Measurement of Green Total Factor Productivity and Its Spatial Convergence Test on the Pig-Breeding Industry in China

Abstract

The pig-breeding industry is one of the pillar industries of China’s agriculture. Improving the green total factor productivity of pig breeding is the basis for ensuring the stable supply of pork, and is also the key to the green transformation of the pig industry. The existing studies about the green total factor productivity of pig breeding lack an analysis of regional coordination and the spillover of spatial technology efficiency at the macro level, and most studies focus on the impact of agricultural production’s environment pollution and other undesirable outputs. Based on the input–output index system of the pig-breeding industry’s green production, the DDF directional distance function model and the Malmquist–Luenberger (ML) productivity index were combined to measure the green total factor productivity of the pig-breeding industry. Moran’s I-Theil index model was used to measure and reveal the technical efficiency differences among the dominant regions of the pig-breeding industry in China and the σ-convergence test was adopted to reveal the convergence trend of green total factor productivity. The results showed that: (1) The growth level of green total factor productivity of pig breeding in China was generally low from 2006 to 2018, and there were obvious regional and scale differences. (2) The green total factor productivity of pig breeding in each province had spatial autocorrelation; that is, there was technology spillover. From 2006 to 2018, with the advance of time, a pattern of gradual evolution from low-level equilibrium to high-level imbalance was formed. (3) Through the convergence test, the convergence trend of large and medium-scale development between different regions fluctuated, while the convergence trend of small-scale development between different regions was not obvious. Therefore, it is necessary to increase investment in technological innovation, promote the large-scale and standardized development of the pig-breeding industry, and strengthen the promotion of technology in producing areas with advantages in pig breeding.

1. Introduction

In promoting the rapid development of the rural economy, China attaches great importance to the role of agricultural green total factor productivity improvement in achieving rural revitalization and modernized agricultural development [1]. Especially with the continuous expansion in scale of agricultural operations, the problem of rural environmental pollution caused by this cannot be ignored. Agricultural pollution has become the main source of pollution affecting China’s economic and social development, and the main source of agricultural pollution is livestock and poultry farming [2]. The development of livestock and poultry in terms of scale and intensification has not only increased the risk of epidemic disease transmission and the cost and difficulty of waste disposal [2,3], but also of ecological and environmental problems; the pollution of water bodies caused by livestock and poultry manure and urine and wastewater during the breeding process has become increasingly prominent [4]. The pig-breeding industry is a pillar industry of the agricultural economy and has a very important strategic position. China is the world’s top producer of live pigs, and since reform and opening up, the scale of live pig production has been maintained at more than 290 million heads, reaching 412 million heads in 2020, accounting for 30.2% of the total global production of live pigs (FAO, 2021). In terms of pig industry development, large-scale and intensive breeding has become an inevitable trend. At the same time, although large-scale breeding can increase economic benefits by improving efficiency, the large amount of by-products (manure, etc.) produced during the breeding process has brought a heavy burden to the fragile rural ecological environment, which has seriously affected the realization of the civilization development goal of “production development, rich living and good ecology” in rural areas [5,6]. Therefore, the development of China’s pig industry is no longer limited to how to ensure the basic supply and demand balance of pork products under the rigid constraints of resources, but must also fully consider its resource-carrying capacity and the ecological and environmental disasters that may result [7,8]. There is an urgent need for a green transformation in the development approach of China’s traditional pig-breeding industry and for improving green total factor productivity.

2. Literature Review

Improving the green production efficiency of pig breeding is the basis for ensuring a stable supply of pork. Modern economic growth theory and practice show that technological progress and productivity improvements are the driving forces of long-term economic growth [9]. Therefore, the healthy and sustainable development of China’s pig industry, especially the improvement of pork production and supply capacity, is driven by productivity improvements [10]. Currently, China’s pig industry is facing multiple constraints from resources, the environment, epidemics and changes in market conditions [11] that directly affect the efficiency of pig breeding and even the overall efficiency of pork production. Compared to the increase in output due to the expansion of farming scale and the increase in input factors, the intensive output growth due to the improvement of production efficiency is the key element to ensuring a healthy increase in production for the Chinese pig industry and of pork products [12,13]. Sustained growth in pig production efficiency relies on two mechanisms: first, a significant increase in the productivity of pig breeding in different sizes, which will result in higher output levels [14]; and second, a restructuring of pig production that drives the allocation of industry resources from low-productivity to high-productivity regions [15]. Therefore, when evaluating pig production efficiency, it is necessary to introduce variables related to the environmental impact of green efficiency measurement, which have important theoretical and practical significance for guiding the green development of pig production, further optimizing the spatial layout of breeding and achieving quality and efficiency improvements.

The evaluation and estimation of agricultural production efficiency have long been a hot topic of academic research, and assessment methods have been continuously updated and made more comprehensive. While the traditional research paradigm did not consider the by-products of the industry as environmental costs, Chung (1997) first incorporated environmental cost variables into the model analysis framework of production efficiency [16], which provided a new research perspective for the comprehensive assessment of environmental efficiency as well as green total factor productivity. Subsequently, most scholars at home and abroad have considered environmental costs in their studies of agricultural productivity [3,17,18,19], and along with the increasingly prominent problem of environmental pollution in animal husbandry, the inclusion of resource and environmental constraints in the evaluation of total factor productivity has become a new trend [20,21,22,23,24,25,26,27].

Given the strategic position of the pig industry in China’s rural economy, the measurement of the total factor productivity of pig breeding is also a hot issue in current academic circles. In terms of assessment methods, most scholars have adopted parametric methods such as Stochastic Frontier Analysis (SFA) and non-parametric methods such as Data Envelopment Analysis (DEA). Based on these research methods, most of the literature has then measured technical efficiency, technical progress and total factor productivity, as well as the impact of technical efficiency and technical progress on agricultural productivity using the Malmquist index [27,28,29]. Since the Malmquist productivity index of the traditional distance function does not need to consider the price factor, the Malmquist–Luenberger productivity index can be used to further analyze the dynamic trend of productivity and its influencing factors. Tone also proposed and improved the non-radial and non-angular SBM model [20,21], which on the one hand makes up for the traditional. On the other hand, it solves the relaxation problem of input and output variables, and incorporates the non-expected output “environmental factor variables” in the production process into the measurement of efficiency.

In terms of research results, there is a significant technical efficiency loss in Chinese pig production, both for small-scale free-range farmers and large-scale farms (households), and for economically developed eastern regions or relatively backward remote western regions [30,31,32,33,34]. However, all these studies ignore the efficiency losses caused by environmental pollution, and thus the results may be biased estimates that do not correctly measure and assess the actual efficiency level of the economies concerned. Of course, some scholars have included environmental constraints into the empirical analysis model, and Zhang (2015) used the non-radial concept (Nonradial Notion) to measure the environmental efficiency of pig scale farms (households) by using the nitrogen surplus in pig manure as an example [35]. In addition, the literature on estimating the efficiency of large-scale pig farming by adding environmental constraints or environmental regulations has also emerged [36,37,38,39].

A review of the green development process of pig farming in developed countries shows that there is a compensatory relationship between changes in the scale of pig farming and the number of pig farms [40]. The improvements in pig production efficiency in the United States are mainly due to economies of scale and technological progress [41], and in addition, the regional layout of pig breeding in developed countries has undergone a process of convergence from geographical dispersion to concentration in order to improve production efficiency [42]; as a result, a spatial shift in geographical location has been achieved [43]. Danish pig breeding, on the other hand, suffers from limited scale expansion due to the slow transfer of agricultural land [41]. In contrast, the relatively slow increase in pig breeding efficiency in developing countries is due to factors such as feed costs, transportation and environmental management costs, in addition to technological factors [44]. In addition, the development of pig breeding in remote areas of northern Vietnam has been slow due to poor infrastructure and lagging market news [43,44]. Due to feed resource and environmental constraints, pig breeding regions in China have emerged as areas of functional advantage and sparse areas to facilitate geographical convergence due to technological efficiency spillover or technology diffusion [13], or the spatial convergence of industries [45], which in turn generates economies of scale [46]. Large-scale farms in Thailand are generally more environmentally efficient than retail and small-scale farms [47].

In summary, it can be found that the literature has decomposed technical efficiency, technical progress efficiency and scale efficiency from the total factor productivity index, so as to examine the contribution of each decomposed factor productivity to total factor productivity growth. As an important source of total factor productivity growth, the green production efficiency of pig breeding cannot be ignored as a contribution to the healthy and sustainable growth of the whole pig industry. Therefore, the research on the green efficiency of pig breeding needs to be further enriched. The marginal academic contributions of this paper are mainly reflected in: (1) the combination of the DDF directional distance function model and Malmquist–Luenberger (ML) productivity index under the framework of DEA to construct the pig total green factor productivity index, which provides important methodological support for studying pig breeding green productivity in China; (2) the description of the time-series characteristics of green total factor productivity of pig breeding in the time dimension, and analysis of the spatial autocorrelation of the green production efficiency of pig breeding in China by using Moran’s I-Theil Index model to measure the technical efficiency differences among the dominant regions of the pig industry in China, and to provide a realistic basis for collaboratively improving the green production efficiency of pig breeding in each region; and (3) the use of the σ convergence test to reveal the convergence trend of the green production efficiency of pig breeding, and provide a green total factor productivity perspective for the study of convergence in China.

3. Research Methodology and Data Sources

3.1. Measure of Green Total Factor Productivity of Pigs and Decomposition Method

To overcome the shortcomings of the angular and radial DEA models, Chambers and Chung proposed the DDF model [48,49], which is a method for estimating the relative efficiency of decision units along a pre-determined direction vector without radial constraints. It achieves the goals of increasing economic output and reducing pollutant emissions, and increasing green total factor productivity by optimally adjusting different directions of desired and undesired outputs. According to the research content of this paper, the green production efficiency of pig breeding is measured by setting the following model.

It is assumed that each Decision Making Unit (DMU) uses N factor inputs $\mathrm{x}=\left(x_1,\cdots ,x_N\right)\in R_N^{+}$ to produce M desired outputs $y=\left(y_1,\cdots ,y_M\right)\in R_M^{+}$ and I non-desired outputs $u=\left(u_1,\cdots ,u_l\right)\in R_{\mathrm{l}}^{+}$, then the pig environmental technical efficiency model can be defined as Equation (1).

$$P^t\left(x^t\right)=\left|\begin{array}{c}\left(y^t,u^t\right):{\displaystyle \sum _{k-1}^k}{z}_k^t{y}_{km}^t\ge y_m^t,m=1,\cdots ,M;{\displaystyle \sum _{k-1}^k}{z}_k^t{x}_{km}^t\le x_n^t,n=1,\cdots ,N\\ {\displaystyle \sum _{k-1}^k}{z}_k^t{u}_{ki}^t=u_i^t,i=1,\cdots ,I;z_k^t\ge 0,k=1,\cdots ,K\end{array}\right|$$

(1)

where $P^t\left(x^t\right)$ is the set of production possibilities, y is Desirable Output (e.g., pig staple production), and u is Undesirable Output (e.g., pig manure emissions); t = 1, …, T periods, k = 1, …, K DMUs; Zk is the density variable that reflects the weight assigned to each DMU in each cross-section, and a positive value indicates that the technical structure satisfies the Constant Returns to Scale (CRTS) assumption.

According to the research needs of this paper, it adjusts the desired output (pig main product output) and non-desired output (pig manure emissions) in different directions to achieve the dual output optimization of increasing pig main product output and reducing manure emissions, which can be defined as Equation (2).

$$\overrightarrow{D_0^t}\left(x,y,u;g_y,-g_u\right)=sup\left[\beta :\left(y+\beta g_y,u-\beta g_u\right)\in P_{\left(x\right)}\right]$$

(2)

Then, Max β constraint is

$$s.t. {\displaystyle \sum }_{j=1}^n{\lambda }_j{X}_{ij}⩽X_{i0}-\beta {\mathrm{g}}_x, i=1,2,\dots ..,m$$

$${\displaystyle \sum }_{j=1}^n{\lambda }_j{Y}_{rj}⩽Y_{r0}+{\mathsf{\beta }\mathrm{g}}_y, r=1,2,\dots ..,s$$

$${\displaystyle \sum }_{j=1}^n{\lambda }_j=1, j=1,2,\dots .n$$

$${\lambda }_j⩾0,\hspace{1em}\hspace{1em}\mathsf{\beta } ⩾0$$

where y and u are as above, g = (g_y, −g_u) is the directional variable of output expansion, β is the maximum proportion of the output portfolio (y, u) that can expand and contract simultaneously along the directional vector g, and β ≥ 0. The DMU₀ is efficient and a “best practitioner” when and only when β = 0. Otherwise, it is in the production frontier plane inside and a larger value of this value means that it is far from the P(x) frontier boundary and is inefficient.

Typically, the Malmquist productivity index can be used to evaluate the Total Factor Productivity (TFP) variation of a decision unit. However, the Malmquist index applies to the traditional radial and angular distance functions, which cannot simultaneously consider the decrease in inputs and increase in outputs, and the variables need to vary equally. In order to compensate for these shortcomings, the paper adopts the Malmquist–Luenberger index proposed by Chambers [48] and introduces the environmental pollution output constraint into the productivity measurement process, which can consider both input reduction and output increase without equal proportional changes in each variable. Using the DDF-based data envelopment analysis (DEA) method, the Malmquist–Luenberger index (ML index) can be defined as Equation (3) from period t to period t + 1 to achieve the need to measure the green total factor productivity of pig breeding.

$${ML\_TFP}_0^{t,t+1}=\sqrt{\frac{1+\overrightarrow{D_0^t}\left(x^t,y^t,u^t;g_{y^r},-g_{u^r}\right)}{1+\overrightarrow{D_0^t}\left(x^{t+1},y^{t+1},u^{t+1};g_{y^{r+1}},-g_{u^{r+1}}\right)}·\frac{1+\overrightarrow{D_0^{t+1}}\left(x^t,y^t,u^t;g_{y^r},-g_{u^r}\right)}{1+\overrightarrow{D_0^{t+1}}\left(x^{t+1},y^{t+1},u^{t+1};g_{y^{r+1}},-g_{u^{r+1}}\right)}}$$

(3)

Similar to the Malmquist productivity index decomposition, the ML_TFP index can be further decomposed into the technological progress index (ML_TECH) and the technical efficiency change index (ML_EFFCH), as shown in (4) to (6).

$$ML\_TF{P}_0^{t,t+1}={\left(ML\_TECH\right)}_0^{t,t+1}·{\left(ML\_EFFCH\right)}_0^{t,t+1}$$

(4)

$$ML\_TEC{H}_0^{t,t+1}=\sqrt{\frac{1+\overrightarrow{D_0^{t+1}}\left(x^t,y^t,u^t;g_{y^r},-g_{u^r}\right)}{1+\overrightarrow{D_0^t}\left(x^t,y^t,u^t;g_{y^r},-g_{u^r}\right)}·\frac{1+\overrightarrow{D_0^{t+1}}\left(x^{t+1},y^{t+1},u^{t+1};g_{y^{r+1}},-g_{u^{r+1}}\right)}{1+\overrightarrow{D_0^t}\left(x^{t+1},y^{t+1},u^{t+1};g_{y^{r+1}},-g_{u^{r+1}}\right)}}$$

(5)

$$ML\_EFFC{H}_0^{t,t+1}=\frac{1+\overrightarrow{D_0^t}\left(x^t,y^t,u^t;g_{y^r},-g_{u^r}\right)}{1+\overrightarrow{D_0^{t+1}}\left(x^{t+1},y^{t+1},u^{t+1};g_{y^{r+1}},-g_{u^{r+1}}\right)}$$

(6)

where the technological progress index $ML\_TEC{H}_0^{t,t+1}$ indicates the movement of the technological frontier between period t and period t + 1; the index of technical efficiency changes $ML\_EFFC{H}_0^{t,t+1}$ on the other hand reflect the extent to which the technologically backward regions catch up with the advanced ones on the production possibility frontier.$ML\_TF{P}_0^{t,t+1}$, $ML\_TEC{H}_0^{t,t+1}$, $ML\_EFFC{H}_0^{t,t+1}$ greater than 1 indicate the green total factor productivity increase, efficiency improvement, and technological progress of pigs in that DMU, respectively, and vice versa.

3.2. Spatial Correlation Detection Method

This method is used to measure and test the spatial correlation and distribution state of green total factor productivity of pig breeding in China, i.e., whether there is correlation or convergence between the green production efficiency of pig breeding in one province and region and the efficiency values of neighboring provinces and regions. In this paper, Moran’s I index is used to test the global spatial correlation of green total factor productivity of pig breeding, and the spatial weight matrix is selected as the adjacency matrix. Moran’s I index is calculated as follows:

$$I=\frac{n{{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n{W}_{ij}\left(p_i-\overline{p}\right)\left(p_j-\overline{p}\right)}{{{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n{W}_{ij}{{\displaystyle \sum }}_{i=1}^n{\left(p_i-\overline{p}\right)}^2}$$

$$=\frac{n{{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n{W}_{ij}\left(p_i-\overline{p}\right)\left(p_j-\overline{p}\right)}{S^2{{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n{W}_{ij}}$$

(7)

In Equation (7), the I is the global Moran’s I index. p_i is the green total factor productivity value of pigs in each province and district, and S² is the variance of green total factor productivity of pigs in each province and district (calculated by the formula $S^2$ = $\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{\left(p_i-\overline{p}\right)}^2$), $\overline{p}$ is the mean value of green total factor productivity of pigs in each province and region, and W_ij is the spatial weight matrix of regions i and j, which indicates the proximity of provincial region i and provincial region j, expressed by the geographical distance between them (calculated by the formula $W_{ij}$=1/$d_{ij}^2$, where $d_{ij}^{}$ is the geographical distance between province i and province j). Since different spatial weight matrices can have a large impact on Moran’s I values, in order to obtain relatively more stable Moran’s I index values, the inverse of the quadratic of geographic unit distances is chosen to form the spatial weight matrix. Among them, Moran’s I index takes the value interval of [−1,1], greater than 0 indicates positive spatial correlation, less than 0 is negative spatial correlation, and equal to 0 is no correlation, i.e., randomly distributed in space.

3.3. Spatial Convergence Test Model Construction

In order to examine the evolutionary trend of the green total factor productivity of pigs, this study requires a convergence test. Convergence studies were first focused on economic growth [50], and according to the characteristics of change, convergence can be classified as σ convergence and β convergence. The convergence of green total factor productivity of pigs refers to the trend of the decreasing variance of green total factor productivity of pigs with time. σ convergence mainly describes the absolute value of green total factor productivity, which can visually show the gap between different regions. In this paper, we will use σ convergence to test the trend of the difference of the green total factor productivity of pigs between different regions. The σ convergence model is as follows:

$$\sigma =\frac{\sqrt{{{\displaystyle \sum }}_{i=1}^N{(TFG{P}_{it}-\overline{TFG{P}_t})}^2/N}}{\overline{TFG{P}_t}}$$

(8)

Among them, this means that the green total factor productivity index of pigs in the t period of I province (region) is the average of the green total factor productivity index of pigs in all provinces (regions) in the t period, and N is the total number of provinces (regions).

3.4. Data Sources and Indicator Selection

Given the availability and completeness of data, this paper uses data from 20 provinces, municipalities directly under the Central Government and autonomous regions (excluding Tibet) in China from 2005 to 2018 as a sample and divides them into four categories of regions according to their regional locations (eastern region including: Hebei, Shandong, Jiangsu, Guangdong, Zhejiang; central region including: Shanxi, Anhui, Hubei, Hunan, Henan; western region including Inner Mongolia, Guangxi, Sichuan, Yunnan, Shaanxi, Gansu, Qinghai; northeast regions including: Heilongjiang, Jilin, Liaoning) in order to examine regional differences in the green total factor productivity of live pigs (Figure 1).

(1)

Input factor variables. The quantity of labor (Labor, days/head), weight of litter (Cub, Kg/head), amount of feed concentrate (Js, Kg/head), amount of green roughage (Cs, Kg/head), and other material costs (Fee, yuan/head) (including water and fuel costs, medical and epidemic prevention costs, etc.) were selected as input factor variables. The data of the above variables were obtained from the National Compilation of Agricultural Costs and Returns (2006–2019), and the two costs included in other material costs were deflated according to the price index of agricultural production materials based on the 2005 China Statistical Yearbook in order to eliminate the inflation factor.

(2)

Production output variable. The production output includes desired output and non-desired output. Among these, the desired output is the output of the production of live pigs (Kg/head). The non-desired output is the emission of pollutants per pig, as the manure discharged by pigs is converted into chemical oxygen demand (COD), total nitrogen (TN), total phosphorus (TP), copper (Cu) and zinc (Zn) (unit: Kg/head), etc., which is calculated as

QP = AD × PD × W

(9)

In the above equation, QP is the pollutant emission per pig (kg); AD is average breeding days (days); PD is the emission factor; W is the “actual weight/reference weight” (kg). The data of pig pollutant emissions are based on the production and emission coefficients in the Emission Manual, which provides emission coefficients with different degrees of distinction by province, size and breeding stage (

Table 1. Descriptive statistics of inputs and outputs in different scale.

Scale	Criterion	Index	Unit	Max	Min	Mean	Std.Dev	Obs.
Small	Input	Labor	day/head	19.00	1.52	3.73	1.77	280
		Cub	kg/head	30.37	8.71	16.62	5.57	280
		Js	kg/head	416.48	136.40	295.50	37.55	280
		Cs	kg/head	340.64	95.50	213.99	30.68	280
		Fee	Yuan/head	82.56	15.91	41.61	12.79	280
	Positive output	Main product output	kg/head	151.73	83.80	113.84	10.37	280
	Negative output	Total discharge	kg/head	153.34	12.66	97.17	23.30	280
Medium	Input	Labor	day/head	9.77	0.85	2.44	1.07	280
		Cub	kg/head	29.50	8.30	17.06	5.28	280
		Js	kg/head	396.31	216.40	299.62	35.88	280
		Cs	kg/head	315.24	151.50	217.39	29.85	280
		Fee	Yuan/head	499.60	15.50	47.93	30.84	280
	Positive output	Main product output	kg/head	147.67	92.00	114.44	10.48	280
	Negative output	Total discharge	kg/head	147.29	6.06	65.78	20.89	280
Large	Input	Labor	day/head	6.40	0.42	1.46	0.77	280
		Cub	kg/head	30.40	6.40	17.23	5.57	280
		Js	kg/head	389.82	184.80	285.34	33.22	280
		Cs	kg/head	300.01	123.10	208.08	27.82	280
		Fee	Yuan/head	135.10	15.23	51.11	18.52	280
	Positive output	Main product output	kg/head	152.41	88.80	109.98	10.47	280
	Negative output	Total discharge	kg/head	249.67	32.84	78.12	35.69	280

).

4. Empirical Results and Analysis

4.1. Time Series Characteristics of Changes in China’s Pig Green Total Factor Productivity Index

Based on the above research methods and processing means, MaxDEA 8.0 software was selected for data analysis.

Table 2. Green total factor productivity indices for different sizes of pigs in China, 2006–2018.

Year	$ML\_TF{P}_0^{t,t+1}$			$ML\_EFFC{H}_0^{t,t+1}$			$ML\_TEC{H}_0^{t,t+1}$
	Small Scale	Medium Scale	Large Scale	Small Scale	Medium Scale	Large Scale	Small Scale	Medium Scale	Large Scale
2006	0.9741	0.9634	0.9502	1.0029	1.0160	1.0470	0.9712	0.9482	0.9075
2007	0.9654	1.0227	1.0096	0.9897	1.0006	0.9874	0.9755	1.0220	1.0224
2008	1.0373	1.0163	1.0015	1.0110	1.0066	1.0138	1.0260	1.0097	0.9879
2009	1.0192	1.0679	1.0047	1.0033	0.9971	1.0107	1.0158	1.0710	0.9941
2010	0.9849	0.9098	1.0000	1.0007	1.0123	1.0014	0.9842	0.8987	0.9986
2011	0.9994	1.0119	0.9917	1.0005	1.0067	1.0025	0.9989	1.0051	0.9892
2012	1.0114	1.0166	1.0077	1.0038	0.9984	0.9965	1.0076	1.0182	1.0113
2013	0.9926	0.9931	1.0011	0.9927	1.0010	1.0049	0.9999	0.9921	0.9962
2014	1.0115	1.0026	1.0060	1.0060	1.0010	0.9993	1.0054	1.0016	1.0068
2015	1.0256	1.0096	1.1649	0.9967	0.9975	0.5329	1.0290	1.0121	2.1860
2016	0.9801	1.0100	0.8801	0.9948	0.9999	1.7498	0.9853	1.0101	0.5030
2017	1.0023	1.0017	0.8920	1.0103	1.0005	1.0742	0.9920	1.0012	0.8303
2018	1.0115	1.0059	1.0037	0.9982	1.0009	1.0012	1.0133	1.0049	1.0025
Average	1.0010	1.0018	0.9912	1.0008	1.0030	1.0050	1.0002	0.9988	0.9863

shows the geometric mean of green total factor productivity indices for different sizes of pigs in China from 2006 to 2018.

As can be seen from Table 2, the overall level of green total factor productivity growth of pig breeding in China from 2006–2018 was low. In terms of different scales, (China’s pig-advantageous production areas (including Heilongjiang, Jilin and Liaoning in Northeast China; Jiangsu, Zhejiang, Anhui and Shandong in East China; Shanxi, Hebei and Inner Mongolia in North China; Henan, Hubei and Hunan in Central China; Guangdong and Guangxi in South China; Sichuan and Yunnan in Southwest China; Shaanxi, Gansu and Qinghai in Northwest China, a total of 20 provinces (autonomous regions) the average annual growth rates of green total factor productivity ($ML\_TF{P}_0^{t,t+1}$) for large-scale, medium-scale and small-scale pig breeding were −0.88%, 0.18% and 0.1%, respectively. Among them, the average annual growth rate of total factor productivity of medium-scale pig breeding in dominant production areas was the fastest. If the total factor productivity index (Malmquist–Luenberger index) is further decomposed into the technical efficiency index ($ML\_EFFC{H}_0^{t,t+1}$) and technical progress index ($ML\_TEC{H}_0^{t,t+1}$), it can be concluded that the increasing green total factor productivity of small-scale pig breeding in dominant production areas of China from 2006 to 2018 was driven by the combination of technical production efficiency and technical progress. The increasing green total factor productivity of medium-scale pig breeding mainly depended on improvements in production technology efficiency, while the decreasing green total factor productivity growth rate of large-scale pig breeding was mainly due to the large scale of investment and high demand and requirement for standardized manure treatment technology [51,52,53] and green farming management technology in the process of pig farming. While the current stage of pig farming in China is one of rapid development and transition, technological innovation is still insufficient. However, in general, the main source of the green total factor productivity growth of pig breeding in China is still the continuous improvement in technical efficiency. The growth rate in technical efficiency and technical progress in large-scale pig farming from 2006 to 2018 were 0.5% and −1.37%, respectively. The reasons for this situation were: On the one hand, the investment in technological innovation in China’s pig farming industry is still insufficient, and the investment in technological innovation in agriculture is mainly oriented to the planting industries, while technological innovation investment in the pig industry is neglected. On the other hand, the long-standing crude economic growth model of China’s pig farming industry focuses on the massive input and expansion of production factors to achieve economic growth, while neglecting the quality of economic growth in the pig industry [54,55].

Figure 2 depicts the changing trend of the green total factor productivity index for different sizes of pigs in different farming scales. From 2006 to 2018, the change in the green total factor productivity index of small-scale pig breeding in China basically remained stable; the change in the green total factor productivity index of medium-scale pig breeding fluctuated more before 2011 and tended to a stable change trend after 2011 and almost all exceeded 1; relatively speaking, the change in the green total factor productivity index of large-scale pig breeding was the largest, with the highest value. The new National Environmental Protection Law was formally implemented and the National Pig Production Development Plan (2016–2020) was proposed in 2016, which determined that the proportion of large-scale pig breeding with an annual output of more than 500 head should be increased nationwide, and at the same time about 5 million small- and medium-sized pig farmers in China withdrew from the industry, while agricultural giants accelerated their expansion through mergers and acquisitions, investments. Coupled with the wider application of information technology such as “Internet+”, the transformation and upgrading of the large-scale and standardized pig-breeding industry will be accelerated, which in turn will lead to large changes in the green productivity of large-scale pig breeding.

In terms of different scales of production (Figure 3), from 2006 to 2018, among the 20 dominant pig production areas in China, 12 regions (including Anhui, Gansu, Guangdong, Hebei, Henan, Hubei, Hunan, Jiangsu, Inner Mongolia, Shandong, Shanxi and Sichuan) had a green total factor productivity index of more than 1 for small-scale pig breeding, showing a growing trend of productivity that was related to the local natural resource endowment and economic development level. From the green total factor productivity of medium scale pig breeding in different provinces, medium scale in general showed an obvious trend of a growing green total factor productivity of pig breeding, among which 10 regions (including Guangdong, Henan, Hubei, Inner Mongolia, Qinghai, Shandong, Shanxi, Sichuan, Yunnan and Zhejiang) had green total factor productivity indexes for medium-scale pig breeding above 1, mainly concentrated in the central and eastern regions. In terms of small and medium scale, Guangdong, Henan, Hubei, Inner Mongolia, Shandong, Shanxi and Sichuan are important regions for future standardized and large-scale pig breeding, which is basically consistent with the resource endowment, environmental climate and economic development conditions required for pig breeding. Moreover, at a large-scale, only six regions (including Gansu, Guangdong, Henan, Hubei, Yunnan and Zhejiang) had a pig breeding green total factor productivity index of more than 1; the other regions were below 1, which is related to the strictness of environmental protection officers in these regions towards small-scale farmers [56,57], and the environmental pollution control costs consequently incurred.

In terms of different dominant production areas, from 2006 to 2018, for small-scale pig breeding, the average annual growth rate of the green total factor productivity of pigs in Gansu Province was the fastest at 1.76% and the slowest was −1.34% in Shaanxi; for medium-scale pig breeding, the average annual growth rate of green total factor productivity of pigs in Zhejiang Province was the fastest at 3.25% and the slowest, at −2.09%, was in Shaanxi. For large-scale pig breeding, the average annual growth rate of green total factor productivity of pigs in Zhejiang Province was the fastest, reaching 1.19%, and the slowest was in Qinghai, at only −3.11%. It can be seen that in recent years the average annual growth rate of green total factor productivity of pigs in medium-scale and large-scale pig farms in Zhejiang has been the fastest among the 20 dominant production areas in China, which is related to the influence of local policies and technologies. In Shaanxi, on the other hand, the average annual growth rate of green total factor productivity of pigs in small-scale and medium-scale pig farms has been the slowest among the 20 dominant production areas in China and shows a decreasing trend of production efficiency, which is mainly influenced by the dual results of deteriorating technical efficiency and technological regression.

4.2. Spatial Pattern Characteristics of Green Total Factor Productivity of Pigs in China

(1)

Spatial association characteristics

No green farming of pigs exists in isolation, due to the effect of an industrial association. In order to verify whether there is spatial convergence of green productivity in the process of pig farming, in this paper, using the global spatial autocorrelation formula and the spatial panel data of green total factor productivity of pigs in each province and region from 2006–2018, we can calculate the global Moran’s I value of green total factor productivity of pigs in China from 2006 to 2018. The results in Figure 4 show that, in general, the global Moran′s I value of pig green total factor productivity from 2006 to 2018 is positive, indicating that the pig green total factor productivity of each province and region in China has a significant positive spatial correlation, and there is a certain spatial dependence between provinces and regions, i.e., there is a spatial agglomeration feature. The Moran’s I index values from 2006 to 2011 fluctuate around 0.02, and after 2012 there is a slowly fluctuating upward trend, reaching 0.182 in 2017. The reasons for this phenomenon mainly originate from the scale of pig breeding, the subsidies of national fiscal policy, the improvement of farmers’ education and the promotion of advanced technology use.

(2)

Spatial clustering pattern and technology spillover

To identify the spatial clustering pattern of green total factor productivity of pigs and the technology spillover, the spatial pattern was plotted according to the natural breakpoint method (Figure 4). Overall, the green total factor productivity of pigs in China evolved from a low-level equilibrium to high-level uneven patterns from 2006 to 2018, with the number of high-level types increasing and the number of low-level types decreasing as time progressed. In terms of spatial distribution, the high-level types are concentrated in the north and southeast, while the low-level types are dominated by the northwest, northeast and south- central regions. By 2018, the green total factor productivity and technical progress efficiency of pig farming formed high-level clusters in the northeast, southeast and central regions at the national level, and pure technical efficiency level types were distributed in a band along the Yellow River basin.

As can be seen from Figure 5, Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10: ① In terms of comprehensive efficiency, in 2006, most provinces and regions in the country were of low and lower level types, and only the Inner Mongolia Autonomous Region belonged to the medium level type, which was in a low-level equilibrium overall; in 2018, the spatial pattern changed significantly, the low- level types decreased sharply, only Hunan and Heilongjiang were of lower level types, and the high level and higher level types were distributed in Inner Mongolia, Gansu and Guangdong. The high level and higher level types were distributed in Inner Mongolia, Gansu, Guangdong, Guangxi and Zhejiang, forming a triangular pattern of the south, north and east coast at the national level. ② In terms of technical progress efficiency, the higher level types in 2006 were mainly distributed in Gansu and Shaanxi in the northwest and Jilin and Hebei in the northeast. Except for Heilongjiang and Yunnan, all other regions were low-level types, showing contiguous distribution in 2018; the national level presented three high-level clusters in the north, central and south, showing a non-equilibrium pattern characteristic overall. ③ In terms of pure technical efficiency, in 2006, the high-level types were distributed in Shanxi; only Heilongjiang and Shaanxi belonged to the higher level types, and the rest of the provinces and regions were medium or lower level types, which were in the overall low-level equilibrium stage; in 2018, the number of high level and higher level types increased significantly, mainly distributed in the upstream and downstream areas of the Yellow River Basin, and showed a belt-like distribution, and the number of medium and lower level types sharply decreased.

4.3. Convergence Test for Differences in Green Total Factor Productivity Indices

The analysis of temporal and spatial differences in green total factor productivity conducted earlier shows that there are inter-provincial and regional differences in green total factor productivity of pig farming in China, and they show a certain trend of temporal evolution (see Figure 11, Figure 12 and Figure 13). In order to examine the convergence of different sizes of pigs and regional differences, this paper uses the σ convergence method to test the analysis.

Figure 11 shows that the convergence of three scales, large, medium and small, showed a diverging trend before 2016 and a heterogeneous convergence trend after 2016, indicating that the gap in green production efficiency growth between different scales in each region is gradually narrowing overall. The reason for this stems from the fact that in 2016 the state proposed the National Pig Production Development Plan (2016–2020), which has important theoretical and practical significance for guiding the green development of large-scale farming, further optimizing the spatial layout of farming, and achieving high-quality growth while determining that the proportion of large-scale farming with an annual output of more than 500 pigs nationwide will increase to 52% by 2020. It can be expected that the development of large-scale pig breeding will be faster and faster in the future. At the same time, due to the pressure of environmental protection, some free-range and small-scale pig farmers are gradually banned or merged. Thus, the difference between different scales shows a convergence trend.

In terms of large-scale pig breeding (Figure 12), there are two stages: before 2012, the regional differences in the four regions of eastern, central, western and northeastern China showed a fluctuating divergence trend; after 2013, the differences in the four regions gradually narrowed and showed a convergence trend overall. Among them, the σ convergence coefficient in the eastern region showed a slow decline, but remained stable in general. The central region showed a more volatile evolutionary trend, which was directly related to the shortage of land resources and the severe challenges faced by the water network area in the central part of China, especially in some southern provinces. There were two convergent phases in the middle scale (Figure 13): From 2006 to 2013, four regions, namely the eastern, central, western and northeastern regions, showed fluctuating divergent trends with large regional differences. From 2013 to 2018, all four regions showed convergent trends, indicating that China’s medium-scale pig breeding was in the absolute dominant position. The overall convergence characteristic of small-scale pig breeding is more obvious (Figure 14); before 2009, the four regions showed an obvious dispersion trend, but after 2009, the dispersion trend of the four regions still existed, and the convergence trend was not obvious, which was closely related to the gradual reduction of small-scale farmers and the development of a pig breeding scale and standardization strategy in China under the double constraints of resources and environment.

5. Conclusions and Policy Implications

Based on the relevant statistical data from 2006 to 2018, this paper measured the green total factor productivity of pigs in China by using the DDF directional distance function model and Malmquist–Luenberger (ML) productivity index and analyzed the spatial autocorrelation and spatial pattern characteristics of the green total factor productivity of pig breeding by using Moran’s I-Theil Index model and the natural breakpoint method in comparison. The spatial autocorrelation and spatial pattern characteristics of green TFP were compared by Moran’s I-Theil Index model and the natural breakpoint method, and finally the convergence trend of the green TFP index was examined. The main conclusions drawn in this paper are.

First, the overall level of green total factor productivity growth of pig breeding in China from 2006 to 2018 is low, and there are obvious regional and scale differences. Regionally, it shows that the efficiency of large-scale green production is higher in central and southeastern provinces and regions than in northeastern and southwestern regions. Guangdong, Henan, Hubei, Inner Mongolia, Shandong, Shanxi and Sichuan are important regions for future standardized large-scale pig breeding. In terms of different scales, the average annual growth rate of TFGP on a medium scale is too fast, mainly relying on the improvement in production technology efficiency. Small-scale growth is the second fastest, stemming from the combined effect of technical efficiency and technological progress, while large-scale growth is the slowest, mainly because of the larger scale, higher investment and higher requirements for standardized manure treatment technology and green farming management technology, etc. At this stage, China’s pig-scale farms are in a period of rapid development and transition, technological innovation is still insufficient, and the economic benefits of pig production scale in large-scale farms have not been highlighted.

Second, there is spatial convergence of green total factor productivity of pig breeding in China, i.e., there is spatial autocorrelation of green total factor productivity of pig breeding among provinces and regions. Moreover, from 2006 to 2008, a pattern of gradual evolution from low-level equilibrium to high-level imbalance is formed with the advance of time.

Third, the convergence test reveals that the gap in green total factor productivity growth in pig breeding of different farming scales in China is gradually narrowing in general, but from the four regions of the east, central, west and northeast, the large and medium scales show fluctuating convergence among different regions, and the small scales do not converge significantly among different regions.

Based on the above research findings, this paper tentatively draws the following policy implications. First, there is the need to continue to increase investment in technological innovation in the pig industry, thus promoting technical efficiency and technological progress, especially in large-scale pig farms. There is the need to focus on supporting the cooperation between large- and medium-sized pig farms (households) and research institutes, and to provide a corresponding financial subsidy system to achieve high-quality green development of the pig industry. Secondly, to promote the scale and standardization development of the pig industry according to local conditions, and to properly implement environmental policies for the pig farming industry to comprehensively improve total factor productivity growth, for example, environmental policies such as no-farming zones will need to guide the changes in the spatial pattern of the pig industry. Again, technical promotion in the dominant pig production areas should be strengthened and combined with the local resource endowment conditions so that areas with similar conditions can form a scale effect in terms of technical efficiency, thus improving the technical efficiency of pig breeding. Finally, attention should be paid to the balanced development of the dominant pig production areas to reduce the efficiency differences between the dominant areas and different scales within the dominant areas.