Bayesian Vector Autoregression Analysis of Chinese Coal-Fired Thermal Power Plants

Abstract

Considering the dataset of information related to Chinese coal-fired thermal power plants during the 2005–2017 period, we initially investigated the orthogonalized response of the carbon emission to energy consumption and power generation by using Bayesian vector autoregressions and feedback solutions for impulse control technology. The results showed that the effects of energy consumption and power generation on carbon emissions were significant. The Chinese government has launched a program aimed at curbing carbon emission peaks and neutralizing or decreasing carbon emissions. The causal relationship concludes that China still needs further investment in emission abatement, improvement related to the level of openness to the outside world, and the strengthening of the construction of green zones for industrial transfer to mitigate carbon emissions.

1. Introduction

Recently, rapid economic growth has resulted in great changes in China. It has led to a large increase in energy consumption and carbon emissions (Figure 1). In 2009, China was the world’s largest energy user. According to the IEA (International Energy Agency), global carbon emissions rose less than initially feared in 2022, reaching a new high of over 36.8 GT. The growth of renewable and sustainable energy growth offset much of the impacts of greater coal and oil use. Total carbon dioxide emissions from the consumption of energy in China were relatively flat in 2022, caused in part by the novel coronavirus epidemic disease. Emissions decreased by 20 million tons to around 12 GT.

Global awareness of and concern over climate change was amplified by the formulation of the COP (Conference of the Parties). In 2022, a breakthrough agreement to provide loss and damage funding was adopted at the COP27. To realize sustainable development, the Chinese Government has paid attention to emission reductions: as early as 2006, it first set a target for reducing greenhouse gas emissions in the 11th Five-Year Plan of the People’s Republic of China (reducing emissions per unit of GDP by 20% by 2010, compared to 2005 levels). According to the Chinese government, carbon emissions per unit of GDP had already dropped by 50.8% between 2005 and 2021, increasing the share of non-fossil fuels in primary energy consumption to approximately 16.6%.

Although the goal is close to being attained, binding targets for energy conservation and emission reductions have not yet been realized. Since joining the World Trade Organization in 2001, China has implemented a series of incentives that were very attractive to foreign companies and investors. This alone had a massive impact on the growth of manufacturing industries in China. Cheap and plentiful labor primarily aided in China’s rise as the “world’s factory”. Besides this, an abundance of raw resources and low environmental regulations made it easy for them to grow (Shield Works, https://www.shieldworksmfg.com).

In 2022, the industrial sector accounted for 65 to 72% of China’s total energy consumption [1]. A boom in the electric power industry in China was witnessed to cater for the manufacturing industries. The main cause of this impressive growth was the reform of electricity generation companies. China launched many rounds of reform to form a new market-based pattern of electricity generation. In recent years, government departments (generally the provincial commission of the economy and informatization) assess electricity consumption in the second year and allocate a total power generation amount to each power plant based on an approximately equal quota rule [2]. The companies sign an annual generation contract approved by the provincial departments of development and informatization.

As fossil-fuel electricity generation industries are significant contributors to increased carbon emissions, it is necessary to analyze these companies’ performance. However, this issue has received little attention in previous research, despite a large strand of the literature studying the efficiency or emission performance of China’s regions. Another motivation for focusing on the emission performance of fossil-fuel electricity generation companies is that these sectors have been facing challenges with upgrading and transitioning. Finding better ways to reduce energy consumption and emissions in generation processes is an important piece of this puzzle, as it will allow these industries to contribute to economic and social development.

The purpose of this study is thus to investigate the carbon emission performance of Chinese fossil-fuel electricity generation companies from 2005 to 2017 under the different five-year plans of the People’s Republic of China. For this purpose, this paper proposes a new approach, Bayesian vector autoregressions (BVARs) and impulse response functions (IRFs), to measure greenhouse gas emission performance. This integrated approach has some advantages. First, the Random-Walk Markov Chain Monte Carlo simulation in the BayES program is used. When the iterations approach infinity, the Gibbs sampling methods converge to the actual joint posterior density function. Second, technological heterogeneity can be incorporated into greenhouse gas emission efficiency analysis. Third, by using the Bayesian vector autoregression technology, the discriminating power and comparability of the emission performance function model can be improved. The contributions of this study are threefold. First, this analysis targets Chinese fossil-fuel electricity generation companies, while previous energy efficiency research has mainly focused on different regions. Second, we examine a relatively long period, 2005–2017, which covers several different Chinese five-year plans; as such, this empirical study may yield richer insights. Finally, unlike other efficiency methods, prior knowledge or results of a previous model, can be used to inform our dynamic autoregressions, making a methodological contribution.

The rest of this paper is organized as follows. Section 2 introduces Chinese electricity generation. Section 3 presents the literature review, while Section 4 introduces the methodology, and then Section 5 and Section 6 examine the emission performance of Chinese fossil-fuel electricity generation companies. Section 7 concludes.

2. Greenhouse Gas Emission Reductions in Chinese Electricity Generation Industries

2.1. Energy Consumption Issues in China

With further reform and opening up, China has developed rapidly. High energy consumption and especially high carbon dioxide emissions are two important problems that influence economic growth in 21st century China. Energy consumption represents a fundamental input for economic growth, but limited use of energy may have serious consequences on the environment [3,4,5,6,7,8,9,10,11,12,13]. Since 1978, the Chinese government has launched many electricity generation reforms so that energy efficiency will accelerate the growth of China’s fossil-fuel electricity generation. China is often called the world’s factory, and its electricity industry has played a crucial role in the national economy. Massive domestic demand has induced Chinese power plants to operate at full capacity, increasing generation as well as raw coal consumption. The coal consumption of Chinese power plants has consistently accounted for 57% of total coal consumed in 2021. The generation, energy consumption, and carbon emissions of Chinese power plants have followed upward trends in tandem, not showing the decoupling achieved in developed countries. A milestone was reached in 2001, when China joined the WTO and growth in generation, energy consumption, and carbon emissions accelerated significantly. The world’s largest emitter has not only triggered soaring prices of energy and resources but also threatens the environment and sustainable development.

According to National Development and Reform Committee and National Energy Administration of China, in 2022, coal was the most carbon-intensive of the fossil fuels and accounted for 56.2% of energy used. Therefore, it will be a great challenge to improve the energy efficiency of the Chinese electricity sector, thereby cutting emissions while driving economic growth amid an overall trend of slowing growth following the novel coronavirus disease. However, China’s electricity industries still play a key role in creating job opportunities, so such a shift is also urgently needed.

2.2. Energy Policies in China

China overtook the U.S. as the world’s largest carbon emitter in 2005 (World Bank, https://www.worldbank.org). In 2021, the Glasgow Climate Pact was adopted at the COP26. The Chinese government has made the commitment that by 2030 non-fossil energy will account for 25 percent of its total primary energy consumption, and carbon emission per unit of GDP will be 65 percent lower than in 2005.

When the 14th Five-Year Plan for National Economic and Social Development was released, China made every effort to fulfill its commitment. The Chinese government began taking action to mitigate carbon emissions. It announced that the government aimed to reduce the carbon emitted per unit of GDP by 13.5% during the 5 years; non-fossil energy will rise to 20 percent of national total primary energy consumption by 2025. The government proposed a series of complementary transition plans to phase out fossil-fuel electricity generation companies (

Table 1. Timeline of the transition plan.

Time	Who (Organization Responsible for the Plan)	What (Transition Plan)
–1978	The State Council and Central Committee of the CPC	Management and operation will not be integrated, and power plants and grids will not be affiliated units of the government.
1979–1985	The State Council and Central Committee of the CPC	Electric power companies cannot be solely invested in by the central government. The proposed plans will solve the contradiction between the original vertical monopoly operation mode of the power industry and economic system reform and opening up.
1986–1997	The State Council of the People’s Republic of China	The reform of the investment system will stimulate enthusiasm for power investment, and the power industry will develop rapidly. The total amounts of investment outside of finance will rapidly expand. The primary focus is on alternative energy sources to further explore their relationship with fossil-fuel usage.
1998–2007	The State Council of the People’s Republic of China	The relaxation of restrictions in the field of fossil-fuel electricity generation companies should activate enthusiasm for social capital. The reform of the power investment system should greatly increase the capacity for power investment. China emphasizes the dynamics of the transition from carbon to renewable energy.
2008–2010	The State Council and local management departments	According to the requirements of the 2008 Beijing Olympic Games, some fossil-fuel electricity generation companies will be phased out. The plan for the reform of the electric power system will clarify the key tasks of the reform of the electric power industry.
2011–2013	The State Council and local management departments	The series of complementary transition plans are the separation of power plants and grids, separation of main and auxiliary power, separation of transmission and distribution, and bidding for grid connection.
2014–2022	National Development and Reform Commission, Energy Administration, and local organizations	Important tasks for the development of the power industry: energy conservation, emission reduction, and green development. The Chinese power industry will enter a stage of high-quality development.
2023–	National Development and Reform Commission, Energy Administration, and local organizations	Some fossil-fuel electricity generation companies can be controlled by a foreign capital company. The management departments should pay attention to the development of clean energy generation such as wind power and photovoltaic power. They should promote the comprehensive development of the power industry towards digitization and internationalization.

). Upholding the principle of constructing large units and restricting small ones, China strictly controls the construction of new coal-fired power-generating sets in the BoSea Rim regions (provinces, as well as municipalities directly under the Central Government), including Beijing, Tianjin, and Shanghai, Hubei, Guangdong, and Shenzhen. “It speeds up the elimination of small thermal power units marked by high energy consumption and heavy pollution… to strictly control pollutant emissions from coal-fired power plants” [14]. It has promoted the clean, highly efficient development of energy-saving power plants, “China has been optimizing coal-fired power and upgrading technology to steadily reduce excess capacity. It has improved the early-warning mechanism for risk control in coal-fired power planning and construction, and moved faster to phase out outdated capacity… China has taken action to upgrade coal-fired power plants to reduce emissions, and adopted stricter standards for energy efficiency and environmental protection. The efficiency and pollutants control levels of coal-fired power units are on par with world advanced levels” [15]. It has also commenced the development of hydroelectricity power to improve resource security. The Chinese government had closed down more than 100 million kW of coal capacity. Chinese fossil-fuel electricity generation companies accounted for 52% of total companies in 2019, dropping from 66% in 2012.

Despite China promoting the piloting of low-carbon programs in some regions and supporting an emissions-trading system in the Pearl River Delta, Yangtze River Delta, and BoSea Rim regions, more concrete action is still taken to accomplish these goals.

2.3. Electricity Generation Reform in China

The government proposed a series of complementary transition reforms to develop low-carbon technologies and renewable energy and decrease greenhouse gas emissions in the generation process. Since 1984, the government has initiated many electricity generation reforms to construct large companies and restrict small fossil-fuel electricity generation units.

In 2012, the government began to encourage industrial upgrading. Thermal power generators with a capacity lower than 100 MW all have been closed down. Companies with high energy consumption as well as high pollution have been required to shut down. “In past decades, owing to the rapid growth in power demand, even if the power generation capacity were rapidly expanding, an acceptable capacity factor could be guaranteed. However, the current growth rate in power demand has gradually slowed, and the problem of overinvestment has become acute” [2]. In recent years, the efficiency of power generators has reduced substantially.

2.4. Corruptions and Associated Challenges

Finally, it is worth mentioning that giving absolute power to leaders of Chinese fossil-fuel electricity generation companies is an invitation to absolute corruption. For example, some generation company bosses subcontracted their businesses to their own private corporations or those owned by their relatives. The bosses of China *** Energy Company accept bribes in the coal trade, by “colluding with contractors or suppliers, using their power to seek money or sex”. “Other issues including buying and selling of official positions, wining and dining at public expense, and helping relatives open businesses and obtain illegal profits were discovered in China *** Corporation” (Chinadaily, http://www.chinadaily.com.cn), Southern ***, and other factories. The managers are prone to in-group preferences to secure private benefits. So, nepotism is an epidemic rampant in some companies. The chief officials prefer their relatives who behave like themselves instead of laborious workers.

3. Literature Review

3.1. The Literature on Carbon Emission and Energy Consumption Issues

Carbon emission and energy efficiency play a central role in national economic policies [16]. They are used to calculate and evaluate the economic index in achieving energy efficiency and renewable energy transition in Australia, Belgium, Canada, China, Denmark, France, Germany, the United Kingdom, and the United States. Adekoya et al. use the panel quantile regression technique to examine the nexus across the conditional distribution of the dependent variables. They find that, for a more specific case, economic complexity does not support energy efficiency in all economic groups [17]. Alvarado et al. (2022, 2021), while reviewing data from 18 countries in Latin American and using threshold regressions, prove how economic complexity reduces the consumption of renewable energy [18,19]. Focusing on the linkage among the index of electricity price, energy consumption, and pollution, Qiao et al. show that the rise in carbon and fossil energy prices will reduce the value of the electricity market. But it can ultimately change a series of processes and techniques of natural resource management (at six months), to “reduce carbon emissions” [20].

A number of factors of energy efficiency policies tend to have been met with more empirical attention. Molinos-Senante et al. outline the current state of England’s water industry which “has been undergoing several structural reforms”. It is evident that restricting the cancerous development of monopolistic industries is crucial for government agencies. Assessing the growth and its drivers for the sustainable development of the water industry “has become a significant part of the process of determining the price of the water for urban uses”. The main empirical results can be summarized as follows. It can be seen that the technological index contributed positively to productivity growth, whereas the temporal changes in efficiency catch-up have been the source of deterioration. Moreover, “the transition to private ownership had a positive impact on metafrontier productivity which increased by 2.5% per year” [21,22]. The industrial transfer policy exerts a significant negative impact on carbon emissions. The environmental effects of energy policy could not be underestimated since it may reduce vulnerability to effects of contamination exposure. From a direct investment perspective, the polluting industries will relocate to jurisdictions with less stringent environmental regulations. Meanwhile, firms from investing developed countries contribute to the host country’s reduction in emissions through green technology and economic growth [23,24,25,26,27]. Consistent with prior studies, Tawiah et al. (2023) verify a negative and significant relationship between corruption and green growth [28].

3.2. Approaches for Estimating Efficiency

Owing to the lack of research of the bidirectional cause-and-effect relationship, the classical method for evaluating the efficiency of energy usually used single indicators, and the Malmquist index and Data Envelopment Analysis were used to monitor emission performance in attaining energy and environmental goals [29,30,31,32,33,34,35,36,37,38,39,40,41]. Most previous research has estimated the emissions and energy efficiency of manufacturing industries, ignoring Chinese fossil-fuel electricity generation companies. Meanwhile, these scholars may be unacquainted with the research of the bidirectional cause-and-effect relationship. The estimated energy efficiency may be subjective [42,43]. Later on, Zhang et al. further propose a global meta-frontier distance function that incorporates non-radial slacks as well as group heterogeneity [44].

In the early stage, the efficiency measures will overestimate efficiency without discriminating power. They do not provide ex ante information as they adjust all inputs and outputs by the same probability to meet the efficient targets [45,46,47,48].

Therefore, a large strand of the literature adopting the technical parameter model rather than traditional non-parametric statistics to compare relative performance has emerged in recent years. In this paper, we develop an innovative model. The new technique need not be built entirely through experimentation but requires prior knowledge. The idea is infinitely far superior to the old one. The model of Bayesian vector autoregressions is thus able to precisely improve the discriminating power and comparability of intertemporal observations. It incorporates informative priors, so that prior knowledge, or results of a previous model, can be used to inform the current model. In the remainder of the paper, we apply this Bayesian inference to investigate emission performance among Chinese fossil-fuel electricity generation companies during the 2005–2017 period.

4. Methodology

We set the bidirectional cause-and-effect system AR (lag) with matrix y, and s is the size of the row. I choose the priors for the parameters as flat. The general priors for model are Normal, Inverted Wishart distribution. Supposing that r is an exogenous shock with the identical distribution, the causal programming of economic subject can be expressed as follows:

$$\begin{array}{l}y=z\alpha +r\\ r~N(0,{\tau }^{-1}\otimes I)\end{array}$$

(1)

where

$$y=y(s)=\left[\begin{array}{l}{y}_{lag+1}^{\prime }\\ y_{lag+2}^{\prime }\\ \dots \\ y_s^{\prime }\end{array}\right],z=z(s)=\left[\begin{array}{ccccc}1& y_{lag}^{\prime }& y_{lag-1}^{\prime }& \dots & y_1^{\prime }\\ 1& y_{lag+1}^{\prime }& y_{lag}^{\prime }& \dots & y_2^{\prime }\\ \dots & \dots & \dots & \dots & \dots \\ 1& y_{s-1}^{\prime }& y_{s-2}^{\prime }& \dots & y_{s-lag}^{\prime }\end{array}\right],\alpha =\left[\begin{array}{l}{\alpha }_1^{\prime }\\ {\alpha }_2^{\prime }\\ \dots \\ {\alpha }_{lag}^{\prime }\end{array}\right],\mathrm{and} r=\left[\begin{array}{l}{r}_{lag+1}^{\prime }\\ r_{lag+2}^{\prime }\\ \dots \\ r_s^{\prime }\end{array}\right]$$

During the construction of the matrix of vectorization of y, z, a, and r, first of all, we build a vector stripped of the specified rows. We finally create a matrix of the lagged values.

Based on the iteration, we have the following:

$$\begin{array}{ll}\left|z(s{)}^{\prime }z(s)\right|& =|z_s^{\prime }{z}_s+{\left[\begin{array}{l}{z}_{lag+1}^{\prime }\\ z_{lag+2}^{\prime }\\ \dots \\ z_{s-1}^{\prime }\end{array}\right]}^{\prime }\left[\begin{array}{l}{z}_{lag+1}^{\prime }\\ z_{lag+2}^{\prime }\\ \dots \\ z_{s-1}^{\prime }\end{array}\right]|\\ & =(z_s^{\prime }({\left[\begin{array}{l}{z}_{lag+1}^{\prime }\\ z_{lag+2}^{\prime }\\ \dots \\ z_{s-1}^{\prime }\end{array}\right]}^{\prime }\left[\begin{array}{l}{z}_{lag+1}^{\prime }\\ z_{lag+2}^{\prime }\\ \dots \\ z_{s-1}^{\prime }\end{array}\right]{)}^{-1}{z}_s+1)(z_{s-1}^{\prime }({\left[\begin{array}{l}{z}_{lag+1}^{\prime }\\ z_{lag+2}^{\prime }\\ \dots \\ z_{s-2}^{\prime }\end{array}\right]}^{\prime }\left[\begin{array}{l}{z}_{lag+1}^{\prime }\\ z_{lag+2}^{\prime }\\ \dots \\ z_{s-2}^{\prime }\end{array}\right]{)}^{-1}{z}_{s-1}+1)|{\left[\begin{array}{l}{z}_{lag+1}^{\prime }\\ z_{lag+2}^{\prime }\\ \dots \\ z_{s-2}^{\prime }\end{array}\right]}^{\prime }\left[\begin{array}{l}{z}_{lag+1}^{\prime }\\ z_{lag+2}^{\prime }\\ \dots \\ z_{s-2}^{\prime }\end{array}\right]|\end{array}$$

(2)

Through an appropriate choice of function Ctem, Mean, and Ctr, a challenge in the practical implementation of the long-run prior is the setting up of dummy observations:

$$\left[\begin{array}{cccc}{\displaystyle \frac{1}{Ctem}},& \left(\begin{array}{cccc}{\displaystyle \frac{(CtrMea{n}^{\prime }{)}^{\prime }}{Ctem}}& & & \\ & {\displaystyle \frac{(CtrMea{n}^{\prime }{)}^{\prime }}{Ctem}}& & \\ & & \dots & \\ & & & {\displaystyle \frac{(CtrMea{n}^{\prime }{)}^{\prime }}{Ctem}}\end{array}\right)& ,\dots ,& \left(\begin{array}{cccc}{\displaystyle \frac{(CtrMea{n}^{\prime }{)}^{\prime }}{Ctem}}& & & \\ & {\displaystyle \frac{(CtrMea{n}^{\prime }{)}^{\prime }}{Ctem}}& & \\ & & \dots & \\ & & & {\displaystyle \frac{(CtrMea{n}^{\prime }{)}^{\prime }}{Ctem}}\end{array}\right)\end{array}\right],$$

$$\left[\begin{array}{cccc}{\displaystyle \frac{(CtrMea{n}^{\prime }{)}^{\prime }}{Ctem}}& & & \\ & {\displaystyle \frac{(CtrMea{n}^{\prime }{)}^{\prime }}{Ctem}}& & \\ & & \dots & \\ & & & {\displaystyle \frac{(CtrMea{n}^{\prime }{)}^{\prime }}{Ctem}}\end{array}\right]$$

We use the distribution of $\alpha |{\tau }^{-1},{\tau }^{-1}$:$N(a,\mathsf{\Theta }),IW(\Xi ,g)$.

According to Bayesian Econometrics, the coefficients for each equation will be estimated by the following formula:

$$\begin{array}{l}\exp ((\alpha -a{)}^{\prime }{\mathsf{\Theta }}^{-1}(\alpha -a)+(y-z\alpha {)}^{\prime }(y-z\alpha ))\\ \propto \exp ({\alpha }^{\prime }{\mathsf{\Theta }}^{-1}\alpha -{\alpha }^{\prime }{\mathsf{\Theta }}^{-1}a-a^{\prime }{\mathsf{\Theta }}^{-1}\alpha +{\alpha }^{\prime }{z}^{\prime }z\alpha -{\alpha }^{\prime }{z}^{\prime }y-y^{\prime }z\alpha )\\ \propto \exp ((\alpha -{\displaystyle \frac{z^{\prime }y+{\mathsf{\Theta }}^{-1}a}{z^{\prime }z+{\mathsf{\Theta }}^{-1}}}{)}^{\prime }(z^{\prime }z+{\mathsf{\Theta }}^{-1})(\alpha -{\displaystyle \frac{z^{\prime }y+{\mathsf{\Theta }}^{-1}a}{z^{\prime }z+{\mathsf{\Theta }}^{-1}}}))\end{array}$$

(3)

Letting m be the column size of variables, we may compute the hierarchical log-posterior of the hyperparameters [49] after the observation report:

$$\begin{array}{ll}\log \pi (\alpha ,{\tau }^{-1}|y)=& -\frac{1}{2}\left({\hat{r}}^{\prime }\right({\tau }^{-1}\otimes I{)}^{-1}\hat{r}+(\hat{\alpha }-a{)}^{\prime }({\tau }^{-1}\otimes \mathsf{\Theta }{)}^{-1}(\hat{\alpha }-a))\\ & -\frac{1}{2}\left(\right(\alpha -\hat{\alpha }{)}^{\prime }\left(z^{\prime }\right({\tau }^{-1}\otimes I{)}^{-1}z+({\tau }^{-1}\otimes \mathsf{\Theta }{)}^{-1}(\alpha -\hat{\alpha })+-\frac{1}{2}tr(\Xi \tau )\\ & -\frac{mg}{2}\log \left(2\right)-\log \left({\Gamma }_m\right(\frac{g}{2}\left)\right)+\frac{g}{2}\log \left|\Xi \right|-\frac{m}{2}\log \left|\mathsf{\Theta }\right|\\ & -\frac{s-lag+mlag+m+g+2}{2}\log \left|{\tau }^{-1}\right|-\frac{m(s-lag+mlag+1)}{2}\log \left(2\pi \right)\end{array}$$

(4)

By applying integrating rule, the logarithmic density function is conducted. Integrating out the other variable ${\tau }^{-1},\alpha |{\tau }^{-1}$, we can also similarly obtain another mathematical representation ($\pi (y)$ of logarithmic marginal density) by highlighting the relevant shocks of stochastic volatility of the dynamic system:

$$\begin{array}{ll}\log \pi (y)=& {\displaystyle \frac{s-lag+g}{2}}\log (\left|{({\displaystyle \frac{\Xi +{\widehat{r}}^{\prime }\widehat{r}+(\widehat{\alpha }-a{)}^{\prime }{\mathsf{\Theta }}^{-1}(\widehat{\alpha }-a)}{s-lag+mlag-m+g-1}})}^{-1}{\displaystyle \frac{\Xi }{g-m-1}}\right|)\\ & -{\displaystyle \frac{1}{2}}{\displaystyle \sum _{lag+1}^s\log (\left|\Xi \otimes ({\left[\begin{array}{l}{z}_{lag+1}^{\prime }\\ z_{lag+2}^{\prime }\\ \dots \\ z_s^{\prime }\end{array}\right]}^{\prime }(z_{s-1}^{\prime }{z}_{s-1}+{\mathsf{\Theta }}^{-1}{)}^{-1}\left[\begin{array}{l}{z}_{lag+1}^{\prime }\\ z_{lag+2}^{\prime }\\ \dots \\ z_s^{\prime }\end{array}\right]+1)\right|}\\ & -{\displaystyle \frac{s-lag+g}{2}}\log ({\displaystyle \frac{s-lag+mlag-m+g-1}{g-m-1}})\\ & +\log ({\Gamma }_m({\displaystyle \frac{s-lag+g}{2}}))-\log ({\Gamma }_m({\displaystyle \frac{g}{2}}))\\ & -{\displaystyle \frac{m(s-lag)}{2}}\log (\pi )\end{array}$$

(5)

Random-Walk Markov Chain (RWMC) estimation is used to obtain the parameters. This paper wants to design the transition probabilities between values so that we generate more samples in regions where density is large, and relatively less samples in regions where it is small. To begin with RWMC sampling, the corresponding differential matrix of the hyperparameters has been utilized for the constrained optimization. The matrix of Hessian is regularized (making sure it is positive-definite), the speed of sampling could be probably improved. RWMC sampling accepts the next as a sample if the smallest element taken from one or the next is greater than uniform distribution. An amount of 20,000 is the total number of draws in the sampling. In total, 2000 samples are exercised prior to being put in Bayesian vector autoregression estimation.

We can calculate impulse response series to an exogenous shock in the model, which is stored in the working directory currently in memory. The shock of size is equal to the one standard deviation. Using Cholesky ordering to a shock, the representation (1) delivers precise estimates of the tools of orthogonalized impulse (IMPU) responses based on the variance (Chol) and vecshock (Shock).

$$IMPU(h)=\left\{\begin{array}{ll}\left(CholShock\right)’& if h=1\\ IMPU(h-1)\alpha & otherwise\end{array}\right.$$

(6)

Due to the cumbersome computation of the complete-data likelihood, we use the BayES Software (version 2.5) that has already been compiled by Grigorios Emvalomatis (2020).

5. Empirical Tests

5.1. Data

To resemble the economic and environmental effects under various operations, this study accommodates different endogenous variables to examine how the changes in energy consumption and power generation may alter the performance of carbon emissions. The value from energy consumption, power generation, and emission reduction are based on the official sources. The basic calculation of such parameters can be found from our previous studies [23,44]. In this study, the variables are further modified to reflect the potential climate-induced impacts on economic activities.

This paper uses data of Chinese fossil-fuel electricity generation companies during 2005–2017 to investigate the carbon emission performance. We use a balanced data panel, comprising ninety-one Chinese coal-fired electricity power plants, over a period of thirteen years from 2005 to 2017 (13 × 91 = 1183 observations), and endogenous variables, including carbon emissions, energy consumption, and power generation. All data are constructed based on the homepage websites of the agency of statistic bureau of China (https://data.stats.gov.cn/easyquery.htm?cn=C01, accessed on 3 August 2024) and China Statistical Yearbook [50], etc.

We calculate the CAR through logarithm of carbon emissions, ENE through logarithm of energy consumption, POW through logarithm of power generation, and TIC through logarithm of the installed capacity.

5.2. Results

After performing the Monte Carlo experiment 20,000 times, we obtain the results in the following

Table 2. Parameter estimation results of Bayesian vector autoregression.

	Mean	Median	Sd.dev.	5%	95%
CAR
constant	7.33	7.34	6.80	−3.91	18.38
TIC	−0.21	−0.20	0.67	−1.31	0.88
CAR (−1)	0.34	0.34	0.73	−0.84	1.54
ENE (−1)	−0.05	−0.05	0.23	−0.43	0.33
POW (−1)	−0.30	−0.30	0.76	−1.54	0.95
ENE
constant	16.64	16.78	8.65	2.17	30.70
TIC	0.55	0.54	0.85	−0.84	1.98
CAR (−1)	−1.30	−1.31	0.93	−2.80	0.24
ENE (−1)	−0.41	−0.41	0.29	−0.88	0.07
POW (−1)	1.35	1.37	0.97	−0.25	2.92
POW
constant	2.07	2.03	6.81	−9.09	13.25
TIC	0.63	0.63	0.67	−0.46	1.71
CAR (−1)	−0.04	−0.05	0.73	−1.24	1.14
ENE (−1)	−0.12	−0.11	0.23	−0.49	0.27
POW (−1)	0.19	0.19	0.77	−1.06	1.45
log-ML (Lewis & Raftery)					−18.8171

.

The bottom block of the table presents the result for the precision index of the goodness-of-fit. The higher the value of the log-ML (Lewis & Raftery), the better our model fits a dataset. The two columns on the right-hand side give the endpoints of the 90% credible intervals. The fourth column contains the posterior standard deviations. The third column contains the posterior medians of each parameter, while the second column the corresponding posterior mean. The first column of the table contains the variable name, and the vector associated with the exogenous variable is listed first.

Table 2 presents the value of the log-ML, which is −18.8171, and our model fits well. The regressions of energy consumption on economic growth and carbon emissions then can be algebraically depicted as follows:

$$\left\{\begin{array}{c}POW=\begin{array}{l}2.07\hfill \end{array}\begin{array}{l}-0.04\hfill \end{array}CAR(-1)\begin{array}{l}-0.12\hfill \end{array}ENE(-1)+\begin{array}{l}0.19\hfill \end{array}POW(-1)+\begin{array}{l}0.63\hfill \end{array}TIC\\ ENE=16.64\begin{array}{l}-1.30\hfill \end{array}CAR(-1)\begin{array}{l}-0.41\hfill \end{array}ENE(-1)+\begin{array}{l}1.35\hfill \end{array}POW(-1)+\begin{array}{l}0.55\hfill \end{array}TIC\\ CAR=7.33+0.34CAR(-1)-0.05ENE(-1)-0.30POW(-1)-0.21TIC\end{array}\right.$$

(7)

The coefficients of power generation and energy consumption are −0.04 and −1.30, indicating that, from last time, carbon emissions can decrease the power generation and energy consumption.

Next, we obtain the following:

$$\left\{\begin{array}{c}CAR=7.33+0.34CAR(-1)-0.05ENE(-1)-0.30POW(-1)-0.21TIC\\ POW(-1)=-\begin{array}{l}4.72POW-13.49\hfill \end{array}+1.62CAR(-1)+2.21TIC\\ ENE(-1)=2.21ENE-36.75\begin{array}{l}+2.86\hfill \end{array}CAR(-1)-\begin{array}{l}1.23\hfill \end{array}TIC\end{array}\right.$$

(8)

As shown in representation (8), the endogenous relationship parameters of power generation on emissions are more than zero, which is positive. There exists a significantly negative relationship between energy consumption and carbon emissions.

We then turn to the evaluation of the impulse response functions for an energy consumption shock identified with Cholesky orthogonalization. Figure 2 produces a two-way scatter plot of the IMPU of power generation and energy consumption against carbon emissions. The combined graphs draw the distribution of the impulse response to a one-standard-deviation emission shock: the IMPU at the posterior mode to estimate the simulation of statistical models and evaluate the plausibility (or compare alternative models).

The initial impact of the energy market shock on carbon emissions (ENE→CAR) has steadily diminished from a negative to an increasingly positive reaction. The impulse response does not last for a long time. To the one-unit structural shock of energy consumption, Figure 2 presents the time-varying characteristics of the impulse response (maximum horizon is 20th period). The graph shows that the impulse response of energy consumption reaches the first low point (negative) at period 0 (in the beginning). It reveals that an exogenous increase in energy consumption generates a contraction in carbon emissions. The response reaches the first high point at period 2. The last output competence is almost twice as much as that of 2 years ago. The carbon emissions respond to power generation (POW→CAR) and reachs the first high point and decrease afterwards. With a substantial expansion, the long-term effect is close to zero significantly. The feedback of carbon emissions is a similar line, and the like.

6. Robustness Checks

We apply the fixed and random effects to test the robustness of results. In the fixed-effects model, the constant term is not perpendicular to the variables. In the random- effects model, the constant term is perpendicular to the variables. In the random-coefficients model, each coefficient is associated with group effects. The fixed-effects model is all about separating within-firm difference. We can approximately calculate the model by the within-group dispersion method. Furthermore, the data are transformed within variation in deviations from the group means.

After performing the Monte Carlo experiment 20,000 times, the regressions of energy consumption on economic growth and carbon emissions and then a random-effects linear model can be depicted (

Table 3. Results of random-effects linear model.

	Mean	Median	Sd.Dev.	5%	95%
constant	5.63705	5.63671	0.0823014	5.50259	5.77319
ENE	−0.035816	−0.035774	0.0051327	−0.044221	−0.027397
POW	0.569059	0.568982	0.0203557	0.535759	0.602678
TIC	−0.23297	−0.233016	0.0192314	−0.264334	−0.201116
tau	69.7336	69.6783	2.96024	64.9337	74.6785
omega	22.6448	22.4968	3.63501	16.9904	28.8678
sigma_e	0.119832	0.119799	0.0025469	0.115718	0.1241
sigma_alpha	0.212208	0.210836	0.0173273	0.186122	0.242642
log-ML (Lewis & Raftery)					619.307

and Table 4).

The regression runs a fixed-effects linear model as follows:

Table 4. Results of fixed-effects linear model.

	Mean	Median	Sd.Dev.	5%	95%
dENE	−0.035582	−0.03558	0.0049249	−0.043678	−0.027486
dPOW	0.555856	0.555848	0.0196307	0.523778	0.588278
dTIC	−0.249143	−0.249127	0.0182362	−0.278914	−0.219189
tau	75.8808	75.8441	3.13702	70.7863	81.0935
sigma_e	0.114872	0.114826	0.0023787	0.111047	0.118857
log-ML (Lewis & Raftery)					850.345

Table 4. Results of fixed-effects linear model.

	Mean	Median	Sd.Dev.	5%	95%
dENE	−0.035582	−0.03558	0.0049249	−0.043678	−0.027486
dPOW	0.555856	0.555848	0.0196307	0.523778	0.588278
dTIC	−0.249143	−0.249127	0.0182362	−0.278914	−0.219189
tau	75.8808	75.8441	3.13702	70.7863	81.0935
sigma_e	0.114872	0.114826	0.0023787	0.111047	0.118857
log-ML (Lewis & Raftery)					850.345

The regression runs as follows:

$$CAR=5.63705-0.035816ENE+\begin{array}{l}0.569059\hfill \end{array}POW\begin{array}{l}-0.23297\hfill \end{array}TIC$$

(9)

The fixed and random effects are used to check the robustness of our results. In (9), the technology is an extra exogenous variable. We also follow standard empirical convention to conduct the statistic test. The statistic is calculated with the coefficient, standard error, and credible intervals of the coefficient estimate. The results demonstrate that the effects of energy consumption and power generation on carbon emissions are significant at a 5% critical level. From the economic perspective, the panel of the result shows that the effects of energy consumption and power generation on carbon emissions are significant. As for the carbon emissions, energy shock explains them being positive. Energy consumption has a strong explanation for carbon emissions. There is a powerful interdependence among the variables. To overcome the influence of endogeneity, our dynamic system regression is robust. This model in the paper can effectively identify and capture the dynamic feedback relationship between endogenous variables: energy consumption, economic growth, and carbon emissions.

The comparison with regressions is favorable to our results. The relationship is slightly different, especially in the tail-like part. It indicates that the parameters of our model are reasonable. Furthermore, the methodology may prove, for the most part, useful for the research of a dynamic system. The computation style is also beneficial for analysis on univariate time series and VAR regressions.

This implies that Chinese previous policies of economic growth and the environmental degrading strategy do not have long-term coherence on the whole; the authorities lack the guidance around energy consumption to have reasonable expectations of growth and emissions. Is the goal operationally feasible for China by 2050 to achieve carbon neutrality? The results show that it is maybe difficult to achieve the goal. When the value of power generation increases, carbon dioxide increases significantly. There exists a positive relationship between power generation and carbon emissions. The impact of Chinese power on greenhouse gases dominates energy consumption. So, the long-run influence of Chinese electricity and energy consumption increases greenhouse emissions. Chinese policymakers need to refocus their efforts on achieving economic objectives, including to become carbon-neutral by 2080.

7. Conclusions

This study uses Bayesian vector autoregressions and impulse response to assess the linkage among the carbon emissions, energy structure, and economic growth of a regulated industry. We construct a dynamic system firstly to explain the general causality of energy consumption on power generation and carbon emissions. Through a univariate regression with optimization for the long run, we derive a marginal likelihood to accurately estimate the long-run impact of energy on power generation and carbon emissions, and we then analyze the evolution of power generation in controlling carbon emissions.

This paper constructs a micro-dynamic system and then examines and analyzes the self-motivated effectiveness of the impact of energy consumption on power generation and carbon dioxide emissions from 2005 to 2017. We initially investigated the impact of energy consumption on power generation and carbon dioxide emissions. The results show that the effects of energy consumption and power generation on carbon emissions are significant. The policy lacks a long-term persistent effect.

Based on the empirical findings, the implications are proposed as follows. Firstly, policymakers should increase the implementation and incentives for personnel training in China. It is critically important that at the beginning of every program teachers let trainees know exactly what they will be expected to ameliorate regarding carbon emissions. If you set small, achievable goals the employees and focus on whether or not the learner has made strides toward those goals, employees are able to stay motivated throughout the process. Types of recognition will vary based on relationships, but students can be rewarded for consistent good behavior. You might be surprised at how far a little peak of interest can go, so find a topic for employee training and spark interest in emission abatement. The strengthening of personnel training can effectively prevent and resolve pollution risk, and it is one effective way to coordinate economic development, resource utilization, and environmental protection.

Secondly, the classified guidance and the real-time monitoring technology of carbon emissions should be implemented and improved. Policymakers should also control terminal carbon emissions in a timely and targeted manner, so as to adjust production or improve technology and achieve the goal of carbon emission reduction. It is important to encourage enterprises to implement production process transformation projects and energy-saving and environmental protection technology popularization projects, to support the development of energy-saving and low-carbon new energy and renewable energy industries, and to accelerate the transformation of extensive resource utilization. These things considered, practitioners should also formulate mandatory or incentive policies to regulate the establishment of relevant work processes in industrial parks and promote the efficient and orderly construction of industrial parks. Moreover, strengthening environmental regulation can effectively prevent and resolve the pollution risk of industrial parks, and it is one effective way to coordinate economic development, resource utilization, and environmental protection.

Thirdly, China still needs further investment in improvement related to the level of openness to the outside world. China’s development cannot be achieved without cooperation with other countries or territories. The government will initiate a joint-stock reform to establish modern electricity generation companies. Domestic and foreign ownership can boost each other with foreign ownership as the most basic part. Majority foreign ownership will increase the efficiency of Chinese fossil-fuel electricity generation companies. Practitioners should also strengthen the construction of green demonstration areas for joint-venture companies, actively undertake development of the eco-environmental protection industry and modern service industry, and form a complete sustainable development chain for the pollution halo effect to mitigate carbon emissions. This also requires decision-makers to do an excellent job of examination in this process and strictly promote the sustainable management of ecological red lines and resolutely put an end to the introduction of projects and enterprises with high energy consumption, high pollution, and high emissions, so as to encourage strategies for climate change abatement.

Finally, the Chinese government needs to rollout the blockchain finance networks to explore new models of energy management. Traditional industry management across organizations can involve inefficient transaction reconciliation between energy information. Blockchain finance technology has enabled a new software paradigm for managing digital ownership in partial- or zero-trust environments. It uses cryptocurrencies to exchange verifiable information and achieve coordination across energy companies and on the blockchain finance network. It will, to put it in practical terms, step up efforts to upgrade intelligent photovoltaic generation companies. Chinese photovoltaic products account for nearly 99 percent of the European market share. Policymakers should improve their public service infrastructure and market competition order, optimizing the investment environment, the construction of regional environmental-credit-information-sharing platforms, and supervision channels.

Further research needs to confirm and build on the conclusions reached here by improving on this research. As we used carbon emissions as the only undesirable output in the empirical analysis, firstly, the limitations of this paper suggest directions for new research of pollutants, such as PM 2.5 and SO. Secondly, future research should consider a wider range of transitional characteristics, such as government ownership or corporate governance to better assess the performance of Chinese power industries.