Spatial and Temporal Evolution of the Coupling of Industrial Agglomeration and Carbon Emission Efficiency—Evidence from China’s Animal Husbandry Industry

Abstract

Drawing upon the data of China’s animal husbandry industry from 2000 to 2020 in 30 provinces, an EBM model incorporating non-desired outputs was employed to gauge the carbon emission efficiency of the animal husbandry industry. Coupling degree models, spatial autocorrelation models, and Markov chain models were utilized to assess the coupling degree between the industrial agglomeration of the animal husbandry sector and its carbon emission efficiency, and to analyze its spatio-temporal distribution and evolution. The outcomes showed that (1) the coupling degree of China’s animal husbandry industry agglomeration and carbon emission efficiency exhibited an overall downward inclination. Notably, the diminishing tendency of the coupling degree was more pronounced in the eastern, central, and western parts of the country; (2) the coupling degree of the 30 provinces showed a spatial distribution of “western > central > northeast > eastern”; (3) the coupling degree showed obvious agglomeration distribution characteristics, wherein a substantial quantity of provinces was located in high–high clustering zones and low–low clustering zones; (4) the coupling degree of various provinces remained fairly stable, but after considering the spatial and geographical correlation, the coupling degree of each province would be influenced by the coupling degree of its adjacent provinces. Evidently, there remained a substantial scope for the enhancement of the coupling coordination degree between the industrial agglomeration of China’s animal husbandry and the carbon emission efficiency. This research is capable of furnishing a theoretical allusion for promoting regional cooperation, leveraging agglomeration advantages, and implementing carbon emission abatement regimes and directives to enhance the low-carbon development level of animal husbandry industry agglomeration in China.

1. Introduction

In accordance with the projections of the Sixth Assessment Report of the United Nations Intergovernmental Panel on Climate Change (IPCC), the worldwide emissions of greenhouse gasses in 2030 will lead to an increase in global temperatures of more than 1.5 °C [1]. Exorbitant emissions of greenhouse gasses constitute the proximate determinant of global warming [2]. According to data published by the World Resources Institute (WRI), China has served as the nation that registers the most substantial volume of carbon emissions globally since 2006 [3]. In 2015, China contributed about 28.2% of the total global carbon emissions, with the share rising to 30.7% in 2020 [4]. To cope with global warming, China proposed at the 2020 United Nations General Assembly that it would achieve the goals of peaking carbon emissions by 2030 and achieving carbon neutrality by 2060 [5]. As the largest agricultural nation across the globe, there is a huge potential for agriculture to contribute to China’s carbon reduction efforts. Specifically, within agriculture, in 2020, the output value of China’s livestock sector constituted 29.22% of the aggregate agricultural output value. In 2020, China’s agricultural carbon emissions were approximately 2 billion tons, of which the carbon emissions due to the gastrointestinal fermentation and dung management in the process of livestock breeding were as high as 38.76%, which served as a significant source of greenhouse gas emissions [6]. In consonance with the prognostication furnished by the Food and Agriculture Organization of the United Nations (FAO), the global livestock population will increase by 40% by 2030 compared to 2000. This presages that in the future, while the global livestock industry is providing livestock and poultry products for mankind, the mean value of carbon emissions will experience a substantial augmentation [7]. Unlike the industrial sector, notwithstanding the fact that the livestock industry does not constitute the principal origin of carbon emissions, in light of the modulation of the population’s dietary pattern and the augmentation of the demand for meat, eggs and milk, the growth in carbon emissions engendered by the progression of the livestock industry is by no means to be underestimated [8]. In addition, the FAO pointed out in “Livestock’s Long Shadow: Environmental Issues and Options” that the greenhouse gas emissions from the livestock industry constituted 18% of the aggregate global greenhouse gas emissions [9]. The exorbitant energy consumption, severe pollution, and substantial emissions in animal husbandry production urgently need to be transformed towards low carbon [10].

Due to the existence of scale-based economies, the formation of industrial agglomeration, at the same time, will gradually appear in the production process of standardization and scale, in the industrial agglomeration brought about by resource sharing, in technology spillover, and in other factors, contributing to the advancement of the level of production technology and the elevation of the efficiency of production utilization; industrial agglomeration is considered to promote sustainable development, which is an important factor [11]. Livestock industry agglomeration refers to the economic phenomenon that livestock production and management bodies are organically integrated to better utilize the comparative advantages of production, improve comprehensive production capacity, and form a certain scale of agglomeration in a particular region. The government can take advantage of industrial agglomeration to promote emission reduction and efficiency in livestock production. However, there still exists a certain contradiction between industrial agglomeration and carbon emission efficiency. This is predominantly manifested in the circumstance that the restrictive impact of industrial agglomeration on carbon emission reduction depends, to a large extent, on the dynamic interplay between the scale effect and the congestion effect [12], that is, the strategic interaction between the elevation of production efficiency caused by the standardization and scale of the livestock production process and the diseconomies of scale caused by the over-concentration of elements. If we endeavor to foster the synchronized advancement of industrial agglomeration and emission reduction with increased efficiency, it behooves us to harness the scale effect of industrial agglomeration apropos of carbon emission reduction to the fullest extent [13].

Therefore, currently, there still exists a certain contradiction between the industrial agglomeration of China’s livestock industry and the carbon emission efficiency of the livestock industry. The two are certain to have a reciprocal influence in the course of development. When formulating relevant policies, the development of both should be taken into account. We ought not merely to maximize the salutary function of industrial agglomeration but also to guarantee the steady progress of the carbon emission reduction process within the livestock industry. For this reason, how to enhance the organic combination of the industrial agglomeration of the livestock sector and the carbon emission efficiency of the livestock sector so as to construct a pattern that takes both into consideration in the development process is an exigent issue demanding resolution in promoting the high-caliber advancement process of the livestock sector at present. In consideration of this, this research endeavors to investigate the dynamic relationship between the industrial agglomeration of China’s livestock sector and carbon efficiency, with the expectation of constructing a pattern of the organic combination of the two during the evolutionary course of China’s livestock sector, and providing data references and theoretical bases for propelling the premium-quality evolution of the livestock sector and the attainment of China’s “dual-carbon” goals.

2. Literature Review

2.1. Carbon Emission Efficiency

2.1.1. Carbon Emission Efficiency Measurement Methods

The assessment of carbon emission efficiency encompasses two analytical perspectives: single-factor and total-factor. The single-factor perspective mainly measures carbon emission efficiency through carbon productivity [14]. Compared with the total-factor perspective, it is arduous to precisely gauge carbon emission efficiency based on the single-factor perspective. From the vantage point of the total-factor perspective, scholars mainly use various methodologies, such as stochastic frontier analysis, data envelopment analysis, and optimization models like the SBM model and EBM model, for the quantification of carbon emission efficiency. Zhao [15] used the SFA model to investigate the carbon emission efficiency of Shanxi Province. Wang [16] utilized the DEA model to gauge the carbon emission efficiency of China’s agriculture. Li [17] employed the SBM model predicated on non-desired output to gauge the carbon emission efficiency of the Chinese fisheries industry. Shang [18] used the super-efficient EBM model to dissect the spatio-temporal evolution of the carbon emission efficiency of the animal husbandry industry across the Beijing–Tianjin–Hebei region.

2.1.2. Factors Affecting the Efficiency of Agricultural Carbon Emissions

Regarding the research on the influential factors of agricultural carbon emission efficiency, scholars mainly base these on methods such as the Tobit model and the LMDI model [19,20], which show that the level of agricultural technology, the structure of the agricultural labor force, the extent of economic development, and the degree of industrial agglomeration exert a salutary influence on the agricultural carbon emission efficiency, whereas the labor force size and the market size exercise a detrimental effect on the agricultural carbon emission efficiency [21,22]. Chen [23] and Guo [24], respectively, deployed the Tobit model to dissect the influential factors of carbon emission efficiency in China’s soybean planting industry and pig farming industry. The former found that the level of agricultural technology and the level of financial support for agriculture have a positive effect on carbon emission efficiency, while the latter found that the market scale exerts a negative impact on carbon emission efficiency. Li [25] used the LMDI model to dissect the influencing factors of China’s agricultural carbon emission efficiency and found that the levels of economic development and urbanization have a positive impact on agricultural carbon emission efficiency, while the scale of agricultural labor force and carbon emission intensity exert an adverse influence on the augmentation of agricultural carbon emission efficiency. Du [26] and Wang [27], respectively, analyzed the influencing factors of carbon emission efficiency in China’s livestock husbandry and grain planting industry. They found that the degree of industrial agglomeration exerts a favorable impact on carbon emission efficiency and proposed that the low-carbon emission reduction in livestock husbandry and grain planting industry can be promoted by means of enhancing the degree of industrial agglomeration, establishing policies and regulations, etc.

2.2. Relationship Between Industrial Agglomeration and Carbon Emission Efficiency

Industrial agglomeration reduces transaction costs and brings about external economies of scale through spatial concentration of production, resource sharing, and technological spillovers, which have an impact on environmental governance [28]. Existing research on industrial agglomeration and carbon emission efficiency mainly focuses on areas such as manufacturing, producer services, and traditional agriculture. Research into the correlation between the two centers around the ensuing facets.

Primarily, it is believed that the improvement of the degree of industrial agglomeration in the region exerts a linear influence on carbon emission efficiency, including a positive or negative relationship. For example, Wang [29] found that agricultural industrial agglomeration is capable of enhancing agricultural carbon emission efficiency, drawing on China’s provincial panel data spanning from 2011 to 2020. When Sun [30] studied the impact of industrial clustering on carbon emission efficiency in Chinese cities, he found that the industrial clustering of manufacturing and high-end production service industries had a positive impact on carbon emission efficiency, while the industrial agglomeration of low-end production and living service industries would have a negative impact on carbon emission efficiency.

Secondly, it was postulated that there exists a complex mechanistic relationship between industrial clustering and carbon emission efficiency in the region, including an inverted “U” shape [31] and inverted “N” shape [32]. Liu [33] used a panel bi-directional fixed-effect model to investigate the impact of China’s agricultural production agglomeration on agricultural carbon productivity and uncovered an inverted “U”-shaped correlation between the two. Cheng [34] utilized a spatial autocorrelation model to study the impact of China’s industrial clustering on industrial ecological efficiency and detected an inverted “N”-shaped association between the two.

Thirdly, there is a focus on the study of the spatial spillover effect of industrial agglomeration on the carbon emission efficiency spillover effect. The main research is based on spatial econometrical paradigms to dissect the spatial repercussion of industrial agglomeration on carbon emission efficiency. Liu [35] used spatial panel models and found that the impact of China’s productive service agglomeration on manufacturing carbon efficiency has significant regional heterogeneity. Zhou [36] also reached the same conclusion when studying the impact of China’s tourism industry clustering on carbon emission efficiency.

2.3. Summary

The existing literature provides a reference basis for further research on the coupling degree of the agglomeration of the animal husbandry industry and the carbon emission efficiency of the animal husbandry industry, but there remains a certain margin for improvement. Firstly, focusing on other industries, existing research on industrial agglomeration and carbon emission efficiency mostly focuses on the perspectives of the secondary, tertiary industries and traditional agriculture, and there is a lack of research from the perspective of animal husbandry as a whole. Secondly, regarding bidirectional interaction analysis, there is a dearth. Existing research only analyzes the unidirectional effect of industrial agglomeration on carbon emission efficiency through empirical testing [37], and few scholars have considered the two-way relationship between the two, and there is a lack of attention to the coupling degree. Thirdly, there is a lack of spatial correlation analysis. The existing research lacks analysis of the spatial correlation and evolution law of the coupling degree of industrial clustering and carbon emission efficiency.

Due to the cross-regional nature existing in processes such as breeding and transportation in the livestock industry, the emissions of greenhouse gasses in it have spatial correlations [38]. Chen’s research has found that spatial correlations in the industrial agglomeration of China’s livestock industry also exist [39]. Therefore, the spatial econometric model is applicable to this study. In regard to the choice of model, the EBM model incorporates both radial and non-radial distance functions, which can compensate for the deficiencies of the traditional DEA model and the SBM model in terms of their inability to measure and handle the presence of radial and non-radial input–output relationships [40], and the Markov chain is suitable for the evolution of some regions with no posteriority in the study of the probability of the transfer of state, and it is convenient for the prediction of the long-term trend [41]. Considering this, this article makes use of the data ranging from 2000 to 2020 of 30 provinces within China (with the exclusion of Tibet, Hong Kong, Macao, and Taiwan) to gauge the carbon emission efficiency of the animal husbandry industry using an EBM model based on non-desired outputs. On the basis of a model constructed to explore the coupling degree between the level of industrial agglomeration in the animal husbandry industry and its carbon emission efficiency, this article uses a spatial autoregressive model and a Markov chain model to explore the spatio-temporal distribution characteristics and evolution of the coupling degree, aiming to provide a theoretical foundation and decision-making reference for realizing the coordinated development of industrial agglomeration and low-carbon emission reduction in China’s livestock husbandry.

3. Theoretical Analysis

Coupling represents a condition wherein two systems interact with one another to attain mutual coordination and mutual promotion [42]. The degree of coupling and coordination precisely reflects the degree of mutual promotion and coordination among subsystems, and reflects the dynamical correlative propensity of the subsystems evolving from a state of disorder and dissonance to the development of orderly coordination and mutual promotion. Research on coupling relationships is also an important means of enhancing the collaborative governance capabilities of multiple actors and multiple factors. Generally speaking, a pronounced correlation between industrial development and carbon emissions and environmental sustainability exists. The economies of scale and congestion effects engendered by industrial clustering will act on carbon emission efficiency from diverse directions, and the change of carbon emission efficiency will have a reaction on industrial agglomeration. Therefore, clarifying the coupling and coordination mechanism between the two constitutes a significant theoretical underpinning for facilitating the organic combination of industrial agglomeration and carbon emission efficiency, and it is also a crucial link connecting premium economic development and ecological conservation. The coupling mechanism between livestock industry agglomeration and livestock carbon emission efficiency predominantly encompasses the ensuing two facets.

On the one hand, the agglomeration of the animal husbandry industry will have a supporting, driving, or inhibiting effect on the carbon emission efficiency of the animal husbandry industry.

Firstly, the clustering of the animal husbandry industry will affect the carbon emission efficiency of the animal husbandry industry by exerting economies of scale. Along with the formation of industrial agglomeration, thanks to the influence of the sharing of factor resources in the region, the production efficiency of the livestock industry will be remarkably enhanced, thus reducing the input of factor resources in the production process, improving the output while reducing carbon emissions, and thus enhancing the efficiency of carbon emissions from the livestock industry.

Secondly, the agglomeration of the animal husbandry industry will affect the carbon emission efficiency of the animal husbandry industry by exerting knowledge spillover effects. Industrial agglomeration creates a good communication environment for technology research and development personnel. After close communication and cooperation with other researchers in terms of knowledge, technology, and experience, it is conducive to the effect of knowledge spillover [43], which helps them to make up for their own technical deficiencies or management loopholes, thereby improving technological efficiency and innovative production and management models, and thus reducing the carbon emission efficiency of the animal husbandry industry.

Furthermore, industrial agglomeration in the animal husbandry industry will affect its carbon emission efficiency through the competitive effect. Competition among business entities in industrial agglomerations is extremely fierce, and the pace of innovation and research and development is relatively fast. In order to surpass other competitors in the agglomeration area as soon as possible, gaining a comparative advantage in the production process, and thus maximizing benefits, the research and development of green technology will be accelerated, or the attraction of highly skilled professionals will be increased, improving the level of technological innovation and, thus, the carbon emission efficiency of the animal husbandry industry.

Finally, due to the different natural resource conditions in various regions, there are also significant differences in resource endowments. If a region ignores its regional resource carrying capacity and blindly pursues the output brought about by economies of scale, it will produce a crowding-out effect [44], causing production factors to deviate from the optimal input–output ratio, resulting in the overconsumption of production factors like feed and veterinary drugs, thereby hindering the amelioration of the carbon emission efficiency of animal husbandry.

On the other hand, the carbon emission efficiency of the animal husbandry industry will also exert a certain feedback influence on the agglomeration of the animal husbandry industry.

Firstly, if the carbon emission efficiency of the animal husbandry industry improves, it means that technological progress or management capabilities in the region have improved, which is conducive to accelerating the process of industrial agglomeration, optimizing the level of industrial agglomeration in the region, promoting the development of economies of scale in industrial clustering, and limiting the scope of the crowding-out effect, thereby maximizing the agglomeration effect and promoting the level of regional livestock development. At the same time, it can also set up a regional development benchmark image, which is conducive to increasing exchanges and cooperation with more regions and attracting more foreign investment and policy inclination.

Secondly, if the efficiency of livestock farming carbon emissions is not improved, it means that the negative impact of the irrational allocation of factors in the region, as well as the backwardness of technology level and management mode, is greater than the positive impact of the economy of scale. It will lag behind the industrial development level in terms of environmental protection at the same time, causing great pressure, slowing down its own development, and also having negative externalities on the surrounding areas, which forces the government to develop relevant policies to restrain industrial agglomeration. For example, environmental regulation indicators will be reformulated, or production methods of enterprises in industrial agglomeration areas will be affected through carbon taxes, carbon trading, and other means [45], for the purpose of propelling the improvement of the regional livestock industry level and ensuring environmentally sustainable development.

The coupling mechanism diagram between the industrial agglomeration of animal husbandry and the carbon emission efficiency of animal husbandry is shown in Figure 1.

4. Research Methods and Data

4.1. Data Sources and Processing

In light of the accessibility of data, the temporal scope of this research is from 2000 to 2020. The data on capital input, intermediate consumption, total mechanical power, the output value of animal husbandry, the output value of agriculture, forestry, animal husbandry, and fishery, and the labor input are from the China Rural Statistical Yearbook; the GDP is from the China Statistical Yearbook; and the data on carbon emissions from animal husbandry are from the China Animal Husbandry and Veterinary Medicine Yearbook, the National Compilation of Data on Costs and Returns of Agricultural Products, and the China Rural Statistical Yearbook. All the above data are derived from the official website of the China Statistics Bureau. Since linear interpolation approximates the original function by constructing a primary polynomial such that the error at the interpolating node is zero, linear interpolation was utilized to replenish the scant missing data.

Furthermore, with the intention of ensuring the comparability of the data, the agglomeration data were normalized using the range standardization method. The specific formula is shown in Equation (1):

$$Y_{ij}={\displaystyle \frac{x_{ij}-min{x}_j}{max{x}_j-min{x}_j}}+0.01$$

(1)

In Equation (1), Y_ij is the normalized index value, x_ij is the value of the jth index in the ith year, and maxx_j and minx_j are the maximum and minimum values of the jth index, respectively.

4.2. Construction of an Indicator System for the Efficiency of Carbon Emissions in Livestock Husbandry

In this study, labor input, intermediate consumption, capital input, and total machinery power were selected as the input indicators of the carbon emission efficiency of animal husbandry; and the total output value of the animal husbandry and carbon emission of animal husbandry were determined as the intended output and non-intended output indicators of the carbon emission efficiency of animal husbandry. The specific livestock industry carbon emission efficiency input and output indicator system is shown in

Table 1. Descriptive statistics of input–output indicators of carbon emission efficiency in livestock industry.

Indicator	Variable Name	Unit	Average	Standard Deviation	Maximum	Minimum
Input indicator	Labor input	Million people	287.220	250.220	1265.875	5.317
	Capital investment	Billions of yuan	572.050	856.602	5964.420	2.340
	Intermediate consumption	Billions of yuan	341.342	323.055	1479.600	0.900
	Total mechanical power	Million kilowatts	849.880	866.112	3851.328	15.677
Expected outputs	Gross output value of livestock	Billions of yuan	690.219	639.893	3613.800	23.500
Non-expected outputs	Carbon Emissions from livestock	Million tons	664.554	481.395	2181.051	24.274

.

Labor input: Denoted as the personnel headcount engaged in the animal husbandry domain. In accordance with the research conducted by Wu [46], the employee quantity within the agriculture, forestry, animal husbandry, and fishery industry was calculated by multiplying the number of individuals employed in said industry by the ratio of the output value of animal husbandry to the total output value of the agriculture, forestry, animal husbandry, and fishery industries. The unit was denominated by ten thousand individuals;

Intermediate consumption: Referring to the study of Lin [47], it includes material consumption such as veterinary drugs, feed, energy use, and labor expenditure in the material sector, as well the as expenditure on livestock production services. It is adjusted for the price index of agricultural production materials in billions of dollars;

Capital inputs: With reference to the study by Donckt [48], the perpetual capital method was used to calculate the specific formula as shown in Equation (2)

$$K_t=\left(1-{\mathsf{\delta }}_t\right)K_{t-1}+I_t$$

(2)

In Equation (2), K_t is the current capital stock, I_t is the current investment, and δ_t is the capital depreciation rate; the initial agricultural capital stock K₀ is expressed by the amount of investment in agriculture, forestry, animal husbandry, and fishery fixed assets, and the value of agricultural capital depreciation rate δ is taken as 5.42% [49]. Additionally, this is in accordance, to the proportion of the total output value of the livestock industry to the total output value of agriculture, forestry, animal husbandry, and fisheries, multiplied by the amount of investment in fixed assets of agriculture, forestry, animal husbandry, and fisheries as a measure of the current year’s investment in livestock assets I_t, which was adjusted for the price index of the agricultural production materials in billions of yuan;

Total machinery power: Expressed as the total machinery power of the animal husbandry industry. Referring to the study of Zhang [50], the aggregate power of agricultural machinery in each province was used as a benchmark, multiplied by the ratio of the gross value of animal husbandry to the gross value of agriculture, forestry, animal husbandry and fisheries; subsequently, the aggregate mechanical power of animal husbandry was computed in 10,000 kilowatts;

Desired output: Represented by the aggregate output value of the livestock industry. Referring to the study of Tian [51], it was deflated by the production price index of the agricultural products in billions of yuan;

Non-desired output: Expressed in terms of carbon emissions from the animal husbandry calculated via the full life cycle approach (LCA). A portion of scholars have adopted the carbon emissions generated through the emission factor method [52] or the enteric fermentation and manure management link [53] of livestock and poultry to represent the carbon emissions of the animal husbandry sector. Nevertheless, the carbon emissions of the livestock industry ought not to merely focus on a solitary phase within the pre-production, production, and post-production procedures of the livestock industry. Rather, comprehensive deliberation should be afforded from perspectives such as the procurement of raw materials, product manufacturing, and the consequences following the utilization of products. In this paper, we drew on Sun’s [54] method of calculating carbon emissions from the whole life cycle approach (LCA), and divided the carbon emissions generated in the whole life cycle of the livestock industry into seven segments in accordance with the traits of the production segments within the livestock industry, including the cultivation of feed grains, the transportation of feed grains, the gastrointestinal fermentation of livestock and poultry, the manure management system, the energy consumption of livestock and poultry feeding, the processing of livestock products, and the carbon sinks of plants. Pigs, poultry, rabbits, dairy cows, non-dairy cows, horses, mules, donkeys, mules, goats, sheep, camels were mainly selected as the carbon emission sources of animal husbandry, and the carbon emission coefficients of each link of the whole life cycle of animal husbandry in this paper referred to the studies of Sun [55], Hu [56], and Ma [57], and the coefficients of the plant carbon sinks refer to the study of Tian [58], and the specific Equations are as shown in Equation (3):

$$\begin{array}{ll}{TC}_{TOTAL}={TC}_{CZ}& +{TC}_{CY}+{TC}_{SW}+{TC}_{CD}+{TC}_{SC}+{TC}_{SG}-C\\ & =[{TC}_{CZ}+{TC}_{CY}+{TC}_{SW}·{GWP}_{CH4}\\ & +\left({TC}_{mc}·{GWP}_{CH4}+{TC}_{md}·{GWP}_{N2O}\right)+{TC}_{SC}+{TC}_{SG}-C]·e_{tpf}\end{array}$$

(3)

In Equation (3), TC_TOTAL represents the total standard carbon emissions from livestock; TC_CZ, TC_CY, TC_SW, TC_CD, TC_SC, TC_SG, and C, respectively, signify the standard carbon emissions ascertained from the seven domains: forage crop cultivation, forage crop conveyance, fermentation occurring within the gastrointestinal tracts of livestock and poultry, manure management framework, energy consumption in the process of livestock and poultry rearing, livestock product manufacturing, and plant carbon sequestration; the global CH₄, N₂O global warming potential (GWP_CH4 and GWP_N2O) was divided into 31 and 210; the coefficient of conversion of the unit CO₂ equivalent to standard carbon (e_tpf) was 0.2728 from IPCC.

4.3. Research Methodology

4.3.1. Coupling Degree Model

This study utilizes the research method of Yu [59] to set the functional form of the degree of development, which is shown in the form of Equation (4):

$$T=\lambda f{\left(x\right)}^{\theta }g{\left(y\right)}^{1-\theta }$$

(4)

Equation (4) represents the development degree of livestock industry carbon emission efficiency—livestock industry agglomeration. In Equation (4), λ is an exogenous variable, f(x) is the carbon emission efficiency of the livestock industry, and g(y) is the level of livestock industry agglomeration; θ and 1 − θ are the importance degree of the carbon emission efficiency of the livestock industry and the livestock industry agglomeration in the development model, respectively. 0 ≤ T ≤ 1, and the bigger the value of the degree of development T, the better the degree of development of both.

This study utilizes the research approach of Chen [60] to set the functional form of the degree of coordination, which is shown in Equation (5):

$$C={\left[{\displaystyle \frac{4f\left(x\right)g\left(y\right)}{{\left(f\left(x\right)+g\left(y\right)\right)}^2}}\right]}^2$$

(5)

Equation (5) indicates the coordination degree of both the carbon emission efficiency of the animal husbandry and animal husbandry industry agglomeration; f(x) and g(y) have the same meaning as in Equation (4). 0 ≤ C ≤ 1, the larger the value of the coordination degree C, the better the coordination between the two, and when C assumes a value of 0, it signifies the absence of a coordination relationship between the two; on the contrary, if C = 1, it indicates that the two have the optimal coordination status.

From the above analysis on the development degree and coordination degree, it is observable that the coordination degree function C is capable of measuring the divergence of carbon emission efficiency and industrial structure upgrading. However, it fails to mirror the development level of the two. Conversely, the development degree function T can assess the development level, but it is unable to exhibit the coordination status of the two. Thus, it is requisite to examine both the development level and the coordination level when measuring the coupling degree. We drew on the study of Weng [61]. Therefore, the coupling degree in this study is as depicted in Equation (6):

$$CD=\sqrt{C\times T}$$

(6)

The were different couplings for different coupling levels, as depicted in

Table 2. Coupling measures and levels.

Coupling	0 < D ≤ 0.5	0.5 < D ≤ 0.6	0.6 < D ≤ 0.8	0.8 < D ≤ 1
Coupling degree	On the verge of becoming dysfunctional	Elementary coordination	Intermediate coordination	Advanced coordination
Grade code	I	II	III	IV

.

4.3.2. Measurement Model of Livestock Industry Agglomeration Level

In light of the accessibility of data, this study draws on the research method of Wang [62], which utilizes the production value to gauge the location entropy, thereby facilitating the assessment of the significance of animal husbandry within the overall economic framework of a region. Then, the location entropy is employed to appraise the level of industrial clustering, and a greater value of location entropy implies a more elevated level of industrial agglomeration. The specific formula is shown in Equation (7):

$$M_{it}={\displaystyle \frac{e_{it}/e_{jt}}{E_{it}/E_{jt}}}$$

(7)

In Equation (7), M_it is the degree of agglomeration of the animal husbandry industry in the i province in the t year; e_it is the output value of the animal husbandry industry in the i province in the t year; e_jt is the output value of the animal husbandry industry in the whole country in the t year; E_it is the GDP of the i province in the t year; and E_jt is the GDP of the j province in the t year.

4.3.3. EBM Model for Non-Desired Outputs

The SBM model represents a frequently employed approach for computing multi-factor efficiency. It possesses the characteristics of multiple inputs and multiple outputs. Moreover, it does not necessitate the setting of a functional form and is extensively utilized for the calculation of efficiency. The EBM model proposed by Tone [63] in 2010 can solve radial and non-radial problems while including non-desired outputs. Therefore, this study constructs the EBM model containing non-expected outputs to gauge the optimal value of carbon emissions from animal husbandry, and the formula of the specific model is shown in Equation (8):

$$\begin{array}{c}\begin{array}{ll}\rho *=& min{\displaystyle \frac{\theta -{\epsilon }_x\sum _{t=1}^T\sum _{i=1}^I\frac{{\omega }_i^{-}{s}_i^{-}}{x_{ki}}}{\delta +{\epsilon }_y\sum _{t=1}^T\sum _{n=1}^N\frac{{\omega }_n^{+}{s}_n^{+}}{y_{kn}}+{\epsilon }_b\sum _{t=1}^T\sum _{z=1}^Z\frac{{\omega }_z^{b-}{s}_z^{b-}}{b_{kz}}}}\\ & s.t.{\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{j=1}^K}{\lambda }_j^t{x}_{ji}^t+s_i^{-}=\theta x_{ki}, i=1,2,\dots ,I\\ & {\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{j=1}^K}{\lambda }_j^t{y}_{jn}^t-s_i^{+}=\delta y_{kn}, n=1,2,\dots ,N\\ & {\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{j=1}^K}{\lambda }_j^t{b}_{jz}^t+s_i^{b-}=\delta y_{kz},z=1,2,\dots ,N\end{array}\\ {\lambda }_k^t\ge 0,s_i^{-}\ge 0,s_n^{+}\ge 0,s_z^{b-}\ge 0\end{array}$$

(8)

In Equation (8), ρ* represents the optimal efficiency value measured by the EBM model, satisfying 0 ≤ ρ* ≤ 1; x_ki, y_kn, and b_kz represents the values of the input, expected output, and non-expected output factors; ${\omega }_i^{-},{\omega }_n^{+},{\omega }_z^{b-}$ denote the weight vector; $s_i^{-},s_n^{+},s_z^{b-}$, respectively, denote the surplus variables corresponding to the ith input (i.e., the input redundancy variable), the nth input–output (i.e., the desired output insufficiency variable), and the zth non-desired output (i.e., the undesired output redundancy variable); t denotes the year; θ and ϵ denote the radial and non-radial parameters, respectively, and 0 ≤ ϵ ≤ 1.

4.3.4. Spatial Autocorrelation Model

Global Autocorrelation Model

The global Moran index was utilized to depict the average level of correlation among all the spatial units with their surrounding area across the entire region, as well as to ascertain the distribution and spatial relevance of the area variables. Drawing on the study of Liu [64], this study utilizes the global Moran index to execute an analysis regarding the overall distribution of the coupling between the carbon emission efficiency of the livestock industry and livestock industry agglomeration in order to determine the degree of association and saliency of all the spatial objects. The computational formula is shown in Equation (9):

$$I={\displaystyle \frac{\sum _{i=1}^n\sum _{j=1}^n{w}_{ij}(Y_i-\overline{y})(Y_j-\overline{y})}{S^2\sum _{i=1}^n\sum _{j=1}^n{w}_{ij}}}$$

(9)

In Equation (9), I is the global Moran’s index, and Y_i and Y_j represent the coupling degree of the carbon emission efficiency and industrial agglomeration of the animal husbandry in each province, respectively. $\overline{y}$ is the mean value, S² is the variance, n represents the quantity of regions, and W_ij denotes the spatial weight matrix. This study uses the spatial geographic weight matrix.

Local Autocorrelation Model

Given that the global Moran index cannot describe the specific regions where the phenomenon of aggregation and disaggregation occurs, this study draws inspiration from the research of Xu [65] and introduces the local Moran index to dissect the local spatial correlation of the coupling of carbon emission efficiency of the livestock industry and the agglomeration of the livestock industry. As shown in Equation (10):

$$I_i={\displaystyle \frac{\left(Y_i-\overline{y}\right)}{S^2}}{\sum }_{j=1}^n{W}_{ij}\left(Y_j-\overline{y}\right)$$

(10)

In Equation (10), I_i is the local Moran index, and Y_i, Y_j, n, W_ij, and S² are the same as the global Moran index.

4.3.5. Markov Chain

Traditional Markov Chain

A Markov chain constitutes a stochastic process within which both time and space are discretized. Continuous numbers are discretized into k types, and the distribution of each type along with its alterations are computed. The transfer between the attribute types at different times can be expressed by a k × k probability transition matrix. Therefore, a Markov probability transfer matrix can be constructed to describe the dynamic evolutionary traits of the coupling degree. Drawing on the research of Zhang [66], the specific formula is shown in Equation (11):

$$m_{ij}={\displaystyle \frac{n_{ij}}{n_i}}$$

(11)

In Equation (11), m_ij is the probability that a region categorized as type i at moment t is transposed to type j at moment t + 1; n_ij represents the aggregate of the number belonging to the regions of type i at moment t transitioned to type j at moment t + 1; and n_i is the sum of the number of regions of type i at all the moments of moment t in the course of the investigation period.

Spatial Markov Chain

Considering that there may be a spatial–geographical correlation between the carbon emission efficiency of animal husbandry and the degree of industrial agglomeration of animal husbandry in China’s provincial regions, we draw on the research of Zhou [67] and introduce a spatial Markov chain for discussion. As opposed to the traditional Markov chain, the spatial Markov chain introduces the concept of “spatial lag”, which can explore the interactions between regions under different geographical conditions, such as the likelihood of an upward or downward shift, so as to better characterize the spatial correlation and dependence of the indicator with neighboring regions during the dynamic evolutionary process. Specifically, the traditional Markov chain decomposition of the coupling degree can be decomposed into kk × k Markov probability transition matrices. In the kth matrix, m_ij(k) represents the probability that an area α of type i at time t and spatial lag of k will transition to type j at time t + 1. The spatial lag term of area α is the spatially weighted average of the property values of the neighboring areas of area α. The specific calculation formula is shown in Equation (12):

$${Lag}_{\alpha }=\sum _{\theta =1}^n{L}_{\theta }{W}_{\alpha \theta }$$

(12)

In Equation (12), Lag_α is the spatial lag value of region α, which indicates the field state of region α; θ is the field; L_θ is the original attribute value of field region θ; n is the aggregate number of regions; furthermore, W_αθ is the spatial weight matrix of the spatial connection between region α and region θ. This study will employ the spatial geographic weight matrix to substitute into the Equation.

5. Results and Analysis

5.1. Analysis of the Current Situation of Carbon Emission Efficiency in the Livestock Industry

Based on Equation (8), MATLAB software was utilized to evaluate the carbon emission efficiency of animal husbandry in 30 provinces in China from 2000 to 2020, and in accordance with the method of dividing China’s four major economic regions, the 30 provinces in the country were grouped into four regions, namely, eastern, central, western and northeastern regions, and the results of the carbon emission efficiencies in part of the year as well as the average of the carbon emission efficiencies in 21 years are presented in

Table 3. Carbon emission efficiency of animal husbandry in 30 provinces of China, 2000–2020.

Region	Province	2000	2005	2010	2015	2020	Average	Ranking
	Beijing	1.000	0.902	0.475	0.544	1.000	0.719	8
	Tianjin	0.893	0.818	0.450	0.454	0.854	0.605	22
	Hebei	0.743	0.633	0.489	0.473	0.636	0.554	28
	Shanghai	1.000	0.935	0.899	0.811	0.927	0.921	1
	Jiangsu	0.705	0.782	0.825	0.836	0.897	0.811	4
	Zhejiang	0.768	0.698	0.716	0.524	1.000	0.692	12
	Fujian	1.000	0.916	0.765	0.819	1.000	0.892	2
	Shandong	0.704	0.662	0.551	0.460	0.563	0.569	25
	Guangdong	0.872	0.907	0.804	0.661	1.000	0.831	3
	Guangdong	0.681	0.719	0.811	0.891	1.000	0.810	5
East		0.837	0.797	0.679	0.647	0.888	0.740
	Shanxi	0.755	0.669	0.488	0.401	0.689	0.561	26
	Anhui	0.822	0.759	0.633	0.501	0.693	0.646	18
	Jiangxi	0.948	0.794	0.569	0.558	0.894	0.695	10
	Henan	0.858	0.784	0.562	0.536	1.000	0.664	17
	Hubei	0.927	0.872	0.674	0.628	0.807	0.738	7
	Hunan	1.000	0.759	0.638	0.487	0.857	0.672	16
Central		0.885	0.773	0.594	0.518	0.823	0.663
	Guangxi	0.938	0.825	0.632	0.513	0.718	0.691	13
	Inner Mongolia	0.851	0.591	0.518	0.483	0.567	0.554	27
	Chongqing	0.819	0.787	0.510	0.521	0.827	0.634	20
	Sichuan	1.000	0.849	0.592	0.496	0.803	0.709	9
	Guizhou	0.885	0.835	0.684	0.705	0.794	0.752	6
	Yunnan	0.894	0.765	0.547	0.551	1.000	0.693	11
	Shaanxi	0.694	0.626	0.555	0.522	0.726	0.600	24
	Gansu	0.796	0.678	0.685	0.630	0.827	0.689	14
	Qinghai	0.855	0.632	0.681	0.652	0.786	0.682	15
	Ningxia	0.575	0.400	0.433	0.419	0.538	0.444	30
	Xinjiang	0.690	0.563	0.620	0.654	0.660	0.619	21
West		0.820	0.683	0.572	0.527	0.699	0.626
	Liaoning	0.820	0.761	0.557	0.573	0.617	0.644	19
	Jilin	0.957	0.709	0.500	0.498	0.661	0.601	23
	Heilongjiang	0.566	0.542	0.414	0.512	0.720	0.520	29
Northeast		0.782	0.671	0.490	0.528	0.666	0.589
National		0.835	0.739	0.602	0.544	0.745	0.657

.

Throughout the research period, the mean value of carbon emission efficiency within the livestock sector of 30 provinces in China stood at 0.657, which implies that there is still a substantial scope for enhancing the carbon emission efficiency of China’s livestock industry. Sub-regionally, the average value of the carbon emission efficiency of China’s animal husbandry industry from 2000 to 2020 shows the distribution trend of east > west > center > northeast, among which the average value of carbon emission efficiency in the east is 0.740, significantly superior to the national level, and the mean value of carbon emission efficiency in the northeast is 0.589, significantly inferior to the national level. This might be attributed to the circumstance that the eastern region is economically prosperous, has a higher level of livestock farming scale and management, and is more concerned about the environmental pollution of the livestock industry, while the northeastern region is not sufficiently concerned about the environmental pollution of the livestock industry, which leads to a large difference in the regional average carbon emission efficiency value.

Specifically, from a provincial perspective, substantial disparities exist in the carbon emission efficiency of the livestock industry among different provinces within the same region during the research period. For example, in the eastern region, there are provinces such as Shanghai and Fujian, which are at the leading level in the country, and there are also provinces such as Hebei and Shandong which are lower than the national average level. There also exist significant discrepancies in the carbon emission efficiency of the livestock sector across various cities within diverse regions. Moreover, the average value of carbon emission efficiency in the livestock industry of Shanghai, Fujian, and Guangdong provinces is considerably higher than the national average during the study period. Within the span of the research period, the average values of the carbon emission efficiency of animal husbandry in Shanghai, Fujian, Guangdong, and other provinces were 0.921, 0.892, 0.831, respectively, which were at the top level of the country, while the mean values of the carbon emission efficiency of animal husbandry in Hebei, Heilongjiang, Ningxia and other provinces were 0.554, 0.520, 0.444, respectively, which were at the bottom level of the country; from this, it can be discerned that there exists a substantial disparity in the carbon emission efficiency among the provinces within the same region, as well as across different regions of the country.

5.2. Spatio-Temporal Characterization of the Coupling Degree of Livestock Husbandry Industry Agglomeration and Livestock Husbandry Carbon Emission Efficiency

According to Equations (4)–(6), the coupling degree of animal husbandry industry agglomeration and animal husbandry carbon emission efficiency in 30 provinces in China from 2000 to 2020 was calculated, and its rank and type were clarified. In this study, we consider livestock industry clustering and livestock industry carbon emission efficiency to be equally important, so we set θ = 0.5 and λ = 1 in Equation (4). The specific results are shown in

Table 4. Coupling of carbon emission efficiency of animal husbandry and industrial agglomeration of animal husbandry in 30 provinces of China, 2000–2020.

Province	2000	2005	2010	2015	2020	Average	Ranking
Beijing	0.273	0.188	0.205	0.098	0.012	0.141	29
Tianjin	0.212	0.302	0.199	0.161	0.151	0.201	28
Hebei	0.877	0.805	0.742	0.713	0.718	0.757	13
Shanxi	0.543	0.419	0.538	0.523	0.502	0.479	23
Inner Mongolia	0.953	0.793	0.759	0.721	0.779	0.771	11
Liaoning	0.634	0.728	0.779	0.718	0.716	0.727	16
Jilin	0.989	0.860	0.749	0.751	0.859	0.797	7
Heilongjiang	0.560	0.718	0.670	0.758	0.897	0.721	17
Shanghai	0.012	0.013	0.013	0.014	0.015	0.013	30
Jiangsu	0.503	0.367	0.409	0.306	0.184	0.353	25
Zhejiang	0.191	0.238	0.310	0.199	0.093	0.219	27
Anhui	0.886	0.817	0.815	0.709	0.632	0.773	10
Fujian	0.489	0.443	0.479	0.376	0.352	0.437	24
Jiangxi	0.894	0.776	0.769	0.651	0.565	0.730	14
Shandong	0.679	0.629	0.696	0.621	0.528	0.640	21
Henan	0.919	0.861	0.793	0.747	0.622	0.790	9
Hubei	0.732	0.748	0.785	0.707	0.569	0.728	15
Hunan	0.943	0.875	0.816	0.698	0.730	0.800	6
Guangdong	0.347	0.297	0.381	0.287	0.219	0.302	26
Guangxi	0.960	0.886	0.843	0.740	0.726	0.829	2
Hainan	0.803	0.819	0.890	0.803	0.718	0.815	3
Chongqing	0.792	0.737	0.664	0.582	0.485	0.648	20
Sichuan	0.975	0.953	0.820	0.748	0.779	0.857	1
Guizhou	0.888	0.809	0.821	0.782	0.682	0.796	8
Yunnan	0.858	0.802	0.786	0.772	0.877	0.808	5
Shaanxi	0.636	0.588	0.682	0.603	0.494	0.602	22
Gansu	0.695	0.664	0.701	0.638	0.664	0.661	19
Qinghai	0.895	0.771	0.845	0.781	0.862	0.815	4
Ningxia	0.770	0.648	0.674	0.624	0.699	0.665	18
Xinjiang	0.755	0.677	0.807	0.797	0.767	0.761	12
National	0.689	0.641	0.648	0.588	0.563

.

As is observable from Figure 2, the coupling degree of the 30 provinces in China during the study period was low overall. Most of the provinces are in the coupling degree level between endangered dysfunction and intermediate coordination, and the number of provinces with advanced coordination is small. In terms of the mean value of the provinces, the coupling degree of the 30 provinces ranged from 0.01 to 0.85, with a large gap between the provinces. The average value of Sichuan’s coupling degree was the first one, 0.857, indicating that its livestock industry agglomeration and livestock industry carbon emission efficiency were better coupled, and the two were more synchronized to achieve high-quality development; Guangxi, Hainan, Qinghai, and Yunnan were ranked from 2 to 5 in that order; corresponding to this, Shanghai’s coupling degree had the lowest mean value of 0.013; Beijing, Tianjin, Zhejiang, and Guangdong were ranked in the penultimate 2 to 5 in that order.

We selected five years during the study period, 2000, 2005, 2010, 2015, and 2020, to analyze the trends in the coupling of animal husbandry carbon emission efficiency and animal husbandry industry agglomeration in China as a whole and in the four regions.

As can be seen in Figure 3, from a national perspective, the coupling degree of livestock industry agglomeration and carbon emission efficiency showed a small decline from 2000 to 2005, from 0.689 in 2000 to 0.641 in 2005, with a decline of 6.97%; from 2005 to 2010, the coupling degree rebounded slightly, from 0.641 to 0.648, with an increase of 1.09%. From 2010 to 2020, there was a large decline, from 0.648 in 2010 to 0.563 in 2020, and in 2020, the national coupling decreased by 13.12% and 18.29% compared to 2010 and 2000, respectively. Sub-regionally, in 2000, the coupling degree in the western region attained the highest level, trailed by the central and northeastern regions, whereas the coupling degree in the eastern region was at the lowest ebb, indicating that the interaction and coordination between the industrial agglomeration of animal husbandry and the carbon emission efficiency were better in the early stage of the study in the western region of China; from 2005 to 2015, the trend of the coupling degree changed in the east, but the central region and the western region were the same, which exhibited a tendency of decline, and subsequent augmentation, followed by a further decline, with an overall downward trajectory. Compared to 2005, in 2015, the coupling degree of the three regions decreased by 12.75%, 10.24%, and 6.47%, respectively, and the coupling degree change trend of the Northeast demonstrated a propensity of initial increment, subsequent decrement, and subsequent re-increment, but the general trend was a small decline, with a decline of 3.4%; from 2015 to 2020, the coupling degree of the east and the central part of the country decreased again, respectively, by 16.43% and 10.3%, while the coupling in the northeast showed an upward trend, with an increase of 10.94%, and the coupling in the west showed a slight upward trend, with an increase of 0.28%. Compared to 2000, in 2020, the coupling degree in the east, center, and west decreased by 31.89%, 26.46%, and 14.87%, respectively, and the coupling degree in the northeast increased by 13.19%. It can be discerned that throughout the research period, the coupling degree of industrial agglomeration and the carbon emission efficiency of the animal husbandry in the east, central, and west showed an overall decreasing trend, the coupling degree in the northeast demonstrated an overall ascending tendency, and the coupling degree of the industrial agglomeration and carbon emission efficiency of China’s animal husbandry sector as a whole demonstrated a declining tendency.

In this study, the 21-year study period was divided into two phases, and the average values of the coupling degree of 30 provinces in 2000–2010 and 2011–2020 were calculated, respectively, as exhibited in Figure 4. From the viewpoint of spatial distribution, the coupling degree between the animal husbandry industry agglomeration and the carbon emission efficiency of the animal husbandry in 30 provinces in China had a spatial distribution pattern of “West > Central > Northeast > East”. Specifically, from 2000 to 2010, the coupling degree of the 30 provinces was in the range of imminent dissonance, intermediate coordination, and advanced coordination. Among them, eight provinces were on the verge of becoming dysfunctional, with the exception of Shanxi, which is located in the central part of the country, and all of them are located in the eastern part of the country; twelve provinces had an intermediate level of harmonization, with two in each of the eastern, central, and northeastern regions, and the remaining six are located in the western part of the country; and ten provinces had advanced levels of harmonization, with one in each of the northeastern and eastern regions, three in the central part of the country, and five in the western part of the country. Between 2011 and 2020, the coupling of the 30 provinces with coupling degrees at all the four coupling degree levels were distributed. Compared to the previous period, the number of provinces on the verge of dislocation declined to seven, all in the eastern region; the quantity of provinces with primary coordination was three, with one in the central region and two in the western region; the number of provinces with intermediate coordination rose to 17, with no change in the eastern region, five in the central region, seven in the western region, and three in the northeastern region; and the number of provinces with advanced coordination declined to three, with no change in the eastern region, and a decline in the western region by 2.

Taken together, the coupling degree of the western region is the highest, the coupling degree of the central region and the northeastern region is lower than that of the western region, and the coupling degree of the eastern region is the lowest. At present, the coupling degree of most provinces is not optimistic, except for Zhejiang, Fujian, Guangdong, and other provinces that have long been on the verge of dislocation of the grade; the coupling degree of the big provinces of animal husbandry, such as Sichuan, Henan, Anhui, and other provinces, is difficult to stabilize in a state of advanced coordination. This is because there is vast land and there are abundant grassland resources in western China for livestock breeding, which is conducive to the agglomeration of the livestock industry and large-scale breeding and production. Conversely, the grassland resources in the central, northeastern, and eastern regions are relatively scarce, making it difficult to support the large-scale agglomeration of the livestock industry. Moreover, the national and local governments have introduced a series of support policies for the western region, such as breeding subsidies, fine breed subsidies, and other support measures. These policies have attracted a substantial number of farmers and enterprises to congregate in the western region. Against the backdrop of emphasizing sustainable development, the western region encourages farmers to adopt ecological breeding models, strengthening the harmless treatment and resource utilization of livestock and poultry manure, and propelling the development of the livestock industry towards a green and low-carbon orientation. The implementation of these policies has a positive impact on the coupling between the clustering of the livestock industry and carbon emission efficiency in the western region. However, due to the relatively high level of economic development and the more complex industrial structure in the central, northeastern, and eastern regions, the focus of policies may be more on industries such as industry and service sectors, and the coupling degree between the agglomeration of the livestock industry and carbon emission efficiency is correspondingly inferior to that in the western region.

5.3. The Characterization of the Spatial Correlation of the Coupling Degree of Animal Husbandry Industry Agglomeration and Animal Husbandry Carbon Emission Efficiency

5.3.1. Global Spatial Autocorrelation Analysis

The global Moran index of the coupling degree of animal husbandry industry agglomeration and animal husbandry carbon emission efficiency in each province of China from 2000 to 2020 was computed via Stata 17 software, and the relevant outcomes are presented in

Table 5. Global Moran’s index of the coupling of the carbon emission efficiency of animal husbandry and animal husbandry industry agglomeration in China, 2000–2020.

Year	Moran’s I	Z-Value	p-Value	Year	Moran’s I	Z-Value	p-Value
2000	0.074	3.009	0.003	2011	0.100	3.796	0.000
2001	0.078	3.149	0.002	2012	0.102	3.850	0.000
2002	0.081	3.234	0.001	2013	0.103	3.859	0.000
2003	0.075	3.062	0.002	2014	0.104	3.878	0.000
2004	0.074	3.021	0.003	2015	0.106	3.924	0.000
2005	0.080	3.200	0.001	2016	0.107	3.948	0.000
2006	0.087	3.409	0.001	2017	0.111	4.043	0.000
2007	0.078	3.118	0.002	2018	0.115	4.176	0.000
2008	0.087	3.380	0.001	2019	0.114	4.111	0.000
2009	0.099	3.766	0.000	2020	0.121	4.283	0.000
2010	0.098	3.748	0.000

. From the examination period, it is easy to find that the global Moran index value of the coupling degree of animal husbandry industry agglomeration and animal husbandry carbon emission efficiency is in an upward trend, although there are some fluctuations, and all the years have successfully met the significance test at the 1% level. It is observable that the spatial allotment of the coupling degree between the industrial agglomeration of animal husbandry and the carbon emission efficiency of animal husbandry in China is characterized by obvious agglomeration distribution, i.e., the provinces boasting high values are abutting against other high-value provinces, and the provinces with low values are abutting against those of the low-value type as well.

5.3.2. Local Spatial Autocorrelation Analysis

The mean values of the coupling between 2000 and 2010, and 2011 and 2020 for the 30 provinces were used to examine the agglomeration of each province, and the Moran scatter plot of the province-specific distribution of each type of agglomeration is presented in Figure 5.

As is discernible from Figure 5, the number of provinces located in the high–high agglomeration area and low–low agglomeration area during the study period was high, and the spatial correlation is obvious. Compared to 2000–2010, the quantity of provinces encompassed within the high–high agglomeration area remained unchanged in 2011–2020, with only Jiangxi and Chongqing changing while the rest of the provinces remained unchanged. From the perspective of regional distribution, the provinces in the high–high agglomeration area are mainly concentrated in the west and northeast, which belong to the advantageous production areas of animal husbandry, and the linkage between the provinces has gradually formed a neighborly and mutually reinforcing relationship. The quantity of provinces in the low–high agglomeration area remained unchanged, with Shaanxi being replaced by Chongqing in 2011–2020, while the rest of the provinces remained unchanged, probably due to the high coupling degree of the neighboring provinces and, thus, the siphoning effect, which led to the outflow of population and resources from the provinces in the region, and in the long run, the gap with the neighboring provinces gradually widened. No changes occurred in the provinces in the low–low clustering area, and the coupling degree of these provinces has remained at a relatively low level over an extended period, which may be associated with the inferior positioning of the livestock industry’s development within the provincial development plan, thus leading to the overall strength of the livestock industry being weak. The quantity of provinces in the high–low clustering area remained unchanged, with Jilin being replaced by Jiangxi in 2011–2020 and the remaining provinces remaining unchanged. The provinces in this region have better livestock industry agglomeration and livestock carbon emission efficiency, but they do not drive the coupling of neighboring provinces to increase, probably because they have not been able to form a mechanism to drive the coupling of neighboring provinces to increase, and the trickle-down effect on the coupling of neighboring provinces is very small, which leads to a widening of the gap.

5.4. Trend Analysis of Transfer of Coupling Degree of Livestock Industry Agglomeration and Livestock Carbon Emission Efficiency

5.4.1. Traditional Markov Chain Analysis

After clarifying the spatio-temporal evolutionary traits of the coupling degree of animal husbandry industry agglomeration and animal husbandry carbon emission efficiency in each province of China, the next step involved the analysis of the dynamic change law of the coupling degree of animal husbandry industry agglomeration and animal husbandry carbon emission efficiency in the years of 2000–2020, based on the hierarchical division of the coupling degree in the previous section, and the introduction of the traditional Markov chain with a lag of one period. Among them, the values on the diagonal of the matrix represented the probability that the coupling degree would not shift after t + 1 years; the values on the non-diagonal of the mean denoted the likelihood that the coupling degree would shift. The results of the likelihood transfer matrix pertaining to the traditional Markov chain are presented in

Table 6. Traditional Markov chain probability transfer matrix for coupling of 30 provinces in China, 2000–2020.

Observations	Degree	I	II	III	IV
148	I	0.973	0.027	0.000	0.000
39	II	0.179	0.641	0.179	0.000
285	III	0.000	0.039	0.884	0.077
128	IV	0.000	0.000	0.242	0.758

.

Combined with Table 6, it can be seen that (1) from the observed values, the number of provinces at the endangered dysfunction, primary coordination, intermediate coordination, and advanced coordination levels in 2000–2020 were 148, 39, 285, and 128, respectively, indicating that the number of provinces at the intermediate and lower levels of the coupling degree grades was still relatively high, and that there is a large room for improvement in general. (2) The values on the diagonal were all much larger than those off the diagonal, with the smallest value on the diagonal being 0.641 for primary coordination, indicating that the probability that the coupling degree grade would not change was at least 64.1%, and that the phenomenon of grade solidification was gradually taking shape. (3) The probability of reverse transfer for the provinces that were initially in senior coordination was 24.2%, which was higher than the probability of reverse transfer for the other ranks, indicating that there was a more likely risk of falling for such ranks, while junior coordination possessed a higher probability of rank jumping compared to intermediate coordination and near-dislocation. (4) The non-diagonal non-zero data were all immediately adjacent to the diagonal, which suggests that all the changes in coupling were limited to between the neighboring grades, which leads to the conclusion that the development of coupling grades is a gradual process, and it is difficult for leapfrogging to occur.

5.4.2. Spatial Markov Chain Analysis

The traditional Markov chain was built on the basis that variables are independent of each other and do not affect each other, but that there is geospatial correlation among provinces, and the development of the coupling degree not only depends on its own production factors, but also has a close connection with neighboring provinces. Therefore, this study takes the spatial lag value of the initial year 2000 as the basis for classification, and introduces a spatial Markov chain to analyze the dynamic progression of the coupling degree of animal husbandry industry clustering and animal husbandry carbon emission efficiency from 2000 to 2020, and the results of the spatial Markov chain likelihood transfer matrix are shown in

Table 7. Spatial Markov chain probability transfer matrix of coupling for 30 provinces in China, 2000–2020.

Type of Spatial Lag	Observed Value	Degree	I	II	III	IV
I	21	I	1.000	0.000	0.000	0.000
	1	II	0.000	1.000	0.000	0.000
	9	III	0.000	0.000	1.000	0.000
	0	IV	NaN	NaN	NaN	NaN
II	81	I	0.975	0.025	0.000	0.000
	13	II	0.231	0.615	0.154	0.000
	115	III	0.000	0.052	0.896	0.052
	22	IV	0.000	0.000	0.273	0.727
III	46	I	0.957	0.043	0.000	0.000
	25	II	0.160	0.640	0.200	0.000
	161	III	0.000	0.031	0.870	0.099
	106	IV	0.000	0.000	0.236	0.764
IV	0	I	NaN	NaN	NaN	NaN
	0	II	NaN	NaN	NaN	NaN
	0	III	NaN	NaN	NaN	NaN
	0	IV	NaN	NaN	NaN	NaN

Note: When MATLAB calculates the transfer probability, if there are no members in a particular club, there will be a denominator of zero in the calculation of the probability, in which case the MATLAB result will be output as NaN.

.

Through a comparison of the results presented in Table 6 and Table 7, it becomes evident that (1) the probability transfer matrices under different spatial lag classifications exhibit discrepancies and deviate from the traditional Markov probability transfer matrices, which implies that spatial geography constitutes a significant factor that exerts an impact on the dynamic evolutionary principles of coupling. (2) After taking spatial geography into consideration, the values located on the diagonal of the spatial Markov probability transfer matrix were also steadily larger than those on the off-diagonal, and the phenomenon of transfer inertia was still more severe. (3) The coupling degree of each province in China showed a “spatial spillover” effect, in which the coupling degree of each province interacted with the coupling degree of the neighboring provinces. If a province is adjacent to a province with a higher coupling grade, the likelihood of its own coupling grade will increase, and in the event that it is adjacent to a province possessing a lower coupling grade, the likelihood of its own coupling grade will be lowered. For example, the probability of a province at the endangered dislocation rank crossing upward increases from 0 to 2.50% and 4.30% when it is contiguous to a region of an equivalent rank, primary coordination, or intermediate coordination rank; the probability of a province at the primary coordination rank shifting upward increases from 15.4% to 20.0% when it is adjacent to a region of the same type and intermediate coordination rank; in contrast to this, the probability that a province at the intermediate level of coordination will shift downward increases from 3.10% to 5.20% when it is adjacent to a region of the same type and lower level of coordination. It is observable that the coupling degree of China’s animal husbandry industry agglomeration and animal husbandry carbon emission efficiency shows a certain degree of “the strong are getting stronger and stronger, the weak are getting weaker and weaker” Matthew Effect. However, we can also utilize the “spatial spillover” effect of the coupling degree of each province to help the provinces with lower coupling degree to realize their grade crossing.

6. Conclusions and Suggestions

6.1. Conclusions

Based on the data of 30 provinces in China from 2000 to 2020, this study measured the carbon emission efficiency of the livestock industry using the EBM model of non-expected output, measured the level of coupling between the industrial agglomeration of the livestock industry and the carbon emission efficiency of the livestock industry using the coupling degree model, the spatial autocorrelation model, and the Markov chain model, and analyzed the characteristics of its spatial–temporal distribution and the law of evolution. The main research findings are as follows: first, the carbon emission efficiency of China’s animal husbandry industry as a whole shows a distribution pattern of east > west > center > northeast, with large regional differences, and there exists substantial disparities in the carbon emission efficiency both within the same region and among the provinces in different regions across the country. Second, from a temporal perspective, although the coupling degree between the industrial agglomeration of China’s animal husbandry and the carbon emission efficiency of animal husbandry fluctuates over time, it generally shows a downward trend. Third, spatially, the coupling degree between the industrial agglomeration of animal husbandry and the carbon emission efficiency of animal husbandry in 30 provinces in China follows a spatial distribution pattern of “west > center > northeast > east”. Fourth, the spatial coupling degree shows the obvious characteristics of agglomeration distribution, the number of provinces located in the high–high agglomeration area and low–low agglomeration area is larger, and the spatial correlation characteristics are obvious. Fifth, the coupling degree rank of animal husbandry industry agglomeration and animal husbandry carbon emission efficiency in Chinese provinces is relatively stable in a short period of time, but after considering the spatial geographic correlation, the coupling degree of each province will be affected by the coupling degree of the neighboring provinces. Provinces with higher coupling grades will exert favorable spillover impacts on adjacent provinces, and vice versa will have negative spillover effects. This causes the stable coupling-degree grade of each province to be shaken, showing a certain degree of the Matthew Effect to some extent.

6.2. Suggestions

In light of the research findings, this paper makes the following policy suggestions:

Firstly, establish and consummate the policy regime for the industrial agglomeration and the abatement and efficiency augmentation of livestock husbandry, impelling the concerted development of industrial agglomeration and carbon-emission curtailment within the livestock husbandry ambit. On the one hand, each province should fully exploit its think tanks and expert echelons to conduct scientific disposition and programming for the tasks associated with industrial agglomeration, emission reduction, and efficiency elevation in the livestock husbandry. Moreover, correlative ancillary policies should be refined to probe into the optimal equipoise between industrial agglomeration and low-carbon evolution. On the other hand, the government should steer the orderly dilation of the scale of industrial agglomeration in the livestock husbandry through environmental regulation, governmental subsidies, and other measures. The low-carbon development objectives should be integrated into the industrial agglomeration blueprint to attenuate its negative influence on the low-carbon production modality of the livestock husbandry. Concurrently, the investment in the public infrastructure of livestock husbandry should be ramped up to ensure the full manifestation of the positive effect of industrial agglomeration on carbon emission mitigation in the livestock husbandry;

Secondly, drive the upgrade of livestock husbandry production technologies by taking advantage of industrial agglomeration. To make the most of the benefits of industrial agglomeration, it is essential to facilitate the transformation and upgrading of livestock husbandry industrial agglomeration, overcome the “congestion effect” and “lock-in effect” resulting from low-level industrial agglomeration, and achieve the transition from “quantity-based growth” to “quality-driven improvement” in livestock husbandry industrial agglomeration, thus creating a favorable environment for scientific research and development. On this basis, accelerate the digital production technologies in livestock husbandry, and hasten the research, application, and popularization of technologies such as the digital-based scientific feeding of livestock and poultry, the comprehensive utilization of livestock and poultry breeding manure, and the digital monitoring of livestock and poultry-breeding environments. Fully unleash the promotional effect of industrial agglomeration on improving carbon emission efficiency, and gradually form a rational livestock husbandry development pattern with regional characteristics;

Thirdly, fully utilize the spatial spillover effect and continuously optimize the win—win cooperation mechanism among provincial areas. Research findings reveal that there is a significant spatial dependence in the coupling degree of the industrial agglomeration of animal husbandry and the carbon emission efficiency of animal husbandry among various provinces in China. Consequently, it is imperative for each province to place a significant emphasis on the spatial interaction effects with neighboring provinces. Each province should make the most of its comparative advantages in resource endowment, establish an exchange platform, and enhance the exchange of experiences in the construction of livestock–husbandry industrial agglomeration and in livestock husbandry emission reduction and efficiency improvement among provincial areas. This will promote the balanced development of livestock husbandry industrial agglomeration and low-carbon emission reduction among provincial areas. Provinces with a higher coupling degree should actively create favorable conditions, such as setting up sample demonstration zones, to spread their experiences. Provinces with a lower coupling degree should also actively learn from the advanced ideas of those with a higher coupling degree and gradually improve their own coordinated-development mechanism for livestock husbandry industrial agglomeration and carbon emission reduction.

7. Discussion

Global warming is a major challenge facing mankind today. In order to break through the shackles of environmental resources, promoting low-carbon green development has become the consensus of global economic and social development. As an important participant in global climate governance, China has made a commitment to “peak carbon and carbon neutrality” at the 2020 United Nations General Assembly. As an important part of China’s agriculture, animal husbandry is also an important source of greenhouse gas emissions. Since the feces and gastrointestinal fermentation of livestock and poultry produce large amounts of greenhouse gas emissions, and the livestock industry does not have the carbon sink attributes possessed by the plantation industry and does not have the ability to sequester carbon, this will result in a growth in the pressure to reduce carbon emissions from China’s animal husbandry industry. In this context, the 2022 Implementation Plan for Agricultural and Rural Emission Reduction and Carbon Sequestration points out that to promote the low-carbon and green development of the animal husbandry industry, it is necessary to promote the large-scale breeding of livestock and poultry, and the industrial agglomeration of the livestock industry can play a role in the economies of the scale of the animal husbandry industry production and operation through the reduction in costs, the effect of technological diffusion, and other ways, so as to improve the efficiency of the carbon emissions of the livestock industry, and the improvement of the efficiency of the carbon emissions will further produce a certain feedback effect on industrial agglomeration. Consequently, delving into the functional mechanism between the industrial agglomeration of the livestock sector and carbon emission efficiency holds substantial significance for attaining “dual-carbon” objectives and facilitating the low-carbon transition of the livestock industry.

In contrast to prior studies that analyzed the unidirectional impact of industrial agglomeration on carbon emission efficiency, this study is different in that it constructs a coupled model of the “carbon emission efficiency of animal husbandry-industrial agglomeration of animal husbandry” and analyzes the spatial and temporal distribution and evolution of the coupling between the two. In the industrial planning of animal husbandry and carbon emission management, the coupling model of the two is utilized to analyze the interactions between the scale and intensification of the animal husbandry industry and the ecological environment, as well as how to balance the relationship between them through coordinated development. It is of profound significance to furnish policy guidelines for the government to sustain low-carbon and environmentally amicable production concurrent with the elevation of the livestock industry’s industrial echelon. This is instrumental in spurring the synchronized progression of economic augmentation and low-carbon abatement within the livestock industry.

However, owing to the constraints of data acquisition and research methods, there is still room for expansion as follows. First of all, in this research, the Location Quotient method was adopted to calculate the industrial agglomeration indicators. Although this method has been commonly used in current studies, regional heterogeneity exists. There are some differences among various regions in terms of natural environment, economic development level, and the functional orientation of the livestock industry. In addition, there is also some research in which the Location Quotient is calculated based on the number of employees. Consequently, this method might not be able to fully present the overall situation of the industrial agglomeration of the livestock industry in a region. Secondly, the carbon emissions of the livestock industry in this study were measured by the relatively accurate full life cycle method. Although this method has fully considered gastrointestinal fermentation and manure management systems, the largest source of carbon emissions from livestock [68], the boundaries of the life cycle stages in actual production are difficult to determine [69], and may not adequately take into account the mobility of livestock production between different provinces, resulting in some room for improvement in the accuracy of carbon emission measurement in the livestock sector. Thirdly, the Markov chain adopted in this study presumes, within its model, that the transition probabilities between states are invariable, thus disregarding the influences of external factors such as those that are environmental, economic, and policy-related, and technological progress elements. However, in the practical environment, the impacts of various external factors on state transition probabilities are usually in dynamic variation. Hence, it may be impossible to fully consider the influencing factors of the transition probabilities.

Consequently, future research should concentrate on the improvement and innovation of the industrial agglomeration level of animal husbandry, carbon emission measurement methods, and state-transition probability models. In addition, duly considering the regional heterogeneity of the coupling association between them in a comprehensive manner, and continuously optimizing the influence mechanism of this coupling relationship, thus provides more accurate theoretical and decision-making bases for the realization of low-carbon emission reduction in animal husbandry.