Effects of eco-environmental damage compensation system with multi-stakeholder engagements: a DSGE perspective from China

Eco-environment is a natural capital that pursues effective allocation like labour, capital, land, and other economic factors (Xin and Sun 2018, Xin 2019). The 'polluter pays principle' states that whoever is responsible for damage to the environment should bear the costs associated with it. (Taking Action, The United Nations Environmental Programme), which is consistent with the theory of ecological compensation (Gastineau et al 2021, Vaissière and Meinard 2021). The EDCS is oriented to investigate the liability for damage, strengthen the responsibility of the illegal subject, improve the illegal cost, which fully reflects the connotation of the system of severe punishment for consequences. As far as the system itself is concerned, EDCS is more represented in legal issues such as legal disputes between the claimant and the compensation subject, interest consultations, and liability attribution. At present, many scholars have studied such topics. Specifically, taking the oil spill as an example, Liu and Zhu (2014) made a detailed analysis of the legislation of EDCS and discussed how to improve the existing marine eco-environmental quality. However, the corresponding results are rarely mentioned in terms of the implementation effect and green governance effect. So, these issues need to be further explored. Based on the mentioned-above research gaps, we intend to carry out corresponding research on the implementation effect of EDCS.

Eco-environment is regarded as particular public goods. The Public Goods Theory of Marxism emphasizes that the essence of public goods lies in public welfare and its characteristics are non-competitive and non-exclusive (Oakland 1987). In addition, public goods are also products that satisfy the needs of production and life, so they have use value (Seo 2020). From the implementation principles of EDCS, damage to the eco-environment means damage to the value of public goods. So, the Public Goods Theory of Marxism provides reasonable explanation and beneficial guidance for the EDCS. Public goods have special properties such as public welfare and integrity, which determines that the governance of public goods cannot adopt a single model, and it needs to adopt a social multi-cooperative development mode. From the current research status at home and abroad, the concepts of collaborative governance, public governance, and multi-governance illustrate those mentioned-above multiple cooperative development models to varying degrees. For example, Ansell and Gash (2008) used meta-analysis methods to analyse collaborative governance in-depth, used proper cases to find the key variables that affect collaborative governance, and then elaborated their contingency model. Davies and White (2012) elaborated on the cooperative relationship between various stakeholders, including common goals and strategies, shared responsibility and resources. Besides, Tosun et al (2016) believed that co-governance is a dynamic interaction between public and private actors, and its specific forms are cooperation, competition and conflict. It is further discussed that the degree of collaboration and competition mainly depends on the existing regulatory arrangements and the consistency of different objectives.

As an essential concept in public management, multi-stakeholder engagement has accumulated a wealth of theoretical results and practical experience, providing a necessary reference for countries to improve their environmental governance level. Tracing back to previous literature, some scholars have analysed the multi-stakeholder engagement models, expounding the decision-making behaviour of the government, enterprises, and the public, constructing the logic of check and balance between stakeholders. Finally, the concrete practice path is given according to the practical problems. For example, Fu and Geng (2019) constructed a multi-stakeholder environmental governance system and analysed the innovative model of ecological civilisation's diversified collaborative governance, and provided new ideas for solving the conflicts of interests encountered in the process of green development. Rajesh (2020) took micro-enterprises as the research object, explored the sustainability of the supply chain by using the score of environment, society and governance, and then analysed the interest mechanism between various subjects.

In summary, multi-stakeholder engagements provide a realistic basis for accelerating the implementation of EDCS. On the one hand, the EDCS with multi-stakeholder engagements provides a coordination platform for multi-stakeholder. On the other hand, the EDCS with multi-stakeholder engagements attaches much significance to pre-prevention thought and preventive supervision. Therefore, this paper incorporates the EDCS into the multi-stakeholder engagements system and explores its operating mechanism and green development effect in line with the realistic requirements of promoting green development and promoting harmonious coexistence between man and nature.

In the multi-stakeholder engagements system, households participate in the governance through damage supervision. Households' social and public influence will play an essential role in firms' emission reduction efforts and the government's environmental supervision. The transmission path of a household's participation can be summarised in two ways as follows. (i) supervise by households -- reduce emissions independently by firms -- the environment will be improved, (ii) supervise by households -- submit feedback to relevant departments -- carry out regulation measures by the government. Specifically, the transmission effect results are reflected in the household utility function through the variables of actual pollution level and government pollution control expenditure, as shown in equation (1). Referring to the existing literature (Chan 2020, Liu and He 2021), it is assumed that households are homogeneous in consumer preference, investment and saving, and they have intertemporal decision-making behaviour (Golosov et al 2014). Therefore, based on the consideration of labour supply, pollutant emission, and government's pollution control expenditure, the CRRA (Constant Relative Risk Aversion) utility function of representative households is established. The original formula of CRRA is $u\left(c\right)=\tfrac{{c}^{1-\theta }-1}{1-\theta },$ which is a standard analysis model based on Neoclassical economic. Therefore, refer to the existing literature (Argentiero et al 2018), we further improve the formula of CRRA and present it as follows:

$$\begin{eqnarray}&&U={E}_{0}\left\{\displaystyle \sum _{t=0}^{\infty }\beta \left(\displaystyle \frac{{{C}_{t}}^{1-{\theta }_{1}}}{1-{\theta }_{1}}-\displaystyle \frac{{N}_{t}^{1+{\theta }_{2}}}{1+{\theta }_{2}}-\mu \,\mathrm{ln}\,C{E}_{t}+\eta \,\mathrm{ln}\,{G}_{t}\right)\right\}\end{eqnarray} \tag{ 1 }$$

where ${E}_{0}$ represents the conditional expectation operator based on period 0; $\beta$ represents the discount rate; ${C}_{t}$ represents household consumption; ${N}_{t}$ represents household labour supply; ${\theta }_{1}$ and ${\theta }_{2}$ represent the relative risk aversion elasticity coefficients of consumption and labour, respectively; $\mu$ represents actual pollution emission The negative utility coefficient of the household; $\eta$ represents the positive utility coefficient of the government expenditure on pollution control to households.

Based on the comprehensive consideration of household consumption, investment, labour remuneration, and capital gains, the budget constraints of the household sector are expressed as follows:

$$\begin{eqnarray}&&{C}_{t}+{I}_{t}={W}_{t}{N}_{t}+{R}_{K,t}{K}_{t}\end{eqnarray} \tag{ 2 }$$

where ${I}_{t}$ represents the actual investment of the family, which mainly includes productive investment; ${W}_{t}$ represents unit labour compensation; ${K}_{t}$ represents capital; ${R}_{K,t}$ represents the rate of return on capital.

In addition, the capital accumulation equation of the household sector can be written as equation (3). By combining equations (2) and (3), the budget constraint equation of the household sector can be further written as the following equation (4):

$$\begin{eqnarray}&&{K}_{t+1}=\left(1-\delta \right){K}_{t}+{I}_{t}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{C}_{t}+{K}_{t+1}=\left(1-\delta +{R}_{K,t}\right){K}_{t}+{W}_{t}{N}_{t}\end{eqnarray} \tag{ 4 }$$

On the premise of satisfying the maximisation of household utility, rational choices are made based on consumer preferences, capital accumulation equations and budget constraint balance relationships, and the optimal decisions for household behaviour are made. Assuming that the marginal utility of wealth ${\xi }_{1,t}$ is the Lagrange multiplier, then construct the Lagrange function shown in equation (5) to obtain the optimal allocation condition of the household sector.

$$\begin{eqnarray}&&\begin{array}{l}L={E}_{{\rm{t}}}\left\{\displaystyle \sum _{t=0}^{\infty }{\beta }_{t}\left(\displaystyle \frac{{{C}_{t}}^{1-{\theta }_{1}}}{1-{\theta }_{1}}-\displaystyle \frac{{N}_{t}^{1+{\theta }_{2}}}{1+{\theta }_{2}}-\mu \,\mathrm{ln}\,C{E}_{t}+\eta \,\mathrm{ln}\,{G}_{t}\right)\right\}\\ \,+\,{\xi }_{1,t}\left[{C}_{t}+{K}_{t+1}-\left(1-\delta +{R}_{K,t}\right){K}_{t}-{W}_{t}{N}_{t}\right]\end{array}\end{eqnarray} \tag{ 5 }$$

By solving the optimisation problem of the household sector, the following first-order conditions can be obtained:

$$\begin{eqnarray}&&{\xi }_{1,t}=-{C}_{t}^{\left(1-{\theta }_{1}\right)-1}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&{N}_{t}^{{\theta }_{2}}={C}_{t}^{\left(1-{\theta }_{1}\right)-1}{W}_{t}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&\displaystyle \frac{{{C}_{t}}^{\left(1-{\theta }_{1}\right)-1}}{{C}_{t+1}^{\left(1-{\theta }_{1}\right)-1}}=\beta \left(1-\delta +{R}_{K,t}\right)\end{eqnarray} \tag{ 8 }$$

In equation (6), ${\xi }_{1,t}$ represents the marginal utility of household consumption, equation (7) is the optimal labour supply in the household sector, and equation (8) represents that the marginal utility of household consumption in the current period is equal to the discounted value of utility brought about by consumption in the next period.

The firm's goal is to maximise profit, and its profit per period is the difference between revenue and cost. When the price is normalised to 1, the firm's revenue equals its output. Firms carry out production activities under the conditions of technology, labour, and capital. Refer to the Cobb-Douglas function to set the firm's output function as follows:

$$\begin{eqnarray}&&{Y}_{t}={A}_{t}{K}_{t}^{{\alpha }_{1}}{N}_{t}^{{\alpha }_{2}}{S}_{t}^{1-{\alpha }_{1}-{\alpha }_{2}}\end{eqnarray} \tag{ 9 }$$

where ${A}_{t},$ ${K}_{t},$ ${N}_{t}$ and ${S}_{t}$ represent the technical level, capital, labour supply, and resource input of the firm, respectively; ${\alpha }_{1}$ and ${\alpha }_{2}$ are the output elasticity of capital and the output elasticity of labour, respectively; ${A}_{t}$ is regarded as an exogenous shock, which satisfies the first-order autoregressive process, namely:

$$\begin{eqnarray}&&\mathrm{ln}\,{A}_{t}=\left(1-{\rho }_{A}\right)\mathrm{ln}\,{A}^{\ast }+{\rho }_{A}\,\mathrm{ln}\,{A}_{t-1}+{\varepsilon }_{A,t}\end{eqnarray} \tag{ 10 }$$

where ${\rho }_{A}$ represents the first-order autoregressive coefficient of the technical level, ${A}^{* }$ represents the steady-state value of the technical level, and ${\varepsilon }_{A,t}$ satisfies $N\left(0,{\sigma }_{A}^{2}\right).$

The EDCS usually punishes firms or individuals who cause environmental damage. To simplify the model, firms are mainly responsible for compensation, and the government's supervision objects are also firms. Generally, firms may cause environmental damage to rivers, lakes, soil, atmosphere and so on, which results in the deterioration of eco-environmental quality. Referring to the previous research (Annicchiarico and Di Dio 2015), the pollutant emission level is positively correlated with the firm's current output ${Y}_{t},$ so the pollution level can be expressed as $\kappa {Y}_{t},$ and $\kappa$ represents the pollution proportion based on production.

Firms that cause environmental damage shall be liable for compensation, and the responsibility for restoring eco-environmental damage shall be actively fulfilled. In addition, the system stipulates that the obligee of compensation makes repairs by himself or a third party. The obligor of compensation shall bear the expenses for the investigation and evaluation. Suppose the eco-environment damage caused by the obligor of compensation cannot be repaired. In that case, the compensation fund shall be used as the government's non-tax revenue, which shall be turned over to the local treasury in total and included in the local budget management. Based on this, it is assumed that the EDCS is regarded as an exogenous environmental regulation shock. Some firms, who do not actively carry out environmental governance or fail to reach the emission standards, need to bear the corresponding compensation liability. Therefore, the shock of EDCS may force firms to conduct eco-environmental government to avoid damage compensation liability. In this paper, we assume that the firm's emission reduction efforts $E{R}_{t},$ the emission reduction amount $R{X}_{t},$ and the final pollution emissions $C{E}_{t}$ are negatively correlated, and the firm's compensation expenditure $E{P}_{t}$ and compensation ratio ${\omega }_{t}$ are positively correlated. So, the pollutant emission amount $C{E}_{t}$ can be expressed as equation (11), the emission reduction amount $R{X}_{t}$ can be defined as equation (12), and the compensation expenditure $E{P}_{t}$ can be expressed as equation (14).

$$\begin{eqnarray}&&C{E}_{t}=\kappa {Y}_{t}\left(1-{\chi }_{t}E{R}_{t}\right)\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&R{X}_{t}={\chi }_{t}\kappa {Y}_{t}E{R}_{t}\end{eqnarray} \tag{ 12 }$$

where ${\chi }_{t}$ represents the environmental supervision of the public and government departments. Suppose it is an exogenous shock and satisfies the first-order autoregressive process, as shown in equation (13).

$$\begin{eqnarray}&&\mathrm{ln}\,{\chi }_{t}=\left(1-{\rho }_{\chi }\right)\mathrm{ln}\,{\chi }^{\ast }+{\rho }_{\chi }\,\mathrm{ln}\,{\chi }_{t-1}+{\varepsilon }_{\chi ,t}\end{eqnarray} \tag{ 13 }$$

where ${\rho }_{\chi }$ represents the first-order autoregressive coefficient of environmental supervision; ${\chi }^{* }$ represents its steady-state value; ${\varepsilon }_{\chi ,t}$ satisfies $N\left(0,{\sigma }_{\chi }^{2}\right).$

$$\begin{eqnarray}&&E{P}_{t}={\omega }_{t}\left(C{E}_{t}-E{P}_{0}\right)=\left\{\begin{array}{l}{\omega }_{t}\left(C{E}_{t}-E{P}_{0}\right),\,\\ 0,\end{array}\right.\,\,\begin{array}{c}C{E}_{t}\gt E{P}_{0}\\ C{E}_{t}\leqslant E{P}_{0}\end{array}\end{eqnarray} \tag{ 14 }$$

Under the EDCS, the damage compensation of the firm is related to the degree of pollution, as shown in equation (14). When the pollutant emission is higher than the threshold $E{P}_{0},$ the firm needs to pay compensation to the government. When the pollutant emission is lower than the threshold $E{P}_{0},$ the firm will conduct regular independent emission reduction efforts to reach the qualified standard. $E{P}_{0}$ is an environmental rule set by the government, regarded as an exogenous restraint shock to firms. If the actual pollution discharge is higher than the threshold, the firm shall compensate for the excess part. The local environmental protection department usually determines the compensation ratio ${\omega }_{t}$ jointly with a third-party assessment agency, which is regarded as an exogenous random variable. Specifically, the first-order autoregressive equations of $E{P}_{0}$ and ${\omega }_{t}$ are set as follows:

$$\begin{eqnarray}&&\mathrm{ln}\,E{P}_{0t}=\left(1-{\rho }_{E{P}_{0}}\right)\mathrm{ln}\,E{P}_{0}^{\ast }+{\rho }_{E{P}_{0}}\,\mathrm{ln}\,E{P}_{0t-1}+{\varepsilon }_{E{P}_{0},t}\end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray}&&\mathrm{ln}\,{\omega }_{t}=\left(1-{\rho }_{\omega }\right)\mathrm{ln}\,{\omega }^{* }+{\rho }_{\omega }\,\mathrm{ln}\,{\omega }_{t-1}+{\varepsilon }_{\omega ,t}\end{eqnarray} \tag{ 16 }$$

In addition, referring to the research of Annicchiarico and Di Dio 2015, it is assumed that the cost of pollutant control by firms satisfies the following conditions:

$$\begin{eqnarray}&&{Z}_{t}={\nu }_{1}{\left(E{R}_{t}\right)}^{{\nu }_{2}}{Y}_{t}\end{eqnarray} \tag{ 17 }$$

Where ${\nu }_{1}\gt 0$ and ${\nu }_{2}\gt 0$ are the technical parameters of pollutant control cost.

Therefore, the firm's profit function based on the principle of profit maximisation can be expressed as:

$$\begin{eqnarray}&&\begin{array}{l}Max\pi =\left(1-{\tau }_{Y,t}\right){Y}_{t}-{N}_{t}{W}_{t}-{R}_{K,t}{K}_{t}\\ \,-\,{P}_{S,t}{S}_{t}-E{P}_{t}-{Z}_{t}\end{array}\end{eqnarray} \tag{ 18 }$$

where ${\tau }_{Y,t}$ represents the output tax rate; ${W}_{t}$ represents the unit labour remuneration; ${P}_{S,t}$ represents the price of resource elements; ${P}_{S,t}$ is regarded as an exogenous shock, subject to the first-order autoregressive process shown in equation (19); ${\rho }_{{P}_{S}}$ represents its steady-state value, and ${\varepsilon }_{{P}_{S,t}}$ satisfies $N\left(0,{\sigma }_{{P}_{S}}^{2}\right).$

$$\begin{eqnarray}&&\mathrm{ln}\,{P}_{S,t}=\left(1-{\rho }_{{P}_{S}}\right)\mathrm{ln}\,{P}_{S}^{* }+{\rho }_{{P}_{S}}\,\mathrm{ln}\,{P}_{S,t-1}+{\varepsilon }_{{P}_{S,t}}\end{eqnarray} \tag{ 19 }$$

Based on the above conditions, the first-order conditions that firms need to meet to achieve optimal decision-making are as follows:

$$\begin{eqnarray}&&\begin{array}{l}{W}_{t}=\left[1-{\tau }_{Y,t}-{\nu }_{1}{\left(E{R}_{t}\right)}^{{\nu }_{2}}-{\omega }_{t}\kappa \left(1-{\chi }_{t}E{R}_{t}\right)\right]\\ \,\times \,{\alpha }_{2}{A}_{t}{K}_{t}^{{\alpha }_{1}}{S}_{t}^{1-{\alpha }_{1}-{\alpha }_{2}}{N}_{t}^{{\alpha }_{2}-1}\end{array}\end{eqnarray} \tag{ 20 }$$

$$\begin{eqnarray}&&\begin{array}{l}{R}_{K,t}=\left[1-{\tau }_{Y,t}-{\nu }_{1}{\left(E{R}_{t}\right)}^{{\nu }_{2}}-{\omega }_{t}\kappa \left(1-{\chi }_{t}E{R}_{t}\right)\right]\\ \,\times \,{\alpha }_{1}{A}_{t}{K}_{t}^{{\alpha }_{1}-1}{N}_{t}^{{\alpha }_{2}}{S}_{t}^{1-{\alpha }_{1}-{\alpha }_{2}}\end{array}\end{eqnarray} \tag{ 21 }$$

$$\begin{eqnarray}&&\begin{array}{l}{P}_{S,t}=\left[1-{\tau }_{Y,t}-{\nu }_{1}{\left(E{R}_{t}\right)}^{{\nu }_{2}}-{\omega }_{t}\kappa \left(1-{\chi }_{t}E{R}_{t}\right)\right]\\ \,\times \,\left(1-{\alpha }_{1}-{\alpha }_{2}\right){A}_{t}{K}_{t}^{{\alpha }_{1}}{N}_{t}^{{\alpha }_{2}}{S}_{t}^{\left(1-{\alpha }_{1}-{\alpha }_{2}\right)-1}\end{array}\end{eqnarray} \tag{ 22 }$$

$$\begin{eqnarray}&&E{R}_{t}={\left(\displaystyle \frac{{\omega }_{t}\kappa {\chi }_{t}}{{\nu }_{1}{\nu }_{2}}\right)}^{\displaystyle \frac{1}{{\nu }_{2}-1}}\end{eqnarray} \tag{ 23 }$$

To simplify the model, we assume that the government's income includes tax and eco-environmental damage compensation from firms, while the expenditure consists of the pollutant supervision and governance expenditure. The above two aspects constitute the balance of payments function, as shown in equation (24). In addition, based on the relevant theories of welfare economics, the social welfare function is defined as: under the condition of meeting the government's balance of expenditures, the utility of households and firms is considered optimal, as shown in equation (25).

$$\begin{eqnarray}&&{\tau }_{Y,t}{Y}_{t}{P}_{t}+E{P}_{t}={G}_{t}\end{eqnarray} \tag{ 24 }$$

$$\begin{eqnarray}&&SE=U+\pi \end{eqnarray} \tag{ 25 }$$

Where ${\tau }_{Y,t}{Y}_{t}$ represents government tax revenue; ${P}_{t}$ represents the ratio of pollutant control expenditure to tax revenue, which reflects the government's pollution control efforts to some extent. It is also an exogenous shock that satisfies the first-order autoregressive process shown in equation (26), ${\rho }_{P}$ represents its steady-state value, and ${\varepsilon }_{P,t}$ satisfies $N\left(0,{\sigma }_{P}^{2}\right).$

$$\begin{eqnarray}&&\mathrm{ln}\,{P}_{t}=\left(1-{\rho }_{P}\right)\mathrm{ln}\,{P}^{* }+{\rho }_{P}\,\mathrm{ln}\,{P}_{t-1}+{\varepsilon }_{P,t}\end{eqnarray} \tag{ 26 }$$

Finally, the following Lagrange function shown in equation (27) is constructed based on equations (24) and (25). The first-order optimal condition of government pollution control expenditure is obtained, as shown in equation (28).

$$\begin{eqnarray}&&{L}_{g}={E}_{0}\left\{\displaystyle \sum _{t=0}^{\infty }{\beta }^{t}\left[U+\pi +{\xi }_{2,t}\left({\tau }_{Y,t}{Y}_{t}{P}_{t}+E{P}_{t}-{G}_{t}\right)\right]\right\}\end{eqnarray} \tag{ 27 }$$

$$\begin{eqnarray}&&{G}_{t}=\eta {P}_{t}\end{eqnarray} \tag{ 28 }$$

According to the previous analysis, EDCS is a new environmental regulation system in environmental law. It aims to improve the eco-environmental quality through punishment and force firms to independently reduce pollutant emissions, thereby enhancing the level of green development. Innovation, coordination, green, openness, and sharing in China constitute five development concepts that play an increasingly important role in economic and social development. Green development and the other four concepts are interdependent and synergistic, involving resource utilisation, production, living, environmental governance, and other aspects. According to Fang et al (2020) and Weng et al (2020), we integrate decision variables of the DSGE model into the green development system to form a measurement index system, which includes input, pollution emission, pollution control expenditure, household consumption, per capita income, labour force, and economic output. Specific measurements of indicators are shown in table 1.

The green development level index is the key variable of this paper, which expands the traditional DSGE model and represents the green governance effect of EDCS. Therefore, based on the above indicator system of green development level, we construct a linear model as shown in equation (29). Among them, ${Q}_{t}$ represents green development level, ${q}_{1},{q}_{2},\mathrm{......}{q}_{7}$ represent the weight of each decision-making variable in turn.

$$\begin{eqnarray}&&\begin{array}{l}{Q}_{t}={q}_{1}{S}_{t}-{q}_{2}C{E}_{t}+{q}_{3}{G}_{t}+{q}_{4}{C}_{t}\\ \,+\,{q}_{5}{W}_{t}+{q}_{6}{N}_{t}+{q}_{7}{Y}_{t}\end{array}\end{eqnarray} \tag{ 29 }$$

Based on the general equilibrium theory, when stakeholders satisfy the optimal decision, the output market, labour market, and capital market will reach a common equilibrium, and the state of market clearance will be formed simultaneously.

$$\begin{eqnarray}&&{Y}_{t}={C}_{t}+{K}_{t+1}-\left(1-\delta \right){K}_{t}+{G}_{t}+{P}_{S,t}{S}_{t}\end{eqnarray} \tag{ 30 }$$

In this paper, parameters are assigned in the following ways: First, static parameters need to be calibrated based on the previous literature. Second, dynamic parameters need to be calibrated using Bayesian estimation based on China's actual economic data. Third, use China's macroeconomic data to estimate the weight coefficient of the indicator system of green development level.

Static parameters include the subjective discount rate $\beta ,$ the relative risk aversion elasticity of household consumption and labour supply ${\theta }_{1}$ and ${\theta }_{2},$ the capital-output elasticity ${\alpha }_{1},$ the labour output elasticity ${\alpha }_{2},$ the capital depreciation rate $\delta ,$ the pollution emission coefficient per unit of output $\kappa ,$ and the emission reduction cost parameters ${\nu }_{1}$ and ${\nu }_{2}.$ The specific parameter calibration values and references are shown in table 2.

Table 2. The results of static parameters calibration.

Parameter	Meaning	Value	References
$\beta$	Discount coefficient	0.95	Refer to Punzi (2019)
${\theta }_{1}$	Relative risk aversion coefficient of consumption	0.8	Refer to Li and Peng (2020)
${\theta }_{2}$	Relative risk aversion coefficient of labour	3	Refer to Xiao et al (2018)
$\delta$	Capital depreciation rate	0.11	Refer to Chan (2019)
${\alpha }_{1}$	Capital elasticity coefficient	0.6	Refer to Pan et al (2020)
${\alpha }_{2}$	Labour elasticity coefficient	0.3	Refer to Pan et al (2020)
$\kappa$	Pollutant emission coefficient per unit	0.16	Refer to Annicchiarico and Di Dio (2015)
${\nu }_{1}$	Abatement cost parameters	0.185	Refer to Annicchiarico and Di Dio (2015)
${\nu }_{2}$	Abatement cost parameters	2.8	Refer to Annicchiarico and Di Dio (2015)

In this section, we select output and consumption as external observation samples. The original data comes from the National Bureau of Statistics and China Economic Network database from 2000 to 2018. We use MATLAB to estimate dynamic parameters, including the negative utility coefficient of pollutant emission, the positive utility coefficient of government's expenditure in pollution control, the first-order autoregressive coefficients, and the random error terms of each exogenous shock. According to the estimation result of previous literature and the characteristics of policy shocks, we set the prior mean value of the first-order autoregressive coefficient as shown in table 3. We refer to the previous research (Smets and Wouters 2007, Khan and Tsoukalas 2009). In addition, this paper sets the first-order autoregressive parameters to obey the Beta distribution, and the random fluctuation term follows the Inv. Gamma distribution, the specific estimation results are shown in table 3, and the corresponding prior distribution and posterior distribution are shown in figure 2.

Table 3. Bayesian estimation results of dynamic parameters.

Parameter	Parameter description	Prior mean	Prior distribution	Posterior mean	Confidence interval
$\mu$	Negative utility coefficient of pollutant emissions	0.300	Normal	0.3006	[0.2853,0.3165]
$\eta$	Positive utility coefficient of pollution control expenditure	0.120	Normal	0.1231	[0.1087,0.1388]
${\rho }_{A}$	First-order autoregressive coefficient of technology	0.350	Beta	0.3796	[0.3462,0.4119]
${\rho }_{PS}$	First-order autoregressive coefficient of resource price	0.300	Beta	0.2991	[0.2665,0.3344]
${\rho }_{\omega }$	First-order autoregressive coefficient of the firm's compensation ratio	0.300	Beta	0.3027	[0.2690,0.3356]
${\rho }_{\chi }$	First-order autoregressive coefficient of household and government supervision	0.300	Beta	0.2968	[0.2573,0.3277]
${\rho }_{E{P}_{0}}$	First-order autoregressive coefficient of pollutant emission threshold	0.300	Beta	0.3014	[0.2730,0.3336]
${\rho }_{P}$	The first-order autoregressive coefficient of government's pollution control efforts	0.300	Beta	0.2993	[0.2690,0.3383]
${\varepsilon }_{A,t}$	Random disturbance term of technology	10	Inv. Gamma	9.7921	[7.5364,12.1308]
${\varepsilon }_{PS,t}$	Random perturbation term of resource price	1	Inv. Gamma	0.7438	[0.2937,1.3194]
${\varepsilon }_{\omega ,t}$	Random disturbance term of firm's compensation ratio	1	Inv. Gamma	0.9321	[0.2947,1.6001]
${\varepsilon }_{\chi ,t}$	Random disturbance term of household and government supervision	1	Inv. Gamma	0.6772	[0.2867,1.0976]
${\varepsilon }_{P,t}$	Random disturbance term of government's pollution control efforts	24	Inv. Gamma	23.7556	[21.1098,26.1274]
${\varepsilon }_{E{P}_{0},t}$	Random disturbance term of pollutant emission threshold	1	Inv. Gamma	1.0522	[0.2767,2.2944]

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According to equation (29), the indicator system of the green development level includes seven variables: output, consumption, resource input, labour, pollution control expenditure, and pollutant emission. The data are from China Statistical Yearbook, China Environmental Statistical Yearbook, and China Energy Statistical Yearbook from 2000 to 2018. As some variables involve secondary indicators, we intend to use the standardisation method to carry out dimensionless indicators of each dimension and then use the entropy method to get the contribution weight for indicators of each dimension. Finally, use the linear weighted method to work out the overall green development level. Specifically, the estimation results of correlation coefficients are shown in table 4.

Table 4. The weight coefficient estimation results of green development level.

Parameter	${q}_{1}$	${q}_{2}$	${q}_{3}$	${q}_{4}$	${q}_{5}$	${q}_{6}$	${q}_{7}$
Weights	0.1079	0.0709	0.0799	0.2276	0.2388	0.0545	0.2204