Decoupling Effect, Driving Factors and Prediction Analysis of Agricultural Carbon Emission Reduction and Product Supply Guarantee in China

: Under the requirements for high-quality development, the coordinated promotion of agricultural carbon emission reduction and agricultural product supply guarantee in China is crucial to hold the bottom line of national food security as well as promote agricultural green transformation and development. Based on such situation, from the perspective of decoupling effect, driving factors and the prediction, this paper uses panel data of 30 provinces in China from 2011 to 2020, takes the carbon emission formula, the “two-stage rolling” Tapio decoupling elasticity coefﬁcient method, the spatial Durbin model and the Grey model optimized by the Simpson formula background value to quantify the relationship between agricultural carbon emission and agricultural product supply, analyze the driving effects of agricultural carbon emission reduction and agricultural product increase, and predict the decoupling state of agricultural carbon emission and agricultural product supply between 2021 and 2025, so as to draw a scientiﬁc basis that is conducive to the coordinated promotion of agricultural carbon emission reduction and agricultural product supply guarantee in China. The result shows that: (1) The decoupling state of agricultural carbon emission and agricultural product supply shows generally “the eastern and central regions are better than the western regions” in China, and the decoupling state has improved signiﬁcantly year by year. Green technology innovation (GTI), agricultural carbon emission and agricultural product supply in China have signiﬁcant spatial differences and spatial auto-correlation, which shows the spatial factors cannot be ignored; (2) Green technology innovation and agricultural carbon emission in local and adjacent provinces are both in an inverted “U-shaped” relationship, meaning that high level green technology innovation is an effective way to reduce carbon emission. Though green technology innovation and agricultural product supply in local and adjacent provinces are both in a positive “U-shaped” relationship, but the minimum value of lnGTI is greater than 0, which indicates that current level of green technology has been raised to a certain level, effectively improving the output of agricultural products; (3) Compared with those in 2016–2020 in China, it is projected that in 2021–2025 the decoupling state of agricultural carbon emission and agricultural product supply will be improved signiﬁcantly, and the provinces below the optimal state will leave the extremely unreasonable strong negative decoupling state, mainly show recessionary decoupling and recessionary connection. Our ﬁndings provide Chinese decision-makers with corresponding references to formulate accountable and scientiﬁc regional policies in order to achieve high-quality development of agriculture and realize “Double carbon” target in China.


Introduction
Since the goals of "Carbon Peak" and "Carbon Neutrality" is proposed by Chinese central government, the coordination between environmental protection and economic growth has become the focus of academic discussion.After the industrial revolution started in 1750s, intensifying global warming enables the development model of "Economy Sustainability 2022, 14, 16725 2 of 22 Replacing Environment" to be no longer applicable, so many countries around the world begin to put forward respective plans to tackle the challenge from climate change and address other environmental issues [1].Especially, the green and low-carbon strategy is crucial to comprehensively mitigate global warming, as the guidance and goal to enhance the capacity to achieve sustainable development [2,3]."The 2022 World Food Security and Nutrition Report" showed that though world food production kept pace with population growth, but 828 million people might be affected by hunger and about 2.3 billion people (29.3%) around the world might face moderate or severe food insecurity in 2021.In the continuation to promote the activities of carbon emission reduction in agricultural field, it is necessary to ensure that everyone can buy and afford the basic food they need at any time [4][5][6][7].In March 2022, the newspaper of "Farmer's Daily" in China, reported "How to Balance Agricultural Carbon Emission Reduction and Growth under the 'Double Carbon' Goal?-Dialogue with Zhao Lixin, Jin Shuqin and Huang Xianjin", and pointed out that agricultural carbon emission (ACE) reduction and agricultural product supply (APS) guarantee are dialectical unity, and the responsibility for agricultural production cannot be shirked in the name of carbon emission reduction.And agricultural activity owns both natural and social attributes, which should not blindly reduce carbon emission at the cost of such aspect as crop cultivation, hinder farmers' income growth and decrease agricultural output, but hold the bottom line of food security and ensue the supply of major agricultural products [8].In June 2022, the Ministry of Agriculture and Rural Affairs and the National Development and Reform Commission in China jointly issued the policy of "Implementation Plan to Redue and Fix Carbon in Agricultural and Rural Areas" in the country, which proposed that food security and stable supply of major agricultural products not be ignored for any reason in socioeconomic development process.And agricultural and rural carbon emission reduction should be integrated into food security, agricultural modernization and rural revitalization.Meanwhile, scientific and technological innovation support should be strengthened to promote green and low-carbon transformation of agriculture from conventional to high-quality development.In addition, digital economy is ubiquitous in the process of comprehensive promotion of agricultural transformation, which constitutes an important foundation for rural revitalization and common prosperity [9].At 2022 Global Digital Economy Conference it was pointed out that in the face of climate change, resource scarcity, backward technology and other issues, digitalization will play an important role in agricultural production, food systems and ecosystems and so on, effectively ensuring coordinated promotion of food and important agricultural products supply and carbon emission reduction activities [10].Hence, in a word agricultural development should not only follow the trend of times in the face of existing environmental challenges, but also serve for national food security and the supply of major agricultural products.Only by accurately grasping the coordinated relationship between ACE reduction and APS guarantee, can China effectively promote the coordination and unity between efficiently ecological protection and high-quality economic development.So, three following issues are supposedly explored and addressed in this research.Firstly, what is the relationship between current ACE and APS?Secondly, what is the impact of green technological innovation on environmental protection for ACE and APS, and what is the role of digital economy in the process?Finally, what will be the relationship between ACE reduction and APS guarantee in the future, and how could existing issues be addressed?ACE reduction is an inevitable choice to achieve sustainable agriculture development, and also an important method to mitigate global warming.At present, many scholars are actively researching on ACE to deal with worsening global warming and harsh environment, mainly focus on the exploration and analysis of ACE measurement, spatial-temporal characteristics, influential factors and other aspects.Generally, from the perspective of measuring ACE, the calculation formula used is relatively uniform, but the scholars often measure the emissions from specific perspective of embodied carbon emissions like planting, animal husbandry and the like, and then analyze and find the way out of ACE re-duction [11,12].Besides, due to factor flow, regionally differential resources and the others, many scholars have combined spatial and temporal factors and proposed that ACE have significant spatial distribution differences and dynamic sequence evolution characteristics, and adopted exploratory spatial data analysis method (ESDA), spatial distribution map, kernel density estimation, Dagum Gini coefficient, Theil index, Markov chain model, Geary index, Moran index and some methods else to analyze their features, and then SDM, spatial GMM, GTWR model, etc. are used for studying the type of regional emission reduction interaction and spatial-temporal impact [13,14].In addition, there are many factors that affect ACE, including ecological environment, economic development level, technological innovation, factor quality, digital inclusive finance, land management scale, aging, specialization and the others [15][16][17][18].Moreover, technological innovation and ACE as research objects have received extensive attention and become one of current research hot spots.Thus, some scholars point out that regardless of time horizon, technological innovation has always been the main driving force for ACE reduction and ACE fixation, which is conducive to improving the performance and efficiency of ACE, and then promoting ACE reduction [19].However, some scholars believe that technological progress has a non-linear impact on ACE reduction, which implies that the effect of technological innovation on promoting ACE reduction may change under certain specific conditions.For example, technological innovation can only be effectively implemented under appropriate energy intensity [20][21][22].Green technological innovation and digital economy should keep pace with the trend of times.Based on the law of coordination and unification between ecology and economy, green technological innovation emphasizes the importance of environmental protection and green development, which reduces energy consumption and environmental pollution, improve ecological health and save the resources in whole process from raw material of production to the end of product [23][24][25].As a new driving force of economic development, technological improvement, employment security and other aspects, digital economy has received extensive attention from scholars.It has a strong resource integration capability and technological selection effect, and can help to improve information asymmetry and resource efficiency through environmental monitoring, information mutual assistance, industrial structure optimization and other ways to help green technological innovation research, development and utilization, thus promoting coordinated promotion between ACE reduction and APS guarantee [26][27][28].In essence, the coordinated promotion between ACE reduction and APS guarantee is to ensure the efficient unity of environmental protection and economic growth.Thus ACE reduction must be coordinated with agricultural economic development, international trade, environmental resources, food production and the others.Carbon emission reduction activities cannot be at the expense of agricultural productivity and economic growth.That is to say, agricultural development should not only achieve the "Double Carbon" target, but also ensure national food security and the supply of major agricultural products, and then environmentally friendly production modes, low-carbon agricultural and sustainable economy are the inevitable choice for agricultural progress.On one hand, Kaya equation [29], LMDI model [30] and other methods are used for analyzing the driving factors of ACE, which finds that energy intensity, human capital, urbanization and the other factors are critical; on the other hand, considering the relationship between ACE and APS, coupling coordination degree model, Tapio decoupling model and other methods are usually adopted to specifically quantify the decoupling or coupling relationship between ACE and grain production, agricultural economic growth and the others, which indicates that the temporal characteristic is positive while the spatial difference is large, and both closely relate to regional economic development level, agricultural technology innovation and the other factors [31][32][33][34].
From above analysis, we can deduce that the scholars have paid huge attention to equal importance of economic development and environmental protection, while less attention to the relationship between ACE reduction and APS guarantee, which indicates a huge room for the in-depth research leaving us.Thus, this paper, based on the panel data of 30 provinces in China from 2011 to 2020, uses the carbon emission formula and the "two-stage rolling" Tapio decoupling method to respectively calculate the total ACE, and the quantitative relationship between ACE reduction and APS guarantee.Then, using SDM to explore the impact and heterogeneity of green technology innovation on ACE and APS, the changes in the impact of green technology innovation on ACE and APS are analyzed, in which the digital economy plays a regulatory role.In addition, the Grey model with Simpson formula to optimize the background values is used to further predict the decoupling state of ACE and APS in future.Finally, our purpose is to find the best way to reconcile the conflict between environmental protection and economic development, as well as provide academic circle with the references and thinking framework, and the world with Chinese progress and examples.

Measurement Method of ACE
Referring to the carbon emission measurement method of agricultural production by Guo Lili et al. ( 2022), this study defines the ACE sources as the effective irrigation area, the total sown area of crops, the net amount of agricultural chemical fertilizer, the amount of agricultural diesel, the amount of pesticide and the amount of agricultural plastic film [11]; and the corresponding carbon emission coefficients are 25 kg/Cha, 312.60 kg/km 2 , 0.8956 kg/kg [12], 0.5927 kg/kg, 4.9341 kg/kg and 5.18 kg/kg, respectively.The total amount of ACE are calculated according to the following general carbon emission calculation Equation (1): where, NCO 2 is the total ACE, r refers to species of ACE sources (r = 1, 2, . . ., 6) whereas e r and T r denote the carbon emission coefficient and the amount of ACE source used, respectively.

"Two-Stage Rolling" Tapio Decoupling Model
The "decoupling" theory is widely used to evaluate the relationship between environmental condition and economic growth.In this paper, the Tapio decoupling model is used to accurately reflect the sensitivity of ACE to APS in economics.Additionally, considering that there may be some structural impact of period, this paper makes a comparative analysis based on the measurement results of difference between decoupling indexes in relatively long and relatively short term, respectively [35][36][37].The specific calculation formulas are as follows: In Equations ( 2) and ( 3), e t represents the decoupling elasticity index of period t between ACE and APS; ∆ACE and ∆APS represent the growth rate of ACE and APS, respectively; NCO 2,0 and MAP 0 refer to the total ACE and APS in the relatively long-term base period, respectively, whereas NCO 2,t and MAP t to the total ACE and APS in period t, respectively.Consistent with the values of ∆ACE, ∆APS and e t are divided into 1 optimal state and 7 non-optimal states as shown in Table 1.

Measuring the Development Level of Digital Economy
According to "White Paper on China's Digital Economy Development in 2021" issued by the China Academy of Information and Communication Technology, considering the availability and accountability of data, this paper constructs a digital economy development level measurement index system based on the "four-dimension" framework of digital industrialization, industry digitalization, digital governance and data value.As the indicators are of differences in the characteristic scales of different dimensions such as nature, dimension, order of magnitude and other aspects, the Vertical and Horizontal Scatter Degree method (VHSD) is used to measure the digital economy development level using data standardized by the extreme value method to ensure the dual comparability of the measurement results in time and space [38][39][40].The specific steps taken are as follows: Step1: To determine the comprehensive evaluation function.
where, t k refers to the specific year (k = 1, . . ., 10) whereas w j to the weight coefficient of index j; X ij *(t k ) stands for the data of indicator j of province (municipality or region) i in the t k after standardized treatment, and y i (t k ) for the comprehensive evaluation result of province (municipality or region) i in the t k .
Step2: To determine the weight coefficient of each index.
The mathematical representation to sum the squares of total deviations is as follows: (5) The formula of constraint condition is as follows: In the Equations ( 5) and ( 6), e 2 stands for summed squares of total deviations of y i (t k ), whereas W for index weight coefficient vector, and H for m × m symmetric matrix.Obviously, the eigenvector responding to the maximum eigenvalue of H needs to be determined under the constraint of W T W = 1, which means that when the eigenvector responding to the maximum eigenvalue λmax of matrix H is the index weight coefficient vector W, the value of e 2 is the largest.
Step3: To determine the comprehensive evaluation index y i (t k ), which is used for measuring the development level of digital economy, and the specific measurement index system as shown in Table 2. Spatial correlation is the premise to use spatial econometric models.This paper uses global Moran's index widely used in academia to test the overall spatial correlation and spatial difference between regions [41].The mathematical representation is as follows: where, n refers to the total number of spatial units, which is the total number of provinces (municipalities or regions) actually; y i and y j stands for the observed values of province (municipality or region) i and j respectively, whereas y for the mean value of total observed values.W ij is the standardized spatial weight matrix with W ij of adjacent and non-adjacent spatial units being 1 and 0 respectively.The global Moran's index value range is [−1, 1], and the larger the absolute value is, the stronger the agglomeration effect of the spatial correlation of the observed values between adjacent regions will be.When the global Moran's index value being greater than 0, it indicates that the observed values have spatial positive correlation, whereas the value below 0 stands for spatial negative correlation and the value equivalent to 0 for no spatial correlation.

Spatial Econometric Model
Since the spatial Durbin model (SDM) is general and can explain spatial auto-correlation and spatial spillover effects at the same time, so the SDM is preferably considered.The general formula is as follows: In Equation ( 8): Y is the explained variable, whereas W Y is the spatial lag term of explained variable, having the coefficient of ρ 1 ; X is an explanatory variable, having the coefficient of β, whereas W X is the spatial lag term of the explanatory variable, having the coefficient of θ; and ε is an error term.If Equation (10) does not have θW X , it is the spatial lag model (SLM); if Equation (10) does not have ρW Y and θW X , but have ε = σWε + µ, it is the spatial error model (SEM).

Grey Prediction Model
In order to improve the prediction accuracy of Grey prediction model [42], this paper uses the Grey prediction model based on Simpson formula to optimize the background value to predict the decoupling index between ACE and APS.The general representation is shown in the following: In Equation ( 9): a is the development gray level whereas b is the endogenous control gray level; the one-time accumulation sequence x (1) is obtained using the original data accumulated generating operation (k = 1, 2, 3, . . ., n), whereas x (2) (k + 1) is the prediction value.And the nearest neighbor mean value formula is optimized to be x (1)  (k) = 1/6 × [x (2) (k) + 4x (2) [(2k + 1)/2] + x (2) (k + 1)] using Simpson formula.

Variable Selection and Data Sources
Considering the availability, feasibility and accountability of data, the panel data from 30  In this paper, the agriculture we study is of narrow sense (viz.cropping) rather than generalized one (viz.cropping, forestry, animal husbandry and fishery).So, the explained variables are ACE and APS, which are measured by calculating total ACE using previous carbon emission formula and the output of major crop products (mainly including the output of cereals, beans, tubers, cotton, oil crops, hemp and sugarcane), whereas the explanatory variable is green technology innovation.Referring to the "IPC Green Inventory" issued by the World Intellectual Property Organization (WIPO), the data of B61, C10, E04, F02, F03, F24, H1 and H02 from the patent database of the SIPO of China, are collected pursuant to the IPC classification method using green patent applications to measure green technology innovation.The regulating variable is the digital economy and is measured by the digital economy development level using the VHSD, whereas the control variables include the degree of openness, government environmental expenditure, R&D investment, urbanization rate and labor scale.
In order to avoid "false regression" and invalid results due to heteroscedasticity, the standardization for relevant variable data is carried out, meanwhile the stationarity and multicollinearity of all variables are tested and passed, which conforms to the strong balanced panel data applicable to the model.The descriptive statistics of variables are shown in Table 3. Note: TIEAGVAP stands for total import and export of products in gross value of agricultural production.

Temporal and Spatial Distribution Characteristics of Decoupling Effect between Agricultural Carbon Emission Reduction and Product Supply Guarantee
The decoupling elasticity index calculated by the "Two-Stage Rolling" Tapio decoupling model reflects the relationship between China's ACE reduction and APS guarantee, which means the degree of changes in ACE responding to that of APS at certain period in the country.Figure 1 shows the number of optimal and non-optimal provinces (municipalities or regions) in eastern, central and western regions of China in relatively short and relatively long term each year, in which the eastern region includes such 11 provinces (municipalities) as Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong and Hainan, whereas the central region includes such 10 provinces (regions) as Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan and Guangxi, and the western region includes such 9 provinces (municipalities or regions) as Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia and Xinjiang in the country.On the whole, the coordination relationship between ACE reduction and APS guarantee in China is generally good, in which the number of provinces with strong decoupling state gradually increase over time, and the decoupling relationship between the two kinds shows "the eastern and central regions are better than the western region" in general.From temporal perspective, the decoupling elasticity index of ACE and APS showed big and frequent fluctuations from 2011 to 2016.During this period, in either the relatively long-term or relatively short-term decoupling elasticity index, there was at least one year with zero optimal state in eastern, central and western China each, which indicates the ideal situation has yet not been reached in certain year when both the rise of APS and the reduction of ACE continue.The reason is that the policies guided by the Ministry of Agriculture and Rural Affairs of China is to enrich farmers, through agricultural machinery purchase subsidies, grain procurement and the others, which enable farmers to scale up agricultural production with excessive application of pesticides, fertilizers, agricultural diesel, plastic film and so on, thus causing the rise of carbon emissions and other concurrent environmental problems, ultimately making ACE incompatible with the APS, and breaking the coordination between ACE reduction and APS guarantee.After 2016, the number of provinces (municipalities or regions) in eastern, central and western China, in either relatively long-term or relatively short-term, a strong decoupling state between ACE and APS is gradually showed, which indicates that the total amount of ACE reduced while the APS risen.The reason for this is that Chinese governments have attached importance to and implemented coordinated promotion scheme of ACE reduction and APS guarantee, and achieved preliminary results.From spatial perspective, there are obvious differences between the eastern, central and western regions in China.In terms of either relatively long-term or relatively short-term decoupling elasticity index, the Figure 1 shows that the overall coordination between ACE reduction and APS guarantee is better in the eastern and central regions than that in the western region, in which not all provinces in each region have reached the optimal state.In 2018-2020, the proportion of provinces (municipalities or regions) with strong decoupling state in each region in a relatively shortterm presents respectively as follows: in 2018, central region (70.00%)> eastern region (63.64%)> western region (55.56%); in 2019, eastern region (81.81%)> western region (77.78%)> central region (70.00%); in 2020, western region (88.89%)> eastern region (72.72%)> central region (70.00%).In the relatively long-term, the proportion of provinces (municipalities or regions) with strong decoupling state in each region shows respectively as follows: in 2018, eastern region (54.55%)> central region (40.00%)> western region (11.11%); in 2019, central region (60.00%)> eastern region (54.55%)> western region (11.11%); in 2020, central region (60.00%)> eastern region (54.55%)> western region (33.33%).The spatial difference is closely related to the economic development level, scientific and technological level, natural environment and the others in each region, whereas the coordinated progress of ACE reduction and APS guarantee has been steadily proceeded over time.However, not all regions have reached a strong decoupling state from both spatial and temporal perspectives.Therefore, it is necessary to further reduce ACE and increase APS through improving technology, promoting production efficiency and the like, and then properly handle the relationship between economic growth and carbon emission reduction, so as to achieve greater development in the process of promoting green sustainability.In addition, the relatively long-term is defined by the overall 10 years of study as the inspection period, while the relatively short-term done by the previous period as the base period.The decoupling situations in each region are relatively consistent with each other in both the relatively short-term and relatively long-term, but the decoupling situation in the relatively long-term is more severe in comparison with that in the relatively short-term, which indicates that when promoting the coordinated development of ACE reduction and APS guarantee, not only the previous situation should be compared with, but also appropriate ways should be found out to reduce ACE and to ensure APS according to changing level of economic and social development.
(municipalities or regions) with strong decoupling state in each region shows respectively as follows: in 2018, eastern region (54.55%)> central region (40.00%)> western region (11.11%); in 2019, central region (60.00%)> eastern region (54.55%)> western region (11.11%); in 2020, central region (60.00%)> eastern region (54.55%)> western region (33.33%).The spatial difference is closely related to the economic development level, scientific and technological level, natural environment and the others in each region, whereas the coordinated progress of ACE reduction and APS guarantee has been steadily proceeded over time.However, not all regions have reached a strong decoupling state from both spatial and temporal perspectives.Therefore, it is necessary to further reduce ACE and increase APS through improving technology, promoting production efficiency and the like, and then properly handle the relationship between economic growth and carbon emission reduction, so as to achieve greater development in the process of promoting green sustainability.In addition, the relatively long-term is defined by the overall 10 years of study as the inspection period, while the relatively short-term done by the previous period as the base period.The decoupling situations in each region are relatively consistent with each other in both the relatively short-term and relatively long-term, but the decoupling situation in the relatively long-term is more severe in comparison with that in the relatively short-term, which indicates that when promoting the coordinated development of ACE reduction and APS guarantee, not only the previous situation should be compared with, but also appropriate ways should be found out to reduce ACE and to ensure APS according to changing level of economic and social development.

Spatial Connection Intensity of Green Technology Innovation, ACE and APS in 2020
The spatial connection intensity of green technology innovation, ACE and APS can further intuitively reflect their spatial relationship between regions.Therefore, considering the factors flow, spatial spillover effect and so on, this paper uses the classic gravity model to calculate the spatial connection intensity of green technology innovation, ACE

Spatial Connection Intensity of Green Technology Innovation, ACE and APS in 2020
The spatial connection intensity of green technology innovation, ACE and APS can further intuitively reflect their spatial relationship between regions.Therefore, considering the factors flow, spatial spillover effect and so on, this paper uses the classic gravity model to calculate the spatial connection intensity of green technology innovation, ACE and APS between provinces in China and display their distribution using structural map of spatial network.The gravity model is represented as follows: In Equation ( 10): I ij is the spatial connection intensity of the measured elements between region i and region j, whereas M i and M j are the values of measured elements of region i and region j respectively; d ij represents the geographical distance between region i and region j, while b representing the distance friction coefficient that generally is 2, and g representing the gravitational constant that generally is 1.The calculation results are shown in Figure 2, in which Figure 2a-c are the spatial connection network structure map of green technology innovation, ACE and APS between the provinces in China in 2020, respectively.Each one among those pictures has 435 gravity lines, which are divided according to the specific content into such five levels as successively low, relatively low, general, relatively high and high grades.As seen in Figure 2a, China's green technology innovation level is "higher in the east and lower in the west" in 2020.The reason is that the economic development level, science and technology foundation, opening up level and so on in the east are higher than the rest, which is more conducive to support the conditions and platforms for research, development and utilization of green technology innovation.Then the spatial connection of China's green technology innovation between the provinces in the eastern regions shows very similar at high level, and is followed by that in the central regions, whereas that in the western regions showing relatively low.However, both the connection between the central and eastern regions, and that between the western and eastern regions are stronger than that between provinces (municipalities or regions) within either the central or the western regions.The reason is that the better conditions for the development of green technology innovation in the eastern region those in the central and western regions to learn and absorb, and effectively promote the implementation of regional strategies so as to enhance the spatial linkage.The numbers of "low", "relatively low", "general", "relatively high" and "high" spatial connection intensity lines account for 33.10%, 13.56%, 28.74%, 10.11% and 14.48% of total number of lines in the country, respectively, in which Beijing, Shanghai and Zhejiang have most gravity lines, because they are important economic, political and technological development centers in the country and play a leading role in the development among all regions countrywide.It is worth noting that the number of "high" spatial connection intensity is small, which indicates that the overall spatial connection intensity of green technology innovation needs to be improved.As seen in Figure 2b, China's ACE closely relates to whether the region is dominated by agricultural production or not, and those in most regions are at "general" grade.The numbers of "low", "relatively low", "general", "relatively high" and "high" spatial connection intensity lines of China's ACE among the provinces accounted for 25.98%, 52.87%, 14.48%, 1.15% and 5.52% of total number of lines, respectively, which means that China's ACE are dominated by weak spatial connection.However, "relatively high" and "high" spatial connection intensity lines spread from the centre of Chongqing to the others, which shows that the trend of "center radiation highlights" is obvious.The reason is that Chongqing, as the first green financial reform pilot area to realize the goals of "Carbon Peak" and "Carbon Neutrality", has to ensure that the local carbon reduction work is carried out scientifically and effectively, to form effective linkage with the other regions at the same time, and provide practical basis for all regions countrywide.It is worth mentioning that the spatial connection intensity of ACE does not indicate the "good" or "bad" for China's economic and social development, but only indicates that ACE has spatial connection in the country, and spatial factors need to be considered on such purpose.As seen in Figure 2c, APS in China is not ideal as a whole in 2020, and the numbers of "low", "relatively low", "general", "relatively high" and "high" spatial connection intensity lines of APS between the provinces accounts for 43.22%, 17.47%, 29.89%, 8.28% and 1.15% of totallity, respectively.The overall spatial connection intensity of APS is "low in the east and high in the west" in the country, because the eastern counterpart is mainly dominated by secondary industry, supplemented by primary and tertiary industries, and the output of agricultural products is comparatively limited.Regional coordination strategies have received extensive attention either home or abroad, which indicates that, based on above analysis on the spatial connection intensity of green technology innovation, ACE and APS, spatial factors should be taken into account, and regional coordinated development strategy should be promoted comprehensively in China.

Spatial Auto-Correlation Analysis
It can be seen from above analysis that green technology innovation, ACE and APS in China have significant spatial differences and spatial correlations.Therefore, in order to determine the impact and role of green technology innovation on ACE and APS, the spatial auto-correlation of variables in the overall regions were tested using the global Moran's I with time and space dimension before conducting empirical tests.As shown in Table 4, the global Moran index of green technology innovation, ACE and APS all passed the test at 1% significance level, indicating that spatial factors should be considered and spatial econometric models can be used when conducting empirical analysis, and the Geary's c index is shown for comparative analysis.Thus it can be seen that green technology innovation, ACE and APS are indeed of spatial interdependence, which means that when studying the path of green technology innovation to effectively reduce ACE and improve APS, spatial effects should be taken into consideration.

Inspection and Selection of Spatial Panel Econometric Model
As shown in the calculation results of decoupling model, the ideal strong decoupling state is to ensure that ∆ACE < 0 whereas ∆APS > 0, which implies that the coordinated promotion of ACE reduction and APS guarantee is essentially to reduce ACE and increase APS through green technology innovation.In addition, as a new driving force for economic development, technology improvement, employment security and other aspects, the digital economy has received extensive attention from scholars.The digital economy has a strong resource integration capability and technological selection effect, and helps the R&D and utilization of green technology innovation through environmental monitoring, information mutual assistance, industrial structure optimization and other ways to improve information asymmetry, enhance resource efficiency and the others, and then promote the coordinated promotion of ACE reduction and APS guarantee.Therefore, in order to better study the relationship between green technology innovation, ACE, APS and digital economy, the model introduces the quadratic term of green technology innovation and the regulatory variable, and uses the principles of Elhorst (2014) for model selection [24] and the tests of LM-lag, robust LM-lag, Wald and LR to determine the specific choice of spatial econometric models.At the same time, Hausman test and LR test were conducted to determine whether fixed effect model or random effect model could be used and which fixed effect model should be selected for the model.The results are shown in Table 5.When ACE is treated as the explained variable, whether digital economy is introduced as the regulatory variable or not, for which the tests are significant at the level of 1%.Specifically, LM-lag test and robust LM-lag test reject the original hypothesis at the significance level of 1%, indicating that SLM and SEM can be selected.Then the results of the LR test and Wald test are significant at the level of 1%, which indicates that SDM with generality can not be simplified into SLM and SEM, and SDM is the best choice to estimate the spatial panel data.In short, SDM is the best choice when studying the relationship between green technology innovation, ACE and digital economy.To determine the use of SDM, the results of Hausman test and LR test of individual fixed effect and time fixed effect showed that the p-value was less than 1%, which indicates that the double fixed effect model could be selected.This shows that the double fixed SDM is the best choice for the research no matter whether lnDGE is introduced or not.The specific model is represented as Equations ( 11) and ( 12): When APS is treated as the explained variable, whether digital economy is introduced or not, exerts little influence on the test results.Specifically, the robust LM-lag test rejects the original hypothesis at 10% significance level whereas the LM-lag test accepts the original hypothesis, which indicates that SLM and SEM are not applicable.Then, the results of LR test and Wald test both at significant level of 1% indicates that SDM is the best choice.Besides, the results of Hausman test and LR test of individual fixed effect and time fixed effect also show that the p-value is less than 1%, which fully indicates that the double fixed SDM is applicable to studying the relationship between green technology innovation, APS and digital economy.The specific model is represented as Equations ( 13) and ( 14): When the spatial correlation is not taken into consideration, the fixed effect model (FE) and maximum likelihood estimation (MLE) are used for regression analysis.As previously shown in Table 6, the relationship between green technology innovation and ACE shows an inverted "U-shape", and the digital economy has not yet played a significant role in regulating the impact of green technology innovation on ACE.The reason can be understood in a way that green technology innovation and digital economy are both important manifestations of scientific and technological innovation and progress, and effective ways to strengthen Chinese strategic science and technology and enhance the overall effectiveness of national innovation.However, in order to effectively reduce ACE, green technology innovation must reach certain degree and be supported by corresponding talents, funds and basic technologies and the others.Otherwise, blind investment and utilization in green technology innovation will only result in capital waste, incomplete technology system and other losses.Specifically, when the level of green technology innovation is low, though people have recognized the importance of carbon emission reduction, but their purchase power of new technology products is weak, the degree of their trust in this technology is not clear, consistent with the principle to maximize benefits and minimizing costs, they will not tend to use the technology.And even if carbon reduction activities are put into practice, due to the low level of green technology that can be referred and fewer relevant techniques that can be compared simultaneously, it is difficult for them to judge which one is mature and effective.When green technology products are limited by geograph-ical, climate and other factors, their large-scale investment will cause irreversible losses.When green technology innovation reaches certain level, it has already participated in the experiments and obtained the investment in many ways, and its conditions for fund, talent and the like are mature, they can not only obtain economic benefits, but also pursue ecological benefits, so as to obtain the maximum social benefits.The comprehensive promotion of digital economy has an important impact on social and economic development, but the investment and the digital economy in agricultural technology, production and so on in China are still in the preliminary experimental stage and play a limited role.So it is reasonable that the regulatory role of the digital economy is not at significant level in the test.When spatial correlation is taken into consideration, the regression results of double fixed SDM are shown in Table 6, which shows that digital economy does not play a significant role in regulating the impact of green technology innovation on ACE, no matter whether spatial correlation is considered or not.Whether the adjustment of digital economy is considered or not, the acting direction of explanatory variables and control variables on the explained variables remains unchanged, and the coefficient of action varies little.Therefore, according to the regression results without introducing lnDGE, the coefficients of lnGTI, (lnGTI) 2 , W × lnGTI and W × (lnGTI) 2 are 0.136, −0.007, 0.414 and −0.027 at significant level of 1% respectively, which indicates that the green technology innovation of local province (municipality or region) shows an inverted "U-shape" with the ACE in local and adjacent provinces (municipalities or regions).This indicates that when the level of green technology innovation is low, ACE cannot be reduced, but when it reaches certain level, ACE can be effectively reduced.In addition, the inverted "U-shaped" relationship between green technology innovation and ACE in the local and adjacent provinces (municipalities or regions) also indicates that green technology innovation has a "spatial radiation effect".But the lnGTI at the highest impact point of green technology innovation on agricultural carbon emissions in the local and adjacent provinces (municipalities or regions) is 0.025 (=0.007 ÷ 2 ÷ 0.136) and 0.032 (=0.027 ÷ 2 ÷ 0.414) respectively, which indicates that the "spatial radiation effect" has a "spatial lag".Specifically, only when ACE reduction in local province (municipality or region) is effective, can it have an effective effect on that in adjacent provinces (municipalities or regions) through the "technology diffusion effect".The degree of openness and government environmental expenditure have a significant negative impact on ACE in the local.The higher the degree of openness and government environmental expenditure is, the more the financial and technical support required for agricultural carbon reduction activities will be received, which is more conducive to ACE reduction in return.However, R&D investment, urbanization rate and labor scale are characterized by heterogeneity, and show significant regional differences, and have positive impact on ACE in local province (municipality or region) and negative impact on ACE in adjacent provinces (municipalities or regions).The reason is that they pay too much attention to ACE reduction activities and excessive investment in capital, talent and other resources, which makes the "congestion effect" not conducive to the ACE reduction in local province (municipality or region).The coefficient of W × lnACE(rho) is significantly negative at the level of 5%, which is consistent with the results of spatial auto-correlation test, indicating that when the ACE in local region are too high, it will induce the surrounding regions to quickly make decisions and implement ACE reduction in their own.
In order to further explore the influential relationship and spatial spillover effect between green technology innovation and ACE, this paper divides spatial effects into direct effect and indirect one, whose results are shown in Table 7.It can be seen from Table 7 that no matter whether the digital economy is introduced as the regulating variable or not, has little impact on the spatial effect decomposition results.Therefore, consistent with the regression results without the introduction of lnDGE, the direct effect coefficients of lnGTI and (lnGTI) 2 are 0.128 and −0.006 respectively, whereas the indirect effect coefficients are 0.213 and −0.014 respectively, and the total effect coefficients are 0.341 and −0.021 respectively, all at significant level of test.Specifically, the direct effect contributes 47.34% (viz.0.128 ÷ 0.341 ÷ 2 + 0.006 ÷ 0.021 ÷ 2), whereas the spatial spillover effect contributing 52.66% (viz. 1 − [(0.128 ÷ 0.341) + (0.006 ÷ 0.021)]/2), which shows that green technology innovation not only has a first increased and then decreased effect on ACE in local region, but also has the same and even greater effect on adjacent regions.In control variables, the degree of openness and government environmental expenditure mainly show direct effects, which are conducive to ACE reduction in local province (municipality or region).The direct and indirect effect coefficients of R&D investment, urbanization rate and labor scale are all significant at the level of 5%, indicating that they have not only an impact on ACE in local province (municipality or region), but also an spatial spillover effect on ACE in adjacent provinces (municipalities or regions).

Green Technology Innovation, APS and Digital Economy
It is shown in Tables 8 and 9 that: whether the FE model, MLE or SDM are used or not, the regulatory role of the digital economy is not significant; and whether digital economy is introduced into the model as an regulating variable for regression or not, the direction of coefficient remains unchanged and the magnitude fluctuates slightly.This result is consistent with previous analysis of the relationship between green technology innovation, ACE and the digital economy.Thus, the relationship between green technology innovation and APS was analyzed pursuant to the regression results without introducing lnDGE.When the spatial correlation is not considered, the primary conclusions are that the relationship between green technology innovation and APS presents a "U-shape", and the degree of openness, government environmental expenditure, R&D investment, urbanization rate and labor scale all have respective significant impact on APS.Therefore, the most important task to ensure APS is to ensure the stable output of agricultural products.And the APS is measured by the output of agricultural products, which means green technology innovation to improve the output of agricultural products should be perceived as an important step to ensure the coordinated promotion of ACE reduction and APS guarantee.The "U-shaped" relationship between green technology innovation and APS lies in whether green technology innovation at low and high levels can provide strong production conditions for increasing agricultural product output or not.When the level of green technology is low, environment-based green production technology is limited in the output, expensive, and difficult to use, which makes commonly used and mature techniques on the market preferentially chosen for agricultural production.Namely, low level green technology innovation cannot improve the output of agricultural products.When the level of green technology is high, agricultural production will vigorously promote the research, development and utilization of green techniques that are conducive to environmental protection and can improve the output.In this case, not only the government provides funds, talents and other support, but also the participants will improve their core competitiveness through the development and utilization of green technology innovation.When considering spatial correlation, the coefficients of lnGTI, (lnGTI) 2 , W × lnGTI and W × (lnGTI) 2 are −0.07,0.007, 0.055 and −0.028 respectively, but only (lnGTI) 2 and W × (lnGTI) 2 at 10% significant level of test, which indicates that green technology innovation has a positive "U-shaped" relationship with the APS in both local province (municipality or region) and adjacent provinces (municipalities or regions).But the minimum value of lnGTI is greater than 0, which indicates that when the current level of green technology has been raised to certain level, it can effectively improve the output of agricultural products.The degree of openness, government environmental expenditure and urbanization rate play a significant role in agricultural production in local region, but do not have a significant impact on that in adjacent regions.However, R&D investment mainly plays a role in adjacent regions, which reflects the spatial heterogeneity of influential factors.In addition, the coefficient of W×lnAPS (rho) is significantly negative at the level of 1%, which is consistent with the results of spatial auto-correlation test, indicating that those regions with high APS cannot play a role of "diffusion driving effect" in adjacent regions to improve the APS there.The decomposition results of spatial effects are shown in Table 9.The direct effect coefficient of (lnGTI) 2 is 0.008 whereas the indirect one is −0.020, in which both are significant at the level of 10%, indicating that green technology innovation not only promotes the APS in local province (municipality or region), but also has a negative spatial spillover effect on the APS in adjacent provinces (municipalities or regions).The reason is that local region will fully obtain the "technology dividends" brought by green technology innovation, but the technology spillovers to neighboring regions are limited, which leads to the fact that neighboring regions cannot obtain "technology dividends".

Analysis of Grey Prediction
According to the decoupling effect of ACE reduction and APS guarantee in each province (municipality or region) in 2019 and 2020, the remaining provinces (municipalities or regions) after excluding those have reached the optimal state of relatively short-term strong decoupling in this two years, are selected as the objects of prediction.Then, based on the data from 2016 to 2020, we use the Grey model of Simpson formula to optimize the background value to make Grey prediction of ACE and APS in Beijing, Inner Mongolia Autonomous Region, Liaoning, Jilin, Heilongjiang, Shanghai, Anhui, Jiangxi, Hubei, Yunnan and Ningxia, and calculate the decoupling elasticity coefficient of ACE and APS in these provinces (municipalities or regions) through the predicted results, as shown in Table 10.The reason why we forecast ACE and APS instead of directly predicting the decoupling elasticity coefficient, is that the data predicted by the Grey prediction model needs to be in the same direction, the data length of years required is not long, and achieving the coordinated promotion of ACE reduction and APS guarantee is to reasonably reduce carbon emissions and increase agricultural product output.Therefore, it is highly rational to predict and calculate the original data of decoupling states based on the relatively short-term decoupling results.Note: the orange indicates that the strong decoupling is the most ideal state of ACE and APS, while the green indicates that the strong negative decoupling is the most imbalanced state of ACE and APS; the word "decoupling" has been omitted for each specific decoupling state.
Sustainability 2022, 14, 16725 20 of 22 From Table 10, predicted decoupling states in 2016-2020 is basically consistent with the actual, indicating that the prediction results are meaningful and can provide reference to promote the coordinated promotion of ACE reduction and APS guarantee.Compared with that in 2016-2020, the decoupling effect between ACE reduction and APS guarantee is projected to be better in 2021-2025.Comparing the decoupling states each other in the relatively short-term and relatively long-term, it is found that Inner Mongolia, Liaoning, Heilongjiang, Anhui, Yunnan and Ningxia are projected to reach strong decoupling state by 2025.A small number of provinces (municipalities or regions) though have not yet reached the optimal state, but already been away from the extremely unreasonable strong negative decoupling state.Beijing has not yet reached a strong decoupling state in any year from 2016 to 2025, and in most years it remains in a recessionary connection state, a transitional state between decoupling and negative decoupling, which indicates that the growth rate of ACE and APS there is negative, closely relating to the fact that Beijing is a large non-agricultural region.Jilin, Shanghai and Hubei have relatively long-term and relatively short-term prediction results that differ greatly each other.When Jilin and Shanghai fail to reach the optimal state, recessionary decoupling and recessionary connections dominate there; and ACE and APS are in a negative growth state, but the relatively long-term prediction results of other regions reach a strong decoupling state.On the whole, the decoupling state between ACE and APS in China is good.It is expected that most China's provinces (municipalities or regions) can achieve the goal of "Carbon Peak" by 2030.However, it should be aware that the coordinated promotion of ACE reduction and APS guarantee closely relates to regional economic development level, industrial structure, scientific and technological level, agricultural production and other factors.Thus the strategies should be comprehensively adopted to meet the requirements for regional development towards ACE reduction and APS guarantee nationwide.

Conclusions
The coordinated promotion of ACE reduction and APS guarantee is crucial in the green transformation, sustainable development and high-quality development of agriculture, on which we discussed from the perspective of decoupling effect, driving factors and prediction, in order to obtain a scientific basis that is conducive to realizing "Double carbon" target in China.Our main conclusions are as follows.Firstly, from the perspective of temporal-spatial characteristics, the coordination relationship between China's ACE reduction and APS guarantee is generally good, the number of provinces (municipalities or regions) with strongly decoupling state gradually increase over time, but the overall decoupling state distribution of ACE and APS shows "the eastern and central regions are better than the western regions".Secondly, the green technology innovation and the ACE in both local province (municipality or region) and adjacent provinces (municipalities or regions) take on an inverted "U-shaped" relationship.When the level of green technology innovation is low, ACE cannot be reduced; when the level of green technology innovation is high, ACE can be effectively reduced.Though the green technology innovation and the APS in both local province (municipality or region) and adjacent provinces (municipalities or regions) present a positive "U-shaped" relationship, but the minimum value of lnGTI is higher than 0, which indicates that current level of green technology has been raised to certain level, and can effectively improve the output of agricultural products.Whether using FE model, MLE and SDM or not, the regulatory role of digital economy is not significant for the relationship between green technology innovation and ACE, APS.Thirdly, compared with that in 2016-2020, the decoupling state of China's ACE and APS has improved significantly, and the provinces (municipalities or regions) below the optimal state in 2021-2025 have left the extremely unreasonable strong negative decoupling state, and mainly shown recessionary decoupling and recessionary connection.Finally, it is advisable that China establish and improve the relevant technology incubation platform for green technology innovation, give full play to the role of technology spillover and

Figure 1 .
Figure 1.Decoupling effect between ACE reduction and APS guarantee in China.

Figure 1 .
Figure 1.Decoupling effect between ACE reduction and APS guarantee in China.

Figure 2 .
Figure 2. Spatial connection intensity of green technology innovation (a), ACE (b) and APS (c).

Table 1 .
Decoupling states classification criteria between ACE and APS.

Table 2 .
Index system for measuring the development level of digital economy.
provinces (municipalities or regions) in China (excluding Tibet, Taiwan, Hong Kong and Macau) from 2011 to 2020 are used for research objectives.The original data are from China Statistical Yearbook, China Science and Technology Statistical Yearbook, China Environmental Statistical Yearbook, China Rural Statistical Yearbook, the National Bureau of Statistics (http://data.drcnet.com.cn/accessed on 5 November 2022) and the State Intellectual Property Office (https://www.cnipa.gov.cn/accessed on 5 November 2022).

Table 3 .
Results of variable description and descriptive statistics.

Table 4 .
Results of spatial auto-correlation test.

Table 5 .
Statistical tests results of model selection.

Table 6 .
Regression Results of FE model, MLE and SDM on green technology innovation, ACE and digital economy.

Table 7 .
Decomposition results of spatial effect of green technology innovation on ACE.

Table 8 .
Regression results of FE model, MLE and SDM on green technology innovation, APS and digital economy.

Table 9 .
Decomposition results of spatial effect of green technology innovation on APS.

Table 10 .
Grey prediction results of decoupling state of ACE reduction and APS guarantee.