Analysis of regional differences and dynamic mechanisms of agricultural carbon emission efficiency in China's seven agricultural regions

A profound understanding of the present status and regional characteristics of China’s agricultural carbon emissions (ACE) is the basic prerequisite for exploring a pathway to ACE reduction that is compatible with China’s national conditions. This study uses the inter-provincial agricultural industry panel data from 2001 to 2017 and selects the three-stage slack-based measure data envelope analysis (SBM-DEA) model and Malmquist-Luenberger(ML) index model to measure the dynamic efficiency of agricultural carbon emissions (ACE). Additionally, this study uses the Dagum Gini coefficient and the panel vector auto-regression(PVAR) model to analyze the sources of regional differences in dynamic efficiency and the internal structure, respectively. The empirical results reveal the following: (i) The dynamic efficiency of China’s ACE is in a state of “efficiency optimization.” Although both technological change and technological efficiency change are in an “efficient” state, they also show a decline in technological efficiency change and a regression in technological change, respectively. (ii) The overall Dagum Gini coefficient of China’s ACE dynamic efficiency, technological change, and technological efficiency change all demonstrate upward trends. The gap between regions is the main reason for the long-term gap between the dynamic efficiency of China’s ACE, technological change, and technological efficiency change. (iii) Regardless of the time horizon, technological change has always been the main driving force for the continuous growth of dynamic efficiency; the contribution of technological change to dynamic efficiency is far greater than that of technological efficiency change. This conclusion has been verified in samples from different regions of China.


Introduction
As the global climate problem has become increasingly serious, the "low-carbon economy" has become a new schema for global development. According to the IPCC (2018) report, global warming is 1.5°C higher than pre-industrial levels. Moreover, agriculture's share of greenhouse gases cannot be underestimated; approximately 1/4 of the total net artificial greenhouse gas emissions (GHG) and 14% of the total global carbon emissions are related to agricultural activities (IPCC 2007) 1,2 However, due to the widespread and universal nature of agricultural activities suggest that carbon emissions from this sector are an important source of global carbon emissions that must be addressed (Fei and Lin 2016;Dogan et al. 2016). China's agricultural sector accounts for approximately 17% of the country's total carbon emissions (Dong et al. 2008). Reducing carbon emissions and improving unit carbon emission efficiency are important measures for achieving lowcarbon economic development (Beinhocker et al. 2008). Due to the increasing severity of the global climate problem, achieving emission reductions and low-carbon economic development has become matters of concern. The marginal contributions of this paper are as follows: First, the correct division of the study area according to the research question is an important prerequisite for exploring the road to carbon emission reduction in China's agricultural sector. Unlike previous studies, this study conducts an empirical analysis of the regional differences in the dynamic efficiency of ACE and its formation mechanism according to the division of the seven major agricultural regions 3 . Second, in contrast to existing studies on the static efficiency of ACE, this study uses the undesired output super-efficiency three-stage SBM-DEAmodel and the ML index decomposition method to measure the dynamic efficiency of ACE. Third, this study not only focuses on the regional differences and contribution sources of the dynamic efficiency of ACE in various regions but also expands the research perspective to evaluate the internal structure of dynamic efficiency. The findings of this research can be used to diagnose the regional differences in the dynamic efficiency of ACE and their mechanisms and to provide reference about ACE reduction for policy makers and planning of relevant government entities.

Literature review
Many studies on ACE have been conducted. Early literatures focused on the factors that influence ACE. For instance, West and Marland (2002) conducted an in-depth examination of the factors that influence ACE. In contrast, research by Johnson et al. (2007) found that ACE are primarily derived from livestock and poultry gas emissions, manure management, rice cultivation, arbitrary disposal of agricultural waste, and biological combustion. More recently, He and Dai (2016) highlighted that both the agricultural economic structure and the level of agricultural mechanization are leading factors that lead to differences in the spatial structure of agricultural carbon emissions in China. Moreover, Tian and Zhang (2017) found that chemical fertilizers, agricultural lime, pesticides, agricultural irrigation, and seed cultivation were the main sources of ACE.
Decomposition analysis of China's ACE is another area of burgeoning inquiry. Li and Li (2010) measured the amount of carbon dioxide emissions from energy consumption in China's agricultural sector from 1981 to 2007. Furthermore, Han and Zhang (2013) found that the import effect contributes at the greatest rate to China's current carbon emissions related to agricultural energy consumption, followed by the export counter-effect, industrial scale effect, and energy efficiency effect. On this basis, they used the logarithmic mean Divisia index (LMDI) model to decompose carbon emissions; they found that economic growth was the most important driving factor for ACE. The comprehensive measurement of ACE has been used for calculating GHG emissions from energy crop cultivation based on carbon footprint (CFP) approaches. For example, Valin et al. (2013) investigated the effects of crop yield and livestock feed efficiency scenarios on GHG emissions from agriculture and land use change in developing countries. Besides that, Peter et al. (2017) have analyzed the available calculators and approaches according to the goal and scope of the calculator, the methodology used to account for GHG emissions from energy crop cultivation, energy crop cultivation management practices, and the ability to model crop rotation. In addition, Ismael et al. (2018) used annual data for the period 1970 to 2014 to examine the interaction between agricultural technology factors and the environment in terms of carbon emissions in Jordan. Recently, LMDI decomposition and decoupling analysis have been used by researchers such as Liu et al. (2019) to test the changing trends and regional differences in China's ACE.
As research on ACE continues to deepen, scholars have shifted from simple ACE calculations to more comprehensive research on total factor productivity that relies on input and output analysis. Among the representative studies, Guo et al. (2018) used the SBM-undesirable model with undesirable outputs to evaluate the total agricultural carbon emissions and carbon emission efficiency of various provinces in western China, and they found that the total amount of ACE in western China is increasing and that there are obvious spatial differences regarding carbon emissions. In addition, Wang (2020) used the undesired output super-efficiency SBM model to empirically test the agricultural efficiency level and its spatial pattern in Anhui Province, China. Moreover, Lei et al. (2020) empirically tested the non-linear relationship between agricultural technological change and ACE efficiency by constructing a panel-threshold model.
Collectively, the aforementioned studies provide a wealth of theoretical value for exploring the ACE reduction. However, as the understanding of China's agricultural development continues to deepen, research on carbon emissions must move beyond the static level of index calculation and regional difference feature analysis. It is necessary to explore the dynamic efficiency of ACE and the internal mechanism of its formation.
The findings from the existing research on ACE not only lay an important theoretical and methodological basis for this study but also highlight the insufficiency of research on ACE efficiency. In the relevant research on the total factor carbon emission productivity, the parametric method (Färe et al. 2005;Marklund and Samakovlis 2007) and the nonparametric method (Liu et al. 2011;Zhou and Nie 2012;Xu and Luan 2018) are mainly used to measure the carbon emission production efficiency. Among them, non-parametric models are widely used by scholars in the evaluation of total-factor carbon emission efficiency because they do not need to establish functional forms and prior conditions in advance (Song et al. 2012;Molinos-Senante et al. 2016) and can effectively avoid t he subjectivity of parameter weighting (Zhou et al. 2010;Dong et al. 2017). In previous studies on ACE efficiency, most of them adopted the traditional data envelope analysis (DEA) model or SBM-DEA model as their analytical approach. These approaches ignore the influence of the external environment and random interference to a certain extent and only consider the decisionmaking unit (DMU). Therefore, the estimated result is quite different from the actual situation (Tone 2001;Choi et al. 2012;Gómez-Calvet et al. 2014;Iftikhar et al. 2016;Chen et al. 2017;Wu et al. 2019). To compensate for this shortcoming, this study uses the framework of Fried et al. (2002) to propose a three-stage DEA model based on a combination of the traditional DEA model and the stochastic frontier analysis (SFA) method. In addition, to explore the dynamic changes of ACE efficiency, we refer to existing studies (Kortelainen 2008;Wang et al. 2014) and adopt the DEA-Malmquist-Luenberger index method to analyze the dynamics of ACE efficiency. The decomposition analysis explores dynamic efficiency, technological efficiency change, and technological change and uses PVAR model to test the dynamic relationship of these three factors.
In summary, this paper divides China's 30 provincial-level administrative units into seven major agricultural emission regions and uses the three-stage SBM-DEA model and the ML index method to measure the ACE efficiency from a dynamic perspective. In addition, the Dagum Gini coefficient and the PVAR model are used to empirically test the ACE in 30 provinces and regions of China from 2001 to 2017.

Dagum Gini coefficient and its subgroup decomposition method
With reference to existing research, the study area is divided into seven major agricultural regions: Northeast China, Huanghuaihai region, the middle and lower reaches of the Yellow River, South China, Northwest and areas along the Great Wall, Southwest, and Qinghai-Tibet region. Dagum's (1997) methods empirically test the dynamic efficiency, technological efficiency change (EC), and technological change (TC) of ACE and the regional differences among those three factors in China's seven major agricultural regions. Dagum defines Gini coefficient as: In Formula (1), G represents the total Gini coefficient, which measures the total difference of ACE between all provinces. K represents the number of regions, including seven major agricultural regions. y ih and y jr represent the true levels of the dynamic efficiency of ACE of all provinces and cities, and i=1,2,…,K; j=1,2,…,K. μ is the average value of the dynamic efficiency of ACE of all provinces and cities, n is the number of all provinces and cities, and n i and n j are the number of provinces and cities.
G can be decomposed into three parts: intra-regional gap G w , inter-regional gap G rb , and transvariation intensity G t . The three parts satisfy G=G w +G rb +G t . Among them, G w represents the distribution gap of the dynamic efficiency of ACE in the i(j) region. G rb represents the distribution gap of the dynamic efficiency of agricultural carbon emissions between regions i(j). G t represents the impact of the cross term of the dynamic efficiency of ACE between regions on the total Gini coefficient G. If G t =0, it means that the cross term of the dynamic efficiency of ACE between regions does not exist. The specific decomposition formula is as follows: Formula (2) measures the contribution of the difference of dynamic efficiency of ACE within a region to the total Gini coefficient G; Formula (3) measures the net contribution of the extended difference of dynamic efficiency of ACE between regions to the total Gini coefficient G; Formula (4) measures the contribution of the transvariation intensity between regions to the total Gini coefficient G. λ i = n i /n and s i = λ i μ i /μ, and μ i and μ j are the average of dynamic efficiency of ACE.
In Formula (10), D ij =(d ij −p ij )/(d ij +p ij ) is the relative economic affluence between the ith and the jth region, and the gross economic affluence d ij between the ith and the jth region, such as μ i >μ j , is where d ij is under the condition of y ih >y ir , the weighted average of the dynamic efficiency gap (y ih −y ir ) of all ACE under the following conditions. For the continuous density distribution functions f i (y) and f j (y).
p ij is the first-order moment of transvariation intensity between the ith and the jth region, such that μ i >μ j : G ii is the Gini coefficient within region and G ij is the Gini coefficient between regions, i.e., The super-efficiency three-stage SBM-ML model of undesired output The super-efficiency three-stage SBM-ML model of undesired output can be used to analyze the dynamic changes of carbon emission efficiency. The three-stage process is the following: the first stage uses the undesired output superefficiency SBM-DEA model to analyze the changes in total factor productivity; the second stage uses the stochastic frontier method to adjust the input-output variables; the third stage will adjust the input variables, and original output variables are substituted into the undesired output super-efficiency SBM-ML model for measurement.
(1) The first stage: Use the super-efficiency SBM-DEA model of undesired output to calculate the initial efficiency of each decision-making unit (DMU) and the slack variables of input-output. The SBM-DEA model is: subject to where λ is the weight vector. x and y are matrixes that compose the input and output of all DMU, in which y g is the expected output and y b is the undesired output. m is the number of input indicators, and S is the number of output indicators (S 1 represents expected output; S 2 represents undesired output). n is the number of DMU. S − , S g , and S b are the slack variables of input variables, expected output, and undesired output, respectively. ρ is the carbon emission efficiency value, and 0≤ρ≤1. When ρ=1, S − =S g =S b =0. At this time, it is completely efficient for this particular DMU; when ρ<1, it means that the DMU is inefficient, and the input variables and output variables need to be improved to improve efficiency.
From observing the formula, it can be found that inputoutput slack variables are directly substituted into the objective function for calculation. On the one hand, it solves the problem of slackness of input and output variables in the traditional DEA model, and on the other hand, it also effectively solves the problem of expected and undesired output in output variables. Therefore, the SBM model is more effective in evaluating carbon emission efficiency issues.
(2) The second stage: First, construct and use the stochastic frontier analysis (SFA) to decompose the input relaxation value obtained in the first-order stage. The SFA regression model is: where Sij is the slack variable of the ith input of the jth DMU, Zj is the environmental variable, βi is the coefficient of the environmental variable, vij+μij represents the mixed error term, vij is random error, and μij is the managerial inefficiency, which means the influence of managerial factors on the input slack variable, assumed it follows the truncated halfnormal distribution at the zero point, i.e., μ∼N þ 0; σ 2 μ Using the SFA model, the input slack variables of the 30 provincial regions from 2001 to 2017 obtained in the first stage were used as the explanatory variables; economic development level, industrial structure, energy structure, government regulation, technological innovation level, and degree of opening to the outside world which are six environmental factors were used as explanatory variables for regression analysis. Frontier 4.1 was used to obtain SFA regression results. In order to make the calculation results more precise, this paper adopts the method of year-by-year analysis and establishes a total of 54 regression equations.
The input-output slack variable calculated in the first stage is affected by managerial inefficiency, environmental factors, and statistical noise. Therefore, it is necessary to isolate these three effects and eliminate environmental factors and random errors. The specific separation method is as follows: separate environmental factors, managerial inefficiency, and random errors: where In this way, the random error term can be separated from the mixed error term, and the separation equation is: Finally, adjust the input and output variables. Separate managerial inefficiency, environmental factors, and random errors in slack variables in order to put all DMU in the same external environment for efficiency evaluation, so there are two adjustment methods. One is to adjust all DMU to a superior external environment, which can be adjusted by reducing the input and output of other DMU; the other is to adjust to an in-superior external environment and increase the input and output of other DMU. This paper chooses the second adjustment method in view of the operability of the data, and its equation is: The above formula represents adjusted input variable, and X ij represents before adjusted input variable. In summary, all DMU will be placed in the same external environment.
(3) The third stage: The adjusted input value removes the external environment factors and random interference factors, and then recalculate it with the initial output data using the undesired output super-efficiency SBM-ML model. The efficiency value at this time eliminated the influence of environmental factors and random errors and can more accurately reflect the true efficiency of the internal management and investment scale of each DMU.
The undesired output super-efficiency SBM model can only be used to analyze the static environmental efficiency of regions, but it cannot effectively measure the dynamic environmental efficiency of regions. FÄRE et al. (2005) proposed the calculation method of Malmquist index which can be used to analyze the efficiency of dynamic environment. Chung et al. (1997) introduced the directional distance function into the Malmquist index to deal with the problem of undesired output and called it the ML index, which has all the virtues of the Malmquist index model. On this basis, not only the undesired output is taken into account, but also the decrease of undesired output and the increase of expected output are taken into consideration simultaneously. Therefore, this paper adopts the super-efficiency SBM-ML index, which includes undesired output, to measure the dynamic total factor carbon emission efficiency of 30 provincial regions from 2001 to 2017. According to the ML index calculation method proposed by Chung et al. (1997), it is assumed that the "bad" output is weakly disposed and the "good" output is freely disposed. The direction vector g t = (y t ,−b t ), and then the ML productivity index from t period to t+1 is: ML measures the change in productivity from period t to period t+1. If ML<1, production efficiency declines; when ML=1, production efficiency remains unchanged; and if ML>1, production efficiency is ascending. The ML index can be further decomposed into two parts: one part measures technological efficiency change (EC), and the other part measures technological change (TC). The expression is as follows: EC measures how close each observation value is to its respective production frontier, while TC measures the change in the production possibility boundary from period t to period t+1. Among them, EC>1 means that the technological efficiency is improved; EC<1 means that the technological efficiency is reduced. TC>1 indicates technological improvement; TC<1 indicates technological regression. ML>1 indicates that the efficiency has increased; ML<1 indicates that the efficiency has decreased.

Index selection
Based on the panel data of 30 provinces, municipalities, and autonomous regions in China from 2001 to 2017 4 . According to the classification standard of the "National Economic Industry Classification 5 ," this paper focuses on the dynamic efficiency of ACE and uses undesired output. The superefficiency three-stage SBM-ML model. The required data mainly comes from the 2001-2017 China Statistical Yearbook, China Energy Statistical Yearbook, China Science and Technology Statistical Yearbook, local statistical yearbooks, and bulletins. Part of the missing data is supplemented by research methods such as interpolation, exponential smoothing, and mean method. In order to test the interval difference in the dynamic efficiency of agricultural carbon emissions, the study divided the regions according to the seven major agricultural regions and conducted empirical analysis on samples from different regions. The specific variables are selected as follows: (1) Selection of input-output variables. From the research of Li et al. (2020), this paper takes labor, capital stock, and total energy consumption as input variables and regional agricultural production and carbon dioxide emissions as output variables. The specific description of the variables is shown in Table 1. It should be noted that for the calculation of capital stock, we use the perpetual inventory method to estimate with the base period of 2000 and the depreciation rate of 10.96%.
(2) Selection of environment variables. For the selection of environmental variables in the three-stage DEA model, the main criterion is that the selection has a significant impact on the efficiency of carbon dioxide emissions, but it is also a factor that cannot be controlled by the DMU. Based on comprehensive consideration of data availability, representativeness of variable indicators, and existing research (Chen et al. 2017; Huang and Bai 2019), this study focuses on economic energy and institutional environment, and six indicators are selected as the environmental variables in this paper. They are economic development level, industrial structure, energy structure, government regulation, technological innovation level, and degree of openness to the outside world. This paper uses regional GDP per capita to express the level of regional economic development.
The level of economic development. For the crude economic development mode, the higher level of economic development means greater energy consumption and more carbon emissions, Therefore, it is certain that the level of economic development is one of the factors that affect carbon dioxide emission efficiency. This paper uses regional GDP per capita to express the level of regional economic development.
Industrial structure. There is a close relationship between carbon dioxide emission efficiency and industrial structure. Industrial structure affects total energy consumption and energy intensity, thereby indirectly affecting carbon dioxide emissions. Meanwhile, the optimization and upgrading of the industrial structure can promote the development of lowcarbon industries and improve carbon emission efficiency. Therefore, this paper uses the ratio of agricultural production value to regional GDP to measure the regional industrial structure.
Energy structure. According to the IPCC (2006), the carbon emissions per unit of coal consumption are 1.33 times than that of oil and 1.73 times than that of natural gas. If the ratio of coal to total energy consumption is high, then carbon emissions will increase rapidly, thereby reducing carbon emission efficiency. Therefore, this paper takes the proportion of coal consumption in agricultural production to the total energy consumption as an indicator of energy structure. Government environmental regulation. Existing studies have shown that environmental regulation is an important factor affecting harmful gas emissions including carbon dioxide (Wang and Xu 2015;Tong et al. 2016). Therefore, this article uses the ratio of provincial government environmental governance investment to GDP to measure government environmental regulation.
The level of technological innovation. Changes in science and technology will improve the efficiency of energy use. Meanwhile, increasing production capacity and promoting the use and development of clean energy will improve the efficiency of carbon emissions. Therefore, this paper selects the ratio of R&D expenditure in agricultural production to GDP in each province to measure the level of technological innovation.
Degree of openness. An important feature of rapidly developing economy is the continuous development of foreign trade. China's intensive foreign trade structure has increased the burden of carbon reduction and has made more contributions to high energy consumption and high carbon emissions. Therefore, the ratio of the total agricultural product's import and export of each province to GDP is used to measure the degree of openness.

Carbon emission estimation method
The carbon dioxide emissions in 30 regions are undesired output, according to the calculation formula in the "Guidelines for National Greenhouse Gas Inventories" compiled by the United Nations Intergovernmental Panel on Climate Change in 2006.
In this formula, E represents the consumption of fossil energy in agricultural production. The data can be directly obtained from statistical data, mainly including 8 major fossil energy sources including coal, coke, and crude oil; NCV represents average low calorific value of fossil energy; all the data comes from the "China Energy Statistical Yearbook"; CEF represents the carbon dioxide emission coefficient of fossil energy in the agricultural production, and its data comes from the carbon content of various types of fuels and effective carbon dioxide emission coefficients provided by IPCC (2006). The figures are shown in Table 2.

Decomposition of regional differences in agricultural carbon emission efficiency in China
Overview of China's ACE efficiency In Fig. 1, in 2001, ML exhibited a spatially distributed orderly pattern, with higher values in western regions and lower in eastern regions and an overall average efficiency of 1.199. Among the 30 regions, 23 regions had ML>1 (efficiency growth areas), and 7 regions had ML<1 (efficiency decline areas), most of which were agglomerated in the middle and lower reaches of the Yangtze River and the Huanghuaihai region. By 2005, ML was distributed in a point-like space, and the overall average efficiency decreased to 0.885, whereas the efficiency growth area was mainly clustered in economically developed areas. By 2009, the spatial distribution of ML showed higher values in eastern and northern regions and The ratio of agricultural production to GDP % Energy structure The ratio of agricultural carbon emissions to total energy consumption b % Government environmental regulation The ratio of government investment in environmental governance to GDP % The level of technological innovation The ratio of R&D expenditure in agricultural production to GDP % Degree of openness The ratio of total agricultural product's import and export to GDP % a Calculation method: First, based on the construction method of Zhang et al. (2004) and Shan (2008) about capital stock, the price deflator of the investment data of various industries in this article is calculated by Xu et al. (2007) deflation index construction method. Then, drawing on the provincial depreciation rate and base period capital stock data calculated by Song and Liao (2014) method, according to the perpetual inventory method, the provincial capital stock data of the three industries in this paper are obtained. Finally, through the calculation of the amount of capital in the base period and the selection of depreciation rates and current investment indicators, the total investment in fixed assets of the whole society is then deflated. b Calculation method: According to the calculation formula in the "Guidelines for National Greenhouse Gas Inventories" compiled by the United Nations Intergovernmental Panel on Climate Change in 2006 (IPCC, 2006)Calculation method: According to the calculation formula in the "Guidelines for National Greenhouse Gas Inventories" compiled by the United Nations Intergovernmental Panel on Climate Change in 2006 (IPCC, 2006) lower values in western and southern regions, and the overall average efficiency increased to 1.034. Efficiency decline areas reduced, with 13 regions in total, whereas efficiency growth areas were mainly distributed in the Northeast, Huanghuaihai region, and the middle and lower reaches of the Yangtze River. By 2013, the overall average efficiency decreased to 0.994; the number of efficiency decline regions increased, and the efficiency growth areas were mainly located in the middle and lower reaches of the Yangtze River. By 2017, the overall average efficiency increased to 1.321; efficiency growth regions also further increased, the distribution was more dispersed, and the efficiency of economically developed regions and agricultural-based regions was higher.
In Fig. 2, in 2001, the overall average EC was 1.065; from the total area, two-thirds were EC growth areas (EC>1), and one-third were efficiency decline areas (EC<1). In 2005, the overall average EC was 1.124, whose spatial distribution showed higher values in central regions and lower values in eastern and western regions. The number of EC decline regions did not considerably change. However, the overall EC of the Northwest and Southwest regions declined. By 2009, EC showed a horizontal band distribution, with an overall average efficiency of 1.013. The areas of EC growth were mainly concentrated along the Yellow River Belt, Northeast China, and Southwest China. The EC decline areas decreased to one-third and were mainly concentrated in the middle and lower reaches of the Yangtze River and the southern coastal regions. By 2013, EC was distributed in a small-scale blocklike spatial structure, with an overall average efficiency of 0.946; technology decline areas further expanded, mainly distributed in the Northwest and areas along the Great Wall, middle and lower reaches of the Yangtze River, Northeast  China, South China, and Southwest China. By 2017, the overall average EC was 1.146, the number of decline areas of EC reduced, and the spatial distribution of increasing efficiency areas moved to the Southwest. It can be seen from Fig. 3 that in 2001, TC in most of the China regions showed a growing tendency, being evenly distributed in the eastern and western regions. The declining areas of TC were distributed in a dot-like pattern, and regions of inefficiency of TC in parts of the middle and lower reaches of the Yangtze River and the southwestern region expanded. By 2005, only three regions remained with TC>1, all of which were agglomerated in the middle and lower reaches of the Yangtze River. By 2009, the number of regions with TC growth gradually expanded, mainly in the Northeast and Huanghuaihai regions. Until 2013, the TC growth-type areas showed an orderly pattern of high TC in the middle and low TC in the east. In South China, TC degraded from growth type to decline type. In 12 regions, concentrated in the Southwest, Huanghuaihai region, and the middle and lower reaches of the Yangtze River, TC upgraded from decline to growth. Finally, by 2017, the growth area of TC showed a flaky-type distribution pattern in the North and South.

Decomposition of regional differences of China's ACE efficiency
The dynamic tendencies of the sources of regional differences in China's ACE are illustrated in Fig. 4.
By analyzing the Gini coefficient of ML (GML), from 2001 to 2017, GML showed an upward tendency of volatility, with an average annual growth rate of 1.729%, which indicates that the gap of ML across China was gradually expanding, and the Gini coefficient of EC (GEC) and TC (GTC) also showed an upward tendency, with average annual growth rates of 2.606% and 2.943%, respectively. In terms of inter-annual changes, GML, GEC, and GTC showed Wshaped fluctuations. It can be observed that the changes in GML were mainly due to the effects of GEC and GTC. However, in different periods, considerable differences were observed between the two contributions to GML fluctuations. Figure 5a, b, and c present the differences in China's ACE dynamic efficiency, technological efficiency change, and technological change among the regions from 2001 to 2017, respectively. It can be seen that the GML changes in various regions were considerably different. Among them, the GML in Northeast and South China showed a downward tendency, upward tendency was observed, with the largest increase (11.973%) in the Huanghuaihai region. From Table 3, it can be seen that during the research period, the inter-region differences of GML, GEC, and GTC were at different levels and the overall tendency of fluctuations was evident. The overall average annual growth rate of the interregion difference of GML ranged from 10.79 to 10.50%. Moreover, the inter-region difference of GML in most regions showed an upward tendency. Among them, the largest increase occurred between Northeast China and the middle and lower reaches of the Yangtze River, with a rate of 10.50%, and the smallest increase occurred between the middle and lower reaches of the Yangtze River and Southwest China (0.40%). The largest decrease was between the Huanghuaihai district and Southwest China, at 10.79%, whereas the Northwest and the areas along the Great Wall and Southwest region had the smallest decline of 0.93%. In contrast to GML, the overall average annual growth rate of the inter-region difference of GEC ranged from 8.529 to 8.483%, and GEC also showed an upward tendency in most regions. Moreover, the average annual increase between South China and the Northwest and the Great Wall was the smallest (0.024%), whereas the Northeast and Huanghuaihai regions had the largest average annual increase (8.483%). Moreover, South China and Southwest China had the largest average annual decrease (8.529%), whereas South China and Southwest China had the lowest average annual decrease (0.207%).
Considering the GTC, the overall average annual growth rate of the inter-region difference ranged from 8.055 to 9.571%. Similarly, most regions showed an upward tendency. The Huanghuaihai region and the middle and lower reaches of the Yangtze River had the largest average annual increase (9.571%), whereas the Northeast and South China had the smallest average annual increase (0.217%). Furthermore, the Northeast and Qinghai-Tibet regions had the largest average annual decrease (8.055%), whereas South China, Northwest, and along the Great Wall had the smallest average annual decrease (−0.457%).
Research on the source decomposition and contribution rate of regional differences of China's ACE efficiency Figure 6a, b, and c exhibit sources of differences between ML, EC, and TC and their contribution rate from 2001 to 2017, respectively.
Considering GML, the contribution to the gap of GML in various parts of China was 46.743%, 39.419%, and 13.840%, for G rb (the inter-region gap), G t (transvariation intensity), and G w (the intra-region gap), respectively. G rb is the main responsible for the gap of GML in China. From the perspective of inter-annual changes, G rb and G t have considerably different contributions to the gap of GML in different periods. Among the years analyzed, for 2003, 2007, 2009, 2012, 2013, 2015, and 2017, the contribution rates of Gt to GML were higher than those of Grb, ranging from 42.638 to 59.338%. G t is mainly used to describe the phenomenon of overlap between regions.
Similarly, in terms of GEC, we found that G rb , G t , and G w , respectively, provided the major contributions to the gap of GML in various parts of China, and G rb contributed the most to the gap of GEC differentiation in various parts of China. However, in the years 2001, 2002, 2005, 2009, 2010, 2013, and 2015, the contribution rate of G t was ranked first, ranging from 43.384 to 58.049%. The contribution rate of G w to GEC fluctuated between 11.297 and 16.398%, with an average annual growth rate of 1.125%.
For GTC, the major contribution to the gap of GTC in various parts of China was still due to G rb , followed by G t and G w . From the perspective of inter-annual changes, G rb and G t alternately became the main contributors for the regional gap of GTC. Moreover, in the two stages of 2007-2008 and 2011-2014, the contribution rates of G t to GTC were higher than those of G rb . Therefore, G t was the main responsible for the regional gap of GTC. In contrast, the contribution rate of G w was stable from 11.808 to 16.113%.
Expansion analysis: quantitative analysis of the sources of regional differences in China's ACE

Stationarity test of variables
The analysis provided explains the static relationship between ML, EC, and TC; however, it does not explain the dynamic relationship between these three factors, which requires a model. As EC and TC are generated by the decomposition of the ML index, there must be an internal connection between the three factors. The vector auto-regression(VAR) model allows each component to be an endogenous variable, and the time span of the data is 17 years, which meets the requirements of time series samples. Therefore, we used the PVAR model to test the dynamic relationships between the three factors. Before analyzing the PVAR model, it is necessary to test the stationarity of each variable and define the optimal post-order. The test results are presented in Table 4 6 . The study found that the variables of each regional sample showed 6 In the stationarity test, we selected the Levin, Lin, and Chu (LLC), Im, Pesaran, and Shin (IPS), augmented Dickey-Fuller (ADF), and Phillips-Perron(PP) test statistics to test whether each variable belonged to a stationary series.    Note: "*," "**," and "***" all indicate passing the test at the significance level of 10%, 5%, and 1%; the P value in square brackets; the empirical results retain three decimal places a stationary series. Therefore, a direct model and analysis of the original data could be performed.

Granger causality test
The above research shows that the data of ML, EC, and TC were stationary series. Thus, in this study, a direct test was performed to evaluate whether there was Granger causality among the three factors. Before the Granger causality test, the optimal lag order must be determined. To ensure the accuracy of the research results, the optimal lag order was determined by adopting the test value that passed the most. The results are listed in Table 5. The results of the Northeast China show that the changes in EC were affected by changes in ML and TC and their combined effects; the results in the Huanghuaihai region show that there was a two-way Granger causality relationship between TC and ML, EC, and TC, manifested as the interaction between the two; EC and ML had a one-way Granger causality relationship, manifested as changes in EC, which were affected by changes in ML; results in the middle and lower reaches of the Yangtze River showed that ML and TC had a two-way Granger causality relationship. However, there was only a one-way Granger causality relationship between EC and TC, which shows that the change in TC was affected by the change in EC. Moreover, there was a two-way Granger causality relationship between ML, EC, and TC in South China, and there was a two-way Granger causality relationship between TC and EC in the Northwest and areas along the Great Wall; the relationship between ML, TC, and EC was only manifested in that the changes in TC and EC were all affected by changes in ML.
The results in the Qinghai-Tibet region show that there was no interaction between ML, EC, and TC.

PVAR model analysis of the dynamic efficiency of China's ACE
Based on the above evaluation, the PVAR model system OLS of ML, EC, and TC and the test results are shown in Table 6. The results in Northeast China show that ML significantly inhibited the development of EC during lag phase 1, whereas TC promoted the development of EC. In South China, ML had a self-weakening mechanism, and EC and TC had significant positive effects on ML. Furthermore, ML had an inhibitory effect on the development of EC, whereas TC had a promoting effect. In addition, ML had an inhibitory effect on TC development. In the middle and lower reaches of the Yangtze River, ML and EC had a self-weakening mechanism, but EC had a long-term self-weakening mechanism, whereas TC had a self-reinforcing mechanism. In the Huanghuaihai zone, TC had a significant positive impact on ML in the lag phase 2. In addition, EC had a self-weakening mechanism, whereas TC had a non-linear change mechanism, which was manifested as a self-enhancement at the initial stage and a selfweakening mechanism at the later stage. In the Northwest and areas along the Great Wall, both ML and EC had a selfweakening mechanism, but the self-weakening mechanism of EC lasted for a long time, whereas TC had a lagging selfenhancement mechanism. In addition, ML had a continuous weakening inhibitory effect on TC, and the promotion effect of ML on EC had a long hysteresis effect. In Southwest China, ML had a self-weakening mechanism, and both TC and EC that lagged in the first stage had a significant positive impact; moreover, TC had a self-reinforcing mechanism, which could effectively inhibit the development of TC, but the growth of EC drove the growth of TC. In the Qinghai-Tibet region, there was no correlation between ML, EC, and TC. Figures 7,8,9,10,11,12,and 13 show the results of impulse response between ML, EC, and TC in seven major agricultural zones in China, where the abscissa is the number of response periods of impact action, which was set to 10. The ordinate represents the degree of influence of the variables. The curve in the figure represents the impulse response function, and the curves on both sides represent the estimated values of the 95% and 5% quantile points, respectively. Figure 7 shows that in the Northeast China, there were significant differences in the response of ML to EC and TC shocks. The response to EC shocks showed an initial positive effect, followed by a negative effect, and the intensity of volatility was weakened. In contrast, the impact of EC on ML and TC was also different. Moreover, the response to ML shock exhibited a continuously weakened positive effect at the initial stage, then turned to a negative effect, and then rebounded. The response to the TC shock showed a continuously increasing positive effect at the initial stage, followed by some small fluctuations. In contrast, in the impulse response analysis of TC, the impacts of ML and EC on TC exhibited severe fluctuations, and the fluctuation directions were completely opposite. Figure 8 shows that in the Huanghuaihai region, the ML response to EC and TC shocks had a large lag; at the same time, there were opposite fluctuations. In the second period, the ML response to EC shocks showed an initially negative followed by a positive effect; the intensity first increased, then decreased, and finally increased again. The reaction of ML to TC shock was the opposite, and the reaction intensity was weak. In the analysis of EC impulse response, the EC response to ML shock showed an initially positive effect followed by a negative effect. Furthermore, the EC response to TC shock had a large hysteresis, which first manifested in the second phase, and showed an initially positive followed by a negative effect. In addition, in the TC impulse response analysis, the  Note: "*," "**," and "***" all indicate that the test passed the test at the significance level of 10%, 5%, and 1%; the P value in brackets; Yes and No, respectively, indicate whether the test passed or not. The empirical results retain three decimal places Table 6 Results of OLS TC response to ML and EC shocks was severe. The response to ML shock showed an initially positive effect followed by a negative effect, and the intensity gradually weakened. However, the response to the EC shock showed an initially negative followed by a positive effect, and the weakening of the intensity was not evident; finally, it remained as a positive effect. Figure 9 shows that in the middle and lower reaches of the Yangtze River, the response of ML to EC shocks showed an initially positive followed by a negative effect, and the intensity first increased and then decreased. In addition, the response to TC shocks showed an initially positive followed by a negative effect, and the intensity gradually weakened. Moreover, in the analysis of EC impulse response, the EC response to ML shock showed an initially positive followed by a negative fluctuation, whereas the response to TC shock was weak. Furthermore, in the impulse response analysis of TC, the response of TC to the shock of ML and EC was severe. In contrast, the reaction to ML shock showed an initially positive effect followed by a negative effect, and the intensity gradually weakened, whereas the reaction to EC shock showed an initially negative followed by a positive effect, and the intensity gradually weakened as well. Figure 10 shows that in South China, the response of ML to EC shocks showed an initially positive followed by a negative effect, with the intensity first increasing and then decreasing. At the same time, the response to TC shocks showed a continuous positive effect, and the intensity first increased and then decreased. Moreover, in the analysis of EC impulse response, the EC response to ML shock showed a continuous weakening positive effect, whereas the response to TC shock showed a continuous positive effect, with the intensity first increasing and then decreasing. Furthermore, in the impulse response analysis of TC, the response of TC to ML shock showed a continuously weakening positive effect, whereas the response to EC shock was very severe, showing an initially negative followed by a positive effect, and the intensity gradually weakened. Figure 11 shows that in the Northwest and along the Great Wall, ML reacted violently to EC shocks, showing a fluctuating pattern of alternating positive and negative effects. Although the intensity weakened, it was not evident. In addition, the response to the TC shock was not significant. In the analysis of EC impulse response, EC showed a continuously weakening positive effect on ML shock. The response to TC shock showed a continuously increasing negative effect at the initial stage and then rebounded to its peak in the fourth period, showing a positive effect. Furthermore, in the impulse response analysis of TC, the response of TC to ML and EC shocks was severe. Moreover, the response to the ML shock showed an initially positive followed by a negative effect, and the intensity gradually weakened, whereas the response to the EC shock showed an initially negative followed by a positive Note: "*," "**," and "***" all indicate that they passed the test at the significance level of 10%, 5%, and 1%; the standard errors are in parentheses effect, the intensity gradually weakened, and finally the shock effect remained positive. Figure 12 shows that in the Southwest China, the response of ML to EC shocks showed a continuous positive effect, with the intensity first increasing and then decreasing. At the same time, the response to the TC shock showed an initially positive followed by a negative effect, and the intensity first increased and then decreased. Moreover, in the analysis of EC impulse response, the response of EC to ML shock showed a continuously weakening positive effect, whereas the intensity of response to TC shock was around zero. In contrast, in the impulse response analysis of TC, the response of TC to the shock of ML and EC was severe. Furthermore, the response to ML shock showed an initially positive followed by a negative effect, and the intensity first decreased, then increased, and decreased again, whereas the response to the EC shock showed an initially negative followed by a positive effect, and the intensity first increased and then decreased. Figure 13 shows that in the Qinghai-Tibet region, the response of ML to EC shocks showed an initially positive followed by a negative effect, and the intensity first increased and then decreased. In addition, the response to TC shocks was weaker, there was a large hysteresis effect, and the negative effect was first identified in the third period. Moreover, in the analysis of EC impulse response, the EC response to ML shock showed an initially positive followed by a negative  effect, and the intensity first increased and then decreased, whereas the response to TC shock showed a steady positive effect at the initial stage and then showed a positive effect. In contrast, in the impulse response analysis of TC, the response of TC to ML and EC shocks was severe. Moreover, the response to the ML shock showed an initially positive followed by a negative effect, and the intensity gradually weakened, whereas the response to EC shocks showed an initially negative followed by a positive effect, and the intensity gradually weakened. Table 7 shows that for the variance decomposition of the ML of ACE in the seven major agricultural regions of China, ML was 100% affected by its own fluctuation shock in the first period, and the impact of EC and TC on ML was first identified in the second period. Except for the Southwest region, the impact of EC on ML in other regions was higher than the impact of TC on ML, and the impact strength continued to increase, indicating that the impact of EC on ML was lagging, long-term, and continuous. In the variance decomposition of EC and TC, each region also had certain commonalities. First, the impact of ML on EC was manifested in the first period, and the impact of TC on EC was first identified in the second period. Second, the impact strength of TC to EC was very small, ranging from 0.013 to 9.654%. Third, the impact of ML and EC on TC was first identified in the first period. Fourth, except for certain periods, the impact of TC on itself

Discussion
There are several elements that influence the sustainable development of agriculture in various regions, such as the carrying capacity of agricultural resources, environmental capacity, ecological types, and development foundations in various regions, resulting in regional differences in China's agricultural development. In the report of China's Sustainable Agricultural Development Plan (2015)(2016)(2017)(2018)(2019)(2020)(2021)(2022)(2023)(2024)(2025)(2026)(2027)(2028)(2029)(2030), China has been divided into three categories: optimized development zone, moderately developed zone, and protected development zone. The direction of sustainable agricultural development in different regions can be better determined by adapting measures to local conditions, cascading advancement, and classifying policies.
Optimized development areas, which were the main production areas of China's bulk agricultural products, include the Northeast China, Huanghuaihai Region, middle and lower reaches of the Yangtze River, and South China. These regions have suitable agricultural production conditions and preferable potential productivity. However, there are also existing  various kinds of drawbacks, for instance, excessive consumption of water and soil resources, environmental pollution, excessive use of agricultural inputs, and low level of resource recycling. For Northeastern China where has vast black land and diverse output of agricultural products (Li et al. 2014;Yang et al. 2018). While with the deepen of the reform and opening-up, the upgrading of industrial structure has lagged behind other regions, agricultural technology is relatively primitive and backward, and low green technology adoption, resulting in high ACE Xia et al. 2019). Therefore, in the Northeast China, changes in EC are affected by dynamic efficiency and TC. The developed agricultural economy and high level of mechanization in the Huanghuaihai area are main factors affecting ACE efficiency, while the pollution of fertilizers and agricultural waste is the main carbon dioxide emission source (Tian et al. 2014). Moreover, in 2015, the ACE efficiency of the eastern provinces in the Huanghuaihai region reached the maximum, which proved that the 2015 "weight loss and drug reduction" policy played a positive role in reducing ACE (Hu et al. 2020). Hence, in this region, there is a significant interaction among EC, ML, and TC. However, the relationship between TC and EC only shows that the former is affected by the latter. For middle and lower reaches of the Yangtze River, the main reasons for intra-group gap of the dynamic efficiency of ACE are that the lower reaches of the Yangtze River Economic Belt are areas close to the east which take the lead in the development strategy. Moreover, these areas have superior geographical location, and the economic and financial development levels are preceded than those in the upper and middle reaches (Lu and Xiong 2021). Financial support has promoted the advancement of agricultural technology. In addition, advanced agricultural technology has increased total efficiency of China's ACE (Hu et al. 2020), consequently leading to a large gap between the level of ACE efficiency in the upstream and downstream areas and the midstream areas.
The Northwest and areas along the Great Wall and Southwest China are divided into moderately developed zones. During the study period, ML of ACE exists in significant differences in different regions, which mainly comes from the changes of policy orientation. Since 2000, the Central Government of China has carried out "Western Development" policy. Specifically, in the year 2007 and 2012, ecological civilization construction as a primary project in these areas. Meanwhile, western agriculture has transformed into a large-scale, intensive mode and even a green and intelligent mode, as well as increasing rural residents' non-agricultural employment income (Guo et al. 2018). As the agglomeration degree of agricultural industry increases, efficiency of China's ACE shows a trend of first improving and then getting worse. The agricultural production areas in the central and western regions are highly concentrated areas of agriculture, and the conditions of groups under different agglomeration levels are different (Cheng et al. 2018). Meanwhile, the efficiency of China's ACE gap in the western provinces is constantly shrinking, but this narrowing trend does not necessarily mean that the efficiency of ACE in the western region has absolutely reduced. There are two reasons for the narrowing of the gap: one is that high-efficiency ACE are moving closer to low-efficiency areas, and the other is that low-efficiency areas are moving closer to high-efficiency areas (Guo et al. 2018;Yue et al. 2018). This is manifested in the narrowing of the gap between groups, and responses of TC to ML and EC showed a positive effect.  Qinghai-Tibet area is a protected and developed zone which is the birthplace of China's major rivers and an important ecological security barrier. The plateau has rich agricultural resources, but the ecology is very fragile. Therefore, the national policy also insists on giving priority to protection, restricting development, and appropriately developing ecological industries and characteristic industries, so that ML of China's ACE in this area is showed to be almost unaffected by TC and EC.

Conclusion and policy implications
This study examines the regional differences in the dynamic efficiency of ACE from 2001 to 2017 in China and empirically analyzes the dynamic effects of the internal structure of dynamic efficiency by using the Dagum Gini coefficient and the PVAR model. The results of this study found the following: (i) the overall dynamic efficiency of China's ACE is in a state of "efficiency optimization," but most provinces in the Southwest and Huanghuaihai regions are in a state of "inefficiency"; numerically, the dynamic efficiency was higher in 2017 than that in 2001. Technological change and technological efficiency change are in a state of "inefficiency" in most areas, and "regions of efficiency decline" present a clustering phenomenon in the spatial structure of emissions in the region. In addition, in the early period of the study (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009), technological change was found to be the main factor leading to dynamic efficiency change, while in the later period (2010-2017), technological efficiency change dominated the dynamic efficiency. (ii) In terms of regional differences, the overall Dagum Gini coefficient of China's ACE dynamic efficiency, technological change, and technological efficiency change all shows upward trends; this indicates that the domestic gap is gradually widening. Among the differences within and between regions, the contribution of technological efficiency change and technological change to the dynamic efficiency of China's ACE varies greatly between regions. In economically developed regions, technological efficiency change drives dynamic efficiency, whereas technological change is the main driver of dynamic efficiency in underdeveloped regions. In terms of the performance of the contribution rate, we found that the gap between regions and the transvariation intensity is the main reason for the gap between dynamic efficiency, technological change, and technological efficiency change in China's ACE. These two factors perform differently in different samples and during different time periods. (iii) In the analysis of the internal formation of dynamic efficiency, we found that the technological change, technological efficiency change, and dynamic efficiency interacted with one another in terms of intensity, direction, and continuity. According to the above analysis, in order to achieve lowcarbon economy and sustainable development goals, the following policy implications may be extracted: (i) For economically developed areas and areas where agriculture accounts for a large proportion of the industrial structure, firstly, precise investment in agricultural fixed assets should be increased. Specifically, for those EC of ACE is the main factors affects dynamic efficiency regions. It is crucial to prevent the decline of EC, for instance, expanding expenditure of research and development funds and adopting innovative low-carbon technology. Secondly, the problem of pesticide abuse is more serious in economically developed areas. It is suggested that the existing agricultural mechanism system should be optimized. It is possible to raise the subsidies of environmental-friendly agricultural materials and technologies. Moreover, improving fertilization methods and encouraging the use of organic fertilizers, biological fertilizers, and green manure planting. (ii) For those TC of ACE which is greatly affected by ML and EC regions, performance evaluation and incentive mechanism of agricultural science and technology innovation should be established. Make full use of market mechanisms to attract social capital and resources to participate in scientific and technological innovation for sustainable agricultural development. (iii) For regions with the low proportion of agriculture and undeveloped economy, differential ACE improvement policies should be formulated according to local conditions, such as protecting the basic ration fields, stabilizing the cultivated areas, and restricting agricultural development. Meanwhile, insisting on giving priority to protection and appropriately developing ecological industries and characteristic industries, so that resources such as grasslands and lakes can be recuperated, and a virtuous cycle of the ecosystem should be promoted.