# Temporal Trend and Regional Disparity of Agricultural Green Total Factor Productivity in China: Data Envelopment Analysis with Biennial Environmental Technology

Authors: Xiuquan Huang; Xi Wang; Baoxin Chen; Fanbo Li; Shaodan Su; Tao Zhang
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

This paper investigates the temporal trend and regional disparity of China’s agricultural green total factor productivity (AGTFP) during 1997-2016. Combined with the green Luenberger productivity indicator, two different data envelopment analysis models with the biennial environmental technology are constructed for robust checks. Compared with the existing literature, more agricultural carbon emissions are used as the undesirable outputs in the models. It is found that AGTFP in the whole of China and all of its sub-regions (the east, the middle, and the west) showed an overall increase, with the drive of high technical progress. The east had the largest AGTFP, and the middle experienced the largest AGTFP growth. More specifically, with respect to AGTFP, the total difference and the gross difference among the three regions as well as the specific difference within regions widened during these periods. There was an absolute convergence trend of AGTFP in the whole of China as well as the middle and the west. The speed of convergence was highest in the west.


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## Body

## 1. Introduction

As the world’s highest carbon emitter, China accounts for about 27% of the world’s annual emissions. Therefore, China’s announcement that it will achieve carbon peak by 2030 and carbon neutrality by 2060 is difficult to achieve but significant because it will have a positive impact on the green economy in China and even the world. In addition, China is a large agricultural country. There are 900 million people registered in agriculture communities, with more than 300 million people engaged in agricultural production. Agriculture is critical to China’s carbon neutrality.At the same time, China’s agriculture has made remarkable achievements since the reform and opening-up began in the 1970s. Its total output of major grains, including rice, wheat, corn, beans, and potatoes, rose from 304.77 million tons in 1978 to 663.84 million tons in 2019, successfully feeding nearly 20 percent of the world’s population on just 9 percent of its arable land. However, it faces increasingly tight resource constraints and environmental pollution pressure. Although China has many natural resources, per capita this is less than half of the world average. Moreover, the per capita resources are decreasing, but the demand for food in China is increasing [1]. China’s agricultural activities account for 16–17% of all greenhouse gas emissions, compared with 13.5% globally [2]. Moreover, China’s Environmental Performance Index (EPI) in 2017, at 43, ranks 118th out of 178 countries (Yale Center for Environmental Law & Policy and Columbia University’s Center for International Earth Science Information Network published global EPI report every two years since 2006). Over the past 40 years, China has accelerated the agricultural modernization process and increased agricultural machinery and materials with low-level technology. For instance, the intensity of pesticides in China is twice that of developed countries [3].Therefore, promoting the green development of China’s agriculture is key to achieving carbon neutrality and improving productivity. Moreover, it can improve air quality, thereby increasing the well-being of residents [4, 5]. China’s agricultural growth should not rely too much on the increase of input factors but should improve agricultural green total factor productivity (AGTFP). What are the spatiotemporal characteristics and growth sources of AGTFP in China? What are their evolution trend and regional differences? The answers to these questions are of theoretical and practical significance for exploring the path of green growth of China’s agriculture and for the government to formulate scientific policies.Total factor productivity (TFP) is typically used to measure the production efficiency of one unit; however, it is no longer feasible to take traditional agricultural TFP as an index to measure agricultural development. The AGTFP, incorporating environmental pollution into the model, is a more reasonable index [6]. The data envelopment analysis (DEA), a mature approach, is used to measure TFP and has three advantages compared with other methods: (1) there is no need to set the form of the production function, which can avoid measurement deviation due to model setting; (2) DEA can consider technical inefficiency; (3) the TFP can be decomposed into several terms, facilitating the in-depth analysis [7].Many studies have analysed the TFP of Chinese agriculture based on the DEA model. Although it has been decades since the first DEA model (CCR model) was published in 1978, the common models are still the basic models (CCR model and BCC model) and the slacks-based DEA model [8–10]. The factor allocation structure in Chinese agriculture was analysed by the CCR model [11]. Li et al. [12] employed the CCR model to evaluate China’s provincial efficiency and improvement potential. The slacks-based DEA model was used to measure agricultural quality development in China [13, 14]. Besides, there are many papers about AGTFP using other DEA models, including the two-stage DEA [15, 16], the three-stage DEA [17], bootstrapped DEA [18–20], the window slack-based DEA [21], the network DEA [22], and the metafrontier DEA [23].DEA models combined with some indexes help the analysis of the dynamic change of TFP, including the Malmquist index and Luenberger index [24]. The models related to the Malmquist index are the most commonly used, and they can calculate the growth rate of TFP directly. Zheng et al. [25] analysed the TFP of fisheries economies in 12 mainland China and Taiwan coastal areas, using the DEA model combined with the Malmquist index. Chen et al. [26] also employed the model to measure the agricultural TFP of the 87 counties in Gansu Province in China from 1988 to 2017.It is essential to select agricultural carbon emission sources (ACESs) directly affecting the accuracy of efficiency measurement. West and Marland [27] considered that agricultural inputs were the primary source, including fertilizers, agricultural limes, pesticides, agricultural irrigation, and seed cultivation. Johnson et al. [28] chose intestinal fermentation of livestock, manure management, rice growth, and arbitrary disposal of agricultural waste as the sources. Li et al. [29] thought that agricultural carbon emissions (ACEs) were mainly from six aspects, including chemical fertilizer, pesticides, agricultural film, agricultural machinery, agricultural plow, and agricultural irrigation. Some scholars have incorporated energy-related CO2 emissions and major agricultural nonpoint-source pollution into the accounting framework [30]. The sources in these studies were not complete, and the ACEs measurement in this study was more extensive and detailed.There is something that can be refined from the previous literature. First, those DEA models employed always have the problem of infeasibility; the unit in periodt is out of the frontier in period t+1[31]. It is usually solved using two production techniques: the global frontier and sequential frontier [30, 32, 33]. Nevertheless, this paper solves it by using the biennial frontier, a better method. The global frontier and the sequential frontier have limits of usage, especially the former, which is not in line with reality [34]. In addition, the biennial technology uses the units in periods t and t+1 to construct frontier, reducing the impact of outliers and improving the accuracy. Second, this study uses more complete ACEs as the undesirable output. This study selects a wide range of ACESs and takes into account the precise types of carbon sources. For instance, we use straw burning as one of the carbon sources, and different kinds of straws have different emission coefficients.This study analysed China’s temporal trend, regional disparity, and growth sources of China’s AGTFP. The main contributions of this study are as follows. First, the study employed the biennial environmental technology to construct two nonradial and nonoriented biennial directional DEA models, which can solve the infeasibility problem and make the calculation result more accurate and more stable. Second, the more complete ACEs were used as the undesirable output, which could also improve the accuracy. To further analyse the characteristics of AGTFP in this paper, kernel density estimation, a nonparametric method, was used to analyse the dynamic distribution of the growth rate, and the Dagum Gini ratio method was used to estimate the difference (within regions and between regions) and the sources of the difference. After the difference analysis, theσ convergence and the absolute β convergence of AGTFP were analysed in China and the three subregions (the east, the middle, and the west).


## 2. Materials and Methods

### 2.1. Selection of Input and Output Indicators

The measurement of TFP requires input and output of each province, which in this paper are shown in Table1, including eight inputs, one desirable output, and one undesirable output. In this study, the ACESs included five categories: (1) agricultural materials; (2) rice cultivation; (3) soil surface releasing when planting crops; (4) livestock and poultry farming; (5) straw burning. The five also include a variety of specific subsources, as shown in Table 2. The study calculated ACEs of agricultural materials and straw burning by carbon emission coefficients from the IPCC report [35]. For other ACESs, their carbon emission coefficients are constructed in terms of the greenhouse effect. Specifically, this study first calculated the amount of N2O and CH4 released with N2O and CH4 emission coefficients and then converted them to standard carbon emissions with the carbon conversion coefficients. The N2O and CH4 emission coefficients mean the amount the corresponding substance per unit source can release. The carbon conversion coefficients of N2O and CH4 mean how many carbons per unit N2O or CH4 are equal in terms of the greenhouse effect. Those coefficients are based on previous papers [35–38]. The ACESs can be converted into ACEs by (1)E=∑i5Ei=∑i5∑jNiQij×cij,where E is the total ACEs, Ei is ACE of the carbon source ii=1,2,3,4,5, and Qij and cij represent the amount and carbon emission coefficients of the carbon subsource j in the source i, respectively.Table 1
Construction of input and output indicators.
FactorIndicatorOutputDesirable output (Y)The actual agricultural productionUndesirable output (C)Agricultural carbon emissionsLabor (L)The number of agricultural practitionersLand (N)Area sown with cropsMachinery (E)Electricity consumption of agricultural machineryInputFertilizer (F)Applying quantity of chemical fertilizer (refractive index)Pesticide (P)Consumption of chemical pesticidesAgricultural film (R)The amount of agricultural film usedAgricultural water (W)Actual irrigation areaFarm animals (A)The number of farm draft animalsTable 2
Agricultural carbon emission sources.
SourcesSubsourcesCoefficientsAgricultural materialsFertilizer, pesticides, plastic sheeting, diesel oil, and energy consumption for irrigationccRice cultivationEarly rice, late rice, and in-season ricecCH4  ∗ tCH4Soil surface releasing when planting cropsPaddy rice, winter wheat, spring wheat, soybean, corn, and vegetablescN2O ∗ tN2OLivestock and poultry farmingCow, buffalo, cattle, mule, camel, donkey, horse, pig, sheep, goat, rabbit, and poultrycCH4  ∗ tCH4+ cN2O ∗ tN2OStraw burningRice, wheat, corn, rape, soybean, and cotton strawccNote: cc, cCH4, and cN2O refer to carbon, N2O, and CH4 emission coefficients. tCH4 and tN2O are the carbon conversion coefficients of N2O and CH4, respectively.


### 2.2. BWMRM and BBAM

The biennial environmental production technology is employed, which considers the negative impact of production on the environment, integrating inputs, desirable outputs, and undesirable outputs in the framework and constructs the production frontier using the two-period decision-making units (DMUs). Suppose thatx, y, and b represent inputs, desirable outputs, and undesirable outputs, respectively.For DMU jj=1…n in period tt=1…T, its input-output set is xj,t,yj,t,bj,t. The biennial environmental production technology allows for technical regression. In addition, it does not need to be recomputed when a new period is added to the data set and can avoid infeasibility, a vital issue in the DEA model [39]. It is in accord with the three assumptions (weak disposability, null-jointness, and the compact set). The technology is shown as (2). Note that z is the intensity variable. ∑j=1nzj=1 and zj≥0 means variable returns to scale (VRS).BWMRM and BBAM are based on the weighted Russell directional distance model and the biennial environmental production technology [39–41]. The difference between the two models is the direction vector [42]. There are three advantages compared with other directional distance function models: (1) the infeasibility can be overcome because of the biennial technology; (2) it is a nonradial and nonoriented inefficiency estimation, so input and output slacks are all included, and different percentage increases or decreases are also allowed (this study measures from the inefficiency side, in which the sum of all the weights to factors is 1; the greater the value of the objective function, the lower the efficiency); (3) it can reduce the impact of outliers on efficiency result. The production frontier is variable over time, and outliers in one period can just influence the result of the period.(2)T=x,y,b:∑j=1nzjtxjit+∑j=1nzjt+1xjit+1≤xji,∑j=1nzjtyjrt+∑j=1nzjt+1yjrt+1≥yjr,∑j=1nzjtbjft+∑j=1nzjt+1bjft+1=bjf,∑j=1nzj=1,zj≥0;∀n,i,r,f.Note that there are two values (βj'tBt and βj't+1Bt) in period t, which are inefficiency measurement. Both values are obtained by using the biennial production frontier in period t as the benchmark. Equations (3) and (4) are the linear programming of βj'tBt for BWMRM and BBAM with VRS according to inputs and outputs (shown in Table 1), respectively. Due to space, the programming of βj't+1Bt for two models is shown in Appendix A. The two types of linear programming are for the DMU j in the period t, and those for other DMUs in another period can be built similarly. The study uses the values to acquire the AGTFP growth, detailed in the next section. M, Q, and H are the total number of inputs, desirable outputs, and undesirable outputs, respectively. sj'xmBt, sj'yqBt, and sj'bhBt are slack variables of them, respectively. The subscript V means VRS.(3)D⟶j′VBtxt,yt,bt;gt=βj′tBt=Max1212M∑m=1Msj′xmBtxmj′t+12Q+H∑q=1Qsj′yqBtyqj′t+∑h=1Hsj′bhBtbhj′t+13M∑m=1Msj′xmBtxmj′t+13Q∑q=1Qsj′yqBtyqj′t+13H∑h=1Hsj′bhBtbhj′ts.t.∑j=1Jzjtxjmt+∑j=1Jzjt+1xjmt+1≤xj′mt+sj′xmBt,for∀m=1,2,…,M∑j=1Jzjtyjqt+∑j=1Jzjt+1yjqt+1≥yj′qt+sj′yqBt,for∀q=1,2,…,Q∑j=1J=1zjtbjht+∑j=1J=1zjt+1bjht+1=bj′ht+sj′bhBt,for∀h=1,2,…,Hzj≥0;sj′yqBt≥0;sj′bhBt≥0;sj′xmBt≥0;∑j=1Jzjt+∑j=1Jzjt+1=1;J=1…J.t=1,2,…,T.(4)D⟶j′VBtxt,yt,bt;gt=βj′tBt=Max1212M∑m=1Msj′xmBtmaxxmt−xmj′t+12Q+H∑q=1Qsj′yqBtmaxyqt−yqj′t+∑h=1Hsj′bhBtmaxbht−bhj′t+13M∑m=1Msj′xmBtmaxxmt−xmj′t+13Q∑q=1Qsj′yqBtmaxyqt−yqj′t+13H∑h=1Hsj′bhBtmaxbht−bhj′t,s.t.∑j=1Jzjtxjmt+∑j=1Jzjt+1xjmt+1≤xj′mt+sj′xmBt,for∀m=1,2,…,M∑j=1Jzjtyjqt+∑j=1Jzjt+1yjqt+1≥yj′qt+sj′yqBt,for∀q=1,2,…,Q∑j=1J=1zjtbjht+∑j=1J=1zjt+1bjht+1=bj′ht+sj′bhBt,for∀h=1,2,…,Hzj≥0;sj′yqBt≥0;sj′bhBt≥0;sj′xmBt≥0;∑j=1Jzjt+∑j=1Jzjt+1=1;J=1….J.t=1,2,…,T.


### 2.3. Green Luenberger Productivity Indicator

The DEA models always combine with some indexes, including the Malmquist index and Luenberger index. This study introduced the green Luenberger productivity indicator (GLPI) to the green performance of agriculture in China because of its higher accuracy level of confidence than the Malmquist index [43, 44], as shown in (5). GLPI is used to measure the dynamic change of AGTFP, for which a value greater than 0 indicates an increase in TFP compared to the previous period, and a value less than 0 indicates the opposite.(5)GLPIVBt+1=D⟶VBtxt,yt,bt;gt−D⟶VBtxt+1,yt+1,bt+1;gt+1=βtBt−βt+1Bt.Furthermore, GLPI can be decomposed into efficiency change (EC) and technology change (TC), essential for studying TFP. What EC measures is the distance between one DMU and the frontier, the gap between actual production and maximum production under the condition of the current technical level unchanged. TC depicts the movement of the production frontier, meaning the change of technical level. The value of each decomposition is more than, less than, and equal to 0, meaning that the indicator deteriorates, is enhanced, and is kept constant, respectively.βt and βt+1 are inefficiency in periods t and t+1, respectively, and the production frontier, which they consider as the benchmark, is constructed using DMUs of single period t or t+1. They can be calculated by the linear programming in Appendix B.(6)ECVB=D⟶Vtxt,yt,bt;gt−D⟶Vtxt+1,yt+1,bt+1;gt+1=βt−βt+1,TCVB=D⟶VBtxt,yt,bt;gt−D⟶Vtxt,yt,bt;gt−DVBtxt+1,yt+1,bt+1;gt+1−D⟶Vtxt+1,yt+1,bt+1;gt+1⟶,=βtBt−βt−βt+1Bt−βt+1,GLPI, EC, and TC are all relative values, so the cumulative TFP (CTFP) based on the value of one year and its decomposition also are used in this study, which enables analysis of AGTFP from a different perspective.


### 2.4. Kernel Density Estimation

The kernel density estimation can reflect the distribution location, morphology, and ductility of a random variable. It uses a smooth peak function to fit the sample data and a continuous density curve to describe the random variable distribution. Suppose the density function of the random variableX is(7)fx=1Nh∑i=1NKXi−xh,where N is the number of observed values and Xi is the observed value. Each Xi is independent of the other and has the identical distribution. K is the kernel function, and h is the window width. The kernel function K is a weighting function or smooth conversion function, which should meet the following requirements:(8)limx⟶∞Kx⋅x=0Kx≥0∫−∞+∞Kxdx=1supKx<+∞∫−∞+∞Kx2dx<+∞.Commonly used kernel functions include Gaussian, Triangle, Quartic, and Epanechnikov, and this study chose Gaussian. This estimation result was sensitive to the selection of window widthh, so an as small as possible window width was chosen to improve the estimation accuracy [45].


### 2.5. Dagum Gini Ratio and Its Decomposition

The Dagum Gini ratio was used to study regional differences of AGTFP [46]. Firstly, the formula for calculating the total Gini ratio G of all subregions is(9)G=∑j=1k∑h=1k∑i=1nj∑r=1nhyji−yhr2n2y¯,where j or h is the subscript of the region and i or r is the subscript of the province. n is the total number of provinces, and k is the total number of regions. njnh is the number of provinces within the region jh. yjiyhr is the TFP index of the province ir in the region jh, and y¯ is the mean of TFP of all the provinces.Before the total Gini ratioG is decomposed by subregions, k regions are sorted according to the TFP mean of each region. G can be decomposed into Gw, Gnb, and Gt, for which the sum of them is equal to G. Gw measures the contribution of the Gini inequality within subregions to the total Gini ratio G. Gnb measures the net contribution of the extended Gini inequality between subregions to the total Gini ratio G. Gt measures the contribution of the income intensity of transvariation between subregions to the total Gini ratio G. The sum of Gnb and Gt is Ggb, measuring the gross contribution of the extended Gini inequality between subregions to the total Gini ratio G. The Gini ratio within the region j is Gjj , and the Gini ratio between the region j and the region h is Gjh. In (11), pj=nj/n and sj=njyj¯/ny¯ , j=1,2,…,k. In (13), Djh is the relative influence of TFP between the region j and the region h, as shown in (15); djh is the difference in TFP between the region j and the region h, the expected value of the sum of all samples with yji−yhr>0 in the region j and the region h, as shown in (16). pjh is the first moment of transvariation, the expected value of the sum of all samples with yhr−yji>0 in the region j and the region h, as shown in (17). Fj and Fh are the cumulative distribution function of AGTFP in the region j and the region h, respectively.(10)Gjj=1/2yj¯∑i=1nj∑r=1njyji−yjrnj2.(11)Gw=∑j=1kGjjpjsj.(12)Gjh=∑i=1nj∑r=1nhyji−yhrnjnhyj¯+yh¯.(13)Gnb=∑j=2k∑h=1j−1Gjhpjsh+phsjDjh.(14)Gt=∑j=2k∑h=1j−1Gjhpjsh+phsj1−Djh.(15)Djh=djh−pjhdjh+pjh.(16)djh=∫0∞dFjy∫0yy−xdFhx.(17)pjh=∫0∞dFhy∫0yy−xdFjx.(18)Ggb=Gnb+Gt.


### 2.6.σ and β Convergence Models

This study tested theσ convergence and the β convergence to investigate the evolution trend of AGTFP difference in China. The σ convergence is the process by which deviation decreases over time. The analysis of the σ convergence mainly uses the coefficient of variation, the ratio of the standard deviation to the mean, to measure the degree of difference of the observed values as shown in (19). The subscript j is the region (j=1,2,3,…,), and the subscript i is the province included in the region. Nj is the number of provinces in the region j, and TFPij¯ is the mean of TFP in the region j.(19)σ=∑iNjTFPij−TFPij¯2/NjTFPij¯.Theβ convergence refers to the fact that underdeveloped regions catch up with developed ones over time because of their higher growth rates and finally reach the convergence state with the same growth rate. The β convergence includes the conditional β convergence and the absolute β convergence. Only the absolute convergence was analysed in this study, and the model is shown as (20). The subscript i is the province, and the subscript t is the time. TFPi,t and TFPi,t+1 are TFP of the region j in the periods t and t+1. β is the convergence coefficient. If β<0 and passes the significance test, it indicates that the β convergence of China’s AGTFP exists. If β>0 and passes the significance test, divergence is indicated. μi, ηt, and εit refer to the spacing effect, the time effect, and the interference term, respectively.(20)lnTFPi,t+1TFPi,t=α+βlnTFPi,t+ui+ηt+εit.


### 2.7. Data

The sample includes data from 31 provinces in China (excluding Hong Kong, Macao, and Taiwan) from 1997 to 2016, obtained from the China Rural Statistical Yearbook, the China Agricultural Yearbook, the China Agricultural Statistics, the China Animal Husbandry Yearbook, and the Statistical Yearbook of China.


## 2.1. Selection of Input and Output Indicators

The measurement of TFP requires input and output of each province, which in this paper are shown in Table1, including eight inputs, one desirable output, and one undesirable output. In this study, the ACESs included five categories: (1) agricultural materials; (2) rice cultivation; (3) soil surface releasing when planting crops; (4) livestock and poultry farming; (5) straw burning. The five also include a variety of specific subsources, as shown in Table 2. The study calculated ACEs of agricultural materials and straw burning by carbon emission coefficients from the IPCC report [35]. For other ACESs, their carbon emission coefficients are constructed in terms of the greenhouse effect. Specifically, this study first calculated the amount of N2O and CH4 released with N2O and CH4 emission coefficients and then converted them to standard carbon emissions with the carbon conversion coefficients. The N2O and CH4 emission coefficients mean the amount the corresponding substance per unit source can release. The carbon conversion coefficients of N2O and CH4 mean how many carbons per unit N2O or CH4 are equal in terms of the greenhouse effect. Those coefficients are based on previous papers [35–38]. The ACESs can be converted into ACEs by (1)E=∑i5Ei=∑i5∑jNiQij×cij,where E is the total ACEs, Ei is ACE of the carbon source ii=1,2,3,4,5, and Qij and cij represent the amount and carbon emission coefficients of the carbon subsource j in the source i, respectively.Table 1
Construction of input and output indicators.
FactorIndicatorOutputDesirable output (Y)The actual agricultural productionUndesirable output (C)Agricultural carbon emissionsLabor (L)The number of agricultural practitionersLand (N)Area sown with cropsMachinery (E)Electricity consumption of agricultural machineryInputFertilizer (F)Applying quantity of chemical fertilizer (refractive index)Pesticide (P)Consumption of chemical pesticidesAgricultural film (R)The amount of agricultural film usedAgricultural water (W)Actual irrigation areaFarm animals (A)The number of farm draft animalsTable 2
Agricultural carbon emission sources.
SourcesSubsourcesCoefficientsAgricultural materialsFertilizer, pesticides, plastic sheeting, diesel oil, and energy consumption for irrigationccRice cultivationEarly rice, late rice, and in-season ricecCH4  ∗ tCH4Soil surface releasing when planting cropsPaddy rice, winter wheat, spring wheat, soybean, corn, and vegetablescN2O ∗ tN2OLivestock and poultry farmingCow, buffalo, cattle, mule, camel, donkey, horse, pig, sheep, goat, rabbit, and poultrycCH4  ∗ tCH4+ cN2O ∗ tN2OStraw burningRice, wheat, corn, rape, soybean, and cotton strawccNote: cc, cCH4, and cN2O refer to carbon, N2O, and CH4 emission coefficients. tCH4 and tN2O are the carbon conversion coefficients of N2O and CH4, respectively.


## 2.2. BWMRM and BBAM

The biennial environmental production technology is employed, which considers the negative impact of production on the environment, integrating inputs, desirable outputs, and undesirable outputs in the framework and constructs the production frontier using the two-period decision-making units (DMUs). Suppose thatx, y, and b represent inputs, desirable outputs, and undesirable outputs, respectively.For DMU jj=1…n in period tt=1…T, its input-output set is xj,t,yj,t,bj,t. The biennial environmental production technology allows for technical regression. In addition, it does not need to be recomputed when a new period is added to the data set and can avoid infeasibility, a vital issue in the DEA model [39]. It is in accord with the three assumptions (weak disposability, null-jointness, and the compact set). The technology is shown as (2). Note that z is the intensity variable. ∑j=1nzj=1 and zj≥0 means variable returns to scale (VRS).BWMRM and BBAM are based on the weighted Russell directional distance model and the biennial environmental production technology [39–41]. The difference between the two models is the direction vector [42]. There are three advantages compared with other directional distance function models: (1) the infeasibility can be overcome because of the biennial technology; (2) it is a nonradial and nonoriented inefficiency estimation, so input and output slacks are all included, and different percentage increases or decreases are also allowed (this study measures from the inefficiency side, in which the sum of all the weights to factors is 1; the greater the value of the objective function, the lower the efficiency); (3) it can reduce the impact of outliers on efficiency result. The production frontier is variable over time, and outliers in one period can just influence the result of the period.(2)T=x,y,b:∑j=1nzjtxjit+∑j=1nzjt+1xjit+1≤xji,∑j=1nzjtyjrt+∑j=1nzjt+1yjrt+1≥yjr,∑j=1nzjtbjft+∑j=1nzjt+1bjft+1=bjf,∑j=1nzj=1,zj≥0;∀n,i,r,f.Note that there are two values (βj'tBt and βj't+1Bt) in period t, which are inefficiency measurement. Both values are obtained by using the biennial production frontier in period t as the benchmark. Equations (3) and (4) are the linear programming of βj'tBt for BWMRM and BBAM with VRS according to inputs and outputs (shown in Table 1), respectively. Due to space, the programming of βj't+1Bt for two models is shown in Appendix A. The two types of linear programming are for the DMU j in the period t, and those for other DMUs in another period can be built similarly. The study uses the values to acquire the AGTFP growth, detailed in the next section. M, Q, and H are the total number of inputs, desirable outputs, and undesirable outputs, respectively. sj'xmBt, sj'yqBt, and sj'bhBt are slack variables of them, respectively. The subscript V means VRS.(3)D⟶j′VBtxt,yt,bt;gt=βj′tBt=Max1212M∑m=1Msj′xmBtxmj′t+12Q+H∑q=1Qsj′yqBtyqj′t+∑h=1Hsj′bhBtbhj′t+13M∑m=1Msj′xmBtxmj′t+13Q∑q=1Qsj′yqBtyqj′t+13H∑h=1Hsj′bhBtbhj′ts.t.∑j=1Jzjtxjmt+∑j=1Jzjt+1xjmt+1≤xj′mt+sj′xmBt,for∀m=1,2,…,M∑j=1Jzjtyjqt+∑j=1Jzjt+1yjqt+1≥yj′qt+sj′yqBt,for∀q=1,2,…,Q∑j=1J=1zjtbjht+∑j=1J=1zjt+1bjht+1=bj′ht+sj′bhBt,for∀h=1,2,…,Hzj≥0;sj′yqBt≥0;sj′bhBt≥0;sj′xmBt≥0;∑j=1Jzjt+∑j=1Jzjt+1=1;J=1…J.t=1,2,…,T.(4)D⟶j′VBtxt,yt,bt;gt=βj′tBt=Max1212M∑m=1Msj′xmBtmaxxmt−xmj′t+12Q+H∑q=1Qsj′yqBtmaxyqt−yqj′t+∑h=1Hsj′bhBtmaxbht−bhj′t+13M∑m=1Msj′xmBtmaxxmt−xmj′t+13Q∑q=1Qsj′yqBtmaxyqt−yqj′t+13H∑h=1Hsj′bhBtmaxbht−bhj′t,s.t.∑j=1Jzjtxjmt+∑j=1Jzjt+1xjmt+1≤xj′mt+sj′xmBt,for∀m=1,2,…,M∑j=1Jzjtyjqt+∑j=1Jzjt+1yjqt+1≥yj′qt+sj′yqBt,for∀q=1,2,…,Q∑j=1J=1zjtbjht+∑j=1J=1zjt+1bjht+1=bj′ht+sj′bhBt,for∀h=1,2,…,Hzj≥0;sj′yqBt≥0;sj′bhBt≥0;sj′xmBt≥0;∑j=1Jzjt+∑j=1Jzjt+1=1;J=1….J.t=1,2,…,T.


## 2.3. Green Luenberger Productivity Indicator

The DEA models always combine with some indexes, including the Malmquist index and Luenberger index. This study introduced the green Luenberger productivity indicator (GLPI) to the green performance of agriculture in China because of its higher accuracy level of confidence than the Malmquist index [43, 44], as shown in (5). GLPI is used to measure the dynamic change of AGTFP, for which a value greater than 0 indicates an increase in TFP compared to the previous period, and a value less than 0 indicates the opposite.(5)GLPIVBt+1=D⟶VBtxt,yt,bt;gt−D⟶VBtxt+1,yt+1,bt+1;gt+1=βtBt−βt+1Bt.Furthermore, GLPI can be decomposed into efficiency change (EC) and technology change (TC), essential for studying TFP. What EC measures is the distance between one DMU and the frontier, the gap between actual production and maximum production under the condition of the current technical level unchanged. TC depicts the movement of the production frontier, meaning the change of technical level. The value of each decomposition is more than, less than, and equal to 0, meaning that the indicator deteriorates, is enhanced, and is kept constant, respectively.βt and βt+1 are inefficiency in periods t and t+1, respectively, and the production frontier, which they consider as the benchmark, is constructed using DMUs of single period t or t+1. They can be calculated by the linear programming in Appendix B.(6)ECVB=D⟶Vtxt,yt,bt;gt−D⟶Vtxt+1,yt+1,bt+1;gt+1=βt−βt+1,TCVB=D⟶VBtxt,yt,bt;gt−D⟶Vtxt,yt,bt;gt−DVBtxt+1,yt+1,bt+1;gt+1−D⟶Vtxt+1,yt+1,bt+1;gt+1⟶,=βtBt−βt−βt+1Bt−βt+1,GLPI, EC, and TC are all relative values, so the cumulative TFP (CTFP) based on the value of one year and its decomposition also are used in this study, which enables analysis of AGTFP from a different perspective.


## 2.4. Kernel Density Estimation

The kernel density estimation can reflect the distribution location, morphology, and ductility of a random variable. It uses a smooth peak function to fit the sample data and a continuous density curve to describe the random variable distribution. Suppose the density function of the random variableX is(7)fx=1Nh∑i=1NKXi−xh,where N is the number of observed values and Xi is the observed value. Each Xi is independent of the other and has the identical distribution. K is the kernel function, and h is the window width. The kernel function K is a weighting function or smooth conversion function, which should meet the following requirements:(8)limx⟶∞Kx⋅x=0Kx≥0∫−∞+∞Kxdx=1supKx<+∞∫−∞+∞Kx2dx<+∞.Commonly used kernel functions include Gaussian, Triangle, Quartic, and Epanechnikov, and this study chose Gaussian. This estimation result was sensitive to the selection of window widthh, so an as small as possible window width was chosen to improve the estimation accuracy [45].


## 2.5. Dagum Gini Ratio and Its Decomposition

The Dagum Gini ratio was used to study regional differences of AGTFP [46]. Firstly, the formula for calculating the total Gini ratio G of all subregions is(9)G=∑j=1k∑h=1k∑i=1nj∑r=1nhyji−yhr2n2y¯,where j or h is the subscript of the region and i or r is the subscript of the province. n is the total number of provinces, and k is the total number of regions. njnh is the number of provinces within the region jh. yjiyhr is the TFP index of the province ir in the region jh, and y¯ is the mean of TFP of all the provinces.Before the total Gini ratioG is decomposed by subregions, k regions are sorted according to the TFP mean of each region. G can be decomposed into Gw, Gnb, and Gt, for which the sum of them is equal to G. Gw measures the contribution of the Gini inequality within subregions to the total Gini ratio G. Gnb measures the net contribution of the extended Gini inequality between subregions to the total Gini ratio G. Gt measures the contribution of the income intensity of transvariation between subregions to the total Gini ratio G. The sum of Gnb and Gt is Ggb, measuring the gross contribution of the extended Gini inequality between subregions to the total Gini ratio G. The Gini ratio within the region j is Gjj , and the Gini ratio between the region j and the region h is Gjh. In (11), pj=nj/n and sj=njyj¯/ny¯ , j=1,2,…,k. In (13), Djh is the relative influence of TFP between the region j and the region h, as shown in (15); djh is the difference in TFP between the region j and the region h, the expected value of the sum of all samples with yji−yhr>0 in the region j and the region h, as shown in (16). pjh is the first moment of transvariation, the expected value of the sum of all samples with yhr−yji>0 in the region j and the region h, as shown in (17). Fj and Fh are the cumulative distribution function of AGTFP in the region j and the region h, respectively.(10)Gjj=1/2yj¯∑i=1nj∑r=1njyji−yjrnj2.(11)Gw=∑j=1kGjjpjsj.(12)Gjh=∑i=1nj∑r=1nhyji−yhrnjnhyj¯+yh¯.(13)Gnb=∑j=2k∑h=1j−1Gjhpjsh+phsjDjh.(14)Gt=∑j=2k∑h=1j−1Gjhpjsh+phsj1−Djh.(15)Djh=djh−pjhdjh+pjh.(16)djh=∫0∞dFjy∫0yy−xdFhx.(17)pjh=∫0∞dFhy∫0yy−xdFjx.(18)Ggb=Gnb+Gt.


## 2.6.σ and β Convergence Models

This study tested theσ convergence and the β convergence to investigate the evolution trend of AGTFP difference in China. The σ convergence is the process by which deviation decreases over time. The analysis of the σ convergence mainly uses the coefficient of variation, the ratio of the standard deviation to the mean, to measure the degree of difference of the observed values as shown in (19). The subscript j is the region (j=1,2,3,…,), and the subscript i is the province included in the region. Nj is the number of provinces in the region j, and TFPij¯ is the mean of TFP in the region j.(19)σ=∑iNjTFPij−TFPij¯2/NjTFPij¯.Theβ convergence refers to the fact that underdeveloped regions catch up with developed ones over time because of their higher growth rates and finally reach the convergence state with the same growth rate. The β convergence includes the conditional β convergence and the absolute β convergence. Only the absolute convergence was analysed in this study, and the model is shown as (20). The subscript i is the province, and the subscript t is the time. TFPi,t and TFPi,t+1 are TFP of the region j in the periods t and t+1. β is the convergence coefficient. If β<0 and passes the significance test, it indicates that the β convergence of China’s AGTFP exists. If β>0 and passes the significance test, divergence is indicated. μi, ηt, and εit refer to the spacing effect, the time effect, and the interference term, respectively.(20)lnTFPi,t+1TFPi,t=α+βlnTFPi,t+ui+ηt+εit.


## 2.7. Data

The sample includes data from 31 provinces in China (excluding Hong Kong, Macao, and Taiwan) from 1997 to 2016, obtained from the China Rural Statistical Yearbook, the China Agricultural Yearbook, the China Agricultural Statistics, the China Animal Husbandry Yearbook, and the Statistical Yearbook of China.


## 3. Results and Discussion

The analysis of AGTFP measured by the two models (BWMRM and BBAM) shows that the results are very similar, so the conclusion is robust. The following section considers the relevant results of BWMRM as the main example to illustrate.


### 3.1. The Trend Analysis of AGTFP and Its Decomposition

Figure1 shows the mean of China’s cumulative GLPI (CGLPI), cumulative TC (CTC), GLPI, and TC calculated using BWMRM and BBAM over the period 1998–2016. As the two models nearly have the same outcomes, the result is generally robust. GLPI and TC always were positive, so CGLPI and CTC increased year by year. Meanwhile, the line (CTC) is always above the line (CGLPI), revealing that cumulative efficiency change (CEC) was always negative. These indicated that AGTFP increased with the drive of TC, and EC was the obstacle to the improvement. That can also be drawn from the way in which the line (GLPI) representing the AGTFP growth in one year or the AGTFP growth rate was always below the line (TC) except the years 1999, 2003, 2005, 2008, and 2013. That corresponded with most research on the green productivity of Chinese agriculture. Since the reform and opening-up in 1978, China has vigorously introduced advanced production technologies, so TC was always positive, and China’s agricultural productivity has been increasing for decades. In addition, since 2005, the “three rural issues” have been the top priority of the central government, and many policies to promote agriculture have been introduced.Figure 1
The dynamic change of AGTFP growth in China.The kernel density estimation was used to analyse the dynamic characteristics of the distribution of AGTFP growth rate in China, and the result is shown in Figure2. First, the midpoint of the distribution curve of the two models has no significant deviation during the observation period, indicating that the GLPI of most provinces fluctuated around zero. Second, the height of the main peak goes through the process “up-down-up-down-up-down,” and the width goes through the process “narrowing-widening-narrowing-widening.” Although the height of the main peak does not have an obvious direction of change, the width becomes wider. In addition, the distance between the rightmost side peaks and the main peak has little change. These phenomena meant that the dispersion degree of GLPI increased.Figure 2
The dynamic distribution of kernel density estimation of GLPI in China.In this study, 31 provincial areas in China were divided into three regions, the east, the middle, and the west, and the sample period was divided into four time periods. The eastern area includes Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan. The middle area includes Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, and Hunan. The western area includes Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang. Table3 shows the mean of GLPI and its components in five periods (including 1998–2016).Table 3
The mean of GLPI and its components.
BWMRMRegionIndex1998–20012002–20062007–20112012–20161998–2016EastGLPI0.01390.01680.02210.03380.0221EC0.00080.00130.00010.00270.0012TC0.01310.01550.02200.03120.0208MiddleGLPI0.01260.04220.04240.04510.0368EC−0.02650.0008−0.00020.0001−0.0054TC0.03920.04140.04250.04500.0422WestGLPI0.02260.02750.00480.03510.0225EC−0.0116−0.0064−0.0069−0.0078−0.0080TC0.03420.03390.01180.04290.0305ChinaGLPI0.01690.02750.02060.03720.0260EC−0.0111−0.0018−0.0027−0.0021−0.0041TC0.02800.02930.02330.03930.0301BBAMEastGLPI0.01480.01580.02690.05700.0294EC0.00090.00140.00010.00270.0013TC0.01390.01440.02680.05430.0281MiddleGLPI0.01330.04590.04320.04750.0387EC−0.02910.0023−0.00030.0014−0.0052TC0.04230.04360.04350.04610.0440WestGLPI0.02580.03040.00670.03580.0246EC−0.0113−0.0064−0.0052−0.0082−0.0076TC0.03710.03670.01190.04400.0322ChinaGLPI0.01870.02920.02330.04630.0299EC−0.0116−0.0014−0.0021−0.0019−0.0038TC0.03020.03060.02540.04820.0338GLPI and TC of China and its three regions were greater than 0 in each period. EC was very small and even negative in two periods of the middle and four periods in the west. Therefore, for the regions, TC was the main driver of AGTFP, and EC played a minor role or even hindered, exactly in line with the conclusion in Figure1. That indicated that although the government vigorously developed and introduced advanced technology, it neglected management experience, organization form, and production scale to improve productivity. GLPI of all the regions increased period by period, meaning that the growth rate got faster and faster, except the western region in the period 2007–2011. GLPI of the west declined precipitously to 0.0048, a meager value compared to the east, 0.0221, and that of the middle, 0.0424, and so did TC; it was just 0.0118 in the period. For the mean of GLPI in entire China, there was also an oscillation in 2007–2011, falling to 0.0206. That was possibly because of many natural disasters in western China during the period. Natural conditions in western China make it more prone to natural disasters, such as earthquakes and debris flow.What GLPI measures is the AGTFP growth rate, which is the growth of one year. This study calculated CGLPI to measure the growth of multiple years to the base year. Table4 shows the mean of CGLPI and its components in five periods. According to CGLPI of the two periods (1998–2016 and 2012–2016), taking 1997 as the base period, the middle experienced the largest AGTFP growth by 2016, followed by the west, and the east was the lowest. The cumulative AGTFP (CAGTFP) was constructed based on the AGTFP in 1997 to compare the absolute AGTFP level of regions or provinces. By comparing the sum of AGTFP in 1997 and CGLPI in each region, this study estimated which region has the largest AGTFP. In BWMRM, the east and the middle had similar CAGTFP, and the west was the least. In BBAM, the east had the largest CAGTFP, followed by the middle and then the west. Although this method is not accurate enough, it can reflect some information, so this study adopted the result of BBAM.Table 4
The mean of CGLPI and its components in three regions.
BWMRMRegionIndex1998–20012002–20062007–20112012–20161998–2016EastCGLPI0.03910.09410.21890.34810.1822CEC0.00320.00030.01300.01070.0070CTC0.03590.09380.20590.33740.1752MiddleCGLPI0.04390.16550.39450.60460.3157CEC−0.0650−0.0985−0.0963−0.1064−0.0929CTC0.10890.26400.49080.71100.4087WestCGLPI0.04610.18380.24660.38010.2230CEC−0.0215−0.0632−0.0923−0.1316−0.0801CTC0.06760.24710.33890.51170.3031ChinaCGLPI0.04300.14730.27490.42670.2325CEC−0.0239−0.0498−0.0560−0.0746−0.0525CTC0.06700.19710.33090.50130.2850BBAMEastCGLPI0.04150.09420.23430.45350.2145CEC0.00360.00060.01380.01150.0075CTC0.03800.09360.22050.44210.2070MiddleCGLPI0.04770.17940.41700.63820.3349CEC−0.0703−0.1027−0.1001−0.1054−0.0959CTC0.11800.28210.51700.74350.4308WestCGLPI0.05590.20680.27740.41850.2493CEC−0.0175−0.0611−0.0887−0.1244−0.0758CTC0.07340.26790.36600.54290.3251ChinaCGLPI0.04870.15980.29810.48760.2591CEC−0.0237−0.0500−0.0553−0.0713−0.0514CTC0.07230.20970.35340.55890.3105The agriculture production efficiency is determined by agricultural resource endowment, policy environment, and many other factors. The east with better resource endowments had the highest AGTFP. However, it did not have the most considerable growth because the high AGTFP resulted in less room for improvement. Overall, in the mountainous area in western China, there is no advantage of large-scale grain cultivation. Although China has introduced “the western development” policy to help the backward western development, the positive effect of the policy does not offset the negative effect of natural agriculture conditions. Therefore, the middle with more plains became the region with the biggest growth.This study also conducted a detailed provincial analysis of AGTFP. Henan, Xinjiang, Sichuan, Hebei, Shandong, and Shaanxi had the best AGTFP performance that their CGLPI and CAGTFP of two periods (2012–2016 and 1998–2016) were the highest, the top 20 percent of provinces. Henan, Sichuan Hebei, Shandong, and Shaanxi, having large populations and fertile plains suitable for farming, are major agricultural provinces in China. As agriculture is their industrial orientation, the government has invested a lot, such as policies and technology, to develop their agriculture. Although Xinjiang has a cold climate and a lot of deserts, the government of China has tilted many policy resources for development, and in addition, there are vast areas and rich water resources for developing characteristic agriculture well.Among the slowest growth areas were Ningxia, Tibet, Hainan, Shanghai, and Qinghai, where the CGLPI of two periods (2012–2016 and 1997–2016) was less than 0.1. Agriculture in Shanghai was a small part of the economy, and the area was economically developed and had advanced agricultural production technology. So, there was little room and impetus for improvement. On the contrary, the economic and technological bases were weak for Ningxia, Tibet, Hainan, and Qinghai. Their natural environment was also unsuitable for agriculture like Xinjiang, which was less attractive to talents, so it was not easy to improve the AGTFP. But their CAGTFP was not very low because of a good performance in 1997. Shanxi, Gansu, and Jiangxi, which also had poor agricultural conditions, had the lowest CAGTFP.According to the above analysis, AGTFP in western China declined significantly in the period 2007–2011. CGLPI in Sichuan (from 0.0916 in 2002–2006 to 0.0295 in 2007–2011) and Qinghai (from 0 in 2002–2006 to −0.0758 in 2007–2011) declined significantly. It may be due to the frequent geological disasters in the two regions from 2007 to 2011, such as the Wenchuan earthquake in 2008, the Yushu earthquake, and the Yushu debris flow in 2010. TC was the drive of AGTFP, and EC always was negative in the middle and the western provinces, except Henan of the middle; its EC was always greater than 0. Although Tables3 and 4 show that EC in the eastern region played a positive role, only Hebei had an excellent performance in EC, and EC of other areas was very small. With a large population, plains with fertile soil, and abundant water, Henan and Hebei are major agricultural provinces in China, so there is a suitable environment for the growth of crops. These places make it easier to scale up agricultural production, improving EC.


### 3.2. The Difference Decomposition of China’s AGTFP

To further reveal the total difference and its sources, this study calculated and decomposed the Dagum Gini ratio of AGTFP. Note that AGTFP here is based on the TFP in 1997, so it is the above CAGTFP. The convergence analysis section also uses the AGTFP. Figures3 and 4 show the Gini inequality within subregions and the net contribution of the extended Gini inequality between subregions of AGTFP, respectively.Figure 3
The dynamic change of Gini inequality within subregions of AGTFP in China.Figure 4
The dynamic change of the net contribution of the extended Gini inequality between subregions of AGTFP in China.The Gini inequality within each region generally widened, although there were slight declines in some years. The inequality in the east was always lower than that in other regions. It decreased continuously from 0.0245 in 1997 to 0.0127 in 2000 and then fluctuated to 0.1336 in 2016. Additionally, the equality in the middle was the largest during 1998–1999 but smaller than that of the western region during 1999–2005. From 2006, it overtook the west, becoming the region with the largest Gini inequality again until 2016. This extended Gini ratio between regions increased on the whole and represented the difference of AGTFP between the two regions, and the larger the value, the more significant the difference. The value of middle-west was the largest, followed by that of east-middle, and east-west was the smallest.This study further analysed the difference of AGTFP among regions for decomposition and quantification, and Table5 shows the result. In general, Gw, the intraregional difference, and Gt, the effect of cross-overlap between different regions on the total difference, increased, and Gnb, the net interregional difference, was just the opposite. Changes in the proportion of each source to the total difference were like the absolute quantities, except that the percentage of intraregional difference grew slowly. For the ratio of sources, the percentage of Gw rose from 22.3 percent in 1997 to 30.48 percent in 2016, about 1.37 times. However, Gw went from 0.0221 in 1997 to 0.073 in 2016, just about 3.3 times, stemming from a significant increase in the total difference. The percentage of the sum of Gt and Gnb, Ggb, in each year was about 65, consistent with the increase of coefficients shown in Figures 3 and 4. So, the total difference between regions was the primary source, accounting for an average of 65 percent per year, and the difference within regions was 35 percent.Table 5
The three components of the total Gini ratio of AGTFP in China.
BWMRMYearGwPGwGnbPGnbGtPGtG19970.009921.070.028460.410.008718.520.047019980.013423.850.026246.670.016529.480.056119990.017726.950.024737.570.023335.480.065720000.013424.200.028351.290.013524.500.055320010.017225.630.035753.300.014121.070.066920020.021628.850.036648.990.016622.160.074820030.024829.260.036543.070.023527.660.084820040.029130.700.037339.320.028429.970.094920050.033130.740.027325.350.047243.920.107620060.037831.600.021117.660.060650.740.119520070.038931.510.012410.030.072158.470.123320080.044031.850.00946.820.084861.340.138220090.045631.780.00725.020.090763.210.143520100.049331.710.00996.370.096361.930.155420110.053131.600.01317.770.101860.630.168020120.056031.510.01659.300.105159.190.177620130.058831.580.01809.680.109458.740.186320140.059331.270.01668.750.113859.980.189720150.063831.390.01708.360.122560.250.203320160.065631.450.01919.140.124059.400.2087BBAM19970.009921.070.028460.410.008718.520.047019980.015024.770.025442.080.020033.150.060419990.020127.870.023833.060.028139.080.072020000.015325.470.030049.820.014924.710.060220010.019226.260.037851.690.016122.040.073120020.023729.050.039147.840.018923.110.081620030.027129.560.038842.360.025728.080.091520040.032731.090.039837.840.032731.080.105220050.036431.050.029224.930.051644.020.117120060.041331.880.024018.530.064249.590.129420070.041031.640.014211.000.074357.370.129520080.046431.870.01258.590.086659.540.145520090.048031.890.00926.120.093361.990.150520100.051231.680.01036.360.100161.950.161520110.053631.560.01378.040.102660.400.169820120.057431.540.01508.270.109560.180.181920130.062031.590.00703.580.127164.830.196120140.065431.790.00964.660.130763.550.205720150.070031.940.01667.570.132660.490.219320160.071431.870.01948.630.133459.490.2242Note:Gw is the Gini inequality within subregions; Gnb is the net contribution of the extended Gini inequality between subregions; Gt is the contribution of the intensity of transvariation between subregions; PGw, PGnb, and PGt are the percentage of Gw, Gnb, and Gt, respectively.The central government has encouraged local governments to pursue GDP following local conditions while ensuring a certain amount of arable land rather than requiring balanced agricultural development. Therefore, the overall difference expanded. Generally, the provinces within a region have more similar agricultural conditions than between regions. So, the difference between regions became the primary source of total difference.


### 3.3. The Analysis of Convergence

This paper employed the coefficient of variation to analyse theσ convergence of AGTFP in China. Due to space limitations, the result of the coefficient of variation is not reported. According to the result, the coefficients of variation of the whole country, the east, the middle, and the west showed a significant upward trend. The average annual growth rate was 8.98%, 7.59%, 11.12%, and 11.54%, respectively. Therefore, there is no trend of σ convergence.Before testingβ convergence, this paper used the Moran index to investigate the spatial correlation of AGTFP, shown in Table 6. However, the result was insignificant, so the spatial lag effect was not included in the β convergence model.Table 6
The absoluteβ convergence test results of AGTFP in China and its subregions.
ModelEastMiddleWestChinaBWMRMβ−0.0230∗−0.0039∗−0.0477∗∗∗−0.0066∗∗∗(−1.8809)(−1.7925)(−3.3800)(−2.8341)Constant2.8397∗∗∗2.8386∗∗∗2.9248∗∗∗2.8189∗∗∗(68.5993)(58.9239)(42.4436)(99.1227)Convergence speed0.02320.00390.04880.0066R-squared0.10.1260.1160.041BBAMβ−0.0031−0.0038∗−0.0441∗∗∗−0.0061∗∗(−0.2948)(−1.7922)(−2.9792)(−2.3540)Constant2.7918∗∗∗2.8578∗∗∗2.9835∗∗∗2.8509∗∗∗(48.7875)(55.0746)(38.4814)(80.998)Convergence speed0.00310.00380.04510.0061R-squared0.1110.1290.0960.043Note:t-statistics in parentheses, ∗∗∗p<0.01, ∗∗p<0.05, and ∗p<0.01.Theβ coefficients of the two models were significant in each region, except that BBAM was not significant in the eastern region. Therefore, it can be concluded that there was an absolute convergence trend of AGTFP in the whole of China, the middle, and the west. In other words, those areas with low AGTFP tended to catch up with areas with high value. In BWMRM, the convergence speed was highest in the west, then in the east, and lowest in the middle. In BBAM, the speed of convergence in the east cannot be determined because the β coefficient was not significant, but the west was certainly faster than the middle. With the gradual implementation of the “western development” policy and the “coordinated development of the regions” policy, the backward provinces in the western region can quickly catch up with the developed provinces faster.This study employed two DEA models with the biennial environment technology to measure AGTFP of China and analyse the features. The DEA models with the biennial environment technology were rarely used, and no studies used the technology to study agricultural efficiency. Other studies on AGTFP in China have used different methods, different indicators, or different sample periods. However, the results of this study are roughly the same as their common results, which demonstrates the robustness of the conclusions [3, 30, 38, 47].


## 3.1. The Trend Analysis of AGTFP and Its Decomposition

Figure1 shows the mean of China’s cumulative GLPI (CGLPI), cumulative TC (CTC), GLPI, and TC calculated using BWMRM and BBAM over the period 1998–2016. As the two models nearly have the same outcomes, the result is generally robust. GLPI and TC always were positive, so CGLPI and CTC increased year by year. Meanwhile, the line (CTC) is always above the line (CGLPI), revealing that cumulative efficiency change (CEC) was always negative. These indicated that AGTFP increased with the drive of TC, and EC was the obstacle to the improvement. That can also be drawn from the way in which the line (GLPI) representing the AGTFP growth in one year or the AGTFP growth rate was always below the line (TC) except the years 1999, 2003, 2005, 2008, and 2013. That corresponded with most research on the green productivity of Chinese agriculture. Since the reform and opening-up in 1978, China has vigorously introduced advanced production technologies, so TC was always positive, and China’s agricultural productivity has been increasing for decades. In addition, since 2005, the “three rural issues” have been the top priority of the central government, and many policies to promote agriculture have been introduced.Figure 1
The dynamic change of AGTFP growth in China.The kernel density estimation was used to analyse the dynamic characteristics of the distribution of AGTFP growth rate in China, and the result is shown in Figure2. First, the midpoint of the distribution curve of the two models has no significant deviation during the observation period, indicating that the GLPI of most provinces fluctuated around zero. Second, the height of the main peak goes through the process “up-down-up-down-up-down,” and the width goes through the process “narrowing-widening-narrowing-widening.” Although the height of the main peak does not have an obvious direction of change, the width becomes wider. In addition, the distance between the rightmost side peaks and the main peak has little change. These phenomena meant that the dispersion degree of GLPI increased.Figure 2
The dynamic distribution of kernel density estimation of GLPI in China.In this study, 31 provincial areas in China were divided into three regions, the east, the middle, and the west, and the sample period was divided into four time periods. The eastern area includes Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan. The middle area includes Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, and Hunan. The western area includes Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang. Table3 shows the mean of GLPI and its components in five periods (including 1998–2016).Table 3
The mean of GLPI and its components.
BWMRMRegionIndex1998–20012002–20062007–20112012–20161998–2016EastGLPI0.01390.01680.02210.03380.0221EC0.00080.00130.00010.00270.0012TC0.01310.01550.02200.03120.0208MiddleGLPI0.01260.04220.04240.04510.0368EC−0.02650.0008−0.00020.0001−0.0054TC0.03920.04140.04250.04500.0422WestGLPI0.02260.02750.00480.03510.0225EC−0.0116−0.0064−0.0069−0.0078−0.0080TC0.03420.03390.01180.04290.0305ChinaGLPI0.01690.02750.02060.03720.0260EC−0.0111−0.0018−0.0027−0.0021−0.0041TC0.02800.02930.02330.03930.0301BBAMEastGLPI0.01480.01580.02690.05700.0294EC0.00090.00140.00010.00270.0013TC0.01390.01440.02680.05430.0281MiddleGLPI0.01330.04590.04320.04750.0387EC−0.02910.0023−0.00030.0014−0.0052TC0.04230.04360.04350.04610.0440WestGLPI0.02580.03040.00670.03580.0246EC−0.0113−0.0064−0.0052−0.0082−0.0076TC0.03710.03670.01190.04400.0322ChinaGLPI0.01870.02920.02330.04630.0299EC−0.0116−0.0014−0.0021−0.0019−0.0038TC0.03020.03060.02540.04820.0338GLPI and TC of China and its three regions were greater than 0 in each period. EC was very small and even negative in two periods of the middle and four periods in the west. Therefore, for the regions, TC was the main driver of AGTFP, and EC played a minor role or even hindered, exactly in line with the conclusion in Figure1. That indicated that although the government vigorously developed and introduced advanced technology, it neglected management experience, organization form, and production scale to improve productivity. GLPI of all the regions increased period by period, meaning that the growth rate got faster and faster, except the western region in the period 2007–2011. GLPI of the west declined precipitously to 0.0048, a meager value compared to the east, 0.0221, and that of the middle, 0.0424, and so did TC; it was just 0.0118 in the period. For the mean of GLPI in entire China, there was also an oscillation in 2007–2011, falling to 0.0206. That was possibly because of many natural disasters in western China during the period. Natural conditions in western China make it more prone to natural disasters, such as earthquakes and debris flow.What GLPI measures is the AGTFP growth rate, which is the growth of one year. This study calculated CGLPI to measure the growth of multiple years to the base year. Table4 shows the mean of CGLPI and its components in five periods. According to CGLPI of the two periods (1998–2016 and 2012–2016), taking 1997 as the base period, the middle experienced the largest AGTFP growth by 2016, followed by the west, and the east was the lowest. The cumulative AGTFP (CAGTFP) was constructed based on the AGTFP in 1997 to compare the absolute AGTFP level of regions or provinces. By comparing the sum of AGTFP in 1997 and CGLPI in each region, this study estimated which region has the largest AGTFP. In BWMRM, the east and the middle had similar CAGTFP, and the west was the least. In BBAM, the east had the largest CAGTFP, followed by the middle and then the west. Although this method is not accurate enough, it can reflect some information, so this study adopted the result of BBAM.Table 4
The mean of CGLPI and its components in three regions.
BWMRMRegionIndex1998–20012002–20062007–20112012–20161998–2016EastCGLPI0.03910.09410.21890.34810.1822CEC0.00320.00030.01300.01070.0070CTC0.03590.09380.20590.33740.1752MiddleCGLPI0.04390.16550.39450.60460.3157CEC−0.0650−0.0985−0.0963−0.1064−0.0929CTC0.10890.26400.49080.71100.4087WestCGLPI0.04610.18380.24660.38010.2230CEC−0.0215−0.0632−0.0923−0.1316−0.0801CTC0.06760.24710.33890.51170.3031ChinaCGLPI0.04300.14730.27490.42670.2325CEC−0.0239−0.0498−0.0560−0.0746−0.0525CTC0.06700.19710.33090.50130.2850BBAMEastCGLPI0.04150.09420.23430.45350.2145CEC0.00360.00060.01380.01150.0075CTC0.03800.09360.22050.44210.2070MiddleCGLPI0.04770.17940.41700.63820.3349CEC−0.0703−0.1027−0.1001−0.1054−0.0959CTC0.11800.28210.51700.74350.4308WestCGLPI0.05590.20680.27740.41850.2493CEC−0.0175−0.0611−0.0887−0.1244−0.0758CTC0.07340.26790.36600.54290.3251ChinaCGLPI0.04870.15980.29810.48760.2591CEC−0.0237−0.0500−0.0553−0.0713−0.0514CTC0.07230.20970.35340.55890.3105The agriculture production efficiency is determined by agricultural resource endowment, policy environment, and many other factors. The east with better resource endowments had the highest AGTFP. However, it did not have the most considerable growth because the high AGTFP resulted in less room for improvement. Overall, in the mountainous area in western China, there is no advantage of large-scale grain cultivation. Although China has introduced “the western development” policy to help the backward western development, the positive effect of the policy does not offset the negative effect of natural agriculture conditions. Therefore, the middle with more plains became the region with the biggest growth.This study also conducted a detailed provincial analysis of AGTFP. Henan, Xinjiang, Sichuan, Hebei, Shandong, and Shaanxi had the best AGTFP performance that their CGLPI and CAGTFP of two periods (2012–2016 and 1998–2016) were the highest, the top 20 percent of provinces. Henan, Sichuan Hebei, Shandong, and Shaanxi, having large populations and fertile plains suitable for farming, are major agricultural provinces in China. As agriculture is their industrial orientation, the government has invested a lot, such as policies and technology, to develop their agriculture. Although Xinjiang has a cold climate and a lot of deserts, the government of China has tilted many policy resources for development, and in addition, there are vast areas and rich water resources for developing characteristic agriculture well.Among the slowest growth areas were Ningxia, Tibet, Hainan, Shanghai, and Qinghai, where the CGLPI of two periods (2012–2016 and 1997–2016) was less than 0.1. Agriculture in Shanghai was a small part of the economy, and the area was economically developed and had advanced agricultural production technology. So, there was little room and impetus for improvement. On the contrary, the economic and technological bases were weak for Ningxia, Tibet, Hainan, and Qinghai. Their natural environment was also unsuitable for agriculture like Xinjiang, which was less attractive to talents, so it was not easy to improve the AGTFP. But their CAGTFP was not very low because of a good performance in 1997. Shanxi, Gansu, and Jiangxi, which also had poor agricultural conditions, had the lowest CAGTFP.According to the above analysis, AGTFP in western China declined significantly in the period 2007–2011. CGLPI in Sichuan (from 0.0916 in 2002–2006 to 0.0295 in 2007–2011) and Qinghai (from 0 in 2002–2006 to −0.0758 in 2007–2011) declined significantly. It may be due to the frequent geological disasters in the two regions from 2007 to 2011, such as the Wenchuan earthquake in 2008, the Yushu earthquake, and the Yushu debris flow in 2010. TC was the drive of AGTFP, and EC always was negative in the middle and the western provinces, except Henan of the middle; its EC was always greater than 0. Although Tables3 and 4 show that EC in the eastern region played a positive role, only Hebei had an excellent performance in EC, and EC of other areas was very small. With a large population, plains with fertile soil, and abundant water, Henan and Hebei are major agricultural provinces in China, so there is a suitable environment for the growth of crops. These places make it easier to scale up agricultural production, improving EC.


## 3.2. The Difference Decomposition of China’s AGTFP

To further reveal the total difference and its sources, this study calculated and decomposed the Dagum Gini ratio of AGTFP. Note that AGTFP here is based on the TFP in 1997, so it is the above CAGTFP. The convergence analysis section also uses the AGTFP. Figures3 and 4 show the Gini inequality within subregions and the net contribution of the extended Gini inequality between subregions of AGTFP, respectively.Figure 3
The dynamic change of Gini inequality within subregions of AGTFP in China.Figure 4
The dynamic change of the net contribution of the extended Gini inequality between subregions of AGTFP in China.The Gini inequality within each region generally widened, although there were slight declines in some years. The inequality in the east was always lower than that in other regions. It decreased continuously from 0.0245 in 1997 to 0.0127 in 2000 and then fluctuated to 0.1336 in 2016. Additionally, the equality in the middle was the largest during 1998–1999 but smaller than that of the western region during 1999–2005. From 2006, it overtook the west, becoming the region with the largest Gini inequality again until 2016. This extended Gini ratio between regions increased on the whole and represented the difference of AGTFP between the two regions, and the larger the value, the more significant the difference. The value of middle-west was the largest, followed by that of east-middle, and east-west was the smallest.This study further analysed the difference of AGTFP among regions for decomposition and quantification, and Table5 shows the result. In general, Gw, the intraregional difference, and Gt, the effect of cross-overlap between different regions on the total difference, increased, and Gnb, the net interregional difference, was just the opposite. Changes in the proportion of each source to the total difference were like the absolute quantities, except that the percentage of intraregional difference grew slowly. For the ratio of sources, the percentage of Gw rose from 22.3 percent in 1997 to 30.48 percent in 2016, about 1.37 times. However, Gw went from 0.0221 in 1997 to 0.073 in 2016, just about 3.3 times, stemming from a significant increase in the total difference. The percentage of the sum of Gt and Gnb, Ggb, in each year was about 65, consistent with the increase of coefficients shown in Figures 3 and 4. So, the total difference between regions was the primary source, accounting for an average of 65 percent per year, and the difference within regions was 35 percent.Table 5
The three components of the total Gini ratio of AGTFP in China.
BWMRMYearGwPGwGnbPGnbGtPGtG19970.009921.070.028460.410.008718.520.047019980.013423.850.026246.670.016529.480.056119990.017726.950.024737.570.023335.480.065720000.013424.200.028351.290.013524.500.055320010.017225.630.035753.300.014121.070.066920020.021628.850.036648.990.016622.160.074820030.024829.260.036543.070.023527.660.084820040.029130.700.037339.320.028429.970.094920050.033130.740.027325.350.047243.920.107620060.037831.600.021117.660.060650.740.119520070.038931.510.012410.030.072158.470.123320080.044031.850.00946.820.084861.340.138220090.045631.780.00725.020.090763.210.143520100.049331.710.00996.370.096361.930.155420110.053131.600.01317.770.101860.630.168020120.056031.510.01659.300.105159.190.177620130.058831.580.01809.680.109458.740.186320140.059331.270.01668.750.113859.980.189720150.063831.390.01708.360.122560.250.203320160.065631.450.01919.140.124059.400.2087BBAM19970.009921.070.028460.410.008718.520.047019980.015024.770.025442.080.020033.150.060419990.020127.870.023833.060.028139.080.072020000.015325.470.030049.820.014924.710.060220010.019226.260.037851.690.016122.040.073120020.023729.050.039147.840.018923.110.081620030.027129.560.038842.360.025728.080.091520040.032731.090.039837.840.032731.080.105220050.036431.050.029224.930.051644.020.117120060.041331.880.024018.530.064249.590.129420070.041031.640.014211.000.074357.370.129520080.046431.870.01258.590.086659.540.145520090.048031.890.00926.120.093361.990.150520100.051231.680.01036.360.100161.950.161520110.053631.560.01378.040.102660.400.169820120.057431.540.01508.270.109560.180.181920130.062031.590.00703.580.127164.830.196120140.065431.790.00964.660.130763.550.205720150.070031.940.01667.570.132660.490.219320160.071431.870.01948.630.133459.490.2242Note:Gw is the Gini inequality within subregions; Gnb is the net contribution of the extended Gini inequality between subregions; Gt is the contribution of the intensity of transvariation between subregions; PGw, PGnb, and PGt are the percentage of Gw, Gnb, and Gt, respectively.The central government has encouraged local governments to pursue GDP following local conditions while ensuring a certain amount of arable land rather than requiring balanced agricultural development. Therefore, the overall difference expanded. Generally, the provinces within a region have more similar agricultural conditions than between regions. So, the difference between regions became the primary source of total difference.


## 3.3. The Analysis of Convergence

This paper employed the coefficient of variation to analyse theσ convergence of AGTFP in China. Due to space limitations, the result of the coefficient of variation is not reported. According to the result, the coefficients of variation of the whole country, the east, the middle, and the west showed a significant upward trend. The average annual growth rate was 8.98%, 7.59%, 11.12%, and 11.54%, respectively. Therefore, there is no trend of σ convergence.Before testingβ convergence, this paper used the Moran index to investigate the spatial correlation of AGTFP, shown in Table 6. However, the result was insignificant, so the spatial lag effect was not included in the β convergence model.Table 6
The absoluteβ convergence test results of AGTFP in China and its subregions.
ModelEastMiddleWestChinaBWMRMβ−0.0230∗−0.0039∗−0.0477∗∗∗−0.0066∗∗∗(−1.8809)(−1.7925)(−3.3800)(−2.8341)Constant2.8397∗∗∗2.8386∗∗∗2.9248∗∗∗2.8189∗∗∗(68.5993)(58.9239)(42.4436)(99.1227)Convergence speed0.02320.00390.04880.0066R-squared0.10.1260.1160.041BBAMβ−0.0031−0.0038∗−0.0441∗∗∗−0.0061∗∗(−0.2948)(−1.7922)(−2.9792)(−2.3540)Constant2.7918∗∗∗2.8578∗∗∗2.9835∗∗∗2.8509∗∗∗(48.7875)(55.0746)(38.4814)(80.998)Convergence speed0.00310.00380.04510.0061R-squared0.1110.1290.0960.043Note:t-statistics in parentheses, ∗∗∗p<0.01, ∗∗p<0.05, and ∗p<0.01.Theβ coefficients of the two models were significant in each region, except that BBAM was not significant in the eastern region. Therefore, it can be concluded that there was an absolute convergence trend of AGTFP in the whole of China, the middle, and the west. In other words, those areas with low AGTFP tended to catch up with areas with high value. In BWMRM, the convergence speed was highest in the west, then in the east, and lowest in the middle. In BBAM, the speed of convergence in the east cannot be determined because the β coefficient was not significant, but the west was certainly faster than the middle. With the gradual implementation of the “western development” policy and the “coordinated development of the regions” policy, the backward provinces in the western region can quickly catch up with the developed provinces faster.This study employed two DEA models with the biennial environment technology to measure AGTFP of China and analyse the features. The DEA models with the biennial environment technology were rarely used, and no studies used the technology to study agricultural efficiency. Other studies on AGTFP in China have used different methods, different indicators, or different sample periods. However, the results of this study are roughly the same as their common results, which demonstrates the robustness of the conclusions [3, 30, 38, 47].


## 4. Conclusion

Based on the BWMRM and BBAM combined with GLPI, this paper investigates the AGTFP with the more complete ACEs as the undesirable output during 1997–2016. The tendencies are analysed using the kernel density estimation, the Dagum Gini ratio method, and convergence models.The main findings can be summarized. First, AGTFP showed an overall increase at the national level during 1997–2016, mainly due to the drive of high TC, and EC was an obstacle to the increase. In addition, the AGTFP growth rate of those provinces had little difference, but the dispersion degree, the total internal difference, increased. At the regional level, AGTFP and the growth in each region increased in the four periods except that GLPI in western China declined strongly in the period 2007 to 2011. In addition, their drivers were different. TC was the drive of all the regions at all the periods, but EC was almost always negative and played a slight positive role in the east. The east has the largest AGTFP, followed by the middle, and AGTFP growth in the middle was highest, followed by that of the west. Henan, Xinjiang, Sichuan, Hebei, Shandong, and Shaanxi had the best AGTFP performance at the provincial level. For Ningxia, Tibet, Hainan, Shanghai, and Qinghai, their AGTFP growth was slow or even regressive.Second, as for AGTFP, the total difference, the gross difference between regions, and the difference within regions had generally widened. Although the net interregional difference continued to decrease, the total interregional difference was the primary source of the total difference, accounting for above 65 percent. From 1997 to 2005, the west had the largest internal difference, followed by the middle. After 2006, the middle became the place with the largest internal difference, followed by the west. The east had the slightest internal difference all the time. As for the interregional difference, the middle-west was the largest, followed by the east-middle, and the east-west was the least on the whole.Third, theβ coefficients were significant except that of BBAM in the eastern region, so there was an absolute convergence trend of AGTFP in the whole of China, the middle, and the west, not including the east. In addition, the speed of convergence was highest in the west, then in the whole of China, and lowest in the middle. That of the east cannot be determined.Some policy implications are also identified. First, the Chinese government should improve AGTFP from a multidimensional perspective. In addition to introducing advanced technology, attention should be paid to drive AGTFP growth by technology efficiency. The government should smooth the cooperation mechanism of industry, university, and research institutes for green agriculture and strengthen the integration of key green technologies based on actual needs. In addition, it should strengthen the application and transformation of green agricultural science and technology innovation and actively carry out the demonstration of new technologies. Moreover, an institutional environment and standard system of inputs and pollutant discharge for green agriculture should be created or improved.Second, the government should scientifically implement a coordinated regional development strategy. Although the difference in agriculture production efficiency among areas has widened, the production level cannot be homogenized unreasonably. Agriculture depends on natural conditions, and the production in each area should be adapted to local conditions. The government should encourage each region to develop its own characteristic agriculture, which is helpful to improve convergence speed for those backward areas. On this basis, agriculture can realize regional coordinated development.Third, the government should improve and innovate agricultural subsidy policies. On the premise of ensuring national food security and sustainable increase in farmers’ incomes, policies should highlight the orientation of green development and give priority to increasing funds to resource-conserving and environment-friendly agriculture. For example, during outbreaks of diseases and insect pests, subsidies in kind are implemented to purchase low-toxicity biological pesticides, which are uniformly distributed to farmers.This study has several limitations. First, this study decomposes GLPI just from the traditional view, as most studies. From the factors-decomposition view, GLPI can be decomposed into the contribution of each factor (inputs and outputs) to the inefficiency, which helps to analyse the drive factors of the growth. Several studies have used this method to decompose efficiency, so it can be a future research direction [48, 49]. Second, straw burning has been banned for a long time, and we still consider it as one of the ACESs because of the lag of the policy and the weak implementation effect. However, the data in this paper has some deviation from the actual situation and needs to be improved. Third, the direction vector affects the accuracy of the efficiency value. The difference between BWMRM and BBAM is just the direction vector [42]. The direction vectors of the two models are commonly used in DEA models. It is hard to figure out which direction vector works best. Therefore, the endogenous direction vector is an important issue, and scholars have made some progress [50–53]. The appropriate methods will be used to select direction vectors in any following research employing the direction distance function.



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*Source: 2219779-2022-04-28.xml*