Inequity in Environmental Pollution of China’s Livestock and Poultry Industry: A Frontier Applications of Spatial Models

: The study’s main aim is to find out the environmental livestock and poultry pollution. The study used data from 31 provinces in China from 2007 to 2019. This paper used two steps for empirical findings. In the 1st step, it conducted an initial analysis of the farmland pollution burden and water pollution that arises from the livestock and poultry industry. After this, through the fair distribution index researcher, the study analyzed the inequity of the environmental pollution burden on the livestock and poultry industry. Finally, by constructing a frontier spatial matrix and spatial econometric model, the study has analyzed the impact of economic development on the in-equity of the environmental pollution burden. The econometrical analysis has provided the following conclusions: (1) China’s arable land is facing a serious pollution burden due to livestock and poultry manure. The results show that the livestock and poultry manure burden value is greater than 1. This value explained the serious environmental threat in 13 areas of China. Water pollution showed a fluctuating trend in four areas of China, while the threat of farmland pollution showed a downward trend. (2) The environmental equity index of the livestock and poultry industry in many regions of China is less than 1. This means one region is producing more pollution than its capacity. So, the pollution has crowded out the environmental capacity of other regions, resulting in an unfair environmental burden. This unfair environmental burden is especially prominent in the western region of China. (3) The phenomenon of environmental pollution-burden inequality has a spatial correlation. The environmental pollution burden inequality of a region has a significant spatial crowding out effect on the surrounding areas at the level of 1%, and the coefficient of spatial effect is −0.909. (4) The per capita GDP of the surrounding areas has a significant “inverted U-shaped” indirect impact on the environmental distribution equity index of the region, with an inflection point of 33,500 yuan/person. The research points out that clear property rights, guidance to regulate emissions trading, control blind pollution transfer, moderate industrial structure adjustment, improving rural residents’ education level, etc., are beneficial to the improvement of the environmental livestock and poultry pollution.


Introduction
With the continuous transformation and upgrading of the consumption structure of agricultural products, the demand for animal husbandry products such as meat, dairy products, and eggs has been continuously rising, which has greatly promoted the rapid development of the livestock and poultry breeding industry (Department of Natural Ecological Protection, State Environmental Protection Administration, 2002) [1]; since 1991, China's meat, eggs, and poultry output have been ranked first in the world [2,3]. However, with the development of the livestock and poultry industry, livestock and poultry breeding pollution has become one of the important causes of agricultural non-point source pollution [4,5]. Research on pollution in China is unavoidable as a big consumption of animal husbandry products. Experience shows that the development of the livestock and poultry industry has mainly brought water pollution and soil pollution. According to the Second National Pollution Sources Census Bulletin issued by China in 2020, the chemical-oxygen demand of water pollutant discharge in China was 100,053 million tons, of which 6.0483 million tons comes from large-scale livestock and poultry farms. The total nitrogen emissions is 596,300 tons, 370,000 tons of which came from the livestock and poultry industry; the total phosphorus emissions reached 119,700 tons, of which 80,400 tons came from the livestock and poultry industry. Census results show that the discharge of livestock manure has been the main source of water pollution in rural areas. In watersheds with serious water pollution in China, rural livestock and poultry breeding is one of the main causes of nitrogen and phosphorus eutrophication in water bodies, and its contribution rate is much higher than that of urban domestic sewage point source pollution and industrial point source pollution [6]. As the carrier of the development of the livestock and poultry industry, the pollution problem of cultivated land is also inevitable. Soil pollution of cultivated land refers to the harmful substances in cultivated land exceeding the purification capacity of cultivated land, which changes the composition and character of cultivated land, leading to the deterioration of cultivated land soil quality and dysfunction. According to the survey results from the China Environmental Protection Administration, the production of livestock and poultry manure in China is twice that of industrial solid waste [7]. With the rapid development of the livestock and poultry industry in China, a large amount of manure discharge is likely to have exceeded the range that the land can bear, causing pollution to the country's water and soil, which deserves great attention.
China's livestock and poultry breeding industry is gradually transferring to resourcerich regions with less developed economies [8], and with the expansion of industrial agglomeration [9], the transfer continues to intensify. The transfer of pig production area is a typical example: according to the research of [10], the pig breeding in Shanghai, Beijing, and some other big cities has been transferred to surrounding or remote areas. Some scholars have verified the "pollution paradise effect" in pig production through empirical analysis and pointed out the transfer of pig industry due to environmental cost savings, that is, the transfer of pig production from areas with strict environmental regulations to areas with looser environmental regulations; so, that is unsustainable and has high environmental risks [11]. The existing layout of livestock and poultry breeding reduces the fairness of resources and environment between regions, and with the gradual transfer of the breeding layout, this asymmetry will continue to expand and result in unfair environmental burdens [12]. The Chinese government have attached a great level of importance to this, and in 2010 issued a "livestock and poultry breeding pollution control technology policy" (2013), that issued the scale of livestock and poultry breeding pollution control ordinance, and then introduced another policy in 2017 to "accelerate the breeding livestock and poultry waste resource utilization", and so on, as a series of regulations to manage the pollution of livestock and poultry industry in China. These policies mainly stipulated how to prevent and control the pollution of the livestock and poultry industry in the region, but did not give clear management methods for the pollution transfer and the unfair environmental burden caused by the livestock and poultry industry.
Based on an extensive review of existing studies, empirical studies on environmental burden inequality are mainly divided into two categories. One is to use income distribution methods. The study [13] verified that pollution transfer would bring serious environmental inequality by simulating China's environmental Kuznets curve. The study [14] used the gene coefficient to measure regional environmental equity in China and proved that environmental inequality in China was on the rise. Another type of study focuses on measuring the emission and transfer of pollution between different regions, such as in this paper, the pollutant discharge coefficient method has been used to calculate the amount of manure produced by livestock and poultry breeding in China, and the current situation and problems of its resource utilization have been analyzed [15]. The metal enrichment factor (EF) was used to measure the watershed distribution of Cu, Zn, Pb, and Cd in sediments in the Wen-Rui Tang urban river system in Wenzhou, Eastern China [16]. This study analyzes pollution emissions and spatial-temporal variations in China's cattle breeding industry [17]. In the study [18], the inequity factors were measured and it was found that the inequity factors of China's resources and environment were mainly concentrated in the economically underdeveloped areas of western China. All these studies have contributed to the study of environmental burden inequality, but pollution has significant spatial transitivity, and environmental inequality itself reflects spatial crowding out from surrounding areas. Unfortunately, little has been written about the extent to which environmental inequity is affected by the surrounding area.
This paper aims to explore whether the pollution caused by the livestock and poultry industry in China has been exceeded by the environmental burden. More importantly, given that pollution is spatially transitive, the study tries to understand how unfairly the environmental load in the surrounding areas affect the region. This study focuses on the unfairness of environmental burdens in different provinces in China and takes the regional economic development level as an entry point to explore the environmental burden and pollution of local and other regions caused by the development of the economic level of each region. Specifically, the environmental burden refers to the pollution of water and soil caused by nitrogen, phosphorus, and chemical oxygen demand emissions from the livestock and poultry industries.
The premise of the application of the spatial model to study space pollution is to build a relatively reasonable and accurate spatial matrix, which is the premise of all spatial research. However, since the construction of the spatial matrix has not formed a unified construction standard in the academic community, most of the existing research mainly adopts a static and cross-sectional spatial matrix. Even if the geographical location of the two regions will not change significantly in a short period of time, the closeness of their relationship is still constantly changing. For example, due to the closed traffic, region A rarely traded with other surrounding areas, but with its economic development, the traffic gradually improved, and then it also starts frequent trade with the surrounding areas. At this time, if the static and cross-sectional spatial matrix was still used, the change in this spatial relationship could not be reflected. Considering that the duration of this study is as long as 13 years, a dynamic and variable endogenous spatial matrix is more in line with the research needs. Therefore, this paper adopts a more cutting-edge spatial matrix construction method to conduct the research, which will be detailed in the following paper.
The main contribution of this study is mainly as follows. First, it discusses the pollution transfer of the livestock and poultry industry in China from the perspective of an unfair environmental burden. It also provides a decision-making basis and pollutiontreatment experience for the development of the livestock and poultry industry in China and even other countries and regions. The second is to apply the cutting-edge spatial matrix construction method and prove its applicability in the spatial change relationship, which provides empirical evidence for the subsequent spatial metrology research.

Data Sources and Description
The data has been used in the study, from 2007 to 2019, in 31 provinces in China, from the National Bureau of Statistics, China Statistical Yearbook, China Rural Statistical Yearbook, China Animal Husbandry and Veterinary Yearbook, China Population and Employment Statistical Yearbook, etc. It should be noted that (1) the annual growth rate of animal husbandry growth in Inner Mongolia in 2017 was zero, which was revised to 0.0001 for calculation needs; (2) in the data released in 2019, only the value-added of agriculture, forestry, animal husbandry, and fishery was published. There is no sub-industry value-added. For research needs, we multiplied the value-added of the total output value of agriculture, forestry, animal husbandry, and fishery by the ratio of the total output value of animal husbandry to the total ones to obtain the value-added of animal husbandry in 2019. (3) During the collection of data, it was found that the unified release of the cultivated land area in each region was only updated to 2017. Considering that the changes in the cultivated land area in each region have been small in the short term, the cultivated land area data in 2018 and 2019 were based on 2017. In the research process, combined with the research needs, use Matlab respectively 2019a, Stata16.0, Arc GIS 10.2 (Version number: 10.2; Environmental Systems Research Institute, Inc.: Redlands, CA, USA), and other software.

Research Methods
This study has been divided into two steps. The first step has to calculate the coefficient of environmental burden unfairness of China's livestock and poultry industry. The second step has to take this coefficient as the dependent variable to analyze the spatial effect of environmental pollution. Therefore, the research method has been also divided into two parts. One part specifically introduces the calculation of water pollution and soil pollution in China's livestock and poultry industry, and the calculation of the unfairness coefficient of the environmental burden. The second part introduces the construction of a frontier spatial matrix and spatial econometric model.

Livestock and Poultry Pollution Coefficient
Regarding the emission and accounting of pollution sources in the livestock and poultry industry, the following two steps must first be completed. Data is used to determine the biological emission coefficients of various livestock and poultry. The second is to determine the calculation cycle of different livestock and poultry according to the growth characteristics of different livestock and poultry. Specifically, the research objective of this paper focuses on the national livestock and poultry industry. To ensure the availability and integrity of various livestock and poultry biological breeding data, the data published by the National Bureau of Statistics is used. Therefore, the livestock and poultry organisms selected in this paper are pigs, cattle, seven types of sheep, horses, donkeys, mules, and poultry. Since there is no uniform standard for the emission coefficient of livestock and poultry manure, to minimize the calculation error, the daily emission coefficient of pigs and cattle in various regions is determined according to the pollution production coefficient of livestock and poultry breeding provided in the "The First National Pollution Source Survey of Livestock and Poultry Industry Pollution Emission Coefficient Manual (in Chinese)". Taking into account the differences in the pollution coefficients of animals in different growth periods, the pollutant discharge coefficient of pigs in the current year is the combination of the coefficients of the nursery period and the fattening period. The calculation is based on the feeding period of 199 days, 1/3 is the nursery period and 2/3 is the fattening period [19,20], the pollutant discharge coefficient of pigs in stock is the average coefficient of the nursery period, fattening period, and breeding period [21]. The calculated breeding period is 365 days, of which 1/3 is the nursery period, 1/3 is the fattening period, and 1/3 is the gestation period. For beef cattle, the pollution coefficients of fattening cattle in various regions provided in the "Coefficient Manual" were adopted, and the feeding period was 365 days. The breeding period of poultry is 210 days. The rest of the livestock and poultry are determined as the standards shown in Table 1 regarding relevant literature because there is no regional coefficient. Among them, pigs and cattle are calculated according to feces and urine. Due to the lack of relevant data, such as the amount of urine contamination of sheep and poultry, only the amount of feces is calculated, which may lead to the calculation result being lower than the actual [22]. The chemical oxygen demand (COD), total nitrogen, and total phosphorus emissions of China's livestock and poultry industry are calculated as follows: In Equation (1), represents the sewage discharge of the livestock and poultry industry in region in period , is COD, total nitrogen and total phosphorus emissions, respectively, represents the number of types livestock and poultry in region , represents the pollution coefficient of type livestock and poultry in region , and is the feeding period.

Accounting Method of Cultivated Land Pollution
To measure the pollution load of livestock and poultry manure in various regions, the discharge amount of various types of livestock and poultry manure is uniformly converted into pig manure equivalent. The alarm value of livestock and poultry manure pollution is calculated according to Equation (2). The specific alarm value classification is shown in Table 2. The results are shown in Table 3.
Among them, r is the alarm value of the load capacity of livestock and poultry manure; q is the arable land load of pig manure equivalent, t/hm 2 ; p is the theoretical maximum suitable fertilizer amount of organic fertilizer, usually 30t*hm 2 . Note: for details see [19].
In Equation (3), W is the regional water environment bearing pressure index; is the amount of surface water resources required to dilute livestock and poultry manure under the given water environment standard.
is the total surface water resource that can be used to dilute pollutants, which can be used to carry water. The total amount of resources is the content of Class I pollutants discharged into the water body by livestock and poultry manure and is the upper limit of the content of Class I pollutants under the established water environment standards. If W > 1, it means that the livestock and poultry manure discharged into the water body exceeds the capacity of the surface water resources in the area. The livestock and poultry breeding causes pollution to the water body; otherwise, it can be considered that no pollution is caused [9].

Fair Distribution Index
The reasonable distribution of pollution rights and social welfare makes the important connotation of environmental fairness. The uneven spatial distribution of pollution emissions is affected by geographical regions and populations. China has a vast territory, and the basic conditions of the different regions are quite different. When studying the measurement of environmental inequity, it is necessary to consider many factors such as population distribution and geographic location in different regions. Therefore, this paper selects the fair distribution index (Equitable Distribution Index, EDI) indicator to measure the degree of environmental inequity in the spatial distribution of various regions, and its calculation equation is: Among them, represents the fair distribution index of the emission of the first type of pollution source in the region. The larger the EDI value, the fairer it is. If the EDI value is lower than 1, it means that the livestock and poultry pollution in the region exceeds the range that its population or land can bear, resulting in the environment not being fair. represents the chemical oxygen demand, total nitrogen, and total phosphorus, respectively, represents the per capita emission of the livestock and poultry industry. in region during period and represents the per capita emission of livestock and poultry industry in China during period .
refers to the emission of the local livestock and poultry industry in period in region , refers to the emission of national livestock and poultry industry in period . A and B are weight coefficients, which are 0.5 and 0.5 in this paper. According to the principle of environmental fairness, if the per capita or land-level livestock and poultry pollution source emissions in a region are higher than the national per capital or land -based pollution source emissions, it means that the region occupies the environmental capacity of other regions. If its livestock and poultry industry pollution discharge scale is inconsistent with its population or land area scale, it causes environmental inequities between regions [18].

The Construction Method of the Space-Time Weight Matrix
With the rise of spatial econometrics, spatial econometrics has been more and more widely used in practical research. This paper takes unfair environmental burdens as the research objective. Based on empirical judgment, we can see that the pollution of the livestock and poultry industry has a certain spatial diffusion. It is said that the inequity of the environmental burden of a region is likely to have a positive or negative impact on the surrounding area in space. If this spatial effect is ignored, it will lead to bias in the research calculations. The environmental burden of the livestock and poultry industry is not fair when carrying out research and analysis. Therefore, this paper selects a spatial econometric model for China.
The construction of the spatial weight matrix is the first and crucial step in the construction of the spatial econometric model. At present, the construction of the spatial weight matrix is still a highly controversial issue, and there is no unified selection and inspection standard. Due to the unobservability of spatial spillover effects, different research experiences and research interests will lead to the subjectivity of the spatial weight matrix setting. At present, most domestic researches use the exogenous spatial weight matrix. The exogenous spatial weight matrix is usually set exogenously based on a certain concept or principle, and its construction and use are generally subjective and arbitrary. Considering this drawback, this paper refers to the construction of the space-time weight matrix proposed by [23]. The weight matrix and the time weight matrix are combined to form a space-time weight matrix by the Kronecker product [24,25] and the setting of the time weight matrix mainly depends on the year of the research object. The ratio of the global Moran index is determined since the global Moran index of the explained variable year represents the spatial spillover effect among all regions in the year. The ratio of the Moran index of two different years must reflect the transfer and conduction effect of the spatial spillover effect over time. Therefore, based on the ratio between the global Moran indices in different years. The influence relationship and conduction path of the spatial spillover effect in time can be accurately depicted, the time weight matrix can be accurately determined based on this. Let the global Moran index be year, then the time weight matrix based on the ratio of Moran index between years can be expressed by Equation (5). where represents the time-influenced period chosen in the study, = 1, 2, … , , = 1, 2, … , .
The elements of the time weight matrix are given by the ratio of the global Moran exponents of the explained variables in the two periods. The principle of setting the elements is as follows: the main diagonal element is always 1, indicating the time shift effect of the spatial spillover effect of the explained variables in the same period. In fact, the ratio of the global Moran index at the same period must also be 1; the upper triangular elements are all 0, which means that the spatial spillover effect of the explained variable is only affected by the spatial spillover effect of the explained variable that precedes the time, and will not be affected by the spatial spillover effect of the explained variable at the later time; the lower triangle element is the ratio between the global Moran index of the year corresponding to the row where the element is located and the global Moran index of the corresponding year of the column, the time weight matrix is standardized, and = ∑ 1/ , = /( + ), = /( + ) . The time weight matrix after row normalization is constructed as shown in Equation (6).
The combined formula of the variable space-time weight matrix is = ՚ ○ ×W, in which ○ × is the Kronecker product. Although the underlying space-time weight matrix is set exogenously, the time-weight matrix of Equation (6) eliminates the influence of the initial setting of the space-time weight matrix. It is determined by the annual global Moran index ratio that is generated endogenously based on the explanatory variable data series, so the space-time weight matrix is also rooted endogenously in the model data itself, and the variable endogenous space-time weight is constructed as follows:

Space Model Construction
This paper first assumes a general spatial econometric model: is the fair distribution index of the region year , is the spatial lag coefficient of the dependent variable, T is the time period, , is the spatial weight matrix (constructed above), is the dependent variable of the t -th year in the i region, is the independent variable of the region year, is the independent variable the influence coefficient, is the independent matrix, is the spatial lag coefficient of the explanatory variable, is the individual effect, is the time effect, M is the disturbance term spatial matrix, and is the spatial error term coefficient when , , are equal in this paper.
To avoid the bias of model selection caused by subjective judgment, this research has first built a general spatial econometric model for regression, and then tested the model as follows: At that time, the model is the Durbin model (S = 0DM), and when ≠ 0 and = 0 when, the model is Spatial Autoregressive Model (SLM); at that time, the model was a Spatial Error Model (S = − EM) to ensure the applicability of model selection [26].

Pollution Analysis of Livestock and Poultry Industry
The pollution caused by livestock and poultry mainly includes the pollution of cultivated land and the pollution of water resources. The pollution of cultivated land mainly refers to the discharge of manure exceeding the suitable amount of organic fertilizer. The pollution of water sources mainly refers to the total amount of surface water resources needed to dilute pollutants in a certain area after livestock and poultry manure enters the water body under the established water quality and environmental standards (refer to the Class III standard of the "Surface Water Environmental Quality Standards") and the area. The ratio of the total amount of surface water resources that can be used to dilute pollutants (calculated at 30% for livestock manure intake) [22].

Measurement Results of Cultivated Land Pollution
The calculation results show that manure discharge exceeding the load of cultivated land is more common in all regions of China. There are 13 regions in the country where a load of livestock and poultry manure poses a serious pollution threat to the environment. Among them, due to the small area of arable land and the large discharge of livestock and poultry manure in Tibet, the livestock and poultry industry poses a serious threat of environmental pollution, the Tibet region ranking first in the country.

Measurement Results of Cultivated Water Pollution
In Table 4 the water pollution caused by livestock and poultry industries in each region is calculated. To make the text concise, only the areas that have caused water pollution and their specific calculation results are listed in the table. The results showed that the W value of chemical oxygen demand (COD) in Beijing, Hebei, Shandong, and Ningxia has been greater than 1, and the phosphorus emission of the livestock and poultry industry in Hebei Province has also been greater than 1. Due to the livestock and poultry industries in this region, the polluted water situation is more serious. In addition, the W values of COD in Beijing and Henan provinces are 0.975 and 0.977, respectively, closer to 1.

Environmental Inequity Analysis of Chemical Oxygen Demand Emissions
According to Equation (4), the fair distribution index of the chemical oxygen demand emission in China's provinces and cities from 2007 to 2019 has been calculated. The annual average value of each region has been calculated to obtain the results in Table 5. The results show that the fair distribution index of chemical oxygen demand emissions from the livestock and poultry industries in the central and western regions, especially in many provinces in the western region, is less than 1.

.2. Environmental Inequity Analysis of Nitrogen Emissions
The fair distribution index of nitrogen emissions from livestock and poultry industries in various regions is shown in Table 6. The results show that the data on the fair distribution of nitrogen emissions from livestock and poultry industries in various regions are not significantly different from COD emissions. Emissions are more equitable than chemical oxygen demand emissions.  Table 7 shows the fairness index of phosphorus emissions from the livestock and poultry industries in each region. The comparison shows that the overall fair distribution index of the three types of pollution sources in the livestock and poultry industry in all regions in China is relatively consistent. Among them are Liaoning, Fujian, Shandong, Guangdong, and Hainan in the eastern region; Jilin, Jiangxi, Henan, Hubei, and Hunan in the central region; and Guangxi, Sichuan, Yunnan, Tibet, and Qinghai in the western region are all three types of pollution source fair distribution index less than 1. The livestock and poultry industries in these areas discharge more than their own environmental capacity and are seeking the development of the livestock and poultry industries at the expense of the environment.

Space-Time Weight Matrix Selection
According to conventional experiences combined with the needs of this research, eight basic space matrices are constructed, namely W1 (01 matrix based on Queen space adjacency relationship), W2 (reciprocal matrix of provincial capital city distance), W3 (reciprocal square matrix of provincial capital city distance), W4 (reciprocal matrix of the distance between regional center points), W5 (reciprocal matrix of the distance between regional center points), W6 (combination matrix of highway distance of provincial capital cities and total population), W7 (matrix of provincial capital city highway distance), and W8 (reciprocal square of provincial capital cities) combined with the total population matrix. Among them, W2, W3, W4, and W5 are calculated according to the Euclidean distance and according to the latitude and longitude of the region or capital city. The eight fundamental matrices are all row-random normalized. Based on these eight basic matrices, according to the above-mentioned principle of constructing the space-time weight matrix. The explained variables are first processed into stacking sequences, and the structure of the processed explained variables is shown in Figure 1. Then, the eight global Moran indices for each year are calculated according to the eight fundamental matrices, and then according to Equations (6) and (7), eight variable endogenous space-time weight matrices are generated, the structure of which is shown in Figure 2. Among them, in the coordinate axis, 1~403 represents the accumulation sequence of the 31 provinces in the country from 2007 to 2019, for example, 1~31 represents the 31 provinces and cities in the country in 2007. To avoid the randomness brought about by subjective selection, Fisher's t-test [27] has been carried out on the eight variable space-time weight matrices according to the principle of effective correlation. The test results are shown in Table 8. The test results show that the eight space-time matrices all pass the Fisher t-test at the 1% level. However, the effective correlation coefficient of the space-time matrix constructed based on the provincial capital city highway distance is 0.807. The correlation coefficient is the highest among the eight matrices, which can be considered the most ideal matrix among the eight basic matrices constructed in this paper. Therefore, the following spatial econometric analysis chooses the provincial capital city highway distance as the spatial matrix.

Spatial Model Construction and Selection
Taking the highway distance of the provincial capital as the spatial matrix. The selection of the spatial model was carried out before the study. The research data was brought into the spatial autoregressive model (SAR) which has been fitted with the double fixed individual period, the double fixed spatial error model in the individual period (SEM), fixed-effects spatial Durbin model (SDM), random-effects spatial Durbin model, and carried out the Wald test and the LR test. The test results are shown in Table 9. The results show that, according to the research data, the model cannot degenerate into a spatial autoregressive model or a spatial error model. The research objective of this paper is suitable to choose the spatial Durbin model with double fixed individual periods.

Variable Selection
1. Dependent variable: In this paper, the emission of chemical oxygen demand, nitrogen, and phosphorus from the livestock and poultry industry are selected to measure the unfairness of the environmental burden. Item index, as the dependent variable of this paper. 2. Independent variables: The unfair environmental burden caused by the discharge of pollutant sources such as chemical oxygen demand, nitrogen, and phosphorus in the livestock and poultry industry is determined by a series of social and economic factors. There are certain differences in management level and residents' awareness of environmental protection. Therefore, the study selects the level of economic development as an independent variable to measure the stage of economic development in different regions and uses the per capita GDP to represent the level of economic development. 3. Control variables: The study selected six indicators as control variables: industry, comparison of income levels of urban and rural residents, local financial science and technology expenditure, number of agricultural meteorological observation sites, per capita cultivated land area, and per capita education years of rural residents. The specific calculation method and data structure are shown in Table 10. From the descriptive statistical results of the variables, the mean values of the three types of fair distribution indexes are all greater than 1, but the gap between the minimum value and the maximum value is large, indicating that there are large differences in the fair distribution indexes between regions and years, and the inequity in some regions was prominent. In the same way, there are also large differences in per capita GDP between regions. Animal husbandry output value in the whole agricultural output value accounted for about 30%, accounting for a relatively large amount. The income comparison of urban and rural residents is 2.805, indicating that the income level of urban residents has 2.8 times that of rural residents. The annual local government expenditure on science and technology has 9.279 billion yuan on average, with a large gap between different years, but the overall investment has constantly increased. Each province has an average of 22.37 agricultural meteorological observation stations. The per capita cultivated land area in the survey area has 291,198 people/10,000 hac, and the difference between different provinces was great. The average length of education of rural residents was 8.862 years, they have mainly completed junior high school education. However, with the passage of time, the level of education of Chinese farmers is constantly improving, and the average length of education in some areas has reached 12 years.

Outcome of Practice
In the table, Models 1 and 2 use an invariant exogenous spatial weight matrix, based on a maximum likelihood estimation. Where Model 2 is corrected for fixed effects bias, Model 3 uses a variable endogeneity spatiotemporal matrix, based on Bayesian estimation. When the spatial spillover effect of the spatial Durbin model is significantly nonzero, the directly obtained main regression results are biased, and its influence effect needs to be decomposed. Available on request.
From the perspective of the economic development level, the regression results show that the spatial effects of each model are significantly negative at the 1% level, indicating the unfairness of the environmental burden among regions has a significant spatial crowding out effect. In Models 1 and 2, both the direct and indirect effects of GDP on the unfair impact of environmental burdens show a U-shaped relationship, that is, in the early stage of economic development, with the increase in GDP, the unfairness of environmental burdens have intensified. After crossing the inflection point, this situation has been reversed. As GDP continues to rise, the environmental burden of the livestock and poultry industry pollution between regions has tended to develop in a more equitable direction. The impact relationship also exists in the impact of neighboring regions on the region. In Model 3, after considering the temporal change of the spatial spillover effect, the situation has changed. The GDP has no significant impact on the inequity of the environmental burden in the region but the inequity in the local environmental burden is significantly affected by the neighboring regions. The specific performance is an inverted U-shaped relationship. That is to say, the increase in the GDP of the surrounding areas has promoted the fairness of the environmental pollution burden in the area in the early stage, but as the GDP of the surrounding areas continues to rise after the inflection point is crossed, it has begun to squeeze the environmental pollution capacity of the area, through pollution transfer and overloading. Pollution and other methods have a significant negative impact on the unfairness of the environmental burden in the region. Similarly, the spatial spillover effects of the three models all show that, on the whole, the inequity of the environmental burden in the region has a significant negative impact on the inequity in the surrounding areas.
From the perspective of other influencing factors: First, the industrial structure. The higher the output value of animal husbandry in the total output value of agriculture and forestry, the more serious the pollution to the environment. From the empirical results of the three models, whether it is a local impact or a neighboring area, the industrial structure has a significant negative impact on the unfairness of the environmental burden, and the impact of the neighboring area is higher than the local one. This also supports the research hypothesized pollution transfer situation of the livestock and poultry industry. Second, the income levels of urban and rural residents are compared. The research shows that the increase in the income ratio of urban residents, is conducive to promoting the fairness of the environmental burden in the region, and it is significant at the 1% level. However, it has a significant negative impact on the surrounding areas. Third, local financial science and technology expenditures. The results of research model 3 show that the local financial science and technology expenditure has no significant impact on the environmental burden. The reason may be that in China, the livestock and poultry industry still adopts a more traditional way of breeding and production, and does not directly utilize related science and technology. Therefore, concerning local financial expenditure on science and technology, the Chinese government should more fully consider supporting the development of science and technology related to livestock and poultry pollution. However, according to the results of Models 1 and 2, the local environmental burden inequity index has been affected by the scientific and financial expenditures of the neighboring areas, which also supports the speculation that the economically developed areas have transferred pollution to the surrounding areas. Fourth, is the per capita arable land area. The results of Model 3 show that the per capita arable land area has no significant impact on the environmental pollution burden. However, the results of Models 1 and 2 show that the per capita cultivated land area in the surrounding area has a significant negative impact on the environmental burden of the area, but the impact is very small. Fifth is the number of years of education per capita. According to the results of Models 1 and 2, the per capita years of education in the region have a significant positive impact on the environmental burden, but the results of Model 3 show that the per capita years of education in the surrounding areas have a significant negative impact on the local environmental burden. Research speculates that this is also related to the level of regional economic development and pollution transfer.

Discussion
According to the above calculation of the cultivated land load and fairness index of the livestock and poultry industries in various regions, in order to further explore the impact of economic development on the unfair environmental burden, the trend of the Rvalue in the three major regions from 2007 to 2019 and the fair distribution represented by COD have been calculated. The trend of the index has been plotted, and Figures 3 and 4 are obtained. Figures 3 and 4 show that, although the alarm R-value of the cultivated land load has a downward trend, the cultivated land load in the eastern region (economically developed region) is at a relatively high level each year, that is, the cultivated land load of the livestock and poultry industry in the more economically developed eastern region has a negative impact on the environment and serious pollution has been produced. The western region (economically backward region) has greatly increased the average R-value of the entire western region because the R-value of Tibet is too high. If Tibet is not included in the calculation, the arable land load of other provinces in the western region is significantly lower than that of other regions. However, it is worth noting that in the context of the arable land load in the western region, where economic development is relatively lagging, is lower than that in the central and eastern regions with higher economic development levels, the environmental fair distribution index in the western region has always been at the lowest level in the 13 years of statistical research. Even after removing the Tibet region with the lowest equitable distribution index value, this situation did not change. Therefore, among the three models that use different spatial matrices to obtain diametrically opposed results, this paper believes that the results of the model (Model 3) constructed by using variable endogenous spatiotemporal weights are more appropriate to the above analysis results.
Therefore, this paper has reason to believe that the level of economic development has no significant direct impact on the environmental equity distribution index of the region, but it will form an inverted U-shaped indirect impact on the surrounding areas. According to the specific analysis of this paper, the western region (the level of economic development that is relatively backward) plays a significant role in promoting the environmental equitable distribution index in the surrounding areas. On the other hand, the central and eastern regions (with a relatively high level of economic development) have a significant inhibitory effect on the environmental equitable distribution index in the western region. However, as per capita GDP in the western region is lower than the national average level, the overall spatial spillover effect is still manifested as the spatial "crowding out effect".  According to the above analysis results, this paper further calculates the inflection point of the non-linear effect of the per capita GDP on the unfair environmental burden. 33,500 yuan per person (Table 11). According to the Figure 5 This result also confirms that Model 3 believes that the result that per capita GDP has no significant direct impact on the research object is more reliable. (1) According to the regression results, the spatial lag terms of the models in the table are all significantly non-zero. At this time, if the spatial Durbin model (SDM) coefficient is used to measure the spatial spillover effect of environmental unfairness, there will be systematic deviations. The partial differential method is used to decompose each spillover effect into three parts: direct effect, indirect effect, and total effect. To ensure the conciseness of the article, the coefficients of the space Durbin model are not listed in this article and are kept for request; (2) The data in parentheses are T-statistics Amount; (3) *** p < 0.01, ** p <0.05, * p < 0.1.

Conclusions and Recommendations
Based on the analysis of the relevant data of the livestock and poultry industry in 31 provinces in China from 2007 to 2019, this paper discusses the arable land load, water pollution, unfair environmental load, and economic development on the environmental load of the livestock and poultry industry in each region. Impact analyses and the following conclusions are drawn.
1. On the whole, China's cultivated land is facing serious pollution. Across them, a load of livestock and poultry manure in 13 regions poses a serious threat to the environment, and the situation in Tibet is particularly serious. In comparison, the water pollution situation in China is relatively optimistic. From the calculated average value from 2007 to 2019, only four regions have water pollution. However, it cannot be ignored that, from a vertical perspective, while the threat of cultivated land load is declining, the water pollution in various regions of China is showing a fluctuating upward trend. 2. The unfair phenomenon of the environmental burden of livestock and poultry industry pollution exists widely in China. The environmental equity index of the livestock and poultry industry in many regions was less than 1, which means that the pollution of the livestock and poultry industry in these regions crowded out the environmental capacity of other regions, resulting in an unfair environmental burden. Due to the difference in economic development levels, this unfair phenomenon has been particularly prominent in the western region of China (which is economically backward). The environmental equitable distribution index of most regions in western China was at the lowest level in the country, with an overall average of 0.92 (COD), indicating that the waste from the livestock and poultry industry in western China exceeds the capacity of its environment. The development of the livestock and poultry industry has been pursued at the expense of the environment. 3. The inequity of the environmental burden in one area has a significant spatial crowding out effect on the surrounding areas, and the influence coefficient is large. The stage of economic development has no significant direct effect on the unfairness of the environmental burden in the region, but the per capita GDP of neighboring regions has a significant inverted U-shaped indirect impact on the region, with an