study has important applications for formulating and implementing policies related to the development of AEE in each region and constructing cross-regional collaborative agricultural production.

Due to the differences in regional resource endowments, agricultural production development, and industrial policies, obvious inter-provincial differences existed in the spatial and temporal evolution of AEE in China. South China and Northwest China reached the peak value of the study period in the 9th FYP. During the 13th FYP period, North China shows a significant growth trend. Therefore, when formulating agriculture-related policies, we should continue to strengthen the agricultural foundation, continue to adjust and optimize the structure of agriculture and rural industries, face the market, rely on science and technology, and take the road of agricultural industrialization (Liu, 2018). Agricultural modernization still faces difficulties in regard to resource conservation and environmental protection. Therefore, the future national agricultural policy should be based on stimulating the vitality of agricultural development while compensating for the regional disadvantages of agricultural development with the strategies of precise poverty alleviation and rural revitalization and on providing full accessing to the backward advantages in the agriculturally backward areas (Liu and Li, 2017).

And we need to improve the efficiency of agricultural resource use while also focusing on the development of ecological environmental protection level (Li et al., 2019). Therefore, agricultural policies were formulated to achieve intensive and sustainable development while continuously improving the land output rate, resource utilization rate, and labor productivity. Special emphasis was placed on building resource-saving and environment-friendly agriculture, Specifically, they focused on two-oriented agriculture, where the new concepts and models of circular agriculture, ecological agriculture, and intensive agriculture are explored by focusing on changing the agricultural development mode and impro-ving the efficiency of resource utilization and ecological environmental protection. AEE is an effective indicator for evaluating the stability and sustainability of agricultural ecosystems. Improving AEE was the target of green and sustainable agricultural development, and it is of key importance to make scientific decisions according to local conditions and agricultural regional types.

This study determined that provincial AEE also had spillover effects, and analyzed the structure and factors influencing the formation these inter-provincial AEE correlations. From 1997 to 2019, there were significant spatial association and spillover effects in China’s AEE, and the network density was increased, but still only 0.318 in 2019. Therefore, the promoting of closer inter-provincial communication and collaboration must still be improved. The spatially associated network possessed improved accessibility, and the network hierarchy and network efficiency were decreased in fluctuation to result in gradual breaking of the hierarchical spatial network structure. This is revelant with the stability of the network structure and the multiple superposition phenomena of spillover effects. The evolution of the AEE network exhibited obvious trends of hierarchization and aggregation, and the complexity of the network continued to escalate. The spatial correlation network structure possessed the spatial aggregation characteristics of dense in the east and sparse in the west, and the network structure changed from monocentric radial to polycentric network where the network nodes chose the more advantageous node with which to connect.

During the spatial and temporal evolution of the AEE spatial correlation network of China, the role played by each provincial region in the network changed in northern, southern, and eastern regions of China such as the Hebei, Guangdong, Jiangsu, Shandong, and Henan. Specifically, these provinces exhibit a strong absorption capacity for agricultural ecological development. These regions possessed a high level of economic development and superior natural conditions, and their levels of agricultural modernization and agricultural mechanization existed in a relatively strong development position. The higher the level of eco-efficiency of these areas and the stronger their absorption capacity, the more they can contribute to the improvement and development of their own AEE greenery. Provinces such as Henan, Hubei, Shandong, Guangdong, Hunan, and Sichuan that are located in different regions of East China, South China, Southwest China, and Central China played a central role in the spatial network of AEE.

The driving factors of AEE networks are discussed from the perspective of multidimensional proximity, which exerts a significant negative effect on the development of the AEE spatial correlation network among provincial regions. Economic, technological, and institutional proximity have significant positive effects on the development of association networks. Cognitive proximity did not significantly affect the development of the association networks.