Measurement of green total factor productivity on Chinese pig breeding: from the perspective of regional differences

China has a vast territory and abundant resources, and there are significant differences in the development of pig breeding in different regions. Chemical oxygen demand (COD), total nitrogen (TN), and total phosphorus (TP) produced in the process of pig breeding will affect China’s environmental quality. In view of this, based on the Minimum Distance to Weak efficient frontier model, this paper constructs Metafrontier-Malmquist-Luenberger (MML) index considering negative output under the common frontier to comprehensively evaluate the green total factor productivity of Chinese pig breeding (GTCP). This has guiding significance for improving China’s pork production and reducing pollution emissions. The results manifest that (1) no matter under the common frontier or the group frontier, GTCP presents large temporal and spatial differentiation characteristics. Compared with the central region and the western region, the eastern region has obvious advantages in GTCP. (2) GTCP has shown an upward trend as a whole, which is mainly due to the technical progress. (3) Compared with small-scale and medium-sized GTCP, large-scale GTCP has apparent superiorities. Based on the above outcomes, this paper finally raises policy recommendations for improving GTCP: (1) give full play to the advantages of pig breeding in different regions, (2) increase the research and introduction of pig breeding clean technology and improve the application efficiency, and (3) give full play to the scale effect and vigorously develop large-scale pig breeding.


Introduction
Pork, as the main component of the daily meat consumption for Chinese residents, has a huge demand in the domestic market (Wu et al. 2002;Zhou et al. 2007;Wang et al. 2016;Leng et al. 2017). At the same time, with the rapid rise in pork prices, China's live hog supply fluctuated greatly (Guevarra et al. 2019;Wang et al. 2020). In order to ensure the demand of Chinese people for pork, this problem can be solved mainly by expanding the hog production scale and improving pig production efficiency (Humphrey and Schmitz 2010;Kaplinsky 2014). This article measures the GTCP in China to improve the production efficiency of hog breeding.
There are two primary phenomena in the process of pig breeding: Firstly, the development of pig breeding industry in different parts of the country has significant difference (Abdalla et al. 1995;Falavigna et al. 2013). There are obvious unlikeness in traffic accessibility, rural human capital level, breeding technology services, biogas projects, urbanization level, and feed price in different localities (Evans et al. 1984;Adams et al. 1994;Ernst 1998;Yue et al. 2017). The eastern region has developed transportation and easy industrial agglomeration (Managi and Kaneko 2006;Xiao et al. 2012); the central region has an ascendant geographical location and is a traffic fortress for population mobility Yuan et al. 2017); the western region has superior environmental conditions, with low labor cost and feed transportation cost (Yue et al. 2014;Wang et al. 2015;Zhang et al. 2016). With the gradual implementation of the policy of "importing hogs from the south to the north" and the differences in environmental carrying capacity, feed resources, and local breed resources in different regions, there are apparent distinctions in pig breeding industry among the three regions (Qiao et al. 2011;Zhao et al. 2015). Secondly, pollutants are generated during hog breeding (Shortle et al. 1998;Burkholder et al. 2007). According to the World Bank's estimation, even if only 10% of livestock manure and urine enter the water body with surface runoff due to stacking or overflowing, the eutrophication contribution rates of ammonia and phosphorus can reach 10-20%. Pathogenic microorganisms and heavy metal elements in wastes can also spread diseases through environmental pollution (Segerson 1998;Campagnolo et al. 2002;Fraison et al. 2013). Thus, this text uses the minimum distance to weak efficient frontier-Metafrontier Malmquist Luenberger (MinDW-MML) model to comprehensively analyze the green total factor productivity (GTFP) of China's pig breeding industry from 2004 to 2018 by adding negative output under the condition of considering the regional heterogeneity.
The second and third parts of this article respectively introduce the study situation of relevant literature, and theoretical basis, including the primary sources of input-output variables and data. Empirical analysis is explained in the fourth part, and the fifth part is the conclusion and related policy suggestions.

Literature review
Previous studies by scholars have focused on pig breeding. While making great contributions to this field, there is a lack of research on the large sample data of pig breeding in China in recent years. Paul (2004) research shows that after the 1980s, the emergence of new technologies and the increase of pig breeding specialization stimulated the continuous expansion of pig farms in the USA. Piot-Lepetit et al. (2005) conducted a study on the production efficiency of the French pig breeding industry. The results revealed that the increase of pig productivity from 1996 to 2001 was mainly attributed to technological progress, and the government's policy intervention did not improve the pig productivity. Onyenweaku and Effiong (2005) measured the technical efficiency and influencing factors of Nigerian pig production in 2004 by Stochastic Frontier Analysis (SFA) method. Key and McBride (2008) conducted an in-depth and systematic study on pig production efficiency in the USA from 1992 to 2004. The results demonstrated that most American farms adopted specialized production modes, with larger farms and fewer numbers. Yan et al. (2019) studied China's pig breeding industry in 2017. Subsequently, Chen et al. (2021) studied the anthropogenic greenhouse gas emission of pig production system from 2000 to 2016. This paper uses the latest year data, which is more in line with the current development and changes in China and can more accurately evaluate the current situation of GTCP. In addition, the existing studies are on the overall situation of China's pig breeding industry, and the three scales are not analyzed separately.
For the calculation of agricultural efficiency, most of the existing study methods focus on SFA, traditional data envelopment analysis (DEA), directional distance function (DDF) model, and slack-based measure (SBM) model. Ali et al. (2000) thought that efficiency was the combined result of transmission efficiency, utilization efficiency, and distribution efficiency. SFA needs to preset a certain function form, but it can separate statistical error and technical inefficiency. Kaneko et al. (2004) evaluated the agricultural water use efficiency in various Chinese provinces based on SFA. The results indicated that there was a big gap between agricultural water use efficiency and production technology efficiency. The factors affecting the efficiency mainly included climate, soil, and other natural conditions, as well as infrastructure construction. However, although SFA method can calculate the efficiency through the partial differential method, it cannot reasonably control the input and output variables and the endogenous problems. It has the disadvantage of needing to set a reasonable production function (Simar and Wilson 1998). Lilienfeld and Asmild (2007) used the traditional DEA method to measure the efficiency and compared the difference with SFA on efficiency. It was concluded that DEA efficiency was easily affected by the input and output in abnormal years. Sueyoshi and Goto (2012) used the traditional DEA method to measure the efficiency level of the power industry. Traditional DEA has non-dynamic characteristics (Simar and Wilson 2000;Mei et al. 2015). Njuki et al. (2016) used greenhouse gases as pollutants and calculated the pig breeding efficiency of farms in the eastern USA by DDF model. It was found that the production efficiency of large farms was higher than that of small farms. However, DDF model cannot calculate the improvement amount and the unreasonable problem of weak disposal of undesired output. Du et al. (2017) used the SBM model to find that coastal areas are more suitable for developing small-sized and medium-sized breeding. The northeast area in China is more suitable for developing large-scale breeding, the central area is more suitable for developing small-scale and middle-scale aquaculture, and the southwest area is more suitable for developing small-scale and largescale aquaculture. Although SBM can correct the slackness problem to the greatest extent, the obtained technical efficiency can also identify the possible relaxation measurement problem of the radial model to the greatest extent (Zhou et al. 2006). However, due to that the set frontier of SBM is too far, most decision-making unit (DMU) cannot catch up or reach the effective frontier in a short time, which frustrates the "enthusiasm" of catching up, and is not conducive to the overall DMU technical progress or the improvement of production efficiency (Yu et al. 2019). MinDW model has many advantages. Because MinDW model does not need to set the function form, it can overcome the limitations of SFA and other parametric methods on input and output variables and the non-dynamic problem of traditional DEA. It can conquer the problems that the DDF model cannot calculate the amount of improvement quantity, and the unreasonable handling of undesired output is weak. It can also put up with the shortcomings of the traditional CCR model and the SBM method based on the slack measure that the frontier is too far, which dampens the ineffective production unit to pursue the "enthusiasm," and avoid the subjective influence of some factors on the research results, such as weight, data outliers, and substantial economic fluctuations, so as to make the results more realistic (Wang et al. 2013). Therefore, this text adopts a newer MinDW model to calculate the efficiency of pig breeding.
The existing studies on pig production efficiency did not consider the importance of regional heterogeneity and environmental factors at the same time for the research of GTCP. Apostolopoulos et al. (2001) analyzed the pig production efficiency in Greece. The results proved that production efficiency is positively correlated with the number of sows and negatively correlated with the equipment usage time. Kliebenstein et al. (2003) pointed out that large-scale breeding has high feeding technology and management skills, and the feeding materials and service fees of pigs have little impact on large-scale breeding. Werf et al. (2007) of Cornell University in the USA demonstrated that with the modern breeding technology being put into live pig production, the pig production efficiency and agricultural labor productivity have been improved, thus reducing labor costs and realizing scale economy. Petrovska (2011) compared and analyzed the pig production efficiency of large-scale and small-scale farms in the Republic of Macedonia by using DEA method combined survey data. The above studies did not take into account the pollutant emission in the process of pig breeding. And Li and Wu (2016), Bava et al. (2017), and McAuliffe et al. (2017) studied the environmental efficiency of pigs, but did not consider regional heterogeneity.
To sum up, the innovation points of this paper are mainly reflected in the following three aspects: (1) In the selection of data and samples, this article selects the input and output data of three scales of pig production from 2004 to 2018 in 17 Chinese major pig producing areas. Compared with the previous research data, the time span is longer, the year is newer, and it is more suitable for the current development and change of China. It can more accurately evaluate the GTCP situation of pig breeding in China's current era. (2) In terms of research methods, considering regional heterogeneity, this text constructs MinDW model based on the common frontier to evaluate GTCPs of different sizes. (3) From the perspective of research, this paper introduces environmental factors into the evaluation system of pig breeding efficiency of different scales, adding negative output and highlighting the significance of environmental issues for pig breeding industry. With a view to putting forward policy suggestions to improve GTCP in 17 major pig producing areas and environmental protection policy suggestions for pig breeding.

MinDW under the common frontier
Minimum distance to weak efficient frontier (MinDW) refers to the nearest distance between the evaluated DMU and the leading edge, regardless of whether its projection point at the frontier is strong-efficient or weak-efficient. It was first proposed by Briec (1999) and Charnes et al. (1996), in which the method can be expressed as n + m linear programming (n is the number of input indicators, m is the number of output indicators), assuming the input variable is x and the output variable is y: e i and e r are constants. In the programming formula, only one e is equal to 1, and the others are 0, that is: The efficiency value of each model is expressed as: The efficiency value of MinDW model is expressed as * max = max * z , z = 1, 2, … , n + m , and the maximum efficiency value corresponds to the minimum β * , that is, the nearest distance to the frontier.
This text uses the MinDW model with negative output. The method can be expressed as n + m + f linear (1) programming (n is the number of input indicators, m is the number of expected output indicators, f is the number of undesired output indicators): e i , e r and e p are constants. In the programming formula, only one e is equal to 1, and the others are 0, that is: The efficiency value of each model is expressed as: The efficiency value of MinDW model is expressed as * max = max * z , z = 1, 2, … , n + m + f , and the maximum efficiency value corresponds to the minimum β * , which means the nearest distance to the frontier.
The efficiency value of MinDW model will not be less than that of directional distance function model with any direction vector or other distance types (such as radial and SBM). In other words, the efficiency value of MinDW model is the largest. Combined with the above process, we can define the regional boundary (β region * ), and the model is as follows: Similarly, the efficiency value of DMU relative to the common frontier (β meta * ) can be obtained by the following model: Finally, in the common frontier model, the technology gap ratio (TGR) is equal to the ratio of the efficiency value of the common frontier to the efficiency value of the group frontier. The formula is as follows: β region * and β meta * represent the optimal solution of formula (7) and formula (8), respectively. TGR is used to measure the distance between the optimal production technology and the potential optimal technology of a group, and whether there are any differences in GTCP under different groups. The closer the TGR is to 1, the closer the technology level is to the optimal potential technology level. Conversely, it is the larger the gap between the technology level and the potential optimal technology level.

Metafrontier-Malmquist-Luenberger index and its decomposition
Malmquist productivity index is widely used in the study of dynamic efficiency change trend and has good adaptability to multiple input-output data and panel data analysis. The actual production process often contains unexpected output. After Chung et al. (1997) proposed Malmquist-Luenberger (ML) index, any Malmquist index with undesired output can be called ML index. Oh (2010) constructed the Global-Malmquist-Luenberger index. All the evaluated DMUs are included in the global reference set, which avoids the phenomenon of infeasible solution in VRS and "technology regression." The global reference set constructed in this article is as follows: This article takes MML index as the GTCP.
Further decompose the MML index into efficiency change (EC) and technology change (TC).
where (x t − 1 , y t − 1 , b t − 1 ) and (x t , y t , b t ) represent the input, desired output, and undesired output of t − 1 and t, respectively. TC t t−1 and EC t t−1 are the devotion to GTCP raise of DMU's technical progress and efficiency improvement from t − 1 to t, respectively. The higher the value is, the larger the devotion is. The MML index is recorded as MI , and the value of MI is the GTCP. The green total factor productivity index of pig breeding under the common frontier and group frontier are as below: For the DMUs with regional heterogeneity, we can calculate the technology gap between the group frontier and the common frontier, which is caused by the specific group structure.

Data and variables
Based on the research of the existing literature, this text chooses five indexes to build the input-output indicator system. Details are as below: 1. Piglet input: piglet weight. The average weight of each piglet that a pig farmer buys outside or raises through his own pig 2. Labor input: the number of employees. The sum number of days of direct labor for agricultural employees and family employees 3. Capital input: namely, expenses investment, including concentrate feed expenses, water and fuel power expenses, medical epidemic prevention expenses. The (12) expenses of concentrate refer to the input expenses of various kinds of concentrate actually consumed by each hog from purchase to fattening, including the total expenses of grain, soybean cake, mixed feed, plant powder, and other expenses. Water and fuel power expenses include water, electricity, coal, and other fuel power expenses. Medical and epidemic prevention expenses include the expenses for disease prevention and control 4. Positive output: the output of the main products, which means the weight of each fattening pig at the time of slaughter 5. Negative output: pollutant discharge. The main pollutants produced in the process of pig breeding include chemical oxygen demand (COD), total nitrogen (TN), and total phosphorus (TP). According to the calculation method of Zuo et al. (2016), total pollutant emission is calculated by Eq. (17). And according to the calculation method of Du et al. (2017), the specific calculation steps are shown in Eqs. (18)- (20): where TPE is the total pollutant emission.
where D A is the average feeding days. CEC, NEC, and PEC are the coefficient of COD emisson, the TN emisson , and the TP emisson, respectively. W R and W A represent the reference weight and the actual weight, respectively.
Piglet weight, labor quantity, concentrate expenses, water and fuel expenses, medical cost, actual weight, average feeding days, and main product output all came from 2004 to 2018 "National Compendium of Agricultural Product Expenses-Benefit Data." Among them, the concentrate expenses, water and fuel expenses, and medical cost are calculated at the price of the current year. In order to eliminate the influence of inflation and other factors, this paper takes 2003 as the base period and flattens it according to the value index of agricultural means of production and fuel power index in "China Statistical Yearbook" from 2004 to 2018.
The reference weight and emission coefficient are derived from the "Discharge Coefficient Manual" released by the Office of the First National Pollution Source Census Leading Group. And the proportion of water feces and dry feces in each province was referred to Du et al. (2017). Meanwhile, according to the above two data on the definition of scale, this text will divide live pig breeding scale into three types: large scale, middle scale, and small scale. Small-scale refers to 30-100 farming households listed annually. Middle scale refers to the annual output of 100-1000 scale farms. Large scale refers to more than 1000 farming area.
In the sample choice, this text chooses 17 major producing provinces of the "Plan of National Pig Production Development (2016-2020)" pig advantage producing areas as the study samples. It is separated into three areas: the Eastern Area (Jiangsu, Zhejiang, Guangdong, Liaoning, Hebei, Shandong), the Central Area (Anhui, Hubei, Hunan, Heilongjiang, Jilin, Henan), and the Western Area (Guizhou, Guangxi, Chongqing, Sichuan, Yunnan).

The overall change of GTCP in China
It can be seen from Fig. 1 that the overall fluctuation trend under the common frontier and the regional frontier is basically the same. The fluctuation amplitude under the common front is larger. In 2016, both GTCP and TC reached a phased peak again. GTCP increased by 1.89% and TC increased by 2.40% under the meta-frontier. Then, GTCP increased by 1.28% and TC increased by 1.54% under the group frontier. After 2016, the GTCP has shown a downward trend, mainly due to the upsurge of investment in pig farming by major enterprises in 2016, which saw hog price spiral through year-round highs. In 2017, piglet sales and pork prices all fell to varying degrees. The price of piglets is affected by pig price, weather factors, and farmers' mentality of filling hurdles. Since the first case of African swine fever was found in China on August 3, 2018, African swine fever has spread rapidly in China. There was a slight decrease in 2017 and 2018 from the boom to the freezing point. The main reason for the sharp decline in investment is the impact of the economic environment. Most China's enterprises have a tight capital chain, and large enterprises have expanded the proportion of breeding in the "company + farmer" mode and purchased a large number of piglets for stocking. It not only improves the scientific and technological content of agricultural products, but also promotes the industrialization of traditional agriculture. In summary, GTCP showed an upward trend in the past 15 years, with an increase of 0.27% under the common frontier and 0.14% under the regional frontier.
As shown in Fig. 2, the fluctuation trends of GTCP and TC are similar under the common frontier and group frontier. The fluctuation range of EC is larger under the meta-frontier. In 2008, the small-scale EC increased and TC decreased, while in the medium-sized, TC rose and EC declined. And in the large scale, the value of TC was also greater than the value of EC. This is mainly because after the Ministry of Agriculture released the Animal manure resource utilization action plan (2017-2020), the nation promoted the resource utilization of livestock and poultry breeding wastes, accelerated the transformation and upgrading of animal husbandry, and constructed a new pattern of sustainable development of farming-breeding combination and farming-pastoral cycle, which improved the standardized breeding technology. In the "Lament" voice of prohibition and restriction breeding, a new way is pointed out for farmers: as long as the waste resources of livestock and poultry can be effectively utilized, the forbidden areas such as water sources can be far away, and the efficient green ecological breeding industry can be developed; pigs can not only be raised, but also own the support of the government. China's environmental protection policy continues to tighten. Driven by both policies and technologies, green ecological transformation and promoting large-scale modern farming must be the theme of the future pig industry. Combined with the actual situation in China, the first half of 2014 and 2015 are the golden opportunities for pig breeding industry to expand against the trend. In 2016, it will make a rich profit, which is the due return of gold opportunities. In 2017, it will earn the return of the expansion of the trend. Of course, there is certainly no downside to profit. 2018 is a loss period, making GTCP decline.
Large-scale GTCP is higher than medium and small scale. The construction of large-scale farm takes about 1 year. It takes about 2 years to introduce sows to produce piglets, and then to develop piglets into commercial pigs. Without sows, there would be no piglets, and the supply of subsequent commercial pigs would not go up. Since 2012, the  reason for technological progress may be that large-scale pig farms gradually introduced to foreign countries and learned the technology to adapt to large-scale pig farms in practice. However, with the scale expansion of pig farms, exceeding the appropriate scale, the unreasonable resource allocation has begun to show the characteristics of decline in technical efficiency. The State Council's "13th Five-Year Plan" on ecological and environmental protection requires that the relationship between pig production and environmental protection should be well handled through "prohibition, restriction, transfer and governance." By the end of 2017, various regions should close or relocate pig farms and specialized breeding households in the forbidden areas according to law. From 2017 to 2018, both the quantity and the price of live pigs in China were low, reflecting the enthusiasm of pig farmers to fill the hurdle is not high, but the enthusiasm is gradually rising.
As can be seen from Fig. 3, under the common frontier, the GTCP of Guizhou (0.9946) and Jilin (0.9989) is lower, while Hubei (1.0104), Guangxi (1.0089), Guangdong (1.0078), and Hunan (1.0072) are higher, all above 1, showing positive growth. Under the regional frontier, the GTCPs of Guizhou (0.9958) and Jilin (0.9987) are also lower, while Hubei (1.0085), Guangxi (1.0075), Guangdong (1.0072), and Sichuan (1.0061) are higher, all exceeding 1, indicating positive growth. Whether in the common frontier or group frontier, the GTCPs of Guizhou and Jilin are all reciprocal, and the growth is negative. The value of EC is also less than 1, indicating that the level of environmental protection farming technical efficiency in these areas needs to be improved. Hubei, Guangxi, and Guangdong ranked the top 4 of the two frontiers, demonstrating that the pig farms in these areas have been upgraded in some aspects (such as animal welfare, environmental protection treatment, and technological innovation). It provides a transformation and upgrading scheme for China's modern agriculture once again. In addition, some pig breeding enterprises have gradually formed a three-dimensional sales system of "online e-commerce + offline supermarket + high-end experience store." The innovative attempt to inject Internet gene into pork sales channels is also of great significance to China's pig industry. Although the tax on solid and water pollution increases the economic burden of the farms, it can promote the reduction of emissions from the source, strengthen the resource utilization of manure, boost the sustainable development, and bring long-term economic benefits. Under the heavy pressure of environmental policies, some local governments have excessive demolition and "one size fits all" phenomenon. In this regard, the leaders at all levels of the Ministry of Agriculture have repeatedly stressed the need to standardize the zoning of prohibited breeding areas, prevent the blind expansion of captivity breeding areas, simply close down the farms, and vigorously stabilize the pig industry.
As shown in Fig. 4, under the meta-frontier, the smallscale (1.0037) GTCP is the lowest, the medium-sized (1.0039) is the second, and the large scale (1.0055) is the highest. The values of the three-scale TC and EC are both positive growth. Under the regional frontier, small-scale GTCP increased 0.22%, medium-sized GTCP increased 0.35%, and large-scale GTCP increased 0.40%. Under the two frontiers, the average annual GTCPs of the whole country are 1.0044 and 1.0033 respectively, which are all positive growth. This is mainly because China has been implementing the promotion of low-carbon farming technology in recent years, with good promotion effect. Most provinces have adopted low-carbon breeding methods, and the overall level of application of modern environmental protection breeding technology in China is high, resulting in the growth of GTCP in the whole country. Whether grouped or not, small-scale farming in Hunan, Hubei, and Sichuan; mediumscale farming in Hubei, Guangxi, and Liaoning; and largescale farming in Guangdong, Jiangsu, and Heilongjiang are all outstanding. Sichuan is a traditional pig province with rapid development of pig industry, so small-scale breeding ranks among the top 3 in China. But the pig industry in Northeast, Henan, Shandong, and other places develops more rapidly. Compared with them, there is a certain gap in large-scale breeding, selection of excellent varieties, and pork quality in Sichuan, resulting in low comprehensive GTCP ranking.
As shown in Fig. 5, from the perspective of time, the fluctuation range of TGR was relatively large before 2012, gradually flattened from 2012 to 2016, hovering around 1, at a high level. It indicates that the frontier of regional frontier is closer to the common frontier. But after 2016, the volatility began to increase gradually. This is mainly because 2017 is a year of ups and downs for China's pig breeding industry. Whether it is the fluctuation of pig prices in the market, the promotion of modern agriculture in policy, the full implementation of prohibition breeding and restriction farming, the innovation and development of breeding technology, or the large-scale expansion at the enterprise level, all involve every enterprise, every practitioner, and even every consumer in the pig industry chain. On January 1, 2018, the "Environmental Protection Tax Law" was formally implemented, and the implementation of environmental protection tax law is a severe test for the breeding industry. The tax law stipulates the main pollution emitted by pig farms with 500 or more pigs is water pollutants and solid pollutants. According to the relevant investigation, a pig farm with 500 pigs on hand in Guangdong should pay the tax of at least 4.6 yuan per pig. In a short time, this will cause some harm to the pig industry. On the whole, the technology presents the trend of regression, and technical efficiency is an increasing trend. The reason may be that with the development of large-scale pig breeding, the technology updates slowly, and the technology adapted to small-scale pig farm cannot adapt to large-scale production, so it is manifested as technological regression. The reason for the progress of technical efficiency is that with the expansion of pig farm scale, it presents the characteristics of scale economy. The GTCPs in most years are positive growth. The slight decline in individual years did not affect the overall positive growth. The eastern and central regions have higher GTCP under the common frontier, while the western region has higher GTCP under the regional frontier. It shows that the eastern and central regions still rely on traditional breeding technology to a large extent, and the level of low-carbon pig breeding technology is low. In recent years, the pig industry has developed well, and the GTCP has shown positive growth as a whole. However, it is obvious that the growth rate of GTCH decreased from 2016 to 2017. The reason is that the periodic imbalance between supply and demand in 2017 has supported the rapid recovery of pig market price. Farmers continue to be reluctant to sell and support the price, the intention of slaughterhouse to reduce the price is obvious, and the domestic pig market supply and demand game situation is intensified. In some areas, the impact of Vietnam pig is huge, and the price has decreased. In terms of demand, the pork sales of northern enterprises are not ideal, and the pork price is difficult to raise. The cost pressure and the intention of price reduction are heavy. The production of southern pickled food is gradually opening up, and the growing demand will also have a certain stimulating effect. In 2018, pig prices continued to decline. This is mainly because, on the one hand, scale farms are still expanding, and the concentration on pig breeding market is gradually increasing, on the other hand, in the context of sufficient pig supply, the demand follows up slowly, the market is oversupplied, and the overall pig price is declining. Although China's GTCP showed a downward trend after 2016, it is still positive growth and expected to recover slowly over time and rise steadily.

The change of GTCP in different regions
As can be seen from Fig. 7, the three-scaled GTCP under the common frontier has a larger fluctuation range than that under the regional frontier, and the fluctuation trend is the same. Under the two frontiers, the GTCP of the eastern region is higher than that of the central and western regions, and the large-scale GTCP is higher than that of the mediumsized and small scale, but there is little difference among the three scales. After 2016, GTCP showed a downward trend. Since 2017, China has paid more and more attention to the environmental protection. Strict control of the environment problems of the aquaculture industry has made it difficult to move forward and narrow the scale. In 2017, raising farm animal welfare has become an essential issue for the pig industry. On October 12, 2017, the World Farm Animal Welfare Conference was held in China. This was the first grand meeting held by the Food and Agriculture Organization of the United Nations for farm animal welfare. The first congress was held in China, which attracted more attention from Chinese breeding enterprises and scientifically understood farm animal welfare, and realized the positive role of practical animal welfare practice in the farming development and pork quality. After the meeting, more and more Chinese breeding enterprises began to practice animal welfare to ensure the sustainable development of breeding. Since the national regulation of implementing environmental protection farming in 2017, Chongqing in the western region, Henan in the central region, and Jiangsu in the eastern region will complete the task indicators ahead of schedule by 2018. Anhui and Hubei in the central region will also complete the task of banning breeding by the end of the year. Guangdong in the eastern region and other places will also complete the relevant work at the beginning of 2018. After the ban, the next step is to promote the recycling of livestock and poultry manure. Many small-scaled and medium-sized farmers have not survived the difficulties, forced to give up pig breeding. Before withdrawing from the market, they will inevitably put live pigs into the market, resulting in a decline of pig prices.
As shown in Fig. 8, under the common frontier, the average annual GTCP of eastern region, central region, and western region is 1.0055, 1.0051, and 1.0022, respectively. Under the regional frontier, the GTCPs of three regions are 1.0037, 1.0033, and 1.0027, respectively. In the western region, although the GTCP is the lowest under the common frontier and regional frontier, it is still positive growth, indicating that the western region has development potential and advantages.
The eastern region is mostly located in the plain areas of various river basins, with developed transportation, broad market, and easy industrial agglomeration. At the same time, the more developed the economy is, the more bulk farming is replaced by large-scale farming. The transformation of production mode is more conducive to the rational use of existing resources, avoid unnecessary cost waste, and maximize profits and benefits. Guangdong Wen's Group occupies a relatively large market share in Chinese pig industry. Its livestock and poultry breeding business mainly focuses on raising pigs and chickens. The enterprise adopts the mode of "company + family farm" and implements the one-stop production and operation mode of whole management process of industrial chain. This makes Guangdong GTCP ahead of the rest of the country. The development of pig breeding industry in the central region is slow, so the investment supported by the government is mainly concentrated in Henan, Liaoning, Heilongjiang, Jiangsu, Guangxi, Hebei, and Shandong. The fluctuation of GTCP is mainly caused by the fluctuation of technical progress index. The fluctuation of technical progress mainly fluctuates with the fluctuation of pig breeding industry, that is, the change of disease and pork price. According to the analysis of relevant statistical data, it is found that the fluctuation of GTCP (technology progress index) has a relatively consistent fluctuation trend with the pork price. The reason is that when the pork market is good, large-scale pig farms have the incentive to research and introduce new technologies. Conversely, existing technologies may be idle.
As shown in Fig. 9, under the meta-frontier, the threesized GTCPs in the eastern region are 1.0041, 1.0049, and 1.0074, respectively; in the central region are 1.0054, 1.0048, and 1.0050, respectively; and in the western region are 1.0013, 1.0017, and 1.0036, respectively. All of them are greater than 1. Among them, the small-scale development in the central region is better, while the large-scale GTCP in the eastern and western regions is greater than that in the small scale and middle scale. Under the group frontier, the GTCPs of small, middle, and large scale in the eastern region are 1.0016, 1.0036, and 1.0058; in the western region are 1.0028, 1.0036, and 1.0035; and in the western region are 1.0024, 1.0032, and 1.0025. Among them, the GTCPs of middle-scale in the central and western regions were higher, indicating that in the case of considering regional factors, the middle-scale breeding in the western region has better development and pays more attention to the ecological effects. The natural breeding conditions in the western region of China are superior. At the same time, the largescale GTCP is higher than the medium-sized GTCP and small-scale GTCP, whether under the common frontier or the group frontier, whether in the eastern area, the central area, or the western area.
Although the economic development in the western region is relatively backward, it is easy to choose sites suitable for large-scale pig farm construction and less damage to the ecological environment in this region. In addition, the intensity of environmental regulation and pollution control investment in the eastern region is higher than that in the central region and western region. Therefore, the average GTCP in the eastern region is higher than that in the central and western regions, with a positive growth. Although the GTCP in the western region is lower than that in the eastern and central regions, the main environmental pollutants produced by pigs are feces and urine, while the western region is a large agricultural province with sparsely populated land, high forest coverage, and large absorption of pollutants. Therefore, the GTCP in the western region is higher than 1.
As shown in Fig. 10, Hunan, Liaoning, and Sichuan have the closest TGR to 1, with a gap of only 0.02%, 0.32%, and 0.56% with the common frontier. From the regional level, the TGR of the eastern region is 0.9760, of the central region is 0.9909, and of the western region is 0.9795. None of the three regions has reached the best frontier technology level, with a gap of 2.40%, 0.91%, and 2.05%, respectively. It shows that relatively speaking, the technical level of the central region is advanced, and the promotion degree of lowcarbon breeding technology is high. The gap between TGR and common frontier in the eastern region is the largest, and there is also the largest room for progress. Although the level of economic development in eastern China is high, most of them focus on scientific and technological industries and pay insufficient attention to agriculture. This is in line with the actual situation in China. The western region is backward in economy, mainly traditional pig breeding model, and the level of clean farming technology is low. The central region, with dense population and superior geographical location, has the power to carry out technological innovation and improve management level.

Conclusions and policy recommendations
Based on the MinDW-MML model, this paper calculates the GTCP under the common frontier and regional frontier of 17 Chinese provinces from 2004 to 2018 and decomposes it into TC and EC. The outcomes show that (1) regardless of the common frontier or the group frontier, the GTCP presents large spatial and temporal differentiation characteristics. Compared with the central region and western region, the eastern region has obvious advantages in GTCP. (2) The overall GTCP shows an upward trend, which is mainly due to the technical progress. (3) Compared with small-scale and medium-sized GTCP, large-scale GTCP has apparent advantages. It highlights the important role of scale advantage in China's pig breeding industry.
According to the current situation of China's pig industry, the following policy implications are put forward: (1) Give full play to the advantages of pig breeding in different regions. The eastern region has developed economy, broad market, and advanced technology. It should develop low-carbon breeding by taking advantage of technological advantages. As the transportation link between the central region and the western region, the central region has no advantages in the climate and topographical conditions. It is necessary to develop large-scale farming on the basis of overcoming natural conditions. Although the economy in the western region is relatively backward and the technical level cannot keep up, it is vast and sparsely populated, and the natural environmental conditions are good. It can develop large-scale breeding by making full use of low-cost labor force and land cost. (2) Increase the research and introduction of pig breeding clean technology and improve the application efficiency. At present, China's pig breeding industry has low technical efficiency, insufficient utilization of existing technology, and insufficient government management on the whole. Therefore, in the future, the government should strengthen the implementation of environmental protection policies and relevant laws and regulations and strengthen the promotion of environmental protection technology in pig breeding. With the increasing pressure of environmental protection, small-scale farmers will accelerate their withdrawal from the market, which will improve the industry concentration, improve the technology application capacity, and speed up the renewal of new technologies for rural pig breeding in China.  relatively not optimistic, and will suffer losses. This is the law of natural elimination of the market. Large-scale breeding plays an extremely important role in improving pig production efficiency and meeting people's pork demand, so as to reduce pollutant emissions and realize low-carbon and high-yield breeding.
At the same time, there are still some room for progress and limitations in this paper. Firstly, considering the reliability, availability, and scientificity of the data, the research object of this paper is 17 major pig producing provinces in China. There are 31 provinces in China. More samples should be added to the future research. Secondly, pork is one of the main foods of people all over the world. The application of this method to calculate the green total factor productivity of pig breeding in other countries is also of certain significance. It is hoped that this paper can promote more research on pig breeding industry.
Author contribution ZS was responsible for the definition of conceptualization and methodology and the use of software. LJW analyzed and interpreted the data and was a major contributor in writing-original draft. ZDH was responsible for the supervision and writing -reviewing. All the authors read and approved the final manuscript.
Funding This research was funded by the National Social Science Foundation Program of China (18AJY016, 19BJY104) and Heilongjiang Philosophy and Social Sciences Project (21JYD272, 21JYE396, 21JLE321).

Data availability
The datasets generated and analyzed during the current study are available in the "National Compendium of Agricultural Product Expenses-Benefit Data" and "Discharge Coefficient Manual" released by the Office of the First National Pollution Source Census Leading Group.

Declarations
Ethics approval and consent to participate Not applicable.

Competing interests
The authors declare no competing interests.