How Does the Carbon Tax Influence the Energy and Carbon Performance of China’s Mining Industry?

Abstract

As the world’s largest energy consumer, China’s CO₂ emissions have significantly risen, owing to its rapid economic growth. Hence, levying a carbon tax has become essential in accelerating China’s carbon neutralization process. This paper employs the two-stage translog cost function to calculate the price elasticity of the mining industry’s energy and input factors. Based on the price elasticity, the carbon tax’s influence on the mining industry’s energy and carbon performance is estimated. In the calculation of energy efficiency, the non-radial directional distance function is adopted. The results express that the carbon tax significantly decreases the mining industry’s CO₂ emissions and promotes its energy and carbon performance. In addition to levying a carbon tax, the government should also strengthen the market-oriented reform of the oil and power infrastructure to optimize the mining industry’s energy structure.

1. Introduction, Literature Review, and Motivation of the Paper

1.1. Introduction

With the goal of carbon neutralization proposed by China’s government, the low-carbon transformation of the energy economy has become an inevitable trend [1]. As the world’s largest energy consumer, China’s CO₂ emissions have risen as a result of its rapid economic growth. According to the 2021 BP World Energy Statistical Yearbook [2], China’s carbon dioxide emissions were 9.90 billion tons in 2020, about 30.66% of the global carbon dioxide emission. Even though China’s CO₂ emission growth rate has slowed down in recent years, achieving the carbon peak goal in 2030 is a difficult challenge especially when industrialization and urbanization are advancing rapidly. According to the Environmental Kuznets Curve (EKC), when the economy grows to a certain extent, the environmental quality will be improved with the continuous growth of per capita income [3]. The EKC has been confirmed in many developed countries. To reduce CO₂ emissions and ensure China’s sustainable development, the energy reform of traditional industries is imperative.

As China’s traditional heavy industry, the mining industry (MI) is vital to the national economy and infrastructure construction. Although the central government has put forward the control for the total energy consumption and intensity and implemented strict control over all kinds of coal power projects, optimizing the energy structure and reducing coal consumption has been a gradual process. At present, coal is still China’s primary energy source. According to the 2021 BP World Energy Statistical Yearbook [2], China’s coal energy consumption accounted for 56.56% of its national energy consumption in 2020. Therefore, ensuring China’s coal supply at this stage is essential for energy security. On the other hand, the MI provides an important material guarantee for China’s industrial development and various infrastructure construction, which makes it a pillar industry for China’s modernization. However, the MI’s CO₂ emission cannot be ignored as a high energy-consuming industry. Based on the China Energy Statistical Yearbook [4], China’s MI’s CO₂ emission in 2019 was about 747 million tons, which exceeded the total CO₂ emission of many countries in 2019. Reducing the MI’s CO₂ emissions and improving its energy efficiency are essential for carbon neutralization.

A variety of policy means must be employed to decrease CO₂ emissions. The carbon trade market and carbon tax have attracted extensive attention in recent years. The carbon trade market means that the government department formulates the total carbon emission and allocates carbon emission quotas to each enterprise participating in the carbon market. If the enterprise’s CO₂ emission is below the quota, the enterprise sells the remaining quota to obtain income. If the enterprise’s CO₂ emission exceeds the quota, it must purchase quotas from other enterprises. Since 2011, China has carried out the pilot work of the carbon market construction in seven provinces and cities, which has taken an essential step towards the national carbon emission reduction and carbon peak goal in 2030 [5,6,7,8]. In 2021, the national carbon emission trading market launched online trading, and more than 2000 key emission units were included in the market. China’s carbon market will become the largest market in the world, covering about 4.5 billion tons of CO₂ emission [9]. However, the carbon market mainly covers the power generation industry and key emission units. Even when the carbon market is mature in the future, it is still difficult to cover the whole industry.

Conversely, allocating carbon emission quotas can also be very complex as the carbon tax is a price policy. The government department stipulates the tax rate, and the market determines the carbon dioxide emission reduction. Although the carbon tax policy cannot control the total amount of carbon dioxide emission, it has a lower administrative cost, broader coverage, and is easier to coordinate with other policies [10]. On the other hand, the carbon tax policy can also increase government revenue to enable the government to continue its investments in emission reduction projects to form a sustainable emission reduction path. As a carbon tax is a valuable way to control carbon emission, Japan, Australia, the Netherlands, Norway, Sweden, and Colombia have successively implemented carbon tax policies [11]. To sum up, the carbon tax is essential for rationalizing the policy system and accelerating China’s carbon neutralization process.

1.2. Literature Review and Motivation of the Paper

In recent years, the carbon tax has been a hot issue in economics. Although China’s government has begun to levy resource taxes on fossil fuels, it has not yet set up a tax aimed explicitly at carbon dioxide emission. The carbon tax is a type of environmental tax, and environmental tax is the general name of a series of tax systems aimed at protecting the ecological environment. The research on environmental tax can be traced back to Arthur Cecil Pigou [12]. Pigou first proposed to make up the gap between the private cost and social cost of polluters’ production through levying a tax, which is the “Pigouvian tax”. Tullock [13] pointed out that the Pigouvian tax can achieve a “double benefit” effect through the internalization of external costs. Pearce [14] proposed the concept of “double dividend” when studying the influence of the carbon tax on global warming. The research pointed out that levying carbon tax can reduce carbon dioxide emission and support environmental protection services or economic development. There has been long-standing research on carbon tax in academia, as most economists believe that carbon tax policy can bring multiple benefits. Newell and Pizer [15] believe that the carbon tax is generally higher than the carbon market under uncertain terms of net social welfare. The research of Wittneben [10] and Goulder and Schein [16] showed that the total administrative cost of carbon tax policy is low, and it is easy to coordinate with other carbon emission reduction policies. However, some scholars question the carbon tax. The enterprises’ profits will reduce because the carbon tax policy raises carbon dioxide emission costs. A relatively higher carbon tax rate may inhibit the development of enterprises, while a relatively lower tax rate cannot reduce carbon dioxide emission [17]. Newell and Pizer [18] believed that a carbon tax will encounter excellent resistance in practice, and levying a carbon tax can be difficult. Chen and Chen [19] think that carbon tax raises the financial burden of enterprises. He et al. [20] showed that a carbon tax will reduce the savings and investment of enterprises and squeeze the living space of small and medium-sized enterprises. In conclusion, the formulation of the carbon tax policy is a very complex problem.

In recent years, as the world pays more and more attention to carbon dioxide emissions reduction, carbon tax policies have begun to attract scholars’ attention. Ghaith and Epplin [21] studied how the carbon tax influences the household electricity cost in the U.S and estimated whether it is sufficient to encourage households to install grid-connected solar or wind energy systems. Chen and Hu [22] explored the behavior strategies of producers under different carbon taxes and subsidies. They found that levying carbon tax can provide more incentives for the manufacturing industry than low-carbon technology subsidies. The research of Zhou, An, Zha, Wu, and Wang [11] showed that adopting the block carbon tax can visibly reduce the tax burden of enterprises and encourage enterprises to produce low-carbon products. Brown et al. [23] showed that the carbon tax policy can increase employment opportunities in the United States. Denstadli and Veisten [24] believed that Norwegian tourists are willing to accept the higher air costs to pay the carbon tax. Cheng et al. [25] studied how the carbon tax influences energy innovation in the Swedish economy. They found that when the rate exceeds a certain point, increasing the carbon tax rate will not promote energy innovation. Gokhale [26] believed that Japan’s carbon tax rate is too low to achieve carbon emission reduction targets in 2030. Hammerle, et al. [27] investigated the citizens’ acceptance of carbon tax. They found that supporting low-income families is conducive to the promotion of the carbon tax policy.

Due to the proposal of China’s carbon peak and carbon neutralization goal, the academic heat on carbon tax policy is gradually increasing. Although China has not officially launched the carbon tax policy, its research has attracted more and more attention from scholars. The research directions mainly focus on the influence of the carbon tax on economic growth and the actual effect of CO₂ emission reduction. Zhou et al. [28] discussed the influence of the carbon tax on China’s transportation industry with the CGE model. They found that the carbon tax can bring the most negligible negative impact on the transportation industry. Shi et al. [29] discussed how different carbon tax rates influence China’s construction industry’s energy consumption. The results showed that when the carbon tax is 60 yuan/ton, it can achieve the emission reduction target and minimize the negative impact. Li et al. [30] took Shanxi Province of China as an example to prove that carbon tax is instrumental in relieving the employment pressure in coal-rich regions. Hu et al. [31] contrasted the resource tax and carbon tax from different aspects. They found that the carbon tax’s comprehensive performance is much better than the resource taxes.

The effect of the carbon tax on CO₂ emission reduction is associated with energy substitution [32]. Levying a carbon tax will cause energy price changes, as the energy cost increases based on its carbon dioxide emission coefficient. Manufacturers will prefer clean energy to replace high-carbon energy. Furthermore, the carbon tax can raise the total energy cost and reduce the relative cost of other input factors, making producers more inclined to use other input factors to replace energy input. Many scholars have studied energy price elasticity and input factors price elasticity in China, but these studies do not consider the relevance between them [33,34,35]. Cho et al. [36] believed that the price change of a single energy type can lead to the substitution among energy and lead to the substitution among input factors. Therefore, the two kinds of price elasticity should be considered. Pindyck [37] proposed a two-stage translog cost function to include the correlation of energy price elasticity and input factors price elasticity. In recent years, many pieces of literature have used this method to calculate price elasticity [38,39,40,41,42,43]. Based on these studies, this paper uses the two-stage translog cost function to estimate the price elasticity of the energy and input factors in the MI. Furthermore, based on the price elasticity, the influence of the carbon tax on the energy and carbon performance (ECP) of China’s MI is also explored. The contributions are as follows. Firstly, different from the previous studies [44,45,46], based on estimating the carbon tax’s influence on carbon dioxide emission reduction, a non-radial directional distance function (NDDF) is adopted to calculate the ECP of the MI and the influence of the carbon tax on ECP is explored. Secondly, the translog cost function is employed to measure the price elasticity of energy and input factors in China’s MI, which supplements the existing literature. Finally, according to the empirical results, corresponding policy recommendations are proposed which are vital to achieving China’s carbon peak and carbon neutralization goals.

The second part describes the methodologies and data while the third part calculates the price elasticity of energy and input factors in China’s MI. The fourth part estimates the MI’s carbon dioxide emission reduction potential and the influence of carbon tax on the MI’s ECP. In the fifth part, the corresponding policy suggestions are put forward according to the empirical results of this paper.

2. Methodologies and Data

2.1. Calculation of the Price Elasticity

Based on Cho, Nam and Pagán [36] and Ma et al. [47], this paper assumes that the MI in each province has a quadratic differentiable total output function, which links the total output (Y) with the capital (K), labor (L) and energy (E). According to Yang, Fan, Yang, and Hu [44] and Li and Sun [48], energy can be combined into three types: coal, oil, and electricity. Assuming that the production function is weakly separable among the main energy, capital, and labor components, a total energy price index is constructed including coal price, oil price, and electricity price. In addition, presuming that all input factors are homogeneous, a homogeneous translog energy cost share equation is specified [36], and the total production function is described as:

$$Y=F\left[K,L,E\left(CO,OI,EL\right)\right]$$

(1)

where CO, OI, and EL represent the MI’s coal, oil, and electricity consumption respectively. If the input factors’ price and the output are exogenous, Equation (1) can also be described by a unique cost function. According to the duality theory, the cost function is also weakly separable.

$$C=G\left[P_K,P_L,P_E\left(P_{CO},P_{OI},P_{EL}\right);Y\right]$$

(2)

where C represents the total cost. $P_K$ and $P_L$ mean the prices of capital and labor. $P_E$ is the total energy price index. Since the translog function is considered as the second-order approximation of any quadratic differentiable cost function. To facilitate estimation, Equation (2) is converted into a non-homogeneous translog cost function [42,49]:

$$\begin{gathered} lnC={\beta }_0+{{\displaystyle \sum }}_i{\beta }_{i}ln{P}_i+{{\displaystyle \sum }}_i{\varnothing }_{i}lnYln{P}_i+\frac{1}{2}{{\displaystyle \sum }}_i{{\displaystyle \sum }}_j{\beta }_{ij}ln{P}_{i}ln{P}_j+{\beta }_{Y}lnY \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\frac{1}{2}{\beta }_{YY}{\left(lnY\right)}^2+{\beta }_{t}t+\frac{1}{2}{\beta }_{tt}{t}^2+{{\displaystyle \sum }}_i{\beta }_{it}tln{P}_i+{\beta }_{Yt}tlnY\left(i,j=K,L,E\right) \end{gathered}$$

(3)

In Equation (3), Y, C, and P represent the output, total cost, and inputs price of the MI, respectively. T represents the time trend. The first year is equal to 1, the second year is equal to 2, and so on. To minimize the cost function, according to Shephard lemma, the demand of input factors is defined as the partial derivative of the total cost function to the corresponding prices, that is:

$$x_i=\frac{\partial C}{\partial P_i}\left(i=K,L,E\right)$$

(4)

In Equation (4), $x_i$ is the i-th input demand. C represents the total cost. $P_i$ represents the i-th input price. To sum up, the cost-share function can be expressed as:

$$S_i=\frac{x_i·P_i}{C}=\frac{P_i}{C}·\frac{\partial C}{\partial P_i}=\frac{\partial lnC}{\partial ln{P}_i}$$

(5)

$S_i$ means the i-th input factor’s share. Bring Equation (3) into Equation (5) and take the partial derivative of the$lnC$ to $ln{P}_i$, then $S_i$ can be expressed as:

$$S_i=\frac{\partial lnC}{\partial ln{P}_i}={\beta }_i+{\varnothing }_{i}lnY+{\displaystyle \sum }_{j=1}^3{\beta }_{ij}ln{P}_j+{\beta }_{it}t\left(i,j=K,L,E\right)$$

(6)

According to Zha, et al. [50], the following regularization conditions need to be set for Equation (6):

$${\beta }_{ij}={\beta }_{ji}foralli\ne j$$

(7)

$${{\displaystyle \sum }}_i{\beta }_i=1;{{\displaystyle \sum }}_i{\beta }_{ij}={{\displaystyle \sum }}_j{\beta }_{ij}=0;{{\displaystyle \sum }}_i{\varnothing }_i={{\displaystyle \sum }}_i{\beta }_{it}=0\left(i,j=K,L,E\right)$$

(8)

By estimating the coefficient in Equation (6), the input factors’ own-price elasticity ${\eta }_{ii}$and cross-price elasticity ${\eta }_{ij}$ can be calculated as:

$${\eta }_{ii}=\frac{{\beta }_{ii}}{S_i}+S_i-1,\left(i=j\right)and{\eta }_{ij}=\frac{{\beta }_{ij}}{S_i}+S_j,\left(i\ne j\right)\left(i,j=K,L,E\right)$$

(9)

To measure the MI’s input factors price elasticity, the total energy price is needed. Based on Pindyck [37], the total cost function and the energy price function are both assumed to follow the translog form. The energy price function can be described as:

$$ln{P}_E={\gamma }_0+{{\displaystyle \sum }}_m{\gamma }_{m}ln{P}_m+\frac{1}{2}{{\displaystyle \sum }}_m{{\displaystyle \sum }}_n{\gamma }_{mn}ln{P}_{m}ln{P}_n+{{\displaystyle \sum }}_m{\gamma }_{mt}tln{P}_m\left(m,n=CO,OI,EL\right)$$

(10)

In Equation (10), m and n represent the energy types. $P_m$ and $P_n$ represent the energy price. $P_E$ represents the total energy price index. By differentiating Equation (10) with various energy prices, the energy share equation can be derived as follows:

$$S_m^{fuel}=\frac{\partial ln{P}_E}{\partial ln{P}_m}={\gamma }_m+{{\displaystyle \sum }}_n{\gamma }_{mn}ln{P}_n+{\gamma }_{mt}t\left(m,n=CO,OI,EL\right)$$

(11)

Like Equation (6), Equation (11) requires the following constraints:

$${\gamma }_{mn}={\gamma }_{nm}forallm\ne n$$

(12)

$${{\displaystyle \sum }}_m{\gamma }_m=1;{{\displaystyle \sum }}_m{\gamma }_{mn}={{\displaystyle \sum }}_n{\gamma }_{mn}=0;{{\displaystyle \sum }}_m{\gamma }_{mt}=0\left(m,n=CO,OI,EL\right)$$

(13)

Based on Equation (11), the own-price elasticity of the three energy types ${\epsilon }_{mm}$ and cross-price elasticity ${\epsilon }_{mn}$ can be calculated as:

$${\epsilon }_{mm}=\frac{{\gamma }_{mm}}{S_m^{fuel}}+S_m^{fuel}-1,\left(m=n\right)and{\epsilon }_{mn}=\frac{{\gamma }_{mn}}{S_m^{fuel}}+S_n^{fuel},\left(m\ne n\right)\left(m,n=CO,OI,EL\right)$$

(14)

Nevertheless, the energy price elasticity is considered with the condition that the total energy consumption is maintained [37]. According to Cho, Nam and Pagán [36] and Floros and Vlachou [51], this paper further considers the feedback effect due to the price change of a single energy type, the energy’s own-price elasticity and cross-price elasticity as specified:

$${\epsilon }_{mm}^{*}={\epsilon }_{mm}+{\eta }_{EE}·S_m^{fuel},\left(m=n\right)and{\epsilon }_{mn}^{*}={\epsilon }_{mn}+{\eta }_{EE}·S_n^{fuel},\left(m\ne n\right)\left(m,n=CO,OI,EL\right)$$

(15)

In Equation (15), ${\eta }_{EE}$ is the energy’s own-price elasticity of the MI, according to Equation (9).

2.2. Calculation of ECP

To measure the impact of CO₂ emissions on the MI’s energy efficiency, the NDDF is employed to benchmark the ECP of the MI. The input factors include capital stock (K), labor (L), and energy (E). The total industrial output value (Y) of the MI is the desirable output, and the carbon dioxide emission (C) is the undesirable output. The production technology set is described as:

$$T = \left\{\left(K,L,E,Y,C\right): \left(K,L,E\right)canproduce\left(Y,C\right)\right\}$$

(16)

According to Zhou, et al. [52], the production technology set can be represented by the following linear constraints:

$$\begin{array}{c}T = \left\{\left(K,L,E,Y,C\right) : \left(K,L,E\right)canproduce\left(Y,C\right)\right\}\\ {\displaystyle {\displaystyle \sum }_{t=1}^T}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\lambda }_{nt}{K}_{nt}\le K\\ {\displaystyle {\displaystyle \sum }_{t=1}^T}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\lambda }_{nt}{L}_{nt}\le L\\ {\displaystyle {\displaystyle \sum }_{t=1}^T}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\lambda }_{nt}{E}_{nt}\le E\\ {\displaystyle {\displaystyle \sum }_{t=1}^T}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\lambda }_{nt}{Y}_{nt}\ge Y\\ {\displaystyle {\displaystyle \sum }_{t=1}^T}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\lambda }_{nt}{C}_{nt}=C\\ {\lambda }_{nt}\ge 0\\ t=1,2,3,\dots ,T\\ n=1,2,3,\dots ,N\end{array}$$

(17)

${\lambda }_{nt}$ can be considered as the intensity variable by using convex combinations. Zhou, Ang and Wang [52] proposed a formal definition of the NDDF:

$$\stackrel{\rightharpoonup }{ND}\left(K,L,E,Y,C;g\right)=\sup \left\{w^T\beta :\left(\left(K,L,E,Y,C\right)+diag\left(\beta \right)·g\right)ϵT\right\}$$

(18)

where $w={\left(w_K,w_L,w_E,w_Y,w_C\right)}^T$ represents the weight given to each factor, and $g={\left(g_K,g_E,g_L,g_Y,g_C\right)}^T$ represents the change direction of each factor. $\beta ={\left({\beta }_K,{\beta }_E,{\beta }_L,{\beta }_Y,{\beta }_C\right)}^T\ge 0$ is the slack vector, representing the rate of increase or decrease of each factor. $diag\left(\beta \right)$ means the diagonalization of $\beta$. To measure the ECP of the MI, this paper sets the weight vector as $w={\left(0,0,\frac{1}{3},\frac{1}{3},\frac{1}{3}\right)}^T$, the direction vector as $g=\left(0,0,-E,Y,-C\right)$, and the slack vector as $\beta ={\left(0,0,{\beta }_E,{\beta }_Y,{\beta }_C\right)}^T\ge 0$. The NDDF’s linear optimization problem can be described as follows:

$$\begin{array}{c}\overrightarrow{ND}\left(K,E,L,Y,C;g\right)=max{w}_E{\beta }_E+w_Y{\beta }_Y+w_C{\beta }_C\\ {\displaystyle {\displaystyle \sum }_{t=1}^T}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\lambda }_{nt}{K}_{nt}\le K\\ {\displaystyle {\displaystyle \sum }_{t=1}^T}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\lambda }_{nt}{L}_{nt}\le L\\ {\displaystyle {\displaystyle \sum }_{t=1}^T}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\lambda }_{nt}{E}_{nt}\le E-{\beta }_E{g}_E,\\ {\displaystyle {\displaystyle \sum }_{t=1}^T}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\lambda }_{nt}{Y}_{nt}\ge Y+{\beta }_Y{g}_Y,\\ {\displaystyle {\displaystyle \sum }_{t=1}^T}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\lambda }_{nt}{C}_{nt}=C-{\beta }_C{g}_C,\\ {\beta }_E,{\beta }_Y,{\beta }_C\ge 0,{\lambda }_{nt}\ge 0\\ n=1,2,3,\dots ,Nt=1,2,\dots ,T\end{array}$$

(19)

According to Equation (19), the optimization result is ${\beta }^{*}={\left(0,0,{\beta }_E^{*},{\beta }_Y^{*},{\beta }_C^{*}\right)}^T$. According to Zhou, Ang, and Wang [52], the energy and carbon performance index (ECPI) can be expressed as:

$$ECPI=\frac{\frac{1}{2}\left[\left(1-{\beta }_E^{*}\right)+\left(1-{\beta }_C^{*}\right)\right]}{1+{\beta }_Y^{*}}$$

(20)

The value of ECPI is between 0 and 1. The higher the value, the better the ECP.

2.3. Impact of the Carbon Tax on MI’s ECP

The carbon tax can cause changes in energy prices. According to Agostini et al. [53], the energy price rise because of the carbon tax is described as follows:

$$\Delta p_i=\frac{t\times e_i}{p_i}\times 100\%\left(i=CO,OI,EL\right)$$

(21)

where $\Delta P_i$ is the increasing rate of the i-th energy’s price. t means the carbon tax rate. $e_i$ represents the CO₂ emission coefficient of the i-th energy. $p_i$ is the initial price of the i-th energy source. Based on similar research [32,44], this paper assumes that the carbon tax price is 50 yuan/ton. According to Chen [54], the calculation of CO₂ emissions can be described as follows:

$$C_t=\sum E_i\times NC{V}_i\times CE{F}_i\times CO{F}_i\times (\frac{44}{12})$$

(22)

where $C_t$ is CO₂ emission. $E_i$ is the consumption of each energy. $NC{V}_i$ represents the average low calorific value; $CE{F}_i$ is the carbon coefficient in the 2006 IPCC report; $CO{F}_i$ is carbon oxidation factor. According to Equation (22), the CO₂ emission coefficient of each energy can be expressed with the following equation:

$$e_i=NC{V}_i\times CE{F}_i\times CO{F}_i\times (\frac{44}{12})$$

(23)

Therefore, levying a carbon tax will change the energy prices as follows:

$$n{p}_i=(1+\Delta p_i)\times p_i\left(i=CO,OI,EL\right)$$

(24)

where $n{p}_i$ is the i-th energy price after levying the tax. The change in energy price will cause the change in energy demand, which can be described as follows:

$$\Delta E_i={{\displaystyle \sum }}_j\Delta p_j\times {\epsilon }_{ij}^{*}\times E_i\left(i,j=CO,OI,EL\right)$$

(25)

Among them, ${\epsilon }_{ij}^{*}$ is the own-price elasticity and cross-price elasticity of each energy type in Equation (15). Changing the consumption of different energy types will lead to changes in the energy structure of the MI, resulting in changing the total energy price index. Therefore, the total energy price index of the MI must be re-estimated with Equations (10) and (13) so that the changes in the labor and capital stock of the MI can be further calculated. The changes of capital and labor are as follows:

$$\Delta D_i=\left(\frac{\Delta P_E}{P_E}\right)·{\eta }_{iE}·D_i\left(i=K,L\right)$$

(26)

$\Delta PE$ represents the change in the MI’s total energy price index. $D_i$ is the original demand of the i-th input factor and ${\eta }_{iE}$ is the cross-price elasticity between energy and the i-th input factor. Finally, due to the change of energy structure caused by the carbon tax, the change of carbon dioxide emission of the MI can be described as follows:

$$\mathsf{\Delta }C{O}_2={{\displaystyle \sum }}_i{{\displaystyle \sum }}_j\Delta p_j\times {\epsilon }_{ij}^{*}\times E_i\times e_i\left(i,j=CO,OI,EL\right)$$

(27)

The changes in ECP of the MI due to the carbon tax can be calculated by Equations (26) and (27).

2.4. Data Processing

The panel data of China’s MI spans from 2004 to 2019. Based on similar research [32,38,42,43,44,46], this paper chooses the main variables which are necessary for calculating the price elasticities with a two-stage translog function, including capital stock (K) and its price ($P_K$), the labor (L) and its price ($P_L$), energy consumption (E) and its classified price ($P_{CO}$, $P_{OI}$, $P_{EL}$), the gross industrial output value (Y), and carbon dioxide emission (C). Considering that some provinces have a small proportion of the MI or lack the data, this paper excludes the observation data from Beijing, Shanghai, Zhejiang, Jiangsu, Hainan, and Tibet to ensure estimation accuracy. All nominal variables in this paper are deflated to the fixed price in 2004.

The gross industrial output value data is taken from China Industry Statistical Yearbook [55]. Since the China Industry Statistics Yearbook from 2012 to 2016 only counts the industrial sales output value of the MI, the average ratio between the gross industrial output value and the industrial sales output value from 2004 to 2011 is adopted to estimate the gross industrial output value from 2012 to 2016. From 2018 to 2019, the statistical subjects of the China Industry Statistical Yearbook have changed. Therefore, this paper uses the operating income of the MI to replace the gross industrial output value. The data in 2017 are measured by the linear interpolation method since they are not counted.

The perpetual inventory method is employed to measure the MI’s capital stock, which is described as follows:

$$K_{it}=K_{it-1}\left(1-{\delta }_{it}\right)+I_{it}$$

(28)

$K_{it}$ represents the capital stock. ${\delta }_{it}$ stands for depreciation rate.$I_{it}$ is fixed asset investment. The depreciation rate is weighted according to the classification of the investment, and the fixed asset investment data of the MI is extracted from China Statistical Yearbook. The price of capital stock is measured as follows [44]:

$$P_K\left(it\right)=r\left(t\right)+\delta \left(t\right)-\pi \left(it\right)$$

(29)

where, $P_K\left(it\right)$ is the price of capital stock in each province. $r\left(t\right)$ means the loan interest rate of the fixed asset. $\delta \left(t\right)$ is the depreciation rate in Equation (28). $\pi \left(it\right)$ means the actual inflation rate calculated according to the consumer price index (CPI) of each province. The loan interest rate and the CPI of each province are extracted from the CEIC database [56].

The labor data is extracted from China Industry Statistical Yearbook [55]. Due to the lack of data on labor in 2011, the linear interpolation method is adopted to supplement the data. The average annual wage of the MI represents the labor price, which is extracted from the China Labor Statistical Yearbook [57].

The energy consumed by the MI includes raw coal, coke, washed coal, other washed coal, crude oil, gasoline, diesel, kerosene, fuel oil, liquefied petroleum gas, natural gas, and electricity. For ease of calculation, this paper combines raw coal, coke, washed coal, and other washed coal into coal consumption; and combines crude oil, gasoline, diesel, kerosene, fuel oil, and liquefied petroleum gas into oil consumption. Because the natural gas consumption of the MI is small and the unit is not easy to be unified with other energy varieties, this paper ignores the natural gas consumption. Electricity consumption in the MI is a separate category. The energy prices are extracted from the CEIC database [56]. Due to the lack of provincial industrial energy price data, this paper takes the energy prices of coal, oil, and natural gas in provincial capitals in 2004 as the benchmark price and uses the provincial energy purchase price index to calculate the energy prices. The power price of each provincial capital city is used as the proxy variable of the power price of the MI. The calculation method of CO₂ emission is the same as that in Zhu and Lin [58], which will not be repeated in this paper. The descriptive statistics of all data are shown in

Table 1. Descriptive statistics of data.

Variables	Unit	N	Mean	Sd	Min	Max
C	104 tons	400	4430.00	5890.00	34.44	32,419.00
Y	108 CNY	400	953.50	971.70	43.69	5249.00
L	104 persons	400	25.95	23.62	1.24	108.40
K	108 CNY	400	1541.00	1344.00	21.07	6441.00
E	104 tons of standard coal	400	1624.00	2140.00	28.62	11,680.00
$P_K$	/	400	0.16	0.02	0.10	0.25
$P_L$	CNY/person	400	49,821.00	26,875.00	10,838.00	144,803.00
$P_{EL}$	CNY/104 KW·h	400	6981.00	1243.00	3640.00	9300.00
$P_{OI}$	CNY/ton	400	6841.00	1512.00	4095.00	12,895.00
$P_{CO}$	CNY/ton	400	679.20	207.10	242.20	1361.00

.

3. Empirical Results

In other similar studies, few scholars paid attention to the control variables when estimating the price elasticity with the two-stage translog cost function. Yang, Fan, Yang and Hu [44] took the industrial structure and economic development level as control variables because they believed those factors can influence the price elasticities. Moreover, based on Lin and Zhu [59], the ownership structure can influence the rebound effect of MI, which may affect its energy price elasticity. Therefore, to eliminate the influence of other endogenous factors, this paper chooses economic development level, industrial structure, and ownership structure as control variables. Industrial structure refers to the proportion of MI in the whole industry in each province. The economic development level refers to the per capita GDP in each province. The ownership structure refers to the proportion of MI’s state-owned capital in each province. This paper employs the step-by-step method to calculate the required parameters to calculate the price elasticity of energy and input factors. First, Equation (11) is estimated by the seemingly uncorrelated regression (SUR) method. The total energy price index is calculated by Equation (10). Finally, the parameters in Equation (6) are estimated using the SUR method. After getting the corresponding parameters, the price elasticity can be calculated through Equations (9), (14), and (15). It should be noted that the energy price used in Equation (6) is the total energy price index calculated by Equation (10). On the other hand, there are two reasons that the constant term in Equation (10) is ignored. Firstly, because Equation (11) is derived from Equation (10), the constant term is eliminated in Equation (11). Secondly, when estimating Equation (6), the logarithm of the total energy price index of the MI is used. Therefore, ignoring the constant term in Equation (10) will not affect the estimation result of Equation (6).

3.1. Estimation Results of Energy Cost Share Equation and Input Cost Share Equation

Equation (11) is estimated by the SUR method. Due to the constraints of Equation (13), when assessing the simultaneous equations, a singular matrix will be generated. Therefore, one of the equations must be deleted. The estimation results are expressed in

Table 2. Estimation results of energy cost share equation.

Variables	${\mathit{S}}_{\mathit{C}\mathit{O}}^{\mathit{f}\mathit{u}\mathit{e}\mathit{l}}$	${\mathit{S}}_{\mathit{E}\mathit{L}}^{\mathit{f}\mathit{u}\mathit{e}\mathit{l}}$
$ln{P}_{EL}$	0.114 ***	0.245 ***
	(3.394)	(7.117)
$ln{P}_{OI}$	0.0261	−0.359 ***
	(0.718)	(−11.08)
$ln{P}_{CO}$	−0.140 ***	0.114 ***
	(−2.681)	(3.394)
t	0.0259 ***	−0.000751
	(6.577)	(−0.273)
Constant	0.274 **	0.470 ***
	(2.112)	(5.531)
Control variables	Yes	Yes
Observations	400	400
R-squared	0.166	0.217

z-statistics in parentheses. *** p < 0.01, ** p < 0.05.

. In the coal cost share equation, except for the coefficient of oil price which is not significant, the coefficient of other energy prices is significant at 1%, and the constant term’s coefficient is significant at 5%. In the electricity cost share equation, the coefficients of all energy prices and constant term are significant at 1%.

According to the estimation results of Equation (11), the total energy price index of the MI can be measured by Equation (10). As for estimating the factor cost share equation, similar to the energy cost share equation, to avoid generating a singular matrix in the estimation process, the energy cost equation is deleted, as the estimation results of capital and labor cost equations are shown in

Table 3. Estimation results of input factor cost share equation.

Variables	SK	SL
lnPK	0.151 ***	−0.0744 ***
	(5.619)	(−5.313)
lnPE	−0.0765 ***	0.0329 **
	(−2.957)	(2.213)
lnPL	−0.0744 ***	0.0414 ***
	(−5.313)	(2.740)
lnY	−0.0537 ***	0.0201 ***
	(−6.833)	(4.769)
t	0.0182 ***	−0.00749 ***
	(6.632)	(−3.584)
Constant	2.038 ***	−0.648 ***
	(7.561)	(−4.341)
Control variables	Yes	Yes
Observations	400	400
R-squared	0.457	0.224

z-statistics in parentheses. *** p < 0.01, ** p < 0.05.

. In the capital cost share equation, the coefficients of all input factor prices and constant term are significant at 1%. In the labor cost share equation, except that the coefficient of total energy price is significant at 5%, the coefficients of other input factor prices and the constant term are significant at 1%. According to the estimation results of the energy cost share equation and input factor cost share equation, most of the coefficients are significant at 1%, indicating that the translog function has an excellent explanatory ability for the energy cost and input factor cost of the MI.

3.2. The Price Elasticity of Energy and Input Factors

According to the coefficients estimated by the energy cost share equation and the input factor cost share equation, the price elasticity of energy and input factors of the MI can be obtained. For the own-price elasticity, if it is positive, the demand for energy or input factors will increase with the price rise. If it is negative, the demand for energy or input factors will decrease with the price increase. For the cross-price elasticity, if it is positive, it means that the two kinds of energy sources or input factors are substitutes. If it is negative, it means that the two kinds of energy sources or input factors are complements.

The improved energy price elasticity of the MI can be measured based on Equation (15). In

Table 4. Own-price and cross-price elasticity of energy.

Own-Price Elasticity		Cross-Price Elasticity
${\epsilon }_{CO-CO}^{*}$	−1.058	${\epsilon }_{CO-EL}^{*}$	0.385
${\epsilon }_{EL-EL}^{*}$	−0.093	${\epsilon }_{CO-OI}^{*}$	0.140
${\epsilon }_{OI-OI}^{*}$	0.879	${\epsilon }_{EL-CO}^{*}$	0.580
		${\epsilon }_{EL-OI}^{*}$	−1.019
		${\epsilon }_{OI-CO}^{*}$	0.369
		${\epsilon }_{OI-EL}^{*}$	−1.781

, except for the oil price elasticity which is positive, the coal and electricity price elasticities are negative for the own-price elasticity. It indicates that the demand for coal and electricity in the MI gradually decreases with the rise of price, while the oil demand gradually increases. The coal own-price elasticity’s absolute value is greater than 1, indicating that China’s MI’s coal demand is very sensitive to price. Coal accounts for the most significant share in the total energy consumption of the MI due to China’s special resource endowment. During the 13th Five Year Plan, the government requires to control the total energy consumption and energy intensity, which means that by 2020, the unit energy consumption will decrease by 15% compared with that in 2015, and the total energy consumption will be limited in 5 billion tons of standard coal. According to the “double control” policy, coal consumption must be limited to reduce energy intensity. For China’s MI, rising coal prices can control coal consumption effectively.

On the other hand, the electricity’s own-price elasticity’s absolute value is the lowest among the three energy sources, implying that the MI’s electricity demand is not sensitive to price changes, which is consistent with the conclusions in Li and Lin [32] and Tan and Lin [42]. Due to the proposal of the goal of carbon neutralization, China is accelerating the process of electrification and expanding the proportion of power in the use of terminal energy in various industries. Therefore, the electricity demand is more rigid than that of coal. As for oil, its own-price elasticity is positive, which indicates that the oil price is distorted. The results are similar to Yang, Fan, Yang, and Hu [44].

There is a substitution relationship between energy types in the MI for the cross-price elasticity between electricity and coal, oil and coal. The cross-elasticity coefficient is less than 1, indicating that these energy sources lack elasticity with each other, and the actual effect of adjusting the mining energy structure by changing the energy prices may be limited. On the other hand, electricity and oil are complementary, indicating that oil and electricity are difficult to replace each other. Since the operation of the MI requires much mechanical equipment, oil and electricity represent the core energy of production and operation. Thus, when the increase of mining equipment causes the rise in oil consumption, the scale of the logistics department also needs to be expanded, so the electricity consumption will also rise.

The price elasticity between input factors can be measured according to Equation (9). In

Table 5. Own-price and cross-price elasticity of input factors.

Own-Price Elasticity		Cross-Price Elasticity
${\eta }_{K-K}$	−0.216	${\eta }_{K-E}$	0.168
${\eta }_{E-E}$	−0.532	${\eta }_{K-L}$	0.048
${\eta }_{L-L}$	−0.592	${\eta }_{E-K}$	0.221
		${\eta }_{E-L}$	0.312
		${\eta }_{L-K}$	0.100
		${\eta }_{L-E}$	0.493

, the own-price elasticity of capital stock, energy, and labor is negative, indicating that the demand for all input factors will decline with the price rising. All input factors’ own-price elasticity’s absolute values are less than 1, meaning that the demands of all input factors are not sensitive to the change of prices. The capital stock has the smallest absolute value, and the labor has the largest. Tan and Lin [42] and Du, Lin, and Li [46] have reached similar conclusions. As the MI is an energy-intensive industry, its fixed assets’ proportion is high such as plants and mining facilities, which is hard to adjust in the short term. Therefore, mining enterprises are more dependent on capital stock. On the other hand, the rigidity of the labor in the MI is the smallest, meaning that the change of labor demand is more sensitive than other input factors.

The cross-price elasticities between all input factors are positive, meaning that there are substitution relationships between all input factors. However, the absolute values of all cross-price elasticity are less than 1, indicating that both labor and capital stock can only finitely replace energy. Similar to the research results of Li and Lin [32] and Du, Lin, and Li [46], among the cross-price elasticities of input factors, the cross-price elasticity between energy and labor is the largest. China has a large population base and rich labor resources. Using labor to substitute for energy consumption can not only reduce CO₂ emission but also alleviate the pressure of social employment. There is a substitution relationship between energy and capital in the MI, which is similar to the research results of Pindyck [37], Ma, Oxley, Gibson, and Kim [39], and Wang and Lin [41]. According to Li and Lin [32], if enterprises update their production equipment, their production efficiency will be improved, as less energy will be consumed under the same output. Therefore, increasing the investment in energy-saving equipment and R&D funds is instrumental in reducing energy investment.

4. Results and Discussion

This part explores the influence of carbon tax on the MI’s ECP. Since the government has not imposed the carbon tax at this stage, this paper follows similar research to set the carbon tax price at 50 yuan/ton. According to Zhu and Lin [58], China’s provinces can be divided into three regions.

Table 6. The area classification.

Region	Provinces
Eastern	Tianjin, Hebei, Liaoning, Fujian, Shandong, Guangdong
Central	Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan
Western	Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang

shows the regional classification.

Due to the different CO₂ emission coefficients, the carbon tax levied per unit consumption of the various energy sources is different under the fixed carbon tax rate. Levying carbon tax will cause changes in energy prices, which will cause changes in various energy consumption in the MI, resulting in changes in CO₂ emission and the total energy price index. The changes in input factors can be calculated according to the own-price elasticity and cross-price elasticity of input factors. Assuming that the desired output of the MI remains unchanged, the change of the MI’s CO₂ emission and ECP can be measured according to the new input factors.

According to Equation (27), the MI’s CO₂ emission reduction potential is calculated in each region. Based on Figure 1, assuming that the carbon tax rates are 50 yuan/ton, in 2019, the MI’s CO₂ emission reduction potential in China is 121.13 million tons. Yang, Fan, Yang, and Hu [44] explored the influence of the carbon tax on China’s CO₂ mitigation. The results show that 197 million tons of CO₂ can be eliminated in 2010 under the 50 yuan/ton tax rate. Li and Lin [32] explored that the carbon tax can cause 311.2 million tons of CO₂ mitigation in 2012 under the 50 yuan/ton tax rate. Liu and Lin [45] explored that China’s building construction industry can mitigate 3.83 million tons of CO₂ in 2012 under the 50 yuan/ton tax rate. Du, Lin, and Li [46] found that levying a carbon tax of 50 yuan/ton can eliminate 62.67 million tons of China’s metallurgical industry’s CO₂ emissions. According to the previous studies, levying a carbon tax can indeed reduce carbon dioxide emission at the national level and the industrial level. Due to the huge amount of CO₂ emission, the MI’s CO₂ emission reduction potential is greater than that of the traditional manufacturing industries. Moreover, the carbon dioxide emission reduction potential in the eastern area is the smallest, while that of the western area is the largest. The carbon tax will increase energy costs and make the mining enterprises use capital and labor instead of energy. The reduction of energy consumption will decrease CO₂ emissions. As the western region is rich in coal, oil, and gas resources and the mining enterprises are mostly concentrated in the western region, the carbon tax takes more conspicuous emission reduction effects in the western area.

The samples under different carbon tax rates are put into one technology set to calculate the ECP. As shown in Figure 2, without the carbon tax, the average value of the ECP is 0.211. When the carbon tax rate is 50 yuan/ton, the average ECP of China’s MI is 0.218, which is 2.86% higher than that without the carbon tax. Among the regions, the ECP of the MI in the eastern region does not increase, while that of the central and western regions significantly improved. Under the carbon tax rate of 50 yuan/ton, the ECP of the MI in the western region increases by 7.24% compared with that without a carbon tax, and the growth rate is the largest among all regions.

Due to the carbon tax, the mining enterprises will prefer capital and labor to energy in the production process. Further, the carbon tax can also optimize the energy consumption structure of mining enterprises and promote enterprises to choose cleaner energy. Without a carbon tax, the ECP of the MI in the eastern region is much higher than that in the central and western regions because the eastern region has a higher level of economic development, a stricter environmental management system, and advanced production technology. Therefore, the carbon tax’s impact on the ECP in the eastern region is not significant. On the other hand, the technological level of the central and western areas is comparatively backward, as they lack talents and capital compared with the eastern region. Therefore, most mining enterprises in the central and western areas use energy to replace capital and labor, resulting in low ECP. Higher energy prices will force the MI in central and western regions to use capital and labor to replace energy consumption. Therefore, the carbon tax policy significantly promotes the MI’s ECP in the central and western regions.

5. Conclusions and Policy Recommendations

5.1. Conclusions

Based on the price elasticity of energy and input factors, this paper estimates the carbon tax’s influence on the ECP of China’s MI. Firstly, the price elasticity of energy and input factors in the MI is estimated with the two-stage translog cost function. Secondly, the changes in MI’s ECP in each region are calculated with NDDF. The conclusions are as follows:

For the energy price elasticity of the MI, except for the oil’s own-price elasticity, which is positive, the own-price elasticities of coal and electricity are negative, meaning that the demand for coal and electricity in the MI decreases with the increase of price. Moreover, except for the cross-price elasticities between oil and electricity, which are negative, the other cross-price elasticities are positive, indicating that oil and electricity are complimentary, while the other types of energy are substitutes. For the price elasticity of input factors in the MI, the own-price elasticity of all input factors is positive, meaning that the demand for capital, labor, and energy decreases with the price increase. The cross-price elasticities of all input factors are positive, meaning that the MI’s capital, labor, and energy are substitutes. It is shown that the carbon tax can significantly decrease the CO₂ emission of the MI and promote its ECP. Under the carbon tax rate of 50 yuan/ton, the ECP of the MI in the eastern area does not raise, while that of the central and western areas significantly improved.

5.2. Policy Recommendations

Based on the calculation results of this paper, the carbon tax cannot only reduce the carbon dioxide emission of the MI but also promote its ECP. Although the carbon trading market has been launched in China, it still needs a long process to cover enough industries. While promoting China’s carbon trading market, the government should join fiscal and tax means to promote carbon emission reduction, such as levying carbon tax on industries not included in the carbon trading market. At present, China only collects resource tax on fossil energy. In 2016, the Chinese government began to implement the resource tax reform, changing the resource tax from quantity-based tax to ad valorem tax [60], which can better reflect the scarcity of mineral resources. However, resource tax is a tax levied on producers, which can only increase the energy cost in the upstream link. If the energy price is distorted, it cannot transfer the negative externalities of energy use to consumers, which has a limited influence on CO₂ emission reduction. Moreover, the resource tax is not designed for CO₂ emission reduction, and its tax rate cannot effectively reflect the CO₂ emission coefficients of different energy types. According to Hu, Dong, and Zhou [31], compared with resource tax, the carbon tax has greater advantages in energy utilization and environmental protection. Therefore, the government should accelerate the process of carbon tax policy.

According to the energy cross-price elasticity of MI, the effect of using electricity to replace coal and oil is limited. Moreover, the absolute value of the input factors cross-price elasticity is small, which indicates that the effect of using labor and capital stock to replace energy is limited. Since the MI is a high energy-consuming industry and the energy demand is rigid, the government should promote the upgrading of the MI’s energy structure. At present, the National Development and Reform Commission encourages electrolytic aluminum enterprises to improve the utilization level of non-aqueous renewable energy such as wind power and photovoltaic power, which should occupy more than 15% of the total power consumption [61]. Therefore, the government should encourage mining enterprises to increase the proportion of renewable energy. Li and Lin [32] believe that government departments should also take a variety of measures to limit the use of fossil energy, such as restricting enterprises from installing and using high-carbon facilities. Further, the government can introduce new fiscal and tax policies to support the development of low-carbon projects in the MI. For example, preferential tax rates can be given to low-carbon projects.

5.3. Limitations and Future Research

This paper has limitations. This paper uses the price elasticity between energy and input factors in the MI to predict the changes in energy structure and input factors caused by the carbon tax. However, the carbon tax may influence the price elasticity and lead to a deviation of the results. The future study will build a CGE model to estimate the influence of exogenous policies on the MI’s energy efficiency.