The impact of environmental regulations on enterprise production——Based on the production game model

doi:10.21203/rs.3.rs-3993323/v1

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The impact of environmental regulations on enterprise production——Based on the production game model

https://doi.org/10.21203/rs.3.rs-3993323/v1

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As an integral part of the modern environmental governance system, environmental regulations have the potential to alter the dynamics of competition and cooperation, resulting in a phenomenon known as the “relatively better” effect. In light of this phenomenon, we have developed a static game model based on incomplete information to analyze its implications. Through the exploration of Nash equilibrium, we have discovered that the "relatively better" effect allows environmentally regulated clean enterprises to transfer a portion of their costs to polluting enterprises. Consequently, clean enterprises experience lower financing costs compared to their polluting counterparts under environmental regulation conditions. This conclusion is supported by empirical analysis conducted using Chinese enterprise data. Furthermore, our research reveals that appropriately designed environmental regulations, including the intensity of regulation and the establishment of emission rights trading systems, can contribute to improving social distribution.

Environmental regulation

Relatively better

Game model

Enterprise behavior

Resource depletion and environmental pollution have become worldwide problems. How to correctly handle the relationship between resources environment and economic development is gradually becoming a hot spot in academic circles. As a new type of government intervention, environmental regulation provides a new method for strengthening environmental protection and promoting green development. This environmental regulation requires enterprises to strengthen the treatment of pollutants and reduce pollution emissions, which may have an impact on the production and operation of enterprises (Ye and Lin 2020; Geng et al. 2023). On the one hand, environmental regulation is a new constraint on the production decision-making of enterprises. Enterprises must increase environmental protection’s investment, which may lead to the increase of enterprise costs and decrease of enterprise profit. On the other hand, properly environmental regulations would stimulate enterprises to carry out technological innovation, which is helpful for enterprises to improve product production efficiency and market competitiveness (Porter, 1991).

In addition, there is a special situation where enterprises actively seek regulation in the market. Because in this way, some enterprises could legitimately use regulatory provisions to attack their opponents. Although the regulated enterprises also face compliance costs. Once the regulation can give competitors greater compliance costs, the enterprises with lower compliance costs would benefit from the regulation. Therefore, environmental regulation is equivalent to administrative license given to clean enterprises, enabling these clean enterprises to obtain benefits (Leard and McConnell 2021). In the situation, a certain external regulation has changed the relative situation and made some enterprises better. We refer to this situation as a “relative better” phenomenon caused by regulation. In the phenomenon of “relative better”, some external regulation changes the relative situation faced by various market entities, causing some entities to improve. Therefore, seemingly unfavorable regulations may also bring unexpected benefits to the regulated objects.

At the same time, academic research on environmental rules is basically based on empirical research and lacks the corresponding theoretical models. (Sun et al. 2013; Xiao 2022; Lu and Zhang 2023; Geng et al 2023). Based on this, We try to start with theoretical construction and explore the “relatively good” phenomena that we are concerned about. Our innovations are mainly as follows: Firstly, the impact of environmental regulation on enterprise behavior is fully considered in the theoretical model, which enriches and expands the theoretical research in the existing literature. Secondly, we notice that using only one policy tool is difficult to achieve the dual goals of environmental protection and enterprise’s development. Therefore, we consider the impact of the two regulatory tools of carbon emission control and carbon tax in the analysis framework. Thirdly, we optimize the setting of the emission reduction cost function and endogenize the emission trading price. At the same time, we focus more on the individual profits of enterprises and explore the different impacts of environmental regulations on clean enterprises and polluting enterprises. Finally, we construct a comprehensive measure method of environmental regulation intensity that considers both pollution discharge indicators and economic input indicators. Based on this method, we explore the impact of environmental regulation intensity on the financing costs of different enterprises.

The follow-up arrangement of this paper is as follows: The second part sorts out the research status from existing literature and reveals the possible impact of environmental regulation on enterprises. The third part analyzes the decision-making behavior and enterprises’ cost situation under environmental regulation. The fourth part conducts a brief empirical analysis using Chinese data. The last is the research conclusion and enlightenment.

In recent years, countries have vigorously advocated green development and paid more attention to the ecological environment. The research of environmental regulation is actively advancing in academic circles. Porter (1991), Porter and Linde (1995) analyzed the role of environmental regulation from a dynamic perspective. They believed that appropriate environmental regulation could stimulate the green development of enterprises. Sun et al. (2020), and Shi et al. (2022) verified this statement through empirical analysis of polluting enterprises. Therefore, increasing the intensity of environmental regulation can effectively reduce carbon emissions (Tan et al. 2013; Hu and Xiong 2021; Gu 2022). On the contrary, some scholars pointed out that the introduction of environmental regulations can exert administrative pressure on enterprises(Dam and Heijdra 2011). These enterprises have to restrain their own pollution discharge behavior under administrative pressure (Vollaard 2017; Yang et al. 2021). The pressure from these environmental regulations could bring a significant negative impact on air pollution emissions (Zhao et al. 2018; Xu et al. 2021).

In addition, some scholars have considered the economic consequences of environmental regulation. They found that environmental regulation policies can effectively promote enterprise R&D activities and improve energy efficiency (Mandal’s 2010; Lanoie et al. 2011; Li et al. 2020). At the same time, environmental regulations could stimulate enterprises with a high degree of environmental protection to enter the market, and force high-polluting and high-emission enterprises to exit the market (Du et al. 2020; Li et al. 2021). Because, the introduction of environmental regulations would significantly increase the entry cost and the capacity adjustment cost (Ryan 2012). Accordingly, environmental regulation was introduced into the theoretical model as an impact factor of enterprise production costs (Millimet and Roy 2016; Tanaka et al. 2020).

However, most of the above studies belong to the category of quasi-natural experimental research. They mainly focused on exploring the effect of specific environmental regulation policies (Keiser and Shapiro 2019). There were few scholars involved in the analysis of the strategic behavior of enterprises in response to environmental regulation. Although Catola and D'Alessandro (2020), Deng et al. (2022) analyzed the social welfare issues caused by enterprise strategic ehavior under environmental regulation, they lacked the exploration of enterprise costs. Here some publications studied environmental regulation and discussed the cost of enterprises. But these discussions are not in-depth and not systematic enough (Yu and Sun 2017). Therefore, we establish the model to fill this research gap.

3.1 Model building

According to the relevant research, environmental regulation policies can be divided into three types: command-control type, market incentive type, and information disclosure type (Li and Shen 2008). In this study, we mainly focus on the control of total carbon emissions ($T$) under the carbon emission trading mechanism, which is a command-control type and market incentive type. Usually, the government’s choice of $T$ is not the result of considering social welfare, but the result of weighing economic growth and environmental protection. Under the goal of green development, government departments are formulating the total carbon emission control target $T$. But whether the choice of $T$ improves social welfare is still unknown. In other words, it is difficult to consider multiple regulatory objectives by only adjusting one exogenous regulatory variable $T$. To solve this problem, carbon tax is levied on the enterprises’ actual emission under the condition of total carbon emission control. The tax rate is $\tau ,\tau \ge 0.$

Assume that the trading price of emission rights is$\theta , \theta \ge 0$. $r$ is affected by the total amount of carbon emissions $T$, the carbon tax rate $\tau$, and the supply and demand relationship in the carbon emissions trading market. Let the initial emission quota of enterprise $i$ be ${t}_{i}$. The enterprise $i$ can use emission rights for production or sell them with a quantity of ${q}_{i}({q}_{i}\le {t}_{i})$ in the emission rights trading market

$$\underset{{y}_{i},{r}_{i},{q}_{i}}{\text{max}}{\pi }_{i}\left({y}_{i},{r}_{i},{q}_{i}|{Y}_{-i},\theta \right)={y}_{i}{p}_{i}\left({y}_{i};{Y}_{-i}\right)+\theta {q}_{i}-{c}_{i}k{q}_{i}{r}_{i}^{2}-\tau k{y}_{i}\left(1-{r}_{i}\right)$$

s.t. $k{y}_{i}\left(1-{r}_{i}\right)\le {t}_{i}-{q}_{i}$

where the decision variables include the output ${y}_{i}$, the emission reduction ratio ${r}_{i}$ and the emission trading volume ${q}_{i}$. ${p}_{i}\left({y}_{i};{Y}_{-i}\right)$ is the product price of the enterprise $i$. $Y$ represents the total output of the industry, and ${Y}_{-i}$ represents other enterprises’ output except the enterprise $i$. $k$ is the industry pollution coefficient, and satisfies $k>0$, which represents the emission by producing per unit of output without emission reduction. The total emission of producing ${y}_{i}$ output is $k{y}_{i}$. At the same time, the emissions’ share ${r}_{i}$ of the enterprise $i$ can be reduced by improving equipment, upgrading technology, etc, $0\le {r}_{i}\le 1$. The enterprise $i$ chooses the optimal ${r}_{i}$ according to its own profit maximization problem. The actual emission is $k{y}_{i}\left(1-{r}_{i}\right)$, and the carbon tax paid is $\tau k{y}_{i}\left(1-{r}_{i}\right)$. Emission reduction needs to pay a certain cost. For the same enterprise, it is difficult to achieve high emission reduction. High emission reduction would result in higher unit emission reduction costs (Levi and Nault, 2004; Subramanian et al., 2007). Therefore, we set the total emission reduction cost as ${c}_{i}k{y}_{i}{r}_{i}^{2}$, ${c}_{i}>0$.

According to the total emission reduction cost setting, the unit emission reduction cost of an enterprise is mainly related to the proportion of enterprise’s emission reduction. Here the unit emission reduction cost is ${c}_{i}{y}_{i}$.

To reflect the mutual competition between enterprises in the same market, the mutual impact of enterprise decision-making behavior must be considered. According to the conventional thinking of industrial organization research, we set the following price function:

$${p}_{i}\left({y}_{i};{Y}_{-i}\right)=\alpha -\beta {y}_{i}-\delta \beta {Y}_{-i}$$

where $0<\delta <1$ indicates the degree of product differentiation. $\delta$ represents the degree of homogeneity and differentiation. Both $\alpha$ and $\beta$ are known parameters greater than zero.

Based on the complementary relaxation properties, the constraint condition needs to be a tight constraint to obtain the maximum value of the formula (1). So, we have $e{q}_{i}\left(1-{x}_{i}\right)={s}_{i}-{t}_{i}$. Combining the formula (2) and the tight constraint, the formula (1) can be simplified as follows:

$$\underset{{y}_{i},{r}_{i}}{\text{max}}{\pi }_{i}\left({y}_{i},{r}_{i}|{Y}_{-i},\theta \right)={y}_{i}\left(\alpha -\beta {y}_{i}-\delta \beta {Y}_{-i}\right)+\theta {t}_{i}+k{y}_{i}\left[-{c}_{i}{r}_{i}^{2}+\left(\theta +\tau \right){r}_{i}-\left(\theta +\tau \right)\right]$$

s.t. $0\le {r}_{i}\le 1$

3.2 Market equilibrium

In the formula (3), ${y}_{i}$ and ${r}_{i}$ are decision variables, where ${r}_{i}$ is only related to the part “$-{c}_{i}{r}_{i}^{2}+\left(\theta +\tau \right){r}_{i}-\left(\theta +\tau \right)$”. To obtain the maximum value of the formula (3), ${r}_{i}=\frac{\theta +\tau }{2{c}_{i}}$ is required. When $0\le \theta +\tau \le 2{c}_{i}$, we have $0\le {r}_{i}\le 1$, ${r}_{i}$ corresponds to the internal solution. When $\theta +\tau >2{c}_{i}$, ${r}_{i}=1$, the formula (3) has a corner solution. Therefore, the following two situations are discussed:

①When $0\le \theta +\tau \le 2{c}_{i}$, the solution of the formula (3) satisfies ${r}_{i}=\frac{\theta +\tau }{2{c}_{i}}$. Substituting ${r}_{i}$ back to the formula (3), then the maximization problem corresponds to the Lagrange equation is:

$${\mathcal{L}}_{i}={y}_{i}\left(\alpha -\beta {y}_{i}-\delta \beta {Y}_{-i}\right)+\theta {t}_{i}-k{y}_{i}\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{i}}\right)$$

First-order condition:

$$\frac{\partial {\mathcal{L}}_{i}}{\partial {y}_{i}}=\alpha -2\beta {y}_{i}-\delta \beta {Y}_{-i}-k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{i}}\right)=0$$

From the formula (5):

$${y}_{i}=\frac{\alpha -\delta \beta Y-k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{i}}\right)}{\left(2-\delta \right)\beta }$$

②When $\theta +\tau >2{c}_{i}$, ${r}_{i}=1$. From ${q}_{i}={t}_{i}-k{y}_{i}\left(1-{r}_{i}\right)$, ${q}_{i}={t}_{i}$. Substituting it back into the formula (3), the Lagrange equation corresponding to the maximization problem is:

$${\mathcal{L}}_{i}={y}_{i}\left(\alpha -\beta {y}_{i}-\delta \beta {Y}_{-i}\right)+\theta {t}_{i}-k{c}_{i}{y}_{i}$$

First-order condition:

$$\frac{\partial {\mathcal{L}}_{i}}{\partial {y}_{i}}=\alpha -2\beta {y}_{i}-\delta \beta {Y}_{-i}-k{c}_{i}=0$$

From the formula (8):

$${y}_{i}=\frac{\alpha -\delta \beta Y-{kc}_{i}}{\left(2-\delta \right)\beta }$$

Notice that the second-order condition $\frac{{\partial }^{2}{\mathcal{L}}_{i}}{\partial {y}_{i}^{2}}=-2\beta <0(\beta >0)$ always satisfy for the internal solution ($0\le \theta +\tau \le 2{c}_{i}$) and the corner solution ($\theta +\tau >2{c}_{i}$). So, the second-order condition of the formula (3) always holds. Therefore, according to the above analysis, we can know that there are two solutions to the profit maximization problem of the enterprise $i$, which are:

①When $0\le \theta +\tau \le 2{c}_{i}$, there is an internal solution.

$${y}_{i}=\frac{\alpha -\delta \beta Y-k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{i}}\right)}{\left(2-\delta \right)\beta }, {r}_{i}=\frac{\theta +\tau }{2{c}_{i}}, {q}_{i}={t}_{i}-k{y}_{i}\left(1-{r}_{i}\right)$$

②When $\theta +\tau >2{c}_{i}$, there is a corner solution.

$${y}_{i}=\frac{\alpha -\delta \beta Y-{kc}_{i}}{\left(2-\delta \right)\beta }, {r}_{i}=1, {q}_{i}={t}_{i}$$

Noted that the solution obtained above is not the final solution to the enterprise profit maximization problem.

On the one hand, the $Y$ on the right side is the summation item of ${y}_{i}$ in the formulas (10) and (11). In other words, ${y}_{i}$ needs to satisfy the condition $Y={\sum }_{i=1}^{n}{y}_{i}$. On the other hand, $\theta$ is regarded as an exogenous variable in the above solution process. But in fact,$\theta$ is determined by the supply and demand of the carbon emission trading market under the given conditions of $T$ and $\tau$.

Generally speaking, environmental regulation becomes stricter with the decrease of total emission quota $T$. Because the supply of emission rights is in short supply, which may drive up the emission trading price $\theta$. From an industry perspective, emissions trading must meet cap constraints and transaction constraints:

$$\sum _{i=1}^{n}{t}_{i}=T\ge 0, \sum _{i=1}^{n}{q}_{i}=0$$

where $\sum _{i=1}^{n}{t}_{i}=T$ represents the total amount constraint of emission allowances. $\sum _{i=1}^{n}{q}_{i}=0$ represents the transaction constraint that the quantity of buying and selling is equal.

From the formulas (10) and (11), whether this optimal solution belongs to the internal solution or the corner solution depends on the relationship between $\theta +\tau$ and $2{c}_{i}$. When ${c}_{i}={c}_{j}$, the two enterprises belong to the same solution. Whether the solution belongs to the internal solution or the corner solution. From the formulas (10) and (11), we can deduce that as long as ${c}_{i}={c}_{j}$, then ${y}_{i}={y}_{j}$, ${r}_{i}={r}_{j}$ and ${t}_{i}-{q}_{i}={t}_{j}-q$.

Based on the above analysis, the main work is to analyze different types of enterprises, and it is not necessary to conduct separate investigations for all enterprises. From the setting of emission reduction costs, the unit emission reduction cost of the same proportion is only related to the parameter $c$ for different enterprises. The smaller $c$ reflects the more advanced pollution control technology of enterprises and vice versa. To simplify the model, we assume that there are only two values of $c$. According to the difference of $c$, we divide enterprises into two types: clean enterprises ($c$ is relatively small, denoted as ${c}_{l}$) and polluting enterprises ($c$ is relatively large, denoted as ${c}_{h}$). Assume that there are $n\ge 2$ enterprises in total, among which, there are $m\ge 1$ clean enterprises and $n-m\ge 1$ polluting enterprises. Here we do not consider the entry and exit of enterprises caused by environmental regulation, so we regard $n$ and $m$ as exogenous variables. All enterprises make decisions about production and emission reduction under the given environmental regulations and the number of enterprises.

As mentioned above, the formulas (10) and (11) are not the final solution to the enterprise profit maximization problem. According to the conditions of $0\le \theta +\tau \le 2{c}_{i}$ and $\theta +\tau >2{c}_{i}$ in the formulas (10) and (11), the final solution needs to be discussed in four cases, namely $\theta +\tau =0$, $0<\theta +\tau \le 2{c}_{l}$, $2{c}_{l}<\theta +\tau \le 2{c}_{h}$ and $\theta +\tau >2{c}_{h}$. Details are as follows:

①When $\theta +\tau =0$,combining with $\theta \ge 0$ and $\tau \ge 0$, we could get $\theta =\tau =0$. According to the solution process of the formulas (10) and (11), we can know that

$${y}_{i}=\frac{\alpha -\delta \beta Y}{\left(2-\delta \right)\beta }$$

There is no carbon tax collection and carbon emission trading. At the same time, there is no need to distinguish polluting enterprises from clean enterprises, $Y=n{y}_{i}$. Thus,

$${y}_{i}=\frac{\alpha }{\left[2+\left(n-1\right)\delta \right]\beta }, Y=n{y}_{i}=\frac{\alpha n}{\left[2+\left(n-1\right)\delta \right]\beta }$$

Here, all enterprises are not motivated to reduce emissions, so ${r}_{l}={r}_{h}=0$. Then the total emission quota is

$$T\ge nk{y}_{i}=\frac{n\alpha k}{\left[2+\left(n-1\right)\delta \right]\beta }\equiv \overline{T}$$

In this case, the environmental regulation is too loose to have any effect ($T\ge \overline{T}$).

②When $0<\theta +\tau \le 2{c}_{l}$, all enterprises correspond to internal solutions according to the formulas (10) and (11), then

$${y}_{l}=\frac{\alpha -\delta \beta Y-k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)}{\left(2-\delta \right)\beta }, {y}_{h}=\frac{\alpha -\delta \beta Y-k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{h}}\right)}{\left(2-\delta \right)\beta }$$

$${r}_{l}=\frac{\theta +\tau }{2{c}_{l}}, {r}_{h}=\frac{\theta +\tau }{2{c}_{h}}$$

Therefore, the total output is

$$Y=m\frac{\alpha -\delta \beta Y-k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)}{\left(2-\delta \right)\beta }+\left(n-m\right)\frac{\alpha -\delta \beta Y-k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)}{\left(2-\delta \right)\beta }$$

Further finishing is

$$\left(2-\delta \right)\beta Y=\alpha n-n\delta kY-mk\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)-(n-m)k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)$$

Simplifying the above formula to get:

$$Y=\frac{\alpha n-mk\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)-(n-m)k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)}{\left[2+\left(n-1\right)\delta \right]\beta }$$

Taking $Y$ back to ${y}_{l}$ and ${y}_{h}$, we get

$${y}_{l}=\frac{\alpha \left[2+\left(n-1\right)\delta \right]-\delta \left[\alpha n-mk\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)-(n-m)k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{h}}\right)\right]-k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)[2+(n-1\left)\delta \right]}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }$$

$${y}_{h}=\frac{\alpha \left[2+\left(n-1\right)\delta \right]-\delta \left[\alpha n-mk\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)-(n-m)k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{h}}\right)\right]-k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{h}}\right)[2+(n-1\left)\delta \right]}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }$$

Organizing the formula into:

$${y}_{l}=\frac{\alpha \left(2-\delta \right)+\left[\delta -2-\left(n-m\right)\delta \right]k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)+\left(n-m\right)\delta k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{h}}\right)}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }$$

$${y}_{h}=\frac{\alpha \left(2-\delta \right)+m\delta k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)+\left(\delta -2-m\delta \right)k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{h}}\right)}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }$$

Notice that in this case, the actual emissions of the industry will use up all the emission quotas. So, there will be no remaining emission rights. Otherwise, some enterprises are willing to sell the emission rights under the current trading price. Then, the trading price of emission rights will decrease until all emission rights are used up or $\theta +\tau$. Therefore,

$$T=mk{y}_{l}\left(1-{r}_{l}\right)+\left(n-m\right)k{y}_{h}\left(1-{r}_{h}\right)$$

which is

$$T=mk{y}_{l}\left(1-\frac{\theta +\tau }{4{c}_{l}}\right)+\left(n-m\right)k{y}_{h}\left(1-\frac{\theta +\tau }{4{c}_{h}}\right)$$

We have noticed that

$$\frac{\partial T}{\partial (\theta +\tau )}=-\frac{mk{y}_{l}}{4{c}_{l}}-\frac{\left(n-m\right)k{y}_{h}}{4{c}_{h}}<0$$

Therefore, we know

$$\underset{\_}{T}\equiv \left(n-m\right)k\left(1-\frac{{c}_{l}}{{c}_{h}}\right)\frac{\alpha \left(2-\delta \right)+\delta m{c}_{l}k+\left(-m\delta -2+\delta \right)(1-\frac{{c}_{l}}{2{c}_{h}})2{c}_{l}k}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }\le T\le \overline{T}$$

In this case, the intensity of environmental regulation is moderate. Clean enterprises and polluting enterprises will not sell all the emission allowances, but will choose to keep a part to meet their own production needs ($\underset{\_}{T}\le T\le \overline{T}$).

③When $2{c}_{l}<\theta +\tau \le 2{c}_{h}$, the clean enterprise corresponds to the corner solution, and the polluting enterprise corresponds to the internal solution, then

$${y}_{l}=\frac{\alpha -\delta \beta Y-{c}_{l}k}{\left(2-\delta \right)\beta }, {r}_{l}=1,{y}_{h}=\frac{\alpha -\delta \beta Y-k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{h}}\right)}{\left(2-\delta \right)\beta },{r}_{h}=\frac{\theta +\tau }{2{c}_{h}}$$

The equilibrium output is

$$Y=\frac{\alpha n-m{c}_{l}k-\left(n-m\right)k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{h}}\right)}{\left[2+\left(n-1\right)\delta \right]\beta }$$

$${q}_{l}=\frac{\alpha \left(2-\delta \right)+\left[\delta -2-\left(n-m\right)\delta \right]{c}_{l}k+\left(n-m\right)\delta k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{h}}\right)}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }$$

$${q}_{h}=\frac{\alpha \left(2-\delta \right)+\delta m{c}_{l}k+\left(-m\delta -2+\delta \right)k\left(\theta +\tau \right)\left(1-\frac{\theta +\tau }{4{c}_{h}}\right)}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }$$

In this case, the environmental regulations are relatively strict. The emission reduction ratio of clean enterprises reaches 100%, and all emission allowances are sold. Polluting enterprises may purchase emission rights or sell emission rights, depending on their initial emission quotas. But at least some polluting enterprises will purchase emission rights, otherwise the formula (2) is not satisfied.

④When $\theta +\tau >2{c}_{h}$, according to the formulas (10) and (11), all enterprises correspond to corner solutions. Then according to $\sum _{i=1}^{n}{q}_{i}=0$ and ${r}_{i}=1$, we can obtain $T={\sum }_{i}^{n}k{y}_{i}\left(1-{r}_{i}\right)=0$. Here, there will be no emissions, and there will be no emissions trading. Enterprises must reduce all emissions to zero. Therefore, the Lagrange function of the enterprise profit maximization problem is

$${\mathcal{L}}_{i}={y}_{i}\left(\alpha -\beta {y}_{i}-\delta \beta {Y}_{-i}\right)-{c}_{i}k{y}_{i}$$

Therefore, we can obtain

$${y}_{i}=\frac{\alpha -\delta \beta Y-{c}_{i}k}{\left(2-\delta \right)\beta }, Y=\frac{\alpha n-m{c}_{l}k-\left(n-m\right){c}_{h}k}{\left[2+\left(n-1\right)\delta \right]\beta }$$

We simplify the formula (30) into

$${y}_{l}=\frac{\alpha \left(2-\delta \right)+\left[\delta -2-\left(n-m\right)\delta \right]{c}_{l}k+\left(n-m\right)\delta {c}_{h}k}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }, {r}_{l}=1$$

$${y}_{h}=\frac{\alpha \left(2-\delta \right)+\delta m{c}_{l}k+\left(\delta -2-m\delta \right){c}_{h}k}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }, {r}_{h}=1$$

In this case, the environmental regulations are so strict that all enterprises cannot emit any emissions. The emission reduction ratio of all enterprises is 100% ($T=0$).

3.3 Equilibrium analysis

Based on the analysis of the above four situations, the carbon emission trading market is only meaningful in the case of ②③ ($0< \theta +\tau <2{c}_{h}$). Therefore, we limit the environmental regulation to the condition of $0< \theta +\tau <2{c}_{h}$, and further analyze the equilibrium output.

< 1 > Further analysis of the equilibrium output in Case ②:

$$\frac{\partial Y}{\partial \theta }=\frac{-mk\left(1-\frac{\theta +\tau }{2{c}_{l}}\right)-\left(n-m\right)k\left(1-\frac{\theta +\tau }{2{c}_{h}}\right)}{\left[2+\left(n-1\right)\delta \right]\beta }$$

$$\frac{\partial {y}_{l}}{\partial \theta }=\frac{\left(n-m\right)\delta k\left(\frac{\theta +\tau }{2{c}_{l}}-\frac{\theta +\tau }{2{c}_{h}}\right)+(\delta -2)k\left(1-\frac{\theta +\tau }{2{c}_{l}}\right)}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }$$

$$\frac{\partial {y}_{h}}{\partial \theta }=\frac{m\delta k\left(\frac{\theta +\tau }{2{c}_{h}}-\frac{\theta +\tau }{2{c}_{l}}\right)+(\delta -2)k\left(1-\frac{\theta +\tau }{2{c}_{h}}\right)}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }$$

From the analysis in Appendix A-1, we can know that $\frac{\partial Y}{\partial \theta }<0$, $\frac{\partial {y}_{l}}{\partial \theta }<0$, but $\frac{\partial {y}_{h}}{\partial \theta }$ may be positive or negative. At the same time, from the formula (22), we have

$$\theta =\frac{2{c}_{l}{c}_{h}}{m{y}_{l}{c}_{l}+\left(n-m\right){y}_{h}{c}_{h}}\left[m{y}_{l}+\left(n-m\right){y}_{h}-\frac{T}{k}\right]-\tau$$

$$\frac{\partial \theta }{\partial T}=-\frac{2{c}_{l}{c}_{h}}{k[m{y}_{l}{c}_{l}+\left(n-m\right){y}_{h}{c}_{h}]}, \frac{\partial \theta }{\partial \tau }=-1$$

Since ${c}_{l},{c}_{h}>0$, $m\ge 1$, $n-m\ge 1$,$k>0$, so $\frac{\partial \theta }{\partial T}<0$, $\frac{\partial \theta }{\partial \tau }<0$.

< 2 > Further analysis of the equilibrium output in the case of ③ ($2{c}_{l}<\theta +\tau \le 2{c}_{h}$):

$$\frac{\partial Y}{\partial \theta }=\frac{-\left(n-m\right)\left(1-\frac{\theta +\tau }{2{c}_{h}}\right)k}{\left[2+\left(n-1\right)\delta \right]\beta }$$

$$\frac{\partial {y}_{l}}{\partial \theta }=\frac{\left(n-m\right)\delta \left(1-\frac{\theta +\tau }{2{c}_{h}}\right)k}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }$$

$$\frac{\partial {y}_{h}}{\partial \theta }=\frac{\left(-m\delta -2+\delta \right)\left(1-\frac{\theta +\tau }{2{c}_{h}}\right)k}{\left(2-\delta \right)\left[2+\left(n-1\right)\delta \right]\beta }$$

From the analysis in Appendix A-2, we have $\frac{\partial Y}{\partial \theta }<0$, $\frac{\partial {y}_{l}}{\partial \theta }<0$, $\frac{\partial {y}_{h}}{\partial \theta }<0$. At the same time, the total emissions are:

$$T=\left(n-m\right)k{y}_{h}\left(1-{r}_{h}\right)=\left(n-m\right)k{y}_{h}(1-\frac{\theta +\tau }{2{c}_{h}})$$

The formula (42) can be arranged as follows:

$$\theta =2{c}_{h}-\frac{2{c}_{h}T}{\left(n-m\right)k{y}_{h}}-\tau$$

$$\frac{\partial \theta }{\partial T}=-\frac{2{c}_{h}}{\left(n-m\right)k{y}_{h}}, \frac{\partial \theta }{\partial \tau }=-1$$

Since ${c}_{h}>0$, $n-m\ge 1$, $k>0$, $\frac{\partial \theta }{\partial T}<0$, $\frac{\partial \theta }{\partial \tau }<0$.

Based on the analysis of the above two cases, $\frac{\partial Y}{\partial \theta }<0$, $\frac{\partial {y}_{h}}{\partial \theta }<0$, $\frac{\partial \theta }{\partial T}<0$,$\frac{\partial \theta }{\partial \tau }<0$, and the sign of $\frac{\partial {y}_{l}}{\partial \theta }$ is positive or negative. From $\frac{\partial \theta }{\partial T}<0$, the emission trading price will decrease with the increase of the industry quota set by the government. With the reduction of the total carbon emission control target $T$, the carbon emission trading price$\theta$ will rise.

Notice that we assume that the emission rights’ trading market is cleared, so enterprises can always buy or sell emission rights when they need to trade. Otherwise, the emission rights trading market will not be cleared. The transaction price $\theta$ will rise or fall. According to $\frac{\partial Y}{\partial \theta }<0$, it indicates that the increase of the carbon emission trading price r will lead to the decline of the total output $T$. Therefore, combining $\frac{\partial \theta }{\partial T}$ and $\frac{\partial Y}{\partial \theta }$, the government’s environmental regulation becomes stronger, the total output of the entire industry will smaller. Similarly, we can infer that the government’s environmental regulation becomes stronger, the output of polluting enterprises will be smaller. In addition, as the sign of $\frac{\partial {y}_{l}}{\partial \theta }$ is positive or negative. As environmental regulations become stricter, the output of clean enterprises may decrease or increase. The reason is that although environmental regulations increase the pollution control costs of enterprises, it reflects the relatively clean nature of clean enterprises. So that clean enterprises may increase output to meet the market demand while polluting enterprises reduce production. After two effects are superimposed, the enhanced environmental regulation of $T$ will lead to the reduction of clean enterprises’ production in some intervals. While the enhanced environmental regulation will lead to an increase of clean enterprises’ production in other intervals. In general, environmental regulation seems to be unfavorable, but it is likely to make clean enterprises better. Because environmental regulation strengthens the advantages of cleaner enterprises.

3.4 Enterprise cost analysis

Further analysis of environmental regulations will change enterprises’ cost in the following two aspects: ①Environmental regulations may increase the cost of enterprise pollution control; ②Emission rights trading may generate costs. From the first point of view, enterprises do not need to control emissions and do not need to pay carbon tax when no environmental regulation. If there is environmental regulation, the cost of enterprise governance will increase. However, environmental regulations have reduced the output of the entire industry, especially polluting enterprises, and reduced their profits. From the second point of view, emission rights trading is a zero-sum game at the industry level. Clean enterprises that sell emission rights increase their income while polluting enterprises that buy emission rights pay the cost. The overall income and expenditure of the industry remain unchanged. Judging from the above two aspects, environmental regulations increase the cost of polluting enterprises and squeeze out their profit margins in the production process. Therefore, investors will lower their future expectations for the polluting enterprises, which may lead to difficulties in financing for these enterprises. In view of this, we propose a theoretical hypothesis here.

Hypothesis

Clean enterprises have lower financing costs than polluting enterprises under environmental regulation. The financing costs’ gap between the two types of enterprises increases with the strength of environmental regulation.

The previous theoretical analysis shows that different types’ enterprises have different financing costs under environmental regulation. To this end, we use Chinese data to conduct empirical research on environmental regulation and enterprises’ financing costs.

4.1 Variable setting

In the study of enterprises’ financing costs, the bonds issued can be used as the research object for analysis. There are two main measurement methods of measuring financing costs: one is the cost discount method; the other is the cost premium method (Zerbib 2019). Nanayakkara and Colombage (2019) pointed out that the cost premium method can obtain the actual financing cost after deducting the macroeconomic impact and can better represent the real financing situation. Therefore, we consider using the cost premium method to measure the financing costs of enterprises under environmental regulation. Here, the cost difference is selected as the financing cost of the bond issuer, and the specific formula is as follows:

$$FC={FC}_{\theta }-{FC}_{\xi }$$

where $FC$ represents the financing cost of enterprise. ${FC}_{\theta }$ indicates the cost of issuing bonds. ${FC}_{\xi }$ represents the issuance cost of national bonds with the same maturity at the same point. The smaller the difference between ${FC}_{\theta }$and ${FC}_{\xi }$, it shows that the enterprise has greater advantages in financing costs.

For the measurement of the intensity of environmental regulation, Zhang and Fu (2008), Zhang et al. (2011), and Han et al. (2016) used the proportion of environmental governance investment in GDP to measure the intensity of environmental regulation. Zhang et al. (2010) used the ratio of pollution control investment to industrial-added value to measure the intensity of environmental regulation. Later, Fu and Li (2010) considered the emission of pollutants as a measurement intensity method of environmental regulation. On this basis, Wang and Liu (2014), Shen et al. (2017) used the emission removal rate to measure the intensity of environmental regulation in the study.

Although the above indicators could measure environmental regulation, a certain indicator usually only emphasizes a certain aspect of environmental regulation. It is difficult to fully reflect the overall environmental regulation status of a region. Based on this, we consider constructing a more comprehensive index of environmental regulation intensity from economic input and governance effect of environmental regulation, to reflect the situation of environmental regulation more comprehensively. Here, we use the ratio of investment in environmental pollution control to local GDP to measure the economic input of environmental regulation. For the effect of environmental regulation, we use the ratio of industrial added value to sulfur dioxide emissions and smoke and dust emissions to measure. It is worth noting that the industrial added value of 2000 is used as the base period to calculate the industrial added value of each region at constant prices. In addition, since the calculation of environmental regulation involves multiple evaluation indicators. How to effectively integrate them is a very important issue. Through a comprehensive comparison of various methods, we choose the entropy method to measure the comprehensive index of environmental regulation intensity. According to each index of the evaluation object, this method calculates the data difference corresponding to the index to determine the weight. The determination of index weights depends entirely on the collected data, which can effectively avoid the interference of subjective factors and objectively reflect the differences between sample data (Fan et al. 2022).

First, different indicators have different dimensional units (Xu 2015). To compare indicators, the data of each indicator needs to be standardized. Here we refer to the treatment methods of Fu and Li (2010) and Shen et al. (2017) to standardize the various environmental regulation indicators in different regions:

$${X}_{ijt}^{s}=\left({X}_{ijt}-\underset{i,t}{\text{min}}{X}_{ijt}\right)/\left(\underset{i,t}{\text{max}}X-\underset{i,t}{\text{min}}{X}_{ijt}\right)$$

where ${X}_{ijt}^{s}$ is the measure of the index $j$ in the year $t$ in the province $i$ after standardization. ${X}_{ijt}$ is the measure of the index $j$ in the year $t$ in the province $i$ before standardization. ${\text{max}}_{i,t}\left({X}_{ijt}\right)$ and ${\text{min}}_{i,t}\left({X}_{ijt}\right)$ are the maximum and minimum measures of the index $j$ respectively.

After the standardization based on the formula (46), calculating the proportion ${P}_{ijt}$ of the $j$-th indicator in the province $i$ in the year $t$, as

$${P}_{ijt}=\frac{{X}_{ijt}^{s}}{{\sum }_{i=1}^{m}{\sum }_{t=1}^{T}{X}_{ijt}^{s}}(i=\text{1,2},\cdots ,m;j=\text{1,2},\cdots ,n;t=\text{1,2}\cdots ,T)$$

Then we calculate the index entropy value ${e}_{it}$:

${e}_{j}=-K{\sum }_{i=1}^{m}{\sum }_{t=1}^{T}{P}_{ijt}ln{P}_{ijt}$ , $k=\frac{1}{\text{ln}m}$ ($m$ is the sample size) (48)

Then we adjust the index, assigning the following weight coefficient to ${P}_{ijt}$:

$${w}_{j}=\frac{1-{e}_{j}}{{\sum }_{j=1}^{n}(1-{e}_{j})}$$

where ${w}_{j}$ is the weight of ${P}_{ijt}$. Using (47) and (49), the environmental regulation intensity of the province $i$ in the year $t$ is:

$${reg}_{it}={\sum }_{j}\left({P}_{ijt}\bullet {w}_{j}\right)$$

In the formula, the larger the value of ${reg}_{it}$, the more economic input is used for environmental protection, the more obvious the output effect, and thus the stronger the intensity of environmental regulation.

4.2 Model setting and sample statistics

To examine the impact of environmental regulation on enterprise’s financing costs, the following multiple regression model is considered here.

Model 1:$FC=\alpha +{\beta }_{1}Ty+{\beta }_{2}Reg+{\beta }_{3}Cont+Fe+\epsilon$

Model 2:$FC=\alpha +{\beta }_{1}Ty+{\beta }_{2}Reg+{\beta }_{3}Ty\times Reg+{\beta }_{4} Cont+Fe+\epsilon$

where $FC$represents the financing cost of the enterprise, $\alpha$ represents the constant item, $\epsilon$ represents the random error, and $Fe$ represents the fixed effect. $Ty$represents the type of enterprise. When the issuing enterprise is a polluting enterprise, the $Ty$ setting value is 0. Otherwise $Ty$ is set to 1. $Reg$ is the intensity of environmental regulation between regions as an independent variable. $Ty\times Reg$ represents the interaction effect of different types of enterprises and environmental regulation on financing costs. $Cont$ represents the control variable. ${\beta }_{1}$ and ${\beta }_{2}$ are the regression coefficients of enterprise type and control variable respectively.

We select bonds issued in all provinces of China except Tibet from January 2016 to December 2021. The data are manually compiled from relevant materials released by the Carbon Emissions Trading Network, China Statistical Yearbook, China Environmental Statistical Yearbook, China City Statistical Yearbook, and the Wind database. After eliminating some samples with missing transaction data, 37,916 bonds issued by polluting enterprises and 2,491 bonds issued by clean enterprises were obtained, as shown in Table 1

Table 1

The number and cost of bond issuance about different types of enterprises
Year	Clean enterprises		Polluting enterprises
Year	Issue number	Issue cost	Issue number	Issue cost
2016	12	0.9334	2332	0.8480
2017	79	1.8744	3875	1.2289
2018	104	1.7207	3311	1.3262
2019	503	1.2776	5547	1.4259
2020	843	0.9081	9038	1.1386
2021	950	0.9299	13803	1.0001
Total	2491	1.0557	37916	1.1379
Source: Authors’ own research.

[Insert Table 1 approximately here]

At the same time, based on the above measure method of the formulas (46)-(50), we calculate the intensity of environmental regulation in China’s 30 provinces except Tibet as Table 2, and show the intermediate value of the calculation process in the appendix B.

Table 2

2015–2020 environmental regulatory intensity by region
Year Region	2015	2016	2017	2018	2019	2020
Beijing	0.0330	0.0476	0.0737	0.1055	0.2283	0.3527
Tianjin	0.0613	0.0724	0.0762	0.1409	0.0907	0.3058
Hebei	0.0162	0.0170	0.0177	0.0222	0.0186	0.0958
Shanxi	0.0455	0.0473	0.0433	0.0435	0.0441	0.0842
Neimenggu	0.0334	0.0359	0.0410	0.0403	0.0424	0.1046
Liaoning	0.0278	0.0348	0.0344	0.0337	0.0355	0.0733
Jilin	0.0561	0.0604	0.0632	0.0679	0.0795	0.0492
Heilongjiang	0.0418	0.0440	0.0452	0.0468	0.0569	0.0504
Shanghai	0.0387	0.0506	0.1042	0.1911	0.0968	0.0359
Jiangsu	0.0223	0.0275	0.0320	0.0317	0.0283	0.0528
Zhejiang	0.0431	0.0541	0.0590	0.0602	0.0513	0.0322
Anhui	0.0208	0.0239	0.0245	0.0238	0.0198	0.0353
Fujian	0.0235	0.0293	0.0355	0.0306	0.0331	0.0277
Jiangxi	0.0130	0.0146	0.0155	0.0142	0.0136	0.0299
Shandong	0.0319	0.0340	0.0377	0.0490	0.0382	0.0255
Heinan	0.0169	0.0210	0.0265	0.0342	0.0202	0.0212
Hubei	0.0239	0.0281	0.0318	0.0337	0.0261	0.0378
Hunan	0.0167	0.0202	0.0225	0.0232	0.0167	0.0234
Guangdong	0.0346	0.0439	0.0488	0.0451	0.0414	0.0388
Guangxi	0.0319	0.0335	0.0322	0.0342	0.0329	0.0252
Hainan	0.0174	0.0185	0.0187	0.0222	0.0184	0.0176
Chongqing	0.0220	0.0293	0.0315	0.0278	0.0232	0.0284
Sichuan	0.0243	0.0266	0.0274	0.0271	0.0222	0.0803
Guizhou	0.0168	0.0177	0.0173	0.0168	0.0156	0.0588
Yunnan	0.0317	0.0325	0.0325	0.0318	0.0278	0.0462
Shanxi	0.0202	0.0229	0.0232	0.0243	0.0211	0.0431
Gansu	0.0591	0.0608	0.0590	0.0565	0.0572	0.0150
Qinghai	0.0126	0.0133	0.0137	0.0143	0.0140	0.0424
Ningxia	0.0403	0.0405	0.0401	0.0400	0.0421	0.0578
Xinjiang	0.0144	0.0152	0.0144	0.0141	0.0134	0.0140
Source: Authors’ own research.

[Insert Table 2 approximately here]

4.3 Regression results

To examine the impact of the intensity of environmental regulation on the financing costs of different types of enterprises, we conduct a regression analysis on the financing costs according to Model 1 and Model 2. At the same time, in order to ensure the rationality of the regression results, the explanatory variables were subjected to mean centering, and the results are shown in Table 3. The first column in the table shows the regression of financing cost on enterprise type and environmental regulation intensity and its control variables. The result 1 shows that there is a significant correlation between the intensity of environmental regulation and enterprise financing costs, that is, the intensity of environmental regulation will directly affect enterprise financing costs. The second column in the table adds the interaction term between enterprise type and environmental regulation based on the sum of the first column. The result 2 shows that the interaction item between enterprise type and environmental regulation intensity is significant at the 99% confidence level, and the regression coefficient is -1.288. This result shows that environmental regulation does have a significant effect on the financing costs of different types of enterprises. The negative effect between enterprise type and financing cost increases with the intensity of environmental regulation.

Table 3

Impact Analysis of Environmental Regulation Strength
Model Variable	Model 1	Model 2
Model Variable	Result 1	Result 2
Ty	-0.099^***	-0.108^***
	(-8.19)	(-8.96)
Reg	-1.399^***	-1.353^***
	(-24.01)	(-23.07)
TyReg*		-1.288^***
		(-8.39)
Constant	2.876^***	2.877^***
	(9.92)	(9.97)
Cont	Yes	Yes
Fixed time	Yes	Yes
Individual fixation	Yes	Yes
Number of samples	35,996	35,271
R-squared	0.674	0.672
Adjusted ${R}^{2}$	0.672	0.672
Source: Authors’ own research.

[Insert Table 3 approximately here]

4.4 Robustness test

According to the previous empirical results, environmental regulation has a significant impact on the financing cost of enterprises. To verify the reliability of these empirical results, we plan to conduct a robustness test on the aforementioned empirical analysis. Here we intend to use the current issuance cost of the enterprise as the financing cost of the enterprise to replace the bond cost difference in Models 1 to 2. If the empirical results obtained after changing the explained variables are not significantly different from the previous empirical results, it indicates that the previous empirical analysis results are stable and reliable. The results of the robustness test after changing the explained variables are shown in Table 4. The results show that the positiveness and significance of the coefficients of each explanatory variable are highly consistent with the previous empirical results. No matter whether the explained variables are changed or not, the same results will still be found. It shows that the empirical results in this paper are robust to a certain extent.

Table 4

Robustness test of the impact of environmental regulation
Variable	Result 3	Result 4
Variable	Rate	Rate
Ty	-0.094^***	-0.103^***
	(-7.87)	(-8.70)
Reg	-1.413^***	-1.367^***
	(-24.16)	(-23.24)
TyReg*		-1.370^***
		(-8.64)
Constant	5.391^***	5.391^***
	(16.56)	(16.62)
Cont	Yes	Yes
Fixed time	Yes	Yes
Individual fixation	Yes	Yes
Number of samples	35,271	35,271
R-squared	0.691	0.691
Adjusted ${R}^{2}$	0.692	0.691
Source: Authors’ own research.

[Insert Table 4 approximately here]

Further consideration should be given to testing the differences in financing costs caused by the different intensity of environmental regulation in different regions. To this end, we conduct a non-parametric test on the eastern, central and western regions. The results are shown in Table 5. The results show that in the eastern region with the strongest environmental regulation, the bonds issued by clean enterprises have lower financing costs than those in the central and western regions, which is consistent with the previous results.

Table 5

Non-parametric test of financing cost differences among regions
Region distribution	Sample size	Median	Mean	Standard deviation
Eastern region	22204	0.790	1.092	0.998
Central Region	9157	0.675	1.177	1.177
Western Region	8271	0.595	1.206	1.312
			P value	0.0001
Source: Authors’ own research.

[Insert Table 5 approximately here]

The above test results are more consistent with the previous empirical analysis results, which shows that the empirical research in this paper has a certain robustness.

Regulatory policies often have a certain orientation, which may bring unexpected situations while guiding the regulated object. For example, encouraging the development of certain industries through policy may lead to overcapacity. Conversely, suppressing the development of certain industries through policy may cause many enterprises to withdraw from the market, which increases the market share of incumbent enterprises in a disguised way. In this way, from the perspective of some regulated persons, regulation is not necessarily a bad thing. In addition to the above-mentioned situations, we propose another situation in which the regulated may benefit from regulation and conduct theoretical research on this situation. The results show that the strengthening of environmental regulations makes clean enterprises have lower financing costs than polluting enterprises. Then we conduct an empirical analysis on the financing costs of different types of enterprises under the environmental regulations in various regions. We have following inspiration:

(1) It is necessary to pay attention to grasp the intensity of environmental regulations in the process of formulating phased emission reduction targets. Judging from our research results, too strict environmental regulation is likely to be counterproductive. Our research shows that market-incentive environmental regulation can improve the situation of the clean enterprise. Therefore, government departments can design regulatory policies that enable enterprises and consumers to actively cooperate and achieve a harmonious and win-win situation.

(2) When formulating specific environmental regulatory policies, the heterogeneity of regulatory objects should be fully considered. The pollution’s degree between enterprises in the industry and the number of polluting enterprises will have an impact on the actual environmental policy effect. This paper demonstrates the different financing costs of different types’ enterprises under the same environmental regulation policy. This result enlightens relevant government departments to avoid “one size fits all” policies in environmental regulation.

(3) Government departments should release more effective incentive policies to promote the green industries’ development and encourage more high-quality enterprises to transform and upgrade. At the same time, enterprises have different transformation needs in different regions, it is necessary to pay attention to the guidance of differentiated policies between regions. Therefore, government department should promote the industrial upgrading of enterprises to adapt to the region’s development.

Noted that we build a static game model with complete information, which abstracts some details such as changes in production costs and enterprises’ investment in emission reduction technologies in the early stage. The in-depth exploration of these details will be the direction of the next research.

Author Contribution

Xuecheng Fan wrote the main manuscript text and Xinxin Wang and Zeshui Xu revised the manuscript. All authors reviewed the manuscript.

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No competing interests reported.

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The impact of environmental regulations on enterprise production——Based on the production game model

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Abstract

1. Introduction

2. Literature review

3. Theoretical model

3.1 Model building

3.2 Market equilibrium

3.3 Equilibrium analysis

3.4 Enterprise cost analysis

4. Empirical analysis

4.1 Variable setting

4.2 Model setting and sample statistics

4.3 Regression results

4.4 Robustness test

5. Conclusions

Declarations

Author Contribution

References

Additional Declarations

Supplementary Files

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