2.1. Pig supply model with herd structure under environmental regulations

Factors of production refer to all the elements and environmental conditions necessary for material production. When analyzing product supply, most studies are based on the C-D production function, constructing a universal supply model, and analyzing the impact of capital, labor, and other factor inputs on production [12]. In the animal husbandry industry, some studies separately analyze factors such as land, epidemic prevention, feed, dams, and young animals to examine the impact of specific factors on production [13, 14]. In order to analyze the impact of herd structure on pig supply, this paper takes sows as a production factor, constructs a pig supply model, and analyzes the relationship between herd structure and pig production under environmental regulations. In the self-breeding and self-raising model, piglets are not only a production factor in the fattening process but also a product that can reproduce sows during the produce process. When reproducing sows and piglets are included in the same framework, it is necessary to analyze the feasibility of both sows and piglets as factors of production at the same time.

First, as an important production factor in the produce process, sows have higher purchase costs and maintenance costs than piglets. The input as a production factor is closer to fixed asset investment. There are mature sows insurances and loan products that use sows as collateral, which shows that sows have better stability in the production process. Second, the production process aimed at traditional products is also longer than piglets. In short-term production, the sows’s products are only piglets. Only when the gestation cycle of the sows and the fattening cycle of the piglet is considered at the same time, its products are traditional products such as slaughter pigs [15, 16]. Third, in actual production, in addition to self-reproduction and self-support, there are also a large number of companies that specialize in fattening or piglet produce. For companies specializing in piglet produce, sows as a production factor are only piglets, and pigs for slaughter are not used as the final product. Based on the above three aspects, the reproductive sows and piglets are used as production factors at the same time to analyze the impact of the adjustment of the herd structure on production in the short term.

In the field research, facing external shocks such as environmental regulation, the major producers will give priority to adjusting the stock of fattening pigs in order to quickly meet the environmental protection requirements, and obtain certain cost compensation through early sales to reduce losses. However, with the increase of external shocks, they will also kill sows. Based on the above facts, when analyzing the adjustment of production input factors, it is assumed that the main produce subject will give priority to adjusting the input of piglets and set short-term and long-term target differences based on whether sows are adjusted or not. The main produce subject generally does not adjust the farming output of sows in the short term, but under the guidance of long-term goals, the main produce subject will strategically adjust sows as a production factor that must be considered separately (Fig 1).

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Fig 1. The changes in the inputs and outputs of the main produce subject.

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Chinese pig production is mainly self-reproduction and self-raising. After considering the contractual relationship between the upstream and downstream of the industrial chain, the non-self-reproducing and self-supporting enterprises can still be approximated as self-reproducing and self-supporting entities for analysis. This kind of subject needs to input the sows X₁ and other production factors X₂ including piglets and feed input in the piglet fattening link to produce with the production function Y = f(X₁,X₂). Its production cost is C = w₁X₁ + w₂X₁, Where w_i is the used price of production factor X_i, the rational peasant theory believes that the producers will take profit maximization and cost minimization as the standard production. Refer to the government’s mandatory environmental regulation conditions set by You J et al. [17] to analyze the production situation of the producers under different environmental regulations, and mark different situations with t. Set t = 0 to indicate that the environmental regulation has not been carried out, t = 1 is the situation of environmental regulation in the short term, t = 2 is the situation of environmental regulation in the long term, and t = 2+k is the context in which the intensity of environmental regulation changes in the long term. The main produce subject produces at the intersection E₀ of the equal-cost line and output isoquant, and the optimal factor input at this time is E_A0 and E_B0 respectively, at t = 1, environmental regulation only affects the production factors X₂, and at t = 2, environmental regulation can affect both production factors X₁ and X₂.

Environmental regulation needs to be concrete as a specific policy tool before it can be applied to pig production. Existing environmental regulation tools include technical level restrictions, total pollution restrictions, and environmental tax on a specific duty, among which technical level restrictions are mainly enforced by national administrative coercive and are hard standards, while total pollution restrictions and environmental tax on specific duty need to rely on market mechanisms, concretely manifested in emission rights and environmental taxes, which are typical marketization environmental regulation tools [18]. Since this paper focuses on the impact of environmental regulation on pig production under the market mechanism, only the two situations of environmental tax collection and the issuance of pollution rights will be explained.

2.2. Non-adjustable factors of production began to adjust

Both the imposition of environmental taxes and the issuance of emission rights require additional costs for factors of production for the main produce subject, which is equivalent to an increase in factor prices. When the production factor cannot be adjusted freely (t = 1), only the production factor X₂ changes and the equal-cost line changes from A₀B₀ to A₁B₀, where A₀A₁ is the additional cost of the main produce subject under environmental regulation, in actual production, this is mainly expressed as the cost of environmental taxes or the purchase of emission rights (Fig 1). The enterprise still produces in the way of maximizing profit and minimizing cost, and its output level is still the tangent point of the isoquant line and the equal-cost line, that is point E₁. At this time, there must be a downward shift of the isoquant line of pigs, that is, the output decreases. At this time, the optimal factor input is E_A1 and E_B0 respectively. In actual production, the producers can reduce production by producing fattening pigs for slaughter and reducing piglets. Among them, slaughter pigs will increase the supply of pigs in the market in the short term and decrease in the long term; reducing piglets will not have an impact on the supply of pigs in the short term, but it will reduce the long-term supply of pigs.

Hypothesis 1: when other conditions remain unchanged, strengthening environmental regulation will lead to a short-term increase and a long-term decrease in the slaughter of pigs.

When the factors of production can freely adjust the (t = 2), considering the substitution effect between production factors, the organic composition of capital can be adjusted (Fig 2). The production factor X₂ is simplified as the input of piglets in the production process to analyze the impact of herd structure and the production of pigs. The main produce subject needs to adjust the input of factors to achieve maximum profit and minimize cost. Since the prices of both the factor X₁ and the factor X₂ have changed, they are recorded as w_i + θ_i, where θ_i is the environmental tax paid by the farming subject for the production factor i. According to the "Taxable Pollutants and Equivalent Value Table", sows and fattening pigs pay the same environmental tax during the fattening process, namely θ₁ = θ₂. At this time, the factor input ratio of the optimal output should be (w₁ + θ₁)/(w₂ + θ₂), which has a greater slope of the equal-cost line than when t = 1 close to -1, as shown in in Fig 2c1. At this time, and are the adjustment of production factors X₂ and X₁, respectively according to the weak axiom of cost minimization (WACM), the change of factors from optimal to non-optimal under equal output will inevitably lead to increased costs. With constant cost constraints, changes in the factors of production toward the optimal combination will promote an increase in output, that is, under the condition that the main produce subject does not increase the input, freely adjusting the configuration of the production input elements X₁ and X₂ can increase the output.

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Fig 2. The effect of whether the factors of production are adjustable on the subject’s input and output under environmental regulation.

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The regulation of total pollutant is different from the collection of environmental tax. The government does not price the pollution generated during the use of every factor of production. Therefore, the main produce subject can produce according to the initial factor price ratio. At this time, the condition for maximizing profit is w₁/w₂. As shown by in Fig 2d1, and are the adjustment of production factors X₂ and X₁, respectively. From the cost minimization axiom, it can be seen that during the produce process, the input elements X₁ and X₂ are allowed to be adjusted, which can increase the output without increasing the main input. Since the total pollution regulation does not change the optimal production conditions, the equal cost line is translated rather than rotated when the total pollution regulation is implemented, that is, pig production only depends on the initial price of the factor.

Hypothesis 2: Under the established production cost of the main produce subject, reasonable adjustment of herd structure can improve pig production under the intensity of specific environmental regulation.

2.3. Pig production changes under environmental regulations

Considering the impact of environmental regulation intensity change on pig production and set it to t = 2+k periods. When the government levies an environmental tax, the produce subject adjusts the inputs of production factors according to the ratio of environmental tax levied on production factors to make them produce under optimal conditions, that is, to ensure that the ratio of factor inputs is equal to (w₁ + θ₁)/(w₂ + θ₂), when θ_i increases as the intensity of environmental regulation increases, the cost for pig production decreases if the total cost of farming remains the same so that the equal-cost line is shifting flat to the lower left. Under the current levy standard , which means that the equal-cost line gradually approaches -1 in the process of translation, the expansion line of the main produce subject with the change of environmental regulation intensity is shown as OQ (Fig 3).

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Fig 3. The effects of changes in the intensity of environmental regulation on the input and output of the subject.

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When the government regulates by selling the total amount of emission rights, it is assumed that the market sells the emission rights in an unlimited amount, and the production function of the main produce subject is shown in Fig 1A. When the intensity of environmental regulation increases and the emission rights τ → 0⁺ are sold, the main produce subject will still produce as described in d1 when it produces, that is, they will approach the origin in a translational manner. At this time, the expansion line of the main produce subject with the intensity of environmental regulation is shown as OQ in Fig 3d2. The intensity of environmental regulation and the herd structure respectively affect the production of pigs, and the intensity of environmental regulation will also affect the production of pigs through the herd structure.

Hypothesis 3: the herd structure has a mediating effect on the impact of environmental regulations on pig production.

3.1. Models and methodology

3.1.1. Methods for estimating the effectiveness of environmental regulation policies.

Policy effectiveness can comprehensively reflect the strictness of environmental regulatory policies, which is one of the important characteristics of environmental regulatory policies. However, since the effectiveness of the policy is difficult to measure, it is necessary to subdivide the indicators [19]. When analyzing China’s energy conservation and emission reduction policies, Zhang G [20] puts forward indicators for the effectiveness of environmental regulatory policies, and it is also decomposed into three dimensions of policy strength, policy objectives, and policy measures for scoring. With the rise of environmental decentralization theory and environmental federation theory, local governments have more discretionary powers in environmental regulation. However, it still needs to be monitored by the central government due to the promotion mechanism [21]. Therefore, this paper introduces policy feedback from indicators measuring environmental supervision into the policy effectiveness evaluation model. Refer to Pan D et al. [22] ’s evaluation criteria for environmental feedback, the four aspects of policy strength, policy objectives, policy measures, and policy feedback are evaluated as shown in Table 1.

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Table 1. Criteria for evaluating the effectiveness of China’s environmental regulation policies.

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In Table 1, policy objectives, policy measures, and policy feedback are used to reflect the effectiveness indicators at the policy formulation level, and the policy strength reflects the effectiveness indicators at the policy implementation level, which are used to ensure that the policy achieves the expected goals. In this paper, based on the relationship among policy objectives, measures, feedback, and strength, the policy effectiveness evaluation model is set as follows.

(1)(2)

Among them, Hjgz_iP is the effectiveness of environmental regulation in the year i of Province P, which is used to reflect the stringency of environmental regulation. is the cumulative effects of environmental regulatory policies at the national level, and is the cumulative effects of environmental regulatory policies at the provincial level in China, S means policy intensity, O is policy objective, M is policy measure, F is policy feedback, and j is the specific environmental regulation policy introduced in the year i.

3.1.2. Econometric model setting.

The existing studies mostly use the step method to analyze the mediating effect [23], This paper builds the mediating effect model based on this, as shown in formula (3).

(3)

Among them, Y is the explained variable, X is the core independent variable, M is the mediator variable, a, b, and c are the regression coefficients, and e is the residual.

Since the number of pigs for column quantity is usually affected by the expectations of the producers when analyzing the production of pigs, it is necessary to consider the impact of pig production itself, that is, a dynamic panel model should be constructed. To ensure the consistency of the estimation, the system Gaussian Mixed Model (GMM) is selected for estimation, and the econometric model for analyzing the impact of environmental regulation on pig production is as follows.

(4)

The mediating effect model is as follows.

(5)

Among them, Szcl is the pig production, Hjgz is the environmental regulation, Yzjg is the herd structure, Wzf, Rgcb and Tdcb are control variables.

3.2. Variables selection and measurement

3.2.2. Independent variable: Pig production.

Environmental regulation. This paper uses the effectiveness of environmental regulation policies to measure the intensity of environmental regulation as the core explanatory variable of this paper. After 2008, the Chinese Government Network began to actively publicize the cur-rent policies. Although there are some early policy announcements, the number of announcements is significantly smaller than after 2008. Taking into account the impact of policy deficiencies on environmental regulation, this paper selects relevant data from 2008 to 2019 for analysis.

According to the above formulae, this paper crawls big data for the website of the Central People’s Government of the People’s Republic of China and 31 official government websites of Chinese provincial units. In the site selection, the crawl uses the keyword search method to search, set the keywords as "pollution", "environment", and "ecology", crawl the policies published from January 1, 2008, to December 31, 2019, and obtain data in total 247,315, and 13429 related policies for the environmental regulation of the pig industry were obtained after screening, and the screening steps are shown in Table 2.

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Table 2. Screening steps of environmental regulation policies.

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Through the previous policy effectiveness evaluation, the results are shown in Fig 4.

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Fig 4. Trends in the effectiveness of China’s pig industry environmental regulation policies.

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In general, the effectiveness of environmental regulation policies for the pig industry began to increase substantially after 2013. Although it declined in 2018, it has reached a high level. It is generally believed that environmental regulation for the pig industry has been gradually strengthened since the State Council issued the Livestock and Poultry Scale Pollution Prevention Regulation in 2013. With the revision of the "Environmental Protection Law" in 2015 and the introduction of the "Guiding Opinions on Promoting the Adjustment and Optimization of the Distribution of Pig Production in Southern Water Net Region " in 2016, the environmental regulation of the pig industry has reached a new height [24, 25]. The effect of the pig industry environmental regulation policy estimated in this paper is the same as this trend, and it can be used as the main indicator to measure the intensity of environmental regulation. Comparing the composition of the effectiveness of environmental regulation policies, the policy feedback and policy objectives are significantly higher than the policy measures and policy intensity. The main reason for this may be because the new environmental protection law specifically strengthens the responsibility for environmental protection at all levels of government. To meet this standard, environmental regulatory policies need not only to refine regulatory goals but also to clarify the responsible units for each objective goal, so that the promotion of policy goals and policy feedback is significantly higher than other components of the effectiveness of environmental regulation policy effectiveness.

3.2.3. Mediator variable: Herd structure.

The herd structure includes three main parts: pigs, sows, and finishing pigs. Gao Y et al. [26] take the sows as the core, construct the pig group number to measure the herd structure of the farm, set the number of pig groups as the ratio of the produce time of the pigs in the corresponding barn to the reproduction rhythm, where the reproductive rhythm involves multiple indicators such as the number of farrowed sows, the number of pregnant sows, the number of sows, the number of suckling piglets, the number of weaning piglets, and the number of fattening pigs. Although this method can effectively identify the herd structure, it is more suitable for the internal production management of the main produce subject due to the complexity of calculation and the short time interval of data requirements. Based on the core definition of the herd structure, this article uses the proportion of the sows to the total sows and fattening pigs as a specific indicator to describe the herd structure for industrial level analysis. The calculation method is as follows.

(6)

Among them, Sows is the number of stock sows at the end of the year, and Pigs is the number of stock pigs at the end of the year. The above data are from the China Animal Husbandry Statistical Yearbook.

3.2.4. Control variables.

In neoclassical economics, the production of products is related to the demand of the product market and the price of the factor market. Therefore, this paper sets control variables from the above two perspectives. Since the market demand for pigs cannot be obtained directly, this paper selects and uses the market pig price as a proxy variable to measure demand for analysis and the factors of pig production are divided into three parts: land, labor, and capital. Select the 50 kg pig column price, land cost, labor cost, and material service fee in the China National Compilation of Cost and Income of Agricultural Products as specific indicators.

The theory of external shocks holds that policy changes are external shocks that affect production. However, for pig production in China, the epidemic situation is also an important external impact. Especially, the outbreak of African swine fever in China in 2019 led to a sharp drop in China’s production capacity. In order to eliminate the influence of this factor on the regression results, we set a virtual control variable ASF to indicate whether there is an African swine fever epidemic. When the variable ASF is 0, there is no African swine fever epidemic, and when the variable ASF is 1, there is an African swine fever epidemic.

In addition, because the China National Compilation of Cost and Income of Agricultural Products does not include statistics on the cost and benefit of Tibetan pigs, and the data for Beijing and Tianjin in 2019 are missing. Therefore, in addition to Beijing, Tianjin, and Tibet, data from 28 provinces in China from 2008 to 2019 were selected for analysis. We use the 2008 CPI as the base period to reduce the price-related data. The statistical description results of each variable after reduction are shown in Table 3.

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Table 3. Selection of indicators for the variables of the empirical analysis.

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4.1. Pre-regression test

Panel data analysis requires data to be stable to ensure that there is no spurious regression in the regression results. Commonly used detection methods include Harris-Tzacalis(HT) test, Levin-Lin-Chu(LLC) test, and Im-Peraran-Shin(IPS) test, respectively for the short panel, long panel, and less samples [27]. Therefore, this article is subject to HT test and IPS test. The specific test results are shown in Table 4.

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Table 4. Unit root test results.

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According to the results of the HT test, the lnSzcl, lnHjgz_t, lnYzjg_t and lnRgcb did not pass the unit root test, that is, the data is non-stationary, and there may be spurious regression in the direct regression analysis. The existing methods include differential processing and cointegration test. Because the differential processing will change the original economic meaning of data, this paper gives priority to the cointegration test Commonly used cointegration test methods include the KAO test, Pedroni test, and WesterLund test. The specific results are shown in Table 5.

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Table 5. Cointegration test results.

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According to the results of the cointegration test, the three test results all show that the variables of the econometric model have a cointegration relationship, cointe-grated data can be directly regressed without spurious regression [28].

4.2. The impact of environmental regulations on pig production

System GMM estimation requires the Sargan test (over-identification) and the Abonda test (sequence correlation), the two-stage system GMM estimation is selected according to the test results, as shown in Regression 2. In the Regression 2, the coefficient of the lnSzjg_t is -0.0567, that is, the slaughter of pigs in the t period will increase with the decrease in the price of slaughter, which is inconsistent with the actual production, which may be caused by the inversion of cause and effect. Zhou J et al. [29] come to a similar view when analyzing the fluctuations in pig production, and analyze the previous period’s price as an instrumental variable. This paper refers to this setting, setting lnSzjg_t as an endogenous variable and lnSzjg_t-1 as an instrumental variable. In order to avoid the endogenous problem between environmental regulations and the slaughter of pigs, the method of introducing lnSzjg_t-1 is used for reference to construct instrumental variables of environmental regulations, variable lnHjgz_t is lagging processing, and lnHjgz_t-1 is used as an instrumental variable for analysis. In order to test the hysteresis of the impact of environmental regulations on pig production, the variable lnHjgz_t-2 is specially introduced, Regression 3 is constructed, and test the nonlinear impact of environmental regulations in Regression 4 and 5. The regression results are shown in Table 6.

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Table 6. Empirical analysis results of the impact of environmental regulations on pig production.

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In Regression 3, the regression coefficient of variable lnSzcl_t−1 is 0.7136, and it is significant at the 1% level, indicating that the pig production in the t period is affected by the pig production in the t-1 period, that is, there is “inertia” in pig production. From the perspective of capital, Wang G et al. [30] believe that the “inertia” is due to the entry and exit barriers of thebehavior of the producers. The regression coefficients of variables lnWzf_t and lnRgcb_t are not significant below the 5% level. Variable lnSzjg_t−1 is significantly positive at the 10% level, and variable lnTdcb_t is significantly negative at the 1% level, indicating that the slaughter of pigs is affected by land costs and price expectations. But it is not affected by material service fees and labor costs. This result verifies the view put forward by Wang H et al. [31] that good price expectations and stable cooperation are positively affecting the slaughter of pigs. The coefficient of the variable ASF is -0.1106, and it is significant at the 1% level. The outbreak of African swine fever will reduce the number of pigs for slaughter by 11.06%. The coefficients of variables lnHjgz_t−1 and lnHjgz_t−2 are 0.0556 and -0.0431, respectively, which are both significant at the 5% level, which proves Hypothesis 1. In Regression 4, the regression coefficients of variable and variable lnHjgz_t−1 are not significant at the 5% level. In Regression 5, the regression coefficients of variable and variable lnHjgz_t−2 are 0.0642 and -0.9653, respectively, and are significant at the 1% level. Combined with the regression coefficients of variables lnHjgz_t−1 in Regression 3, it can be seen that there is a lag effect in the impact of environmental regulations on the slaughter of pigs. That is, in the short term, the strengthening of environmental regulations will increase the slaughter of pigs in short term, but in the long term it will show a positive U-shaped relationship. When the intensity of environmental regulations is lower than 2286.50, the hysteresis effect of environmental regulations is shown to inhibit the slaughter of pigs. When the intensity of environmental regulations is higher than 2286.50, the hysteresis effect of environmental regulations will also increase the slaughter of pigs. When the intensity of environmental regulation is low, environmental regulation will be strengthened through policies such as “prohibition” and “restriction” of produce. In the short term, the production capacity of pigs will be cleared, and the producers will produce a large number of pigs for slaughter, and short-term supply will increase. However, with the reduction of pig production capacity, long-term pig production has been insufficient, showing a long-term inhibitory effect on production. When the environmental regulation is higher than the critical value, the environmental regulation can improve the production efficiency of the producers through the innovation compensation effect, showing the production incentive effect during the production period.

4.3. Analysis of mediating effect of herd structure

To test Hypothesis 2 and Hypothesis 3, the mediation effect model constructed above is used to test the mediation effect of the pig herd structure in the relationship between environmental regulation and pig production, and to control other factors that affect pig production. Due to the lag effect of environmental regulation on pig production, the variables lnHjgz_t and lnHjgz_t−1 are used in the regression model to perform regression to test the mediating effect of environmental regulation at the stage difference. In order to avoid the mutual cause and effect between the herd structure and the lnYzjg_t slaughter of pigs, lnYzjg_t is processed afterwards, and the system GMM is estimated with lnYzjg_t-1 as an instrument variable. The results are shown in Table 7.

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Table 7. Optimal herd structure and U-shaped moderating effect analysis results.

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In Regression 6, the coefficients of the variable lnHjgz_t and the variable lnHjgz_t−1 are 0.0186 and 0.0371 respectively, and both are significant at the 1% level, indicating that there is a hysteresis effect in the impact of environmental regulations on the herd structure, and it is necessary to test whether there is a non-linear effect in stages, and construct Regression 7 and Regression 8. In Regression 7, the coefficients of the variable and the variable lnHjgz_t are 0.0267 and -0.3607, respectively, and both are significant at the 1% level. Comparing the coefficients of the variable and the variable lnHjgz_t−1 in Regressions 8, it can be seen that the impact of environmental regulations on the herd structure is U-shaped. And with the increase of time, the marginal impact of environmental regulations on the aquaculture structure will increase, but it still shows a U-shaped relationship, that is, with the increase of time, the marginal impact of environmental regulations on the aquaculture structure will gradually enlarge. In Regressions 6, 7, and 8, the coefficients of the variable ASF are always positive and significant at the 5% level, indicating that the farmers will give priority to reducing pigs when reducing production capacity after the outbreak. This result also provides factual support for the assumptions of constructing the model.

According to the regression coefficients of variable lnYzjg_t-1 and variable in Regression 9 and Regression 10, we can see that there is a non-linear relationship between the herd structure and the slaughter of pigs. Therefore, further analysis is based on Regression 10. In Regression 10, the coefficients of the variable and the variable lnYzjg_t-1 are both negative and significant at the 1% level, and the variable lnYzjg_t-1 has an inverted U-shaped relationship with the variable lnSzcl_t, and its symmetry axis is -2.2146. That is, when the herd structure level is 0.1092, the slaughter of pigs reaches a maximum value, and there is an optimal herd structure. Hypothesis 2 is proved. Only analyzing the optimal herd structure has limited guiding effect on policy regulation. It is necessary to conduct a comparative analysis based on the current status of pig herd structures in various regions. The results are shown in Fig 5.

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Fig 5. Schematic diagram of adjustment of herd structure in various provinces.

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Comparing the herd structure in the existing provinces in China, in 2018, only Liaoning, Inner Liaoning, Hainan and Xinjiang are located on the right side of the symmetry axis of the inverted U-shaped curve, and the proportion of pig production needs to be adjusted appropriately. The remaining provinces selected for the sample are all located below the optimal herd structure, and the proportion of sows in the stock should be appropriately increased to ensure pig production.

Combining Regression 7 and Regression 10, we can see that there is a U-shaped relationship between environmental regulations and herd structure, and there is an inverted U-shaped relationship between herd structure and pig production, that is, the herd structure has a mediating effect in the impact of environmental regulations on pig production. Hypothesis 3 is proved. According to the regression coefficient analysis, it is found that when the coefficient efficiency of the variable lnHjgz_t is 11.21, the mediation effect of the herd structure will promote the slaughter of pigs. Combined with the current situation of environmental regulations, it can be seen that under the current intensity of environmental regulations, this mediating effect will only amplify the promotion of environmental regulations on the slaughter of pigs.

4.4. Further analysis: Early warning of production fluctuation based on herd structure

In order to further analyze whether the herd structure can warn the fluctuation of pig slaughter, this paper first conducts a feasibility analysis from two aspects of the forecasting ability and the index setting process, and compares the estimation methods of the pork-grain ratio, and gives an early warning interval.

In terms of predictive ability, pig stock and sow stock are used to predict the short-term and mid-to-long-term slaughter of pigs, respectively. L.M. Plà et al. [32] build a Markov model based on the herd structure to provide production decisions for pig companies. In addition, in Regression 9, the significant difference between the variable lnYzjg_t-1 and the variable lnYzjg_t indicates that the herd structure will affect the number of pigs that are lagging in the first period. It can be considered that the herd structure has certain predictability in identifying fluctuations in the slaughter of pigs. Reproductive sows and pigs have decreased in the same proportion. For example, affected by African Swine Fever, China’s pigs and reproductive sows decreased by 38.7% and 37.4% respectively in August 2019 [33]. The herd structure has no significant impact, but it still leads to a shortage of pigs in the market. It has no significant impact on the overall herd structure, but it still leads to a shortage of pigs in the market. The herd structure can be used as a supplementary monitoring indicator to stabilize the supply of pigs, combined with the rate of change in the stock of reproductive sows, to provide early warning of fluctuations in pig production. Among them, the rate of change in the stock of reproductive sows focuses on predicting whether the supply of pigs can meet market demand, and the herd structure focuses on whether the supply of pigs will produce large supply fluctuations. In the indicator setting process, this paper compares the process of setting the pork-grain ratio as an early warning indicator for pig price fluctuations.

Combining existing studies, it is found that as early as 1985, there was research and analysis of the impact of the pork-grain price ratio. By 2020, a relatively reliable forecasting system and method have been formed. For example, Chen Juhong [34] uses the new multiple range test method to test the impact of the pork-grain price ratio and pork price fluctuations and sets an early warning interval of 5.0 to 5.5. Compared with the research on the pork-grain ratio, there are less researches on the herd structure, so this paper will only make a brief analysis here. According to the stock of reproductive sows and pigs monitored by the fixed observation points of the Ministry of Agriculture, the quarterly herd structure in China is estimated. The specific results are shown in Fig 6.

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Fig 6. Trend of China’s pig price and herd structure change and HP breakdown.

https://doi.org/10.1371/journal.pone.0266687.g006

It can be seen from the figure that there are obvious seasonal fluctuations in the herd structure and the number of pigs. The HP filtering method is used to remove seasonal fluctuations, and the herd structure Yzig* and the slaughter of pigs Szcl* after removing the seasonal fluctuations are obtained. Taking into account the growth cycle of fattening pigs and reproductive sows, half a year and one year are selected as the short-term and long-term time ranges for the analysis of slaughter fluctuations, and the difference between short-term and long-term fluctuations in slaughter changes is constructed as , where * means removing seasonal fluctuations, Szcl_t+4 is the amount of pigs to be slaughtered one year later, Szcl_t+2 is the output of pigs after six months. According to the threshold model structure, there is a breakpoint when the herd structure is 0.0980, and the variable Yzjg* in the overall regression result will positively affect the variable Dis* at the 5% significance level. According to the calculation of the coefficient, when the variable Yzjg* is 0.1058, the variable Dis* is 0, that is, there will be no long-term and short-term fluctuations. Early warning is carried out according to the threshold value, and the early warning interval is shown in Table 8.

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Table 8. Early warning interval of herd structure.

https://doi.org/10.1371/journal.pone.0266687.t008

When the herd structure is less than or equal to 0.0980, although the pig industry can guarantee short-term pig supply, there is a long-term supply shortage risk; when the herd structure is greater than 0.0884 but less than or equal to 0.1135, the pig industry can maintain a stable supply; when the herd structure is greater than or equal to 0.1135, the production capacity of the pig industry will increase in the long term, but it may face the risk of short-term supply shortage.

5.1. Conclusions and contributions

Scholars based on the static point of view believe that environmental regulations will increase the production cost of aquaculture enterprises and reduce pollution by reducing production. However, as the main source of meat products in China, insufficient supply will cause a series of social problems. In Porter’s hypothesis and innovation compensation theory, it is believed that environmental regulation can stimulate the innovation ability of enterprises, realize the compensation for the cost of pig production enterprises, and thus stabilize production. Under the two theories, there is no clear basis for the formulation of environmental regulation policies for pig farming. At this time, studying the impact of environmental regulation on pig production is helpful to formulate more accurate environmental regulation policies. We use the organic composition theory of capital for reference, take the community structure as the breakthrough point, analyze the impact of environmental regulation on pig production, and whether we can adjust the impact of environmental regulation on pig production through the community structure, and forecast the fluctuation of pig production in a certain period. The study found that the herd structure is affected by environmental regulations and has a significant impact on pig production. The herd structure can be used as a supplementary monitoring indicator to stabilize the supply of live pigs, and can be used to warn the fluctuation of pig production in combination with the change rate of sow. In the short term, strengthening environmental protection regulations can increase the number of live pigs on the market, but in the long term, the impact of environmental regulations on the number of live pigs on the market is U-shaped. The theoretical and empirical contributions of this paper are as follows:

First, our research complements the environmental regulation theory and applies it to the pig market in China. In the existing regulation theory, environmental regulation mainly includes following the cost theory and Porter hypothesis. This paper uses Marx’s organic composition of capital for reference, and takes the herd structure as an intermediary, and incorporates it into the model of environmental regulation affecting pig production. The results of empirical analysis show that the herd structure is affected by environmental regulations and will also affect pig production. This discovery provides a new starting point for the formulation of environmental regulation policies, namely the industrial adjustment method based on the herd structure. The method can slow down the inhibition effect of environmental regulations on production by adjusting the proportion of sows and fattening pigs in the pig industry, and give consideration to environmental protection and pork supply.

Second, our research verified the regulation and early warning function in the production of live pigs with herd structure. At present, the existing pig early warning system is based on the pig-to-grain ratio. In the “Implementation Plan for Regulation and Control of Pig Production Capacity (Provisional)” dated September 23, 2021, the core regulation index is the change rate of sows capable. However, the supply early warning based on the change rate of sows capable can only predict the change of absolute supply. This system is not sensitive to fluctuations in supply, especially after multiple iterations, the early warning effect on fluctuations is often unrealistic. Based on the analysis of herd structure as an intermediate variable, this paper shows that under a certain level of environmental regulation, there is an optimal herd structure to maximize the slaughter of live pigs, and further analysis results show that there is no significant fluctuation in the slaughter of live pigs corresponding to a specific range of herd structure. The early warning of herd structure is actually a balance between short-term supply and long-term supply of live pigs, which is more advantageous than the existing early warning system in the aspect of early warning supply fluctuation. Based on the above viewpoints, the development of pig industry can be adjusted by adjusting the macro herd structure. For example, the proportion of sows capable in the macro herd structure can be increased by increasing the purchase and elimination subsidies of sows capable by farmers, so as to realize the expanded production of pig production.

Third, our research combed the environmental regulation policies of China’s pig industry from 2008 to 2019, and based on rational policy assessment, constructed the effectiveness indicators of environmental regulation policies only for pig industry from the four angles of objective, measure, feedback and intensity. This attempt not only effectively quantifies the intensity of environmental regulation policies, but also provides a reference for analyzing the policy effectiveness of specific industries.

5.2. Limitations and future research directions

This article has the following short comings: First, only the panel data of a single country, China, are used, and it is worthwhile to further explore the industrial situation of countries with high degree of pig industrialization, such as the United States, Germany, Denmark, etc. Second, due to the limitation of data availability, in this paper, we use virtual variables as the epidemic situation in pig production environment. Although we consider the impact of external shocks, this proxy variable still has limitations and needs further improvement. Third, this paper only focuses on the intermediary role of herd structure in environmental regulation affecting pig production, but this research has not been carried out on the existence and mechanism of other intermediaries. Future research can further explore the intermediary role between regulation of environment and pig production.