Marginal CO₂ and SO₂ Abatement Costs and Determinants of Coal-Fired Power Plants in China: Considering a Two-Stage Production System with Different Emission Reduction Approaches

Abstract

Marginal abatement cost (MAC) plays an essential role in pricing pollutants and guiding environmental policies. Considering the heavy polluting nature of China’s coal power industry, this paper aims at providing companies and policymakers with more comprehensive information on the cost of abatement by estimating the MACs of CO₂ and SO₂ for coal-fired power plants (CFPPs) in China. This study contributes to the literature by considering an interconnected two-stage production system to investigate. The estimation framework is advanced in combining the electricity production and pollution abatement process of CFPPs into a convex quantile regression (CQR) model. The results show that the averages of MAC for CO₂ and SO₂ are estimated to be 367.56 Yuan/ton and 662.30 Yuan/ton, respectively, indicating that the reduction of such emissions is still costly. The heterogeneous analysis then indicates that large CFPPs, central-government-owned power plants (CGOPPs), and low-regulated CFPPs tend to possess lower MACs for CO₂. Regarding SO₂, large and medium-sized power plants show significantly larger MACs than small plants. In addition, the MACs of SO₂ for CGOPPs and high-regulated CFPPs are more concentrated at high levels. In the second part, the Tobit regression analysis was used to discuss the determinants of MACs for CO₂ and SO₂. Factors like carbon emission intensity, load, and operating hours can notably decrease MACs for CO₂, while MACs for SO₂ tend to be positively affected by the total abatement cost and the abatement rate of the FGD equipment. In addition, the MACs for the large CFPPs, CGOPPs, and high-regulated CFPPs are more likely to be affected by the selected influence factors. Based on these results, we conclude with some policy recommendations.

1. Introduction

Over the past few decades, the world has experienced severe greenhouse gas and air pollution emission problems due to the development of coal-fired power plants (CFPPs) to meet the increasing electricity demand. According to IEA [1], CFPPs contributed almost 30% of energy-related carbon emissions, and coal power generation also leads to about two-thirds of pollution emissions growth. In particular, the condition is much worse in China, whose power sector mainly depends on coal burning [2]. In 2019, 5238 Mt CO₂ were emitted in the Chinese electricity and heat production sector, while coal-fired power generation contributed almost 97% of that amount (5078.1 Mt) [3]. Therefore, CFPPs should be the main regulatory objective to improve China’s current carbon emissions condition. Better than carbon emissions, the situation of SO₂ emissions has changed significantly in China since the development of end-of-pipe abatement technology such as the flue gas desulfurization (FGD) system. After being required to install FGD facilities since the 11th FYP, SO₂ emissions per unit of thermal power generation in China has decreased significantly from 6.36 g/kWh in 2005 to 0.16 g/kWh in 2020. However, it is worth noting that China’s electricity and heat supply sector still accounts for 32% of total industrial SO₂ emissions at 805,407 tons [4], indicating that further reduction of SO₂ emissions produced by CFPPs is still of great necessity.

It is inevitable that CFPPs will eventually be phased out as China proposes carbon peak and carbon neutrality targets. However, China still plays an important role in maintaining the stability of the world economy and the global supply chain, especially when facing increasing detrimental factors like COVID-19 and the global supply chain crisis. Therefore, the power sector in China, which is one of the main factors in maintaining the stability and security of the economy and society, must continue its dominant role in meeting the expected increase in demand for various goods and services [5]. In this context, China’s central government should not phase out CFPPs too quickly, by simply focusing on the environmental targets and ignoring the economic and social role of coal-fired power plants.

The Chinese government has made great efforts to improve the environmental performance of CFPPs such as implementing the policy of “replacing small units with large ones” to accelerate the retirement of outdated coal power units and shrink new coal power capacity in construction, and introducing ultra-low emission standards to regulate CFPPs. However, any shift will come at a cost, especially for the coal-fired power sector, which would incur huge sunk costs due to upgrades to generating units or pollution abatement equipment. In order to maintain the enthusiasm of certain companies to reduce emissions, the Chinese government has introduced some market-based environmental policies. An emissions trading scheme is one of the main practical tools to meet the emission goals. In July 2021, the national carbon emission trading scheme (CETS), which encourages firms with lower marginal abatement costs (MACs) to obtain benefits by reducing emissions and those with higher MACs to pay less after purchasing carbon allowances through the carbon market, was officially launched online [6]. Unlike carbon emissions, the desulfurization price subsidy policy is a more general instrument to encourage firms to reduce SO₂ emissions, but a unified SO₂ emissions trading market has not yet been established. Therefore, a plant-level MAC estimate is still necessary to provide market participants with more detail about the actual CO₂ and SO₂ emissions prices.

Extant studies have estimated the marginal abatement costs of hazardous emissions many times, hence providing a theoretical and empirical reference for evaluating the cost of emission reduction in China [7,8,9,10,11,12,13]. Estimating the MAC based on the production process with abundant input and output data is easier in practice and thus more popular [2]. In this content, MAC is regarded as the opportunity cost to reduce undesirable outputs in terms of less desirable outputs or rather more abatement input use [14]. The first and most important step to measure the MAC with an econometric approach is how to integrate undesirable outputs such as CO₂ and SO₂ emissions into the production function. The distance function makes this possible as it can simultaneously satisfy the desirable output increase and undesirable output decrease [15]. Non-parametric and parametric methods are both commonly used methods to estimate the MAC with a “top-down” approach. Since the distance function imposes fewer theoretical assumptions and is consistent with realistic observations, these two types of models have been applied extensively to estimate the MAC of undesirable output at different levels [16,17].

Despite the massive work on MAC estimation in the literature, we still identified some research gaps. First, most previous studies preferred to concentrate on a specific pollutant like CO₂ or SO₂ to conduct their MAC analysis, but rarely estimated the MAC of carbon emissions and other pollutant emissions simultaneously. For example, Lee et al. [18] estimated the shadow price of CO₂ in South Korean power plants using the DEA method. Mekaroonreung et al. [19] took 336 U.S. bituminous coal-burning electricity plants as examples to estimate the shadow prices of SO₂ providing valuable information about market prices of pollution. However, in some pollution-generating sectors such as coal-fired power sector, both CO₂ and SO₂ are the by-product along with the electricity generation because of fuel burning. Therefore, measuring the MAC of CO₂ and SO₂ simultaneously can provide more comprehensive information about further pollution abatement both for companies and policymakers. Second, few studies have noted the difference in the way companies treat CO₂ and SO₂. To the best of our knowledge, the imbalance in the development of end-of-pipe abatement devices for CO₂ and SO₂ often leads companies to take different actions to deal with them. Specifically, with the popularization of end-of-pipe mitigation technologies toward SO₂, companies prefer to install desulfurization equipment to treat SO₂ considering both its technology and cost effectiveness. However, facing the challenge of high energy consumption and the high cost of carbon capture, utilization and storage (CCUS) technology, companies are more likely to reduce carbon emission at the expense of decreasing energy input. This identification is therefore essential, as such a distinction determines what kind of frontier function we can construct to perform the MAC measurement. Third, although both parametric and non-parametric methods have been widely employed, they often project the decision-making units (DMUs) onto the frontier and subsequently derive the MAC based on the frontier. Such a schema tends to ignore the inefficiency that exists in the company itself and causes overestimation. Finally, in past literature, although the determinants of the MACs have been widely studied, most simply identified some industrial or city level factors such as GDP, the environmental regulation stringency, or the industrial structure [20,21,22]; very few studies recognize the influencing factors of MACs on China’s coal-fired power plants and take plant-level elements such as operating hours into consideration.

Therefore, the major contributions of this study are as follows: in addition to the MAC of CO₂ emissions, the MAC of SO₂ is creatively computed in this study. Meanwhile, our paper also considers the different emission reduction characteristics between CO₂ and SO₂, and production and cost frontier functions are constructed to estimate the MAC for CO₂ and SO₂, respectively. Furthermore, according to Kuosmanen et al. [23], we use a novel data-driven approach called the convex quantile regression approach (CQR) to solve the overestimation issue. Instead of projecting DMUs to the frontier, this approach makes it possible to estimate MACs in the production set’s interior based on the specific quantile, which directly takes the inefficiency into account. The price information is then used to explore the determinants of the MACs in our second stage of analysis. Finally, we seek to make policy recommendations based on the empirical results.

The remainder of this paper is organized as follows. Section 2 provides a review of relevant literature. Section 3 describes the proposed method. Section 4 describes the variables we choose and the data we use. Section 5 presents the empirical results. Section 6 develops a discussion about the determinants. Section 7 concludes and proposes policy implications.

2. Literature Review

Previous studies focusing on pollutant emissions reduction have flourished in recent years. In addition to estimating the MACs for some sectors like manufacturing [7,21,24] or agriculture [25,26], or discussing MACs at a national/regional level [8,9,22,27], the MACs of pollutants such as CO₂ and SO₂ generated from CFPPs have also been discussed in the literature many times [2,16,23,28,29,30,31,32,33,34].

Engineering and econometric approaches are two main tools to measure the MACs of various pollutants. The engineering approach is a “bottom-up” approach, which involves technical evaluation of various mitigation measures based on feasible engineering solutions on account of experts’ suggestions [35]. This method will always identify detailed cost information for one unit of pollution abatement and thus can directly provide policymakers with a rich set of pollution control tools. Therefore, several scholars have used it to evaluate the MAC in Poland, Mexico, Ireland and other countries [36,37,38], or on a global level [39]. In the field of thermal power engineering, previous literature has selected specific power plants for the cost assessment of abatement systems to seek the most economical operation [40,41,42,43]. For instance, Luo [44] in particular, established a national primary information database of coal power units in China, which contained 2157 operating coal power units in 2017. Based on this database, he assessed the cost of pollution control in the coal power industry nationwide. The calculations show that the average marginal SO₂ control cost of the coal power industry in all provinces of China is between 1453.2 and 12,306.5 Yuan/ton. Wu et al. [42] took the Beijing-Tianjin-Hebei and the Pearl River Delta regions in China as study areas. They proved that the marginal cost of SO₂ removal technology ranged from 965 Yuan/ton to 6268 Yuan/ton, most of which were less than 5000 Yuan/ton in the power industry. Liu et al. [45] selected 13 key abatement technologies for the Chinese power industry, and evaluated and compared the abatement potential of each and the trend of the MAC of CO₂. The aforementioned studies mainly focused on describing the total or unit cost of desulfurization for a given power unit or plant. If we want to curve the changes of MAC over various power units or plants, it makes more sense to estimate the MAC with econometric methods, which estimate the MACs with the input and output data by assuming the production possibility set..

The most common approach forming a production technology is to portray a black-box production system with several input vectors such as energy, labor, and capital to generate desirable and undesirable outputs simultaneously [16,32,33,34,46,47]. The directional distance function (DDF) approach can perfectly satisfy decision-makers’ expectations about simultaneously increasing desirable output and decreasing undesirable output [48]. Accordingly, the most commonly used framework estimating MACs includes two parts: using distance functions to characterize a certain production technology and obtaining the MACs of undesirable outputs by estimating their shadow prices considering the duality between the output distance function and the revenue function [15]. For instance, Shen et al. [11] evaluated the shadow price of carbon emission for several groups of countries (OECD, ASEAN, BRICS) with the DDF approach. Zeng et al. [12] used the directional output distance function (DODF) to estimate the shadow prices of China’s SO₂ emissions at province level for the period 2001–2013. Du et al. [32] applied the meta-directional output distance function to identify the carbon abatement cost of 648 Chinese coal-fired power plants in 2008. The results showed that state-owned power plants tended to obtain lower marginal abatement costs for CO₂. Liu et al. [29] employed the DODF to derive the shadow price of CO₂ emissions of 92 of China’s large coal-fired power plants in 2010 and considered the different plant scale and provincial carbon intensity targets. All these studies provide a theoretical and empirical reference for MAC analysis toward CFPPs, however, they all focused on one specific pollutant. To the best of our knowledge, there would be multiple undesirable by-products along with the desirable output production in some industries, especially in the coal-fired power industry [49]. Therefore, it is necessary to include both CO₂ and SO₂ in a marginal abatement cost analysis framework as the price information can guide companies and governments to conduct further synergistic emission reduction activities. For example, Zhao et al. [10] jointly evaluated shadow prices of CO₂, SO₂, and NOx for U.S. coal power plants from 2010 to 2017. Wei et al. [30] took 93 Chinese CFPPs as observations, and employed the quadratic directional distance function (QDDF) method to estimate the shadow prices of CO₂ and SO₂, but the data was only from 2005 to 2010.

Another fact about by-produced undesirable outputs is that they may possess different abatement characteristics. With the development of end-of-pipe abatement technology, pollution like SO₂ can be significantly handled by installing FGD facilities. However, since CCUS technology has not realized full application, CO₂ emission reduction is still highly related to controlling carbon-generating input use like coal. Considering this, several studies have proved that it is essential to divide the production system into a production stage with carbon emission and a pollution abatement stage with end-of-pipe treatment [50,51,52,53,54,55,56,57,58,59,60,61]. Previous studies related to CFPPs would treat an undesirable output like SO₂ or CO₂ emissions or an actual energy input as a link variable between production and abatement stages [50,51,52], and assumed that they satisfied a common weak disposability feature, meaning that if the undesired output decreases, the other output will necessarily decrease by some amount [62]. However, Wei et al. [30] pointed out that under different treatment approaches, only CO₂ emission satisfies weak disposability, while FGD technology can change SO₂ from being weakly disposable to strongly disposable, indicating that the desirable output does not need to be reduced in order to reduce the undesired output [19]. Regardless of the difference between assumptions about the disposability of undesirable outputs, all of these studies estimated the MAC of CO₂ and SO₂ from the perspective of the production frontier. However, as we mentioned above, SO₂ emission or abatement is poorly connected with the production stage, but highly relevant to the use of abatement equipment. Therefore, we build production and cost frontiers separately to estimate the MAC for CO₂ and SO₂, respectively. Accordingly, in this study, part of the generated electricity is considered as part of abatement input at the end-of-pipe abatement stage and regarded as the link between the two stages.

Marginal abatement cost has been widely measured both with parametric [16,32,33,34,63,64] and non-parametric approaches [9,22,23,29]. The production frontier constructed by the parametric method mainly includes a parametric stochastic frontier analysis (SFA) and a parametric linear programming (PLP) approach. The SFA approach always demonstrates the production frontier with econometric estimates, meaning that it takes into account statistical noise like measurement errors and random disturbances. Considering this, some studies, for example, Zhang et al. [21], Tian et al. [33], and Wei et al. [16] employed the SFA approach to discuss the MACs of coal-fired power plants. On the other hand, Du et al. [34] pointed out that a PLP approach is more suitable for frontier estimation since it accounts for the constraints of environmental production technologies in its estimation process, although its estimated production frontier is as differentiable as the SFA approach. Based on this method, both Du et al. [32] and Nakaishi [2] estimated the shadow price of coal-fired power plants in China. In addition, a non-parametric data envelopment analysis (DEA) approach is also frequently used in frontier analysis considering its flexibility, such as not assuming the production function form [65]. Based on this, several studies have conducted a MAC estimation for coal-fired power plants, for example, Wang et al. [9] and Kuosmanen et al. [23]. However, the approaches mentioned above strongly rely on the full frontier, where all DMUs are uniformly projected. The estimated MAC derived based on this frontier can cause an overestimation since inefficiencies operating far below the frontier are ignored completely [14]. Therefore, the MACs of pollutants can vary under different efficiency levels even with the same technology [14,66]. To solve this problem, Kuosmanen et al. [23] developed a data-driven approach called the convex quantile regression approach. This approach perfectly accounts for the inefficiency as it estimates the MAC based on a specific quantile, instead of projecting the DMUs onto the full frontier. Kuosmanen et al. [67] then used this method to estimate the average MAC of CO₂ for a panel of 28 OECD countries during the period 1990–2015. Dai et al. [14] estimated the marginal CO₂ abatement costs for 30 Chinese provinces in the period 1997–2015 and then presented a forward-looking assessment of the abatement costs for Chinese provinces for 2016–2020. Following them, we also conduct a convex quantile regression in both stages to curve the quantile frontiers for each power plant (with different efficiency levels) to measure the MACs of CO₂ and SO₂, respectively.

Figure 1 demonstrates a flowchart of our research framework. A three-phase analysis is presented to assess the CO₂ and SO₂ marginal abatement costs and the impact of possible factors on them. First, we estimate the MACs for CO₂ and SO₂ of 221 CFPPs in China in 2018. Unlike previous studies, the MACs of CO₂ and SO₂ are separately derived from the production and cost frontiers based on the input and output index system of the electricity generation stage and the emission abatement stage. Part of the electricity produced in the first stage is used as the variable cost to reduce SO₂ emissions. Furthermore, the convex quantile regression (CQR) is carried out to form quantile frontiers to take the inefficiency into account, which can overcome the shortcomings of overestimation that often occurs in most other methods. Second, plant-level factors such as annual operating hours, load, carbon emission intensity, abatement cost, and abatement rate are considered to affect the MACs. Finally, we identify the diversity of results of empirical studies based on heterogeneous grouping by capacity scale, environmental regulation, and ownership.

3. Methodology

Following Førsund [68], this study divides the production process into two sub-stages—the desirable output production stage and the undesirable output control stage (Figure 2). The production system can be described as follows:

In the economic production stage, the non-pollution-generating inputs such as labor and capital are defined as $x^1\in R_{+}^L$. The pollution-generating input like energy is defined as $x^2\in R_{+}^M$. The inputs can be converted to the desirable output $y^1\in R_{+}^N$, and undesirable output $y^{\mathrm{b}}\in R_{+}^S$ with the traditional production technology $T_1=\left\{\left(x^1,x^2,y^1,y^{\mathrm{b}}\right):f\left(x^1,x^2,y^1,y^{\mathrm{b}}\right)⩽0\right\}$ [69]. Moreover, we assume all the input and desirable output vectors satisfy free disposability, but the undesirable output satisfies cost disposability, consistent with Murty et al. [49], which is detailed in Appendix A. In the abatement stage, the pollution control technology is used to treat undesirable outputs separately from the abatement inputs [68]. Accordingly, the investment cost for the device $x^3\in R_{+}^P$ is denoted as the fixed abatement input, and part of the desirable output $y^1$ used to support the operation of the equipment is regarded as the variable abatement input $y^2\in R_{+}^U$. Considering the removal efficiency of undesirable output control technology cannot reach 100% in practice, and some undesirable output will still remain, we define the treated pollution as $y^4\in R_{+}^Q$.

The marginal abatement cost of pollutants is usually denoted as the cost paid for each additional pollutant reduction unit by reducing desirable outputs or increasing the input use [23]. In this study, we assume different emission reduction approaches for the production and abatement stages, indicating different MAC estimation methods for the two stages.

At the economic production stage, firms aim to achieve the minimum undesirable output only at the cost of reducing desirable output. Therefore, the MAC is regarded as the marginal rate of transformation between the desirable and undesirable outputs: $MA{C}_i=P_{{\mathit{y}}_i}\times MRT\left({\mathit{y}}_i,{\mathit{b}}_i\right)$. We use a benchmark production function $f\left({\mathit{x}}_i\right)$ which satisfies the disposability assumptions and convexity to describe this process [23].

However, traditional DEA techniques always simply estimate the marginal abatement cost using the full frontiers for all individual aspects, including inefficient ones, which neglects the actual performance of each DMU. Following Kuosmanen et al. [23], we conduct the DDF estimator combined with the quantile formulation, which is better able to deal with scattered data, that is, better able to deal with sensitivity to extreme values during frontier construction [70,71].

Therefore, in the economic production stage, for a given quantile τ, we can solve the following linear programming (LP) problem:

$$\begin{gathered} \underset{\alpha ,\beta ,\gamma ,\delta ,{\epsilon }^{+},{\epsilon }^{-}}{\min } \tau {\displaystyle \sum }_{i=1}^n{\epsilon }_i^{+}+\left(1-\tau \right){\displaystyle \sum }_{i=1}^n{\epsilon }_i^{-} \\ s.t. {\mathit{\gamma }}_i^{\prime }{\mathit{y}}_i={\alpha }_i+{\mathit{\beta }}_i^{\prime }{\mathit{x}}_i+{\mathit{\delta }}_i^{\prime }{\mathit{b}}_i+{\epsilon }_i^{+}-{\epsilon }_i^{-}, \forall i=1,\cdots ,n \\ {\alpha }_i+{\mathit{\beta }}_i^{\prime }{\mathit{x}}_i+{\mathit{\delta }}_i^{\prime }{\mathit{b}}_i-{\mathit{\gamma }}_i^{\prime }{\mathit{y}}_i⩽{\alpha }_j+{\mathit{\beta }}_j^{\prime }{\mathit{x}}_i+{\mathit{\delta }}_j^{\prime }{\mathit{b}}_i-{\mathit{\gamma }}_j^{\prime }{\mathit{y}}_i, \forall i,j=1,\cdots ,n \\ {\mathit{\gamma }}_i^{\prime }{g}^y+{\mathit{\beta }}_i^{\prime }{g}^x+{\mathit{\delta }}_i^{\prime }{g}^b=1, \forall i=1,\cdots ,n \\ {\mathit{\beta }}_i⩾0, {\mathit{\gamma }}_i⩾0,{\mathit{\delta }}_i⩾0, \forall i=1,\cdots ,n \\ {\epsilon }_i^{+}⩾0,{\epsilon }_i^{-}⩾0, \forall i=1,\cdots ,n \end{gathered}$$

(1)

The composite error term is broken down into two non-negative components (${\epsilon }_i^{+}$ and ${\epsilon }_i^{-}$) in Model (1). The objective function minimizes the asymmetric absolute deviations from the frontier instead of symmetric deviations. The preassigned weight $\tau$ defines the quantile to be estimated [71]. For example, by setting $\tau$ = 0.05, the function will allow a maximum of 5% of observations to lie above the fitted function and envelope at almost 95% of the observed data points. The first set of constraints is the multivariate regression equation. The second inequality constraint implies the convexity of the production technology. The third set of constraints can be described as the translation property. The fourth constraint imposes the monotonicity assumption. The coefficients ${\mathit{\beta }}_i^{\prime }$, ${\mathit{\gamma }}_i$, and ${\mathit{\delta }}_i$ characterize the shadow prices of ${\mathit{x}}_i$, ${\mathit{y}}_i$, and ${\mathit{b}}_i$ on the efficient frontier under a certain quartile $\tau$. Accordingly, the MAC of undesirable output can be estimated as $MA{C}_i=P_{{\mathit{y}}_i}\times MRT\left({\mathit{y}}_i,{\mathit{b}}_i\right)=P_{{\mathit{y}}_i}\ast \frac{{\mathit{\delta }}_i}{{\mathit{\gamma }}_i}$.

As for the abatement stage, the firm aims to achieve the minimum undesirable output by installing end-of-pipe abatement devices. Therefore, we describe the MAC as the marginal cost of treated pollutants. Following Kuosmanen [72], a cost function $c\left({\mathit{y}}_i\right)$ consistent with the classical axioms including monotonic increasing in all outputs and globally convex is defined in this stage. Similar to the classical DEA approach, we do not assume a specific functional form for either function. According to this, the marginal cost of the treated pollutant in the pollution abatement stage is the first derivative of the cost function, which is estimated with the convex quantile regression model shown in Model (2).

$$\begin{gathered} \underset{\alpha ,\beta ,{\epsilon }^{+},{\epsilon }^{-}}{\min }\tau {\displaystyle \sum }_{i=1}^n{\epsilon }_i^{+}+\left(1-\tau \right){\displaystyle \sum }_{i=1}^n{\epsilon }_i^{-} \\ s.t.{\mathit{c}}_i={\alpha }_i+{\mathit{\beta }}_i^{\prime }{\mathit{y}}_i+{\epsilon }_i^{+}-{\epsilon }_i^{-}, \forall i=1,\cdots ,n \\ {\alpha }_i+{\mathit{\beta }}_i^{\prime }{\mathit{y}}_i⩾{\alpha }_j+{\mathit{\beta }}_j^{\prime }{\mathit{y}}_i, \forall i,j=1,\cdots ,n \\ {\mathit{\beta }}_i⩾0, \forall i=1,\cdots ,n \\ {\epsilon }_i^{+}⩾0,{\epsilon }_i^{-}⩾0, \forall i=1,\cdots ,n \end{gathered}$$

(2)

In Model (2), ${\mathit{c}}_i$ is the vector for the total abatement cost of the treated pollutants for the unit $i$; the coefficient vector ${\mathit{\beta }}_i^{\prime }$ can be described as the marginal abatement cost of the treated pollutants, which is also specific under each quantile $\tau$.

4. Variable Selection and Data Description

Figure 3 shows the distribution of the selected power plants. The samples in this paper include 221 observations from 26 provinces in China in 2018. Considering that coal-rich regions such as Shanxi, Shaanxi, Inner Mongolia, Henan, Anhui, Yunnan, and Guizhou, as well as areas with a high population density such as Shandong, Hebei, Guangdong, Zhejiang, and Jiangsu, tend to have more coal-fired power plants in China, we also include more CFPPs from these areas in our samples, which is sufficiently similar to the overall distribution of CFPPs in China. In addition,

Table 1. Input and output factors.

Sub-Stage	Input/Outpour Factors	Variable	Obs.	Unit	Average	S.D.	Min	Max
Electricity generation stage	Capital	Capacity	221	MW	899.3	867.34	6	5400
	Labor	Labor	221	person	539	446	18	2181
	Energy	Coal	221	ton	1,868,957.9	2,047,343	1064	18,226,977
	Desirable output	Electricity	221	million kWh	393,508.9	436,860.3	304	3,429,007
	Undesirable output	CO2 emission	221	ton	3,867,548.77	4,210,191.33	2107.96	36,110,605.68
Pollution abatement stage	Abatement input	FGD fixed cost	221	yuan	17,455,807.4	15,021,221	140,945.9	92,304,049
		FGD operation cost	221	yuan	8,741,954.5	10,231,604	17,161.3	92,046,010
	Output	SO2 treated	221	ton	30,365.73	738.89	7.81	263,456.26

shows a wide range of the input and output data for the chosen plants. The heterogeneity among these plants provides the possibility to estimate the production and cost frontiers.

Table 1 shows the descriptive statistics of the input and output data for the production and abatement stages. The dataset of Chinese coal-fired plants in this study contains operational data from 221 observations in 2018. As data is missing for Xinjiang, Ningxia, Sichuan, Chongqing, Hainan, Macau, and Taiwan, the research area of this study contains 26 provinces of China. This study only considers the treatment of sulfur dioxide by power plants because the cost data for nitrogen oxide removal equipment and dust removal equipment of each power plant were not available.

We collected the basic information about power plants, such as installed capacity, annual operating hours, coal consumption, and electricity generation, from China Electricity Council and China Electricity Statistical Yearbook. As we all know, coal-fired power plants generate electricity accompanied by carbon emissions. Therefore, the method of calculating carbon emissions from burning coal is described as follows [73]:

$$E_i^{{\mathrm{CO}}_2}=A_i\times E{F}_{k,{\mathrm{CO}}_2}$$

(3)

$$E{F}_{k,{\mathrm{CO}}_2}=C{A}_k\times O\times H_k\times 44/12$$

(4)

where $E_i^{{\mathrm{CO}}_2}$ is the CO₂ emission of the $i$th power plant, $A_i$ is the total coal consumption for electricity generation, and $E{F}_{k,{\mathrm{CO}}_2}$ represents the CO₂ emission factor for province $k$. $C{A}_k$ is the tons of the net carbon content per trillion joules of energy produced (tC TJ⁻¹), $O$ represents the carbon oxidation factor, 44/12 is the molecular weight ratio of CO₂ to carbon, and $H$ is the heating value for coal consumption by the unit of TJ/10⁴ t. In this study, we collected the carbon oxidation factor, the carbon contents, and the heating value data from the Provincial Emissions Inventory Guideline [74].

The fixed cost of desulfurization equipment is the sum of fixed asset investments associated with desulfurization facilities.

Table 2. Investment density of desulfurization equipment.

Capacity (MW)	Yuan/kW
300	230.64
350	195.19
600	167.83
660	164.27
1000	130.14

shows the investment density of the desulfurization device, which is calculated as the rate of the total fixed cost of the FGD equipment and the total installed capacity of each power plant at the 2018 price level. From Table 2, we can see that CFPPs with higher capacities tend to have lower investment densities in desulphurization devices. In particular, the investment density of desulfurization equipment for 1000 MW units could be as low as 130.14 Yuan/kW, while power generation units with 300 MW might only achieve 230.64 Yuan/kW [75].

In this study, we used the concept of annualized investment to calculate the fixed cost of the FGD equipment [76]. The initial investment is equalized over the lifetime of the power plant, and the annual equalized investment is calculated as follows:

$$C_i^{\mathrm{F}}=\alpha \times {\displaystyle \sum }_{j=1}^{n_i}{F}_{i,j}^0$$

(5)

$$\alpha =\frac{r}{1-{\left(1+r\right)}^{-n}}$$

(6)

where $i$ is the $i\mathrm{th}$ coal-fired power plant, $j$ is the $j\mathrm{th}$ coal-fired power unit in the $i\mathrm{th}$ power plant, $C_i^{\mathrm{F}}$is the annually equalized investment of the FGD equipment, $\alpha$ is the annual averaging coefficient. ${\displaystyle \sum }_{j=1}^{n_i}{F}_{i,j}^0$ represents the initial total investment of the FGD equipment in the $i\mathrm{th}$ power plant, which is calculated by summing all the power units’ investments. $r$ is the discount rate, $n$ is the service life of desulfurization equipment in power plants. Referring to Liu [76], we assume a discount rate of 8% and a service lifetime of 20 years for the FGD equipment.

The operation cost of the CFPP mainly includes the cost of materials (absorbent), electricity, water, and labor [77]. Previous studies have proved that electricity consumption of FGD equipment accounts for 76.06–85.9% of the total operating cost [77,78,79]. Therefore, considering the availability of data, we take the electricity cost as the operation cost of FGD equipment, which is calculated by the following equations:

$$C_i^{\mathrm{V}}=P_k^{\mathrm{E}}\times E_i^{Elec}\times \Delta {\eta }_i$$

(7)

where $E_i^{Elec}$ is the power generation of the $i$th power plant, $\Delta {\eta }_i$ represents the electricity consumption rate of the FGD equipment. Each power unit for the $i$th power plant may install the FGD equipment in different years, so we use $\Delta {\eta }_{i,j}$, which indicates the increase of the auxiliary power consumption rate for the $j$th unit from the year before to the year after running the FGD equipment ($\Delta {\eta }_{i,j}={\eta }_{i,j}^{t+1}-{\eta }_{i,j}^{t-1}$) to define the electricity consumption rate of the FGD equipment for the $j$th power unit. Then, for the $i$th power plant, the electricity consumption rate of the FGD equipment $\Delta {\eta }_i$ can be calculated by the weighted average of $\Delta {\eta }_{i,j}$ ($\Delta {\eta }_i={\displaystyle \sum }_{j=1}^{n_i}{w}_i\Delta {\eta }_{i,j}$, where $w_i$ is the proportion of the $j$th coal-fired power unit’s installed capacity to the $i$th power plant’s total installed capacity). According to previous studies, the values of $\Delta {\eta }_i$ in our sample are within a reasonable range. The details of $\Delta {\eta }_i$ can be seen in Appendix B (

Table A2. The reference value of power consumption rate of desulfurization facilities.

	0–300 MW		300–600 MW		600–1000 MW
Related Research	Capacity (MW)	Power Consumption Rate (%)	Capacity (MW)	Power Consumption Rate (%)	Capacity (MW)	Power Consumption Rate (%)
Du et al. [87]	200	1.49	600	1.21	1000	0.95
	300	1.4
Wang et al. [88]	300	1.75
Yang et al. [89]	300	1.78
Li et al. [90]	300	1.5
Yuan [91]	300	1.04	320	1.15	600	1.04
	300	1.01	320	0.96	600	0.97
	300	1.15	320	1.29	600	0.93
	300	1.09	320	1.63	600	0.9
	300	1.2	325	0.9	600	1.27
	300	1.21	325	1.09	600	1.36
	300	1.41	325	0.94	600	1.29
	300	1.47	325	0.99	600	1.6
	300	1.5	325	1.23	600	1.32
	300	1.51	330	1.33	630	1.06
	300	1.77	330	1.56	1000	1.63
			330	1.61
			350	0.93
			350	1.15
			350	1.03
			350	1.3
			350	1.04
			350	1.03
Jiang et al. [92]	300	1.18	315	1.69	600	1.08
	300	1.16	315	1.53	635	0.92
	300	1.21	330	1.44	660	0.82
	300	1.22	330	1.32	660	0.9
	300	1.71	330	1.13	670	2.12
	300	1.97	330	1.1	670	1.93
	300	1.08	335	1.55	1000	1.63
	300	1.93	335	1.55	1000	0.83
	300	1.54	335	1.48	1000	0.86
			335	1.25	1000	1.38
			335	2.02	1000	1.28
Mo et al. [93]			330	1.197
			330	1.205
Xu et al. [94]			350	0.622–1.095
			350	0.612–0.155
Han [95]	430	1.6
Long et al. [96]					600	1.01
					600	1.778
					600	1.98
Yu et al. [97]					600	1.92
Qiu et al. [98]					600	1.13
					600	1.62
Cheng [99]					660	0.6–0.7
Jiang et al. [100]					1000	0.918
					1000	0.973
Xu et al. [101]					1000	1.18
					1000	1.1

). $P_k^E$ is the electricity price in the$k$th province where the $i$th power plant is located. As the on-grid price of each firm was not available, we used the price of each province in 2018 as a substitute—which is shown in Appendix B (

Table A1. Electricity price and sulfur content of coal of each province in 2018.

Province	Electricity Price (Yuan/kWh)	Sulfur Content of Coal (%)
Anhui	0.3828	0.48
Beijing	0.3705	0.56
Fujian	0.3893	0.65
Gansu	0.2953	0.73
Tianjin	0.3519	0.76
Hebei	0.3209	1.02
Shandong	0.4110	1.09
Shanxi	0.3216	1.1
Inner Mongolia	0.2725	0.79
Liaoning	0.3706	0.64
Jilin	0.3654	0.38
Heilongjiang	0.3735	0.33
Shaanxi	0.3268	1.29
Ningxia	0.2487	1.07
Qinghai	0.2802	0.8
Xinjiang	0.2151	0.58
Shanghai	0.4102	0.59
Jiangsu	0.3919	0.79
Zhejiang	0.4163	0.76
Hubei	0.4365	1.27
Hunan	0.4590	1.1
Henan	0.3562	0.77
Jiangxi	0.4182	1.13
Sichuan	0.4403	1.67
Chongqing	0.4126	3.04
Guangdong	0.4411	0.69
Guangxi	0.3994	1.88
Yunnan	0.4125	1.23
Guizhou	0.3324	2.43
Hainan	0.4385	1.08

). Then summing up the fixed cost $C_i^{\mathrm{F}}$ and variable cost $C_i^{\mathrm{V}}$, we can obtain the total abatement cost $C_i$ of the $i$th power plant ($C_i=C_i^{\mathrm{F}}+C_i^{\mathrm{V}}$).

If we do not consider the existence of the desulfurization equipment, the SO₂ generation level is mainly related to the sulfur content of coal [73]. Therefore, we used the following equations to calculate the amount of sulfur dioxide being treated:

$$T_i^{{\mathrm{SO}}_2}=G_i^{{\mathrm{SO}}_2}-E_i^{{\mathrm{SO}}_2}$$

(8)

$$G_i^{{\mathrm{SO}}_2}=A_i\times E{F}_{k,{\mathrm{SO}}_2}$$

(9)

$$E{F}_{k,{\mathrm{SO}}_2}=\left(1-S{R}_k\right)\times S_k\times 2$$

(10)

where $E{F}_{k,{\mathrm{SO}}_2}$ represents the SO₂ emission factor without considering the abatement process of the power plant, $S_k$ is the sulfur content of coal. Since we do not know the specific coal type of each power plant, we used the average sulfur content of the coal in the province where the power plant is located as a substitute [80]. The average sulfur content of coal in each province is also shown in Appendix B (Table A1). $S{R}_k$ denotes the fraction of sulfur retention in ash, which is uniformly assumed to be 15% in this paper due to the unavailability of data [80]. $G_i^{{\mathrm{SO}}_2}$ is the total SO₂ generation, $A_i$ is the coal consumption, and $E_i^{{\mathrm{SO}}_2}$ and $T_i^{{\mathrm{SO}}_2}$ represent final SO₂ emission and the amount of SO₂ being treated, respectively. We collected the SO₂ final emission data for each power plant ($E_i^{{\mathrm{SO}}_2}$) from the annual report of each enterprise on the national emission permit information management platform (Available online: http://permit.mee.gov.cn/perxxgkinfo/syssb/xkgg/xkgg!licenseInformation.action (accessed on 12 July 2022). (In Chinese)).

5. Results

Considering that we divide the power plant production system into two stages, the marginal abatement cost of CO₂ in the power production stage and the marginal abatement cost of SO₂ in the abatement stage are measured in this section. Following the two-stage production system we established in Section 3, the specific input and output vectors for each stage of the power plant are shown in Figure 4.

At the electricity production stage, each power plant has two non-pollution-generating inputs, capacity ($K_i$) and labor ($L_i$), and one pollution-generating input, coal ($A_i$), to produce one desirable output electricity ($E_i^{Elec}$) and one undesirable output CO₂ emission ($E_i^{{\mathrm{CO}}_2}$).

In the abatement stage, abatement technology was used to reduce pollution as much as possible. Abatement inputs like FGD investment cost ($C_i^{\mathrm{F}}$) and operation cost ($C_i^{\mathrm{V}}$) were used to decrease the final SO₂ emission level and the treated SO₂ is defined as $T_i^{{\mathrm{SO}}_2}$.

We then obtained 221 quantile functions with τ = (1/221, 2/221, 3/221, …, 1) by solving the convex quantile regression models (1) and (2). The solution was performed using the software MOSEK. More detailed information is reported in

Table 3. Descriptive statistics of marginal abatement cost of CO₂ and SO₂.

	MAC (CO2)	MAC (SO2)
Unit	Yuan/ton	Yuan/ton
Obs.	221	221
Mean	260.02	641.16
S.D.	167.11	182.63
Min	1.96	106.03
Max	618.94	1085.39

.

Table 3 summarizes the average, standard deviation, and minimum and maximum values of MACs of CO₂ and SO₂. The average MACs of CO₂ and SO₂ for 221 power plants are 367.56 Yuan/ton and 662.30 Yuan/ton, respectively. Referring to other studies on the estimation of MACs, the values of MACs in our study are within a reasonable range. Related references are shown in Appendix B (

Table A3. The reference value of MACs of CO₂ and SO₂.

Related Research	Research Scale	Year	MAC (CO2)	MAC (SO2)
Wu et al. [102]	Power industry	2005–2015	533.71–588.38 Yuan/ton
Liu et al. [45]	Power industry	2020–2035	0.15 Yuan/ton~1133 Yuan/ton
ICCSD [103]	National level	2030–2050	126 Yuan/ton~1364 Yuan/ton
Wang et al. [104]	Provincial level	2015–2020	18.8~37.1 USD/ton
Lu et al. [105]	Plant level	2015		250–800 Yuan/ton
Yang et al. [106]	Plant level	2015		1296–3662 Yuan/ton
Ma et al. [107]	Plant level	2000–2010		1024–1529 Yuan/ton
Luo [44]	Plant level	2017		1453.2–12306.5 Yuan/ton

). However, the average MAC of SO₂ estimated in our study is a little smaller than in other studies as we did not consider the cost of other materials like absorbents, water, and labor. The large standard deviation in the estimated MACs of CO₂ and SO₂ among the 221 power plants indicates substantial heterogeneity in the behavior of the enterprises with regard to reducing emissions. Therefore, following Zhang et al. [21], we explore the distribution differences of the MAC of CO₂ and SO₂ in three dimensions: capacity scale, location, and ownership. We classify the 221 CFPPs into three groups according to their installed capacities: small CFPPs—installed capacities smaller than 300 MW, medium-sized CFPPs—between 300 and 1000 MW capacity, and large CFPPs—capacities larger than 1000 MW. Regarding the provincial CO₂ emission and SO₂ emission reduction targets set in the 13th FYP (2016–2020), we classify the power plants into two groups—high-regulated and low-regulated plants based on the regions in which they are located. Specifically, when discussing the MACs of CO₂, we consider those provinces whose CO₂ emission reduction targets are lower than 19.5% as low-regulated areas, and the others as high-regulated areas. But when exploring the MACs of SO₂, we regard the provinces whose SO₂ emission reduction targets are lower than 20% as low-regulated areas, and the others as high-regulated areas. (Detailed information of the provincial CO₂ emission and SO₂ emission reduction targets for each province is provided in

Table A4. The provincial CO₂ and SO₂ emission reduction targets.

Province	CO2 Emission Reduction Target (%)	SO2 Emission Reduction Target (%)
Anhui	18	16
Beijing	20.5	35
Fujian	19.5	-
Gansu	17	8
Tianjin	20.5	25
Hebei	20.5	28
Shandong	20.5	27
Shanxi	18	20
Inner Mongolia	17	11
Liaoning	18	20
Jilin	18	18
Heilongjiang	17	11
Shaanxi	18	15
Ningxia	17	12
Qinghai	12	6
Xinjiang	12	3
Shanghai	20.5	20
Jiangsu	20.5	20
Zhejiang	20.5	17
Hubei	19.5	20
Hunan	18	21
Henan	19.5	28
Jiangxi	19.5	12
Sichuan	19.5	16
Chongqing	19.5	18
Guangdong	20.5	3
Guangxi	17	13
Yunnan	18	1
Guizhou	18	7
Hainan	12	-

). Concerning firm ownership, we divide the power plants into central-government-owned power plants (CGOPPs) and other-owned power plants (OOPPs) based on the type of beneficial owner following Lam et al. [81].

Figure 5 shows the distribution of kernel densities for the MAC of CO₂ and SO₂ in different groups. Significant differences exist across the scale, the intensity of environmental regulation, and ownership. As Figure 5a shows, the distribution of CO₂ for large power plants is bimodal. The first wave peak is significantly higher than the second, indicating that the share of large plants with lower CO₂ MACs is larger than those with higher CO₂ MACs. Similarly, the small and medium CFPPs also have convergence clubs near the first wave peak of large plants, but both are located to the right of the kernel density curve of large power plants. Considering the difference from the intensity of environmental regulation, as shown in Figure 5b, the kernel density curve of high-regulated CFPPs is to the right of low-regulated CFPPs, indicating that the abatement cost of high-regulated CFPPs is relatively high. This result is consistent with Zhang et al. [21], who demonstrated that high-regulated firms tend to be equipped with a high level of emission reduction technology, thus leading to high MACs. Figure 5c provides the distribution of MACs of CO₂ for CFPPs with different ownerships. The kernel density curve of CGOPPs is obviously to the left of OOPPs, revealing that most CGOPPs show higher carbon emission reduction potential than OOPPs due to their lower MACs of CO₂. This is reasonable because state-owned power plants usually have cheaper abatement costs since they can get more financial support from central and local governments [21,32].

Compared with CO₂, the distributions of kernel densities for the MAC of SO₂ in different groups show different variations (Figure 5d–f). The kernel density curves of large and medium power plants are both to the right of small power plants (Figure 5d), indicating that the MACs of SO₂ of large and medium power plants are significantly larger than that of small ones. This can be explained by the performance gap of FGD equipment in large, medium, and small power plants. Previous studies have demonstrated that large power plants tend to be equipped with more advanced equipment, whether for electricity production or pollution abatement [82,83]. Our study sample also shows that large and medium-sized power plants have higher SO₂ control rates at average levels of 98.6% and 97.83%, respectively, while small power plants only achieve 91.22% at average levels. Figure 5e,f show that the kernel density curves of high-regulated CFPPs and CGOPPs also have narrow widths, indicating that the marginal abatement costs for these two kinds of CFPPs are more convergent to the peak value. This can be attributed to the fact that high-regulated CFPPs and CGOPPs prefer to purchase high-end abatement equipment due to the stricter environmental regulations and the positive response to stronger investment capacity. Their great demands on FGD equipment then give those FGD engineering companies that provide them with desulfurization equipment an inherent advantage and a higher market share. Consequently, a more uniform standard for technical indicators such as emission reduction rate as well as investment intensity for desulfurization equipment may exist in such companies. Therefore, the distribution of MACs for SO₂ can be more concentrated in high-regulated CFPPs and CGOPPs.

6. Discussion

To identify the determinants of the MACs for CO₂ and SO₂, we selected variables to construct a Tobit regression analysis for the marginal abatement costs of CO₂ and SO₂, respectively, and conducted a heterogeneity analysis. The details can be seen in Section 6.1 and Section 6.2.

6.1. Influencing Factors of CO₂ Marginal Abatement Costs

Previous studies have demonstrated that the factors influencing the MAC of CO₂ include emission reduction policies, carbon emissions, carbon intensity, power generation structure, and ownership [9,29,47]. However, considering that this study analyzes factors at the plant level, we also take into account the technical indicators of power plant operation, such as the load and annual operating hours of power plants. Therefore, we assume the following six variables can influence the MAC of CO₂:

CARBON INTENSITY (CEI). We use the CO₂ emissions per unit of electricity generated to describe the carbon emission intensity of each power plant. Given that power plants with high carbon intensity have more room for improvement in carbon emission reduction and are expected to have lower abatement costs, a negative coefficient is predicted for this indicator.

LOAD. An independent variable that indicates the capacity utilization ratio of the power plant, calculated as the ratio of the actual operating capacity to the installed capacity, where the actual operating capacity is defined as the ratio of electricity generation to operating hours. Typically, it is easier for power plants with low electricity generation loads to increase their efficiency by increasing their operating capacity and thus achieve emission reductions [46], which indicates that their abatement costs will be lower, so the coefficient is expected to be negative.

HOUR. An independent variable denotes the annual operating hours of each power plant. This variable has also been illustrated to have a significant positive effect on the efficiency of power plants in other studies [34,84]. Therefore, we assume that it will also have a negative effect on the MAC of CO₂.

POWER GENERATION STRUCTURE (PGS). An independent variable indicates the proportion of clean power generation in the power supply. Accordingly, we denote it by the percentage of clean energy generation in the region where the power plant is located. Generally, the lower the percentage of clean power generation in a region, the more thermal power will be there. Therefore, the more room there is for coal-fired power plants in that region to reduce carbon emissions, the lower the abatement cost. Thus, the coefficient is expected to be positive.

ENVIRONMENTAL REGULATION (ERC). Due to the group heterogeneity between high-regulated and low-regulated CFPPs in terms of the MAC of CO₂, we assume that the local carbon emission reduction targets may have certain impacts on the CO₂ marginal abatement costs.

OWNERSHIP (CGO). To evaluate the effect of ownership on the CO₂ marginal abatement costs, we use dummy variables with 0 and 1 to denote OOPPs and CGOPPs, respectively.

The regression results are shown in

Table 4. Baseline regression analysis.

Factors	MAC (CO2)	MAC (SO2)
CEI	−2.507 ***
	(−9.19)
AC		22.732 **
		(2.32)
AR		11.448 ***
		(5.10)
LOAD	−36.269 ***	−12.156
	(−3.97)	(−0.98)
HOUR	−0.047 ***	0.002
	(−8.21)	(0.19)
CQ		−180.721 ***
		(−5.67)
PGS	258.077 ***	234.605 ***
	(5.24)	(2.93)
ERC	13.548 **
	(2.48)
ERS		−0.338
		(−0.20)
CGO	−42.197 ***	81.655 ***
	(−2.64)	(3.74)
_cons	458.861 ***	−407.538 *
	(3.59)	(−1.65)
No.	221	221
Mean VIF	1.2	1.48
R2	0.5505	0.2667

Note: No. indicates the number of CFPPs. For all variables, values in parentheses are t-statistics. ***, **, and * indicate levels of significance at 1%, 5%, and 10%, respectively. The test for multicollinearity is expressed by the mean VIF (variance inflation factor).

. CEI has a significantly negative effect on the MAC of CO₂ at the 0.01 level, implying that as the intensity of carbon emissions decreases, power plants will have less room to release their carbon reduction potential. On average, an increase of one unit of carbon emission intensity will result in a 2.507-unit decrease in MACs of CO₂. In addition, we find that both technical indicators (LOAD and HOUR) have significant negative effects on the MACs of CO₂. The coefficients are all significant at the 0.01 level, meaning that increasing the capacity utilization ratio and raising the operating hours of a power plant can simultaneously decrease the cost of carbon emission reduction. This is reasonable because the high load and more operating hours can contribute to a more efficient electricity generation [46,84,85]. Additionally, the power generation structure (PGS) can positively affect the MAC of CO₂ with a coefficient of 258.077 at the 0.01 level. The main reason is that a smaller PGS indicates a larger proportion of thermal power in the power generation structure, which can then lead to higher carbon emissions from power generation and a larger potential for emission reduction. Subsequently, the cost of emission reduction is relatively lower.

We found that power plants with different installed sizes, ownership, and environmental regulation intensities exhibit significant variations in the MACs of CO₂. Furthermore, we investigated whether these elements play a role in the effect of the specific factors regressed on the MACs of CO₂. The detailed regression results are shown in

Table 5. Heterogeneity analysis of influencing factors on MACs of CO₂.

	Capacity Scale			Environment Regulation Intensity		Ownership
Factors	Large	Medium	Small	Low-Regulated	High-Regulated	CGOPPs	OOPPs
CEI	−4.159 ***	−2.504 ***	−2.176 ***	−2.284 ***	−3.053 ***	−2.831 ***	−2.374 ***
	(−6.26)	(−5.53)	(−6.55)	(−7.57)	(−5.89)	(−7.69)	(−6.17)
LOAD	−299.452 ***	−192.013 ***	−26.142 ***	−25.231 ***	−152.727 ***	−211.854 ***	−27.566 ***
	(−4.50)	(−2.81)	(−3.48)	(−2.80)	(−4.66)	(−5.01)	(−3.05)
HOUR	−0.058 ***	−0.062 ***	−0.04 ***	−0.048 ***	−0.048 ***	−0.052 ***	−0.045 ***
	(−3.77)	(−5.59)	(−6.36)	(−5.61)	(−5.89)	(−5.66)	(−6.42)
PGS	237.75 ***	219.407 **	76.460	250.579 ***	188.192 **	240.153 ***	193.359 **
	(2.77)	(2.45)	(0.63)	(4.27)	(2.00)	(3.87)	(2.33)
ERC	9.498	8.971	5.159			7.823	15.864 *
	(0.82)	(1.15)	(0.52)			(0.267)	(1.96)
CGO	−49.335 *	−42.287	−51.602 *	−38.266 *	−45.168 **
	(−1.69)	(−1.54)	(−1.84)	(−1.68)	(−2.03)
__cons	1020.981 ***	769.486 ***	574.664 ***	655.03 ***	917.464 ***	760.042 ***	396.639 **
	(3.51)	(3.65)	(2.52)	(11)	(12.83)	(4.28)	(2.12)
No.	89	71	61	100	121	124	97
Mean VIF	1.53	1.21	1.33	1.17	1.07	1.3	1.2
R2	0.59	0.6	0.69	0.63	0.48	0.57	0.55

Note: No. indicates the number of CFPPs. For all variables, values in parentheses are t-statistics. ***, **, and * indicate levels of significance at 1%, 5%, and 10%, respectively. The test for multicollinearity is expressed by the mean VIF (variance inflation factor).

. The cost of reducing CO₂ emissions from large power plants is not only more sensitive to their own technical specifications, such as carbon intensity, capacity utilization ratio and operating hours, but also more affected by external factors. To be specific, CEI, LOAD, and HOUR all have a significant negative impact on the CO₂ marginal abatement costs for large, medium, and small plants but show huge differences in terms of the influencing degree. The CEI factor’s effect on MACs of CO₂ in large power plants (−4.159) is almost twice as large than that of medium and small plants. The LOAD factor, which has an impact on the MAC of CO₂ of large plants with coefficients of (−299.452), is almost 1.5 times larger than that of medium plants (−192.013) and 10 times greater than that of small plants (−26.142). Moreover, the MAC of CO₂ for large and medium-sized power plants can also be positively affected by the power generation structure of the region in which they are located, with coefficients of 237.75 and 219.407. The results in Table 5 additionally indicate that high-regulated CFPPs are more affected by the listed factors, especially for LOAD (−152.727), which is almost six times larger than that of low-regulated CFPPs (−25.231). This can be explained by the fact that some regions may limit the operating hours of CFPPs or require them to operate at low loads to meet the high carbon emission reduction targets and achieve a significant reduction in total carbon emissions, which will also significantly increase the MAC of CO₂. Considering ownership, the coefficient of CEI to the MAC of CO₂ for CGOPPs is larger (−2.831 than −2.374), indicating that the MAC of CGOPPs is more sensitive to a change in CEI. Meanwhile, higher coefficients of LOAD (−211.854) and HOUR (−0.052) for MAC of CO₂ of CGOPPs are in line with our finding that CGOPPs still have a larger space for emission reduction, which can be realized by increasing the load or the operating hours.

6.2. Influencing Factors of SO₂ Marginal Abatement Costs

In addition to the operation indicators LOAD and HOUR, the environmental regulation intensity (SO₂ reduction targets for each province) ERS, electricity supply structure PGS, and ownership CGO influence the MAC of SO₂, so we also consider the following factors:

AVERAGE COST (AC): an independent variable that indicates the cost of reducing one unit of SO₂, calculated as the ratio of the total cost of FGD equipment to the controlled SO₂, where the actual operating capacity is defined as the ratio of electricity generation to operating hours. It has been generally accepted that marginal cost will also increase as the average cost increases. Therefore, we assume there is a positive relationship between AC and the MAC of SO₂.

ABATEMENT RATE(AR): this variable describes the SO₂ abatement rate. A higher abatement rate always represents less room for reducing one more unit of SO₂. Thus, we also assume a positive correlation between AR and MAC of SO₂.

COAL QUALITY (CQ): an independent variable that indicates the sulfur content of coal consumed by each power plant. Given that the higher the sulfur content of the coal, the more sulfur dioxide will be yielded by burning the coal, meaning there is more room for improvement in SO₂ emission reduction, we assume that the sulfur content of coal will have a negative impact on the MAC of SO₂.

From Table 4, we can identify that both AC and AR have a significantly positive effect on the MAC of SO₂ with coefficients of 22.732 and 11.448 at the 0.05 and 0.01 levels, respectively. It is also important to note that the coefficients of operation indicators of CFPPs like LOAD and HOUR are insignificant. Such a difference between CO₂ and SO₂ indicates that considering the existence of abatement constraints, the MAC of SO₂ is more closely linked to the abatement behavior of enterprises including the cost of their abatement inputs and the advancement of their FGD equipment. In addition, we also found that the effects of environmental regulation intensity and ownership on the MAC of SO₂ are the opposite to that of CO₂. Environmental regulation, however, is irrelevant. This can be attributed to the fact that during the 11th FYP and the 12th FYP, the Chinese government strictly required all coal-fired operating units to install FGD facilities. By the end of 2016, the proportion of thermal power units with FGD was close to 100%. As a remarkable result, coal power’s sulfur dioxide emission intensity decreased significantly from 2005 to 2016 [86]. Therefore, the SO₂ reduction targets do not have an obvious incentive on the abatement behavior of the power plant due to the prominent SO₂ reduction effect of the FGD equipment. It is worth pointing out that the coefficients of CGO are quite the opposite between CO₂ and SO₂, implying a large difference between the carbon and pollutant reduction methods in enterprises, especially for CGOPPs. CGOPPs have the advantage of super-enterprise scale and ample capital, which will reduce their MACs of CO₂. However, end-of-pipe abatement technologies may weaken the link between pollutant abatement such as SO₂ reduction and electricity generation. Hence, CGOPPs can acquire advanced abatement devices to achieve higher abatement rates with high MACs of SO₂. Furthermore, the CQ factor shows a significant negative impact on the MAC of SO₂ (−180.721), implying that when CFPPs produce electricity with coal of a lower sulfur content, they are more likely to face a higher MAC of SO₂.

Similarly, to further identify whether the influencing factors exist group heterogeneity, we also conducted several regression models in these three dimensions: capacity scale, location, and ownership. The details are listed in

Table 6. Heterogeneity analysis of influencing factors on MACs of SO₂.

	Capacity Scale			Environment Regulation Intensity		Ownership
Factors	Large	Medium	Small	Low-Regulated	High-Regulated	CGOPPs	OOPPs
AC	78.01 **	46.271 **	31.063 **	34.161 **	1.116	29.234 **	10.092
	(4.30)	(2.53)	(2.42)	(2.37)	(0.08)	(2.16)	(0.68)
AR	−7.456	−5.582	5.049 **	9.79 ***	15.017 ***	12.425 ***	10.773 ***
	(−0.7)	(−1.56)	(1.69)	(2.95)	(4.71)	(4.06)	(3.25)
LOAD	27.156	−53.586	11.695	−4.223	−129.813 **	−157.489 ***	−5.528
	(0.44)	(−1.14)	(0.77)	(−0.29)	(−2.59)	(−3.27)	(−0.36)
HOUR	−0.005	−0.004	0.023	0.014	−0.014	−0.014	0.007
	(−0.29)	(−0.42)	(1.44)	(0.92)	(−1.09)	(−0.96)	(0.51)
CQ	−233.868 ***	−139.786 ***	−96.858	−177.704 ***	−243.352 ***	−160.904 ***	−241.253 ***
	(−6.01)	(−5.42)	(−0.69)	(−4.52)	(−3.39)	(−5.16)	(−3.43)
PGS	99.152	177.813 **	26.638	332.932 ***	211.624 *	177.851 **	222.219
	(0.94)	(2.45)	(0.12)	(3.26)	(1.85)	(0.94)	(1.35)
ERS	0.712	2.589 *	−2.241			0.022	−0.111
	(0.38)	(1.89)	(0.658)			(0.13)	(−0.33)
CGO	29.938	5.408	14.799	118.075 ***	43.661 *
	(1.05)	(0.28)	(0.29)	(3.28)	(1.67)
___cons	1539.191	1295.475 ***	−49.66	−396.1342	−444.896	−231.998	−277.003
	(1.45)	(3.45)	(−0.14)	(−1.05)	(−1.33)	(−0.68)	(−0.75)
No.	89	71	61	100	121	124	97
Mean VIF	1.78	1.6	1.52	1.48	1.48	1.72	1.48
R2	0.58	0.58	0.15	0.35	0.27	0.38	0.21

Note: No. indicates the number of CFPPs. For all variables, values in parentheses are t-statistics. ***, **, and * indicate levels of significance at 1%, 5%, and 10%, respectively. The test for multicollinearity is expressed by the mean VIF (variance inflation factor).

.

As expected, the AC factor has a larger impact on large (78.01) and medium (46.271) CFPPs than on small ones (31.063). Furthermore, we found that coal quality is another key factor influencing the MAC of SO₂ of large and medium-sized power plants. The reason is that large and medium-sized power plants always need to consume large amounts of coal, and the abatement cost of SO₂ is more sensitive to the sulfur content of coal. The coefficient of LOAD is significantly negative for both high-regulated CFPPs and CGOPPs with the values of −129.813 and −157.489, respectively. This implies that end-of-pipe abatement can be affected by the operating condition of power-generating units. Therefore, improving the operation efficiency of power units could achieve a synergistic reduction in the MAC of CO₂ and SO₂.

7. Conclusions and Policy Suggestions

This paper considers a two-stage production system for CFPPs: an electricity generation stage and a pollution abatement stage. Specifically, noting that electricity generation enterprises tend to select different ways to treat CO₂ and SO₂, respectively, we define the MAC of CO₂ as the marginal rate of transformation between desirable and undesirable outputs, and regard the MAC of SO₂ in the pollution abatement stage as the marginal cost of the treated pollutant. After combining the quantile formulation with the traditional DDF estimator and the marginal cost estimation, we further analyzed the heterogeneous characteristics of the MACs in three dimensions: capacity scale, location, and ownership. In addition, the effect of possible influencing factors on the MACs of CO₂ and SO₂ emission is also discussed with a few regression models.

The results show that the average levels of the MACs of CO₂ and SO₂ for 221 CFPPs are 367.56 Yuan/ton and 662.30 Yuan/ton, indicating that it would cost them on average 367.56 yuan and 662.30 yuan to reduce one more ton of CO₂ and SO₂, respectively. The results of the heterogeneous analysis of the CO₂ MACs prove that on the whole large power plants possess lower CO₂ MACs compared with medium and small plants, though some of the large power plants obviously had high MACs of CO₂ with low CO₂ reduction potential. Furthermore, CFPPs not owned by central government (OOPPs) and high-regulated CFPPs have higher MACs of CO₂ than CGOPPs and low-regulated CFPPs. However, the heterogeneous characteristics of SO₂ MACs do not show similar trends. To be precise, the MACs of SO₂ for large and medium-sized power plants are significantly larger than those for small power plants, but the distribution is more concentrated for large power plants. Moreover, the distribution of MACs of SO₂ for high-regulated CFPPs and CGOPPs is also more centrally concentrated at higher levels.

The results of the regression model indicate that factors such as carbon emission intensity, provincial electricity generation structure, and provincial CO₂ emission reduction targets can all positively affect the MACs of CO₂ of CFPPs. The operation indicators of CFPPs like LOAD and HOUR can also significantly decrease the MAC of CO₂, while the SO₂ MACs are less likely to be influenced by such factors, but strongly affected by the emission reduction costs and the abatement rate of certain equipment. In addition, we also explore the differences in terms of the influencing degree of these factors. It can be concluded that large- and medium-sized power plants are likely to spend more for further CO₂ and SO₂ emission reductions. On the one hand, they are more sensitive to the changes of their own carbon emission intensities and external factors like environmental regulation. On the other hand, given their large pollution generation, they are likely to invest more in pollution treatment. Furthermore, improving the operating condition of CFPPs like LOAD and HOUR could more significantly decrease the MACs of CO₂ and SO₂ for both high-regulated CFPPs and CGOPPs.

Based on the above analysis, we propose the following policy recommendations:

First, the electricity generation capacity rather than the installed capacity of China’s CFPPs should be given adequate attention. The overcapacity problem in China’s coal-fired power sector is widespread, but even now electricity shortages can occur seasonally, rooted in a lack of operating capacity at coal-fired power plants. For coal-fired power plants, generating electricity with low load or insufficient hours will significantly harm their comprehensive efficiency levels in terms of increasing the coal consumption per unit of electricity generation or reducing the thermal efficiency of the boiler, which could have a negative impact on their economic and environmental benefits. Therefore, the government should strengthen its guiding role in power planning, carefully analyze the situation around the country and strengthen the rationality and practicality of the national power supply design. A boom in power supply construction should also be avoided, as it would result in wasteful resource allocation and increase the overall cost of the power sector.

Second, the existing large gap in marginal abatement costs for CO₂ and SO₂ across CFPPs suggests that a market-oriented emissions trading system would indeed have considerable benefits for reducing emissions from the coal-fired power sector, in particular encouraging coal-fired power companies to take action to reduce emissions. Therefore, the government should reasonably limit financing support for backward projects of high-emission enterprises with the help of the guiding ability of the market mechanism, and force high-emission enterprises to actively carry out industrial upgrading and transformation to achieve green and coordinated development, which will in turn bring about a sustainable positive impact. In addition, the price formation mechanism should be improved in the design of the national emissions trading market system, and the guiding role of the emissions trading market on the behavior of enterprises should be given full play.

Third, after analyzing the possible factors’ effects on CO₂ and SO₂ marginal abatement costs, we believe that both high-regulated and central-government-controlled CFPPs show larger pollution abatement potentials. Therefore, on the one hand, considering that command-and-control environmental regulation policies have significantly restricted the production activities of high-regulated power plants, the government could prioritize the improvement of market-based mechanisms in the implementation of environmental policies in those high-regulated regions, and maximize the release of the economic dividend effect of the policies through some market-based incentive instruments such as electricity price subsidy policies and emissions trading systems to promote green economic development. On the other hand, the government should pay more attention to the motivation of CGOPPs to reduce emissions, and implement a proper environmental impact assessment system for them to supervise high-pollution projects.

This paper still has limitations. First, we only estimate the MAC of coal-fired power plants in China. For subsequent research, we would consider estimating the MAC of pollutants for firms from other industrial sectors such as the mining and manufacturing industries. Further study could also include more countries in the sample. Second, the data we use in this paper is just cross-sectional data from 2018, which cannot reveal the dynamic characteristics of MACs. Therefore, the usage of an expanded panel data is necessary for further work.