Measurement and Multiple Decomposition of Total Factor Productivity Growth in China’s Coal Industry

Abstract

Optimizing the industry development system and implementing a high-quality development strategy in China’s coal industry require us to grasp the overall status and regional differences of industrial development. Measuring and decomposing the total factor productivity growth of the coal industry is a necessary prerequisite. In this study, we estimated the total factor productivity (TFP) growth of coal industry in 24 major coal-producing provinces in China by constructing a stochastic frontier analysis (SFA) model based on a translog production function and decomposed it into technological progress change (TC), technical efficiency change (TE), scale efficiency change (SE), and factor allocation efficiency (AE). After analyzing the temporal evolution characteristics of TFP growth and its decomposition terms, we also characterized the spatial characteristics by region and province. The results showed that TFP growth in China’s coal industry is on the rise, with TC growth being the main driving factor of this; additionally, the weak growth of SE and AE also plays a limited role in this increase, while the decrease in TE hinders this trend. There are also significant regional differences in the TFP growth of China’s coal industry, with a ranking of central > west > east > northeast. Drivers of TFP growth vary between regions or in different provinces within the same region.

1. Introduction

The steady growth of China’s energy demand due to its rapid economic and social advancements has promoted the rapid development of the energy industry. In recent years, although the proportion of clean energy in China’s energy structure has increased year by year, coal is still one of the most relied-on fuels and plays a pivotal role in the energy sector. In 2021, the national production of raw coal reached 4.13 billion tonnes, an increase of 5.7% year on year, accounting for more than 60% of primary energy production, while national coal consumption increased by 4.6% year on year, accounting for 56% of total energy consumption [1]. It can be seen that China’s reliance on coal for energy will not change for a considerable period of time. As Chinese socialism has entered a new era, China’s economy has entered a new stage of high-quality development from high-speed growth. In the future, sustained and stable economic growth will continue to increase the demand for energy input, which also brings new challenges to the development of the coal industry. At the same time, with the expectation of the “double carbon” goal of achieving carbon peak by 2030 and carbon neutrality by 2060, how to achieve the sustainable and high-quality development of the coal industry has become a real dilemma. At present, the key to achieving the goal of high-quality development is improving total factor productivity through quality reform, efficiency reform, and dynamic reform [2]. Therefore, this country urgently needs to coordinate the “three reforms” of the coal industry to achieve mode transformation, structural optimization, and power conversion, which require accurately measuring and analyzing the total factor productivity growth of China’s coal industry, so as to clarify the overall status quo and regional differences in development, further identify industry development laws and progress barriers, and ultimately realize the optimization of the industrial development system.

Along with the coal industry bringing a series of social and economic problems, how to measure the sustainable or high-quality development of the coal industry has gradually become the research focus of scholars. For example, Neofytou et al. [3] outlined a multi-criteria framework for evaluating a country’s readiness level for the transition to sustainable energy, including eight evaluation criteria under four aspects: social, political, economic, and technical. They also evaluated and ranked 14 countries in different situations and with different levels of sustainable development progress based on the PROMETHEEII and AHP methods to highlight areas for improvement, providing support for policy makers in designing a path towards a green economy. Zhao et al. [4] constructed the Coal Industry Development Index (CIDI) system, including 28 s-level indicators related to six dimensions: resource guarantee, innovation, intelligent efficiency, safety and health, green and clean production, and market operation. Based on grey theory and TOPSIS, a comprehensive evaluation model was constructed to calculate China’s CIDI from 2011 to 2019. Wang et al. [5] built a comprehensive scientific coal productivity evaluation system considering the dimensions of resources, technology, safety, environment, and efficiency based on the Pressure-State-Response (PSR) model and the connotation of scientific coal productivity. They also applied the EVW-TOPSIS-OD analysis method to evaluate and identify the evolutionary characteristics and key influencing factors of scientific coal productivity in China from 2000 to 2016. In addition to the comprehensive evaluation of the high-quality development index of the coal industry, some scholars quantitatively studied the development status and prospects of the coal industry to evaluate policy implementation. Liu et al. [6] constructed the three indicators, namely operational efficiency, environmental efficiency, and unified efficiency, and empirically analyzed the impact of the integration policies of coal enterprises on sustainability in Shanxi and Inner Mongolia provinces from 2005 to 2012 based on data envelopment analysis. Qi et al. [7] used system dynamics (SD) and the Malmquist–Luenberger index to simulate the sustainable effects that green mining construction policy tools, such as environmental taxes, subsidies, and rates, exert. Furthermore, different scholars have analyzed the development status of the coal industry considering green finance [8] and the coupling coordination degree [9,10]. All the studies mentioned above quantitatively analyze the degree of sustainable development of the coal industry in China or other countries at the national level by constructing a comprehensive index system, which serves as a reference for the research of this paper.

However, there are still few studies on the sustainable development of the coal industry measuring total factor productivity growth. Liu et al. [11] used the data of key, state-owned coal mines in 19 regions from 2001 to 2005 to empirically study the technical efficiency of regional coal production and its main influencing factors. Zhao et al. [12] used the stochastic frontier production function model based on MCMC to measure the total factor productivity of coal enterprises in 16 major coal-producing areas in China from 1993 to 2006. Li et al. [13] introduced resource elements into the production function and calculated the contribution of scientific and technological progress of China’s coal industry from 2002 to 2013 using the modified Solow residual value model. Using static analysis, Zhou et al. [14] carried out a triple decomposition of the total factor productivity of coal from 2005 to 2014 in terms of technical efficiency change, technological progress, and scale change. Xue et al. [15] used the Bootstrap-DEA model to measure China’s coal resource efficiency from 2000 to 2015 and analyzed its influencing factors with Tobit. Notably, although these results provided a reference for the development of the coal industry, there is room for optimization. First, the majority of the mentioned studies are focused on the coal industry at the national level without analyzing regional or provincial development characteristics, which does not match the current situation of regional imbalance in the development of China’s coal industry. Second, the coal industry has significantly developed recently, but the observation periods of the above studies do not extend to later than 2015, and so the development of China’s coal industry in recent years has not been described. Third, most of the existing studies are only single-aspect efficiency studies, and the only multifaceted studies carry out a triple decomposition of the total factor productivity, so the comprehensiveness of the studies also needs to be improved.

In this study, we take China’s major coal-producing provinces as the research object and measure the total factor productivity growth of the coal industry in these areas from 2010 to 2020. Then, we conduct a multiple-decomposition analysis to propose a new decomposition framework to decompose the total factor productivity growth and further analyze and identify the driving factors of total factor productivity growth of the coal industry at the national and regional (provincial) levels. The contributions of this paper are as follows: first, we further deepen and refine the literature, and we not only measure and decompose the total factor productivity growth of the coal industry at the national level, but also conduct empirical research by region and province, which depicts the overall situation and regional differences of the industry development at more levels, in line with the reality of the unbalanced development of China’s coal industry. Second, the research observation period extends to 2020, so the actual development of the coal industry in recent years can be taken into account, making this research more informative. Third, the research perspective has been expanded, and the study of the decomposition of total factor productivity growth in the coal industry has been expanded from a single study to a quadruple decomposition, which enriches the selection range for different regions and provinces to identify their own development driving forces. We visualize and analyze the empirical results by region and province, which provide research support for policy formulation “according to circumstances”.

2. Methods

The growth of total factor productivity refers to the portion of output increase that cannot be explained by the increase in the factor input; that is, the growth brought about by the increase in the non-factor input, including technological progress, management level, scale efficiency and factor allocation returns, etc., can be used to effectively measure the development of an industry. The decomposition of total factor productivity provides ideas for the research design of this paper, shown as Figure 1. The research methods used here mainly include the stochastic frontier production function efficiency measurement model based on Battese and Coelli (1992) and the efficiency quadruple decomposition model based on Kumbhakar and Lovell (2000). The BC92 model assumes that the technical inefficiency term changes with time, which overcomes the limitation of technical efficiency not having time-varying characteristics, while the fourfold decomposition model makes the decomposition of total factor productivity growth more refined.

2.1. Measurement Model

The methods of total factor productivity measurement are constantly expanding with the progress of research. Solow [16] first divided economic growth into two major components—factor input growth and total factor productivity growth—and emphasized the long-term contribution of the latter. A growth accounting approach [17] and dual approach [18,19] were used more in early research in this field. Scholars such as Farell [20], Fare et al. [21], and Kumbhakar and Lovell [22,23] also proposed different methods for total factor productivity measurement and decomposition, which promoted the development of total factor productivity being assessed quantitatively. As research has progressed, the frontier function method has become the mainstream in modern efficiency research, mainly including non-parametric methods and parametric methods. The former is represented by data envelopment analysis (DEA), while the main form of the latter is stochastic frontier analysis (SFA). Although DEA can measure efficiency when multiple inputs and multiple outputs are used, it ignores the influence of random errors and has biased evaluation results. However, compared with DEA, which does not require parameters to be determined, SFA determines the specific form of the production function in advance, distinguishes the impact of random error and technical inefficiency on the results, avoids the criticism of the “black box” of the research process, is more consistent with the economic significance of the research process, and also improves the accuracy of the research results.

Therefore, according to Battese and Coelli [24], a stochastic frontier production function model is constructed in this paper, which includes a time-varying inefficiency index, and its general form is shown in Equation (1):

$$y_{it}=f[X_{it}(t);\beta ]\times \exp (v_{it}-u_{it})$$

(1)

$$u_{it}=u_i\times {\eta }_{it}=u_i\times \exp [-\eta \times (t-T)]$$

(2)

Here, $y_{it}$ is the output of region $i$ ($i=1,2,\dots ,N$) in year $t$ ($t=1,2,\dots ,T$); $f(\cdot )$ is the frontier output in the stochastic frontier production function; $X_{it}(t)$ is the factor input of region $i$ in year $t$; $\beta$ is the parameter to be estimated for the frontier function; $v_{it}-u_{it}$ denotes the compound error term, with $v_{it}$ and $u_{it}$ being independent of each other; and $v_{it}$ is the random error term of the frontier function, which represents the error caused by statistical factors, etc., and is subject to independent, identically distributed $v_{it}\sim iid.N(0,{\sigma }_v^2)$. The non-negative term $u_{it}$ is the production technology inefficiency term, which represents the degree of deviation between the actual output and the expected output of the frontier for region $i$ in year $t$. At this time, the technical efficiency can be expressed as $\exp (-u_{it})$.

Equation (2) represents a model with a time-varying technical inefficiency term, where $\eta$ is the time-varying parameter of the technical inefficiency term. When $\eta >0$, $\eta =0$ and $\eta <0$: respectively, the technical efficiency is increasing at a decreasing rate, and is unchanged and decreasing at an increasing rate.

2.2. Decomposition Model

Researchers who decompose TFP growth in the existing literature have mainly used the Malmquist index based on the DEA model [25,26], but this method has the same problem as DEA. To combine the SFA model better, this paper adopts the TFP growth decomposition method provided by Kumbhakar and Lovell [22]. Taking the logarithm of Equation (1) and taking the time derivative, we can obtain Equation (3) (subscripts $i$ and $t$ are omitted to avoid notational clutter):

$$\frac{\partial \ln y}{\partial t}=\frac{\partial \ln f[X(t);\beta ]}{\partial t}+{\displaystyle {\sum }_j\frac{\partial \ln f[X(t);\beta ]}{\partial \ln X_j}}·\frac{\partial \ln X_j}{\partial t}-\frac{\partial u}{\partial t}$$

(3)

where the left-hand term of the equation denotes the rate of output growth change ($\Delta y$) and the first term on the right-hand side of the equation is the technological progress change (TC), indicating the degree of change in technology over time under the condition of constant factor input change. The second term measures the change in the frontier output caused by the change in the factor input. $X_j$, ${\epsilon }_j=\frac{\partial \ln f[X(t);\beta ]}{\partial \ln X_j}$, and $\Delta X_j=\frac{\partial \ln X_j}{\partial t}$ represent the input amount, output elasticity, and input growth rate of factor $j$, respectively. The third term, $-\frac{\partial u}{\partial t}$, represents the technical efficiency change (TE), which measures the change rate of the ratio between the actual output and expected output of the frontier with time, under the condition that the frontier technology level and factor input are unchanged. In this case, Equation (3) can be rewritten as:

$$\Delta y=TC+{\displaystyle {\sum }_j{\epsilon }_j}\Delta X_j+TE$$

(4)

Total factor productivity (TFP) growth is known to express the part of the increase in output that cannot be explained by the increase in factor inputs, which leads to Equation (5):

$$TFP=\Delta y-{\displaystyle {\sum }_j\frac{X_j{P}_j}{{\displaystyle \sum X_j{P}_j}}\Delta X_j}=\Delta y-{\displaystyle {\sum }_j{S}_j\Delta X_j}$$

(5)

where $S_j$ represents the proportion of the input cost of factor $j$ in total input cost—that is, the share of the input cost of factor $j$ in total input cost—and represents the actual factor input level. $X_j$ is the input amount of factor $j$ and $P_j$ is the price of factor $j$. By substituting Equation (4) into Equation (5), we obtain Equation (6):

$$\begin{array}{cc}\hfill TFP& =TC+{\displaystyle {\sum }_j{\epsilon }_j}\Delta X_j+TE-{\displaystyle {\sum }_j{S}_j\Delta X_j}\hfill \\ & =TC+TE+{\displaystyle {\sum }_j({\epsilon }_j-S_j)\Delta X_j}\hfill \\ & =TC+TE+({\displaystyle {\sum }_j{\epsilon }_j}-1){\displaystyle {\sum }_j\frac{{\epsilon }_j}{{\displaystyle {\sum }_j{\epsilon }_j}}}\Delta X_j+{\displaystyle {\sum }_j(\frac{{\epsilon }_j}{{\displaystyle {\sum }_j{\epsilon }_j}}-S_j})\Delta X_j\hfill \\ & =TC+TE+(RTS-1){\displaystyle {\sum }_j{\lambda }_j}\Delta X_j+{\displaystyle {\sum }_j({\lambda }_j-S_j})\Delta X_j\hfill \end{array}$$

(6)

where the third term represents the scale efficiency change (SE) and $RTS={\displaystyle {\sum }_j{\epsilon }_j}$ is the sum of the output elasticities of all factors. The fourth term represents the factor allocative efficiency change (AE) and ${\lambda }_j=\frac{{\epsilon }_j}{{\displaystyle {\sum }_j{\epsilon }_j}}$ is the output elasticity share of factor $j$ and represents the optimal factor input level. $({\lambda }_j-S_j)$ represents the deviation degree between the actual input level and the optimal input level of factor $j$, which is used to measure the allocation distortion degree of factor $j$.

Ultimately, TFP growth can be decomposed into four components: technological progress change (TC), technical efficiency change (TE), scale efficiency change (SE), and factor allocative efficiency change (AE), as shown in Equation (7):

$$TFP=TC+TE+SE+AE$$

(7)

3. Variable Selection and Model Test

As of 2020, seven provinces—Beijing, Tianjin, Shanghai, Hainan, Tibet, Guangdong, and Zhejiang—had withdrawn from the coal mining and washing industry. Chongqing also withdrew from the coal mining and washing industry in 2021 [27], but it remains in this paper to present a more accurate portrayal of the coal industry because the research period of this paper ends in 2020. Thus, we selected 24 provinces in China (excluding Hong Kong, Macao, and Taiwan) as research samples and the input–output panel data of coal mining and washing industry from 2010 to 2020 for analysis. In order to compare samples and combine this information with the regional characteristics of coal production in China, the selected provinces were divided into four regions: the east, comprising Shandong, Jiangsu, Hebei, and Fujian; the central region, made up of six provinces, Shanxi, Anhui, Jiangxi, Henan, Hunan, and Hubei; the west, with 11 provinces, namely Sichuan, Chongqing, Yunnan, Guizhou, Shaanxi, Gansu, Qinghai, Ningxia, Guangxi, Xinjiang, and Inner Mongolia; and the northeast, including Heilongjiang, Jilin, and Liaoning provinces.

3.1. Variable and Data

3.1.1. Variable Selection

The variables used in the total factor productivity growth measure include two main categories: input variables and output variables.

(1)

Input variables

The input variables in the coal industry include capital, labor, energy, management, and policy, etc. Given the availability of data, the input variables selected in this paper include capital input and labor input.

Capital ($K$): The average annual balance of the net fixed assets in the coal mining and washing industry [28,29] was selected and calculated from the original cost of fixed assets minus accumulated depreciation, in billions of yuan.

Labor ($L$): The average number of all employees in the coal mining and washing industry that is generally accepted by academia was selected [28,30,31].

(2)

Output variables

Raw coal production ($Y$): Various output variables are used in the coal industry. Some studies use the gross industrial output value, industrial added value, or industrial sales output value, while some other studies use raw coal production as the output [32,33]. Considering that the price level of coal fluctuates greatly, and raw coal production is statistically not affected by the price level, this paper selects each province’s raw coal production as the output variable, in million tons.

3.1.2. Data Source and Processing

(1)

Quantities of input–output

The average number of all employees, original value of fixed assets, and accumulated depreciation data are from the China Industry Statistical Yearbook [34]. The state did not issue the China Industrial Statistical Yearbook in 2019 and 2018, so the fixed assets data of the coal industry in 2018 are from the China Economic Census Yearbook 2018 [35], the data of 2017 were obtained from the statistical yearbooks of all provinces, and other missing data are replaced by the arithmetic average of the two years before and after. Raw coal production data are from the China Energy Statistical Yearbook [36].

Apart from this, for the calculation of the change rate of the factor allocation efficiency, factor price information is required [37,38]. The factor price data were processed as follows:

(2)

Capital price

The capital price ($P_k$) is usually calculated using a mathematical formula that includes the depreciation rate of fixed assets and the interest rate of bank loans. Since the annual average balance of the net value of fixed assets selected in this paper was used in the calculation of depreciation, only the interest rate of bank loans over five years [39] in the current year was used to represent the capital price. If the interest rate of the current year was adjusted many times, its annual arithmetic average value was taken. To eliminate the effect of price factors, capital prices were deflated using the fixed asset price base index (2010 = 1) by province. The data on bank loan interest rates above five years are from the official website of the People’s Bank of China [40], and the fixed asset price index by province is from the Statistical Yearbook of the Chinese Investment in Fixed Assets [41].

(3)

Labor price

The labor price ($P_l$) is expressed using the average annual wage of employees in the coal industry [42]. Similarly, to eliminate the effects of inflation, labor prices were deflated using the average real wage base index (2010 = 1) for urban units of employment for the studied years. The data of the annual average wage of employees were obtained from the China Labor Statistics Yearbook [43], and the data of the average real wage index for urban employees are from China Price Statistics Yearbook [44].

3.2. Model Setting and Formula Initialization

3.2.1. Model Setting

SFA is a parameter estimation method. The efficiency frontier function needs to be set before efficiency measurements can be made. Compared with the Cobb–Douglas production function, the translog production function not only overcomes the limitation of the constant elasticity in the substitution of factor inputs, but also relaxes the Hicks-neutral assumption, and the functional form is more adaptive and the measurement results are more realistic. Therefore, we chose to use the translog production function, which includes capital and labor inputs, with $t$ representing the time trend of technological progress. The specific form is shown as Equation (8):

$$\begin{array}{c}\ln Y_{it}={\beta }_0+{\beta }_1\ln K_{it}+{\beta }_2\ln L_{it}+{\beta }_{3}t+{\beta }_4{(\ln K_{it})}^2+{\beta }_5{(\ln L_{it})}^2+{\beta }_6{t}^2\\ +{\beta }_7\ln K_{it}\ln L_{it}+{\beta }_{8}t\ln K_{it}+{\beta }_{9}t\ln L_{it}+(v_{it}-u_{it})\end{array}$$

(8)

where $Y_{it}$ is the real output; $K_{it}$ is the capital factor input; $L_{it}$ is the labor factor input; $t$ represents the time trend term; and $v_{it}$ and $u_{it}$ have the same meaning as above. In order to consider factor interactions and non-neutral technological progress, the squared and interaction terms of capital, labor, and time trend are introduced in this function.

3.2.2. Formula Initialization

After setting the specific functional form, we can realize the preliminary setting of various calculation formulas in the theoretical model in the previous section. According to Equation (6), the measurement and decomposition of TFP growth requires the following variables to be calculated first:

(1)

$\Delta X_{itj}$

The growth rate of input factors is measured by the ratio between the input growth amount of factor $j(j=k,l)$ in region $i$ in the current year and the input amount in the previous year.

Growth rate of capital input factor:

$$\Delta X_{itk}=\frac{X_{itk}-X_{i(t-1)k}}{X_{i(t-1)k}}$$

(9)

Growth rate of labor input factor:

$$\Delta X_{itl}=\frac{X_{itl}-X_{i(t-1)l}}{X_{i(t-1)l}}$$

(10)

(2)

${\epsilon }_{itj}$ and ${\lambda }_{itj}$

The output elasticity of factors refers to the percentage change in output caused by increasing a certain input factor by a given percentage when the input level remains unchanged and represents the sensitivity of the output to changes in the amount of input of a certain factor.

The output elasticity of capital factor:

$${\epsilon }_{itk}=\frac{\partial \ln f[X(t);\beta ]}{\partial \ln K}={\beta }_1+2{\beta }_4\ln K+{\beta }_7\ln L+{\beta }_{8}t$$

(11)

The output elasticity of labor factor:

$${\epsilon }_{itl}=\frac{\partial \ln f[X(t);\beta ]}{\partial \ln L}={\beta }_2+2{\beta }_5\ln L+{\beta }_7\ln K+{\beta }_{9}t$$

(12)

The share of a factor’s output elasticity shows the proportion of the output elasticity of a certain input factor in the total factor output elasticity at a given input level.

Share of capital factor output elasticity:

$${\lambda }_{itk}=\frac{{\epsilon }_{itk}}{{\epsilon }_{itk}+{\epsilon }_{itl}}$$

(13)

The share of labor factor output elasticity:

$${\lambda }_{itl}=\frac{{\epsilon }_{itl}}{{\epsilon }_{itk}+{\epsilon }_{itl}}$$

(14)

(3)

$C_{itj}$ and $S_{itj}$

The cost of input factor refers to the value of a certain factor input, which is calculated by multiplying the amount of factor input by its price.

The cost of capital factor:

$$C_{itk}=X_{itk}{P}_{itk}$$

(15)

The cost of labor factor:

$$C_{itl}=X_{itl}{P}_{itl}$$

(16)

The share of the factor cost refers to the proportion of a certain factor input cost of the total cost of the factor input.

The share of capital factor cost:

$$S_{itk}=\frac{C_{itk}}{C_{itk}+C_{itl}}$$

(17)

The share of labor factor cost:

$$S_{itl}=\frac{C_{itl}}{C_{itk}+C_{itl}}$$

(18)

3.3. Model Test

3.3.1. Model Test Method

The SFA model is sensitive to functional form and conditional assumptions. To ensure the measurement results are accurate, we need to test the model settings in order to select the most appropriate functional form for the sample data. Thus, this paper uses the maximum-likelihood ($LR$) statistical test method to test the parameters of the stochastic frontier production function and inefficiency function. In the constructed statistic $LR=-2[LR(H_0)-LR(H_1)]$, $LR(H_0)$ and $LR(H_1)$ represent the log-likelihood function of the original hypothesis $H_0$ and the alternative hypothesis $H_1$, respectively. When the original hypothesis holds, $LR$ obeys the mixed chi-square distribution, and its degree of freedom n is the number of constrained variables. When $LR>{\chi }^2(n)$, the original hypothesis is rejected; otherwise, the original hypothesis is accepted.

(1)

Test 1: Parameters of the deterministic frontier production function

The basic model and several hypotheses set in this paper are listed as follows:

Basic model: the complete functional form of Equation (8) is used, and the coefficients in this equation are not zero.

Hypothesis 1.

$H_0:{\beta }_4={\beta }_5={\beta }_6={\beta }_7={\beta }_8={\beta }_9=0$; i.e., the coefficients of all interaction terms and square terms are 0, and there is no interaction between factors, denoted as Model 1.

Hypothesis 2.

$H_0:{\beta }_3={\beta }_6={\beta }_8={\beta }_9=0$; i.e., the coefficient of the interaction term containing the time variable is 0 and there is no technological progress, denoted as Model 2.

(2)

Test 2: Parameters of the inefficiency function

The main aim of this part of the study is to assess whether the values of the parameters $\gamma$, $\mu$, and $\eta$ are equal to 0. The meaning of the parameter $\eta$ is the same as explained above. The parameter $\gamma$ mainly reflects the proportion of technical inefficiency in the compound error term, and its value is between 0 and 1. The closer its value is to 1, the more errors of the stochastic frontier production function come from technical inefficiency rather than statistical errors and other external influences. The value of the parameter $\mu$ is used to judge the distribution of the technical inefficiency term.

Hypothesis 3.

$H_0:\gamma =\mu =\eta =0$; i.e., there is no technical inefficiency term, denoted as Model 3.

Hypothesis 4.

$H_0:\mu =\eta =0$; i.e., there is no time-varying technical efficiency, and the technical inefficiency term follows a half-normal distribution, denoted as Model 4.

Hypothesis 5.

$H_0:\mu =0$; i.e., the technical inefficiency term follows a half-normal distribution, denoted as Model 5.

Hypothesis 6.

$H_0:\eta =0$; i.e., the technical efficiency has no time-varying characteristics, denoted as Model 6.

3.3.2. Model Test Results

The parameters of the stochastic frontier production function were estimated using Frontier 4.1, and the results of parameter estimation for each model under the basic model and hypothesis conditions are shown in

Table 1. Frontier production function model and its parameter estimation results.

Variables	Parameter	Frontier Production Function				Inefficiency Function
		Basic Model	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
Constant	${\beta }_0$	8.277 ***	2.663 ***	6.211 ***	7.350	13.934 **	17.034 ***	8.324 ***
$\ln K$	${\beta }_1$	1.685 ***	0.211 **	1.728 ***	1.892	2.735 **	3.602 ***	1.628 ***
$\ln L$	${\beta }_2$	−1.103 ***	0.582 ***	−0.663 **	−0.744	−2.493	−3.242 **	−1.141 ***
$t$	${\beta }_3$	−0.251 ***	0.005		−0.482	−0.328	−0.390 *	−0.221 ***
${(\ln K)}^2$	${\beta }_4$	0.070 **		0.072 **	0.205 **	0.087	0.099 *	0.059
${(\ln L)}^2$	${\beta }_5$	0.111 ***		0.097 ***	0.082	0.200 **	0.241 **	0.116 ***
$t^2$	${\beta }_6$	0.008 ***			0.012 **	0.007 **	0.007 **	0.008 ***
$\ln K\ln L$	${\beta }_7$	−0.178 **		−0.199 ***	−0.266	−0.295 *	−0.375 **	−0.170 *
$t\ln K$	${\beta }_8$	−0.007			−0.008	−0.011	−0.034 *	−0.002
$t\ln L$	${\beta }_9$	0.017 **			0.026	0.027	0.047 *	0.012
${\sigma }^2={\sigma }_u^2+{\sigma }_v^2$		0.592 ***	0.590 ***	0.683 ***	0.320	4.066 ***	6.845 ***	0.631 ***
$\gamma ={\sigma }_u^2/{\sigma }^2$		0.885 ***	0.902 ***	0.910 ***	0	0.984 **	0.991 ***	0.895 ***
$\mu$		1.448 ***	1.459 ***	1.577 ***	0	0	0	1.503 ***
$\eta$		−0.010	−0.014 *	−0.009	0	0	−0.031 ***	0
Samples Log-likelihood		264	264	264	264	264	264	264
		−70.93	−89.96	−76.10	−219.13	−76.26	−72.10	−76.26

*, **, and *** indicate significance levels of 10%, 5%, and 1%, respectively.

, while

Table 2. Results of hypothesis tests for the frontier production function model.

Models	Hypothesis	LR Value	Degree of Freedom	Critical Value	Decision
Model 1	${\beta }_4={\beta }_5={\beta }_6={\beta }_7={\beta }_8={\beta }_9=0$	38.08	6	16.81 ***	Reject
Model 2	${\beta }_3={\beta }_6={\beta }_8={\beta }_9=0$	10.35	4	9.49 **	Reject
Model 3	$\gamma =\mu =\eta =0$	296.41	3	11.34 ***	Reject
Model 4	$\mu =\eta =0$	10.66	2	9.21 ***	Reject
Model 5	$\mu =0$	2.36	1	2.71 *	Accept
Model 6	$\eta =0$	8.32	1	6.63 ***	Reject

*, **, and *** indicate significance levels of 10%, 5%, and 1%, respectively. Critical values are from the table of critical values of cardinal distribution.

shows the results of the maximum-likelihood (LR) statistical tests for the corresponding models.

(1)

Result 1

First, the basic model rejects the hypothesis that there is no interaction between variables—i.e., it rejects Model 1—and shows that the interaction between input factors in the coal industry is also affecting the industry output. Second, the basic model also rejects the hypothesis that there is no technological progress—i.e., it rejects Model 2—which shows that the choice of the translog production function form containing the time trend term is reasonable. Finally, most of the estimated parameters of the basic model are significant at the 5% level, and the high value of the log-likelihood function indicates that the form of function setting is realistic, which makes it appropriate for use in the basic model with the translog production function.

(2)

Result 2

Except for hypothesis 5, the test results strictly rule out the other hypotheses related to the inefficiency function, which indicates that not only is there technical inefficiency present in China’s coal industry, but also that it follows a half-normal distribution and has strong time-varying characteristics. In other words, the technology used in the coal industry was not efficient enough to put all provinces on the production frontier in 2010–2020. The value of $\gamma$ for Model 5 is 0.991 and is significant at the 1% level, which indicates that 99.1% of the compound error of the frontier production function comes from technical inefficiency; i.e., there was a significant loss in time-varying technical efficiency in China’s coal industry in 2010–2020.

In summary, Model 5 was chosen as the model to measure TFP in this paper. First, the estimated value of coefficient ${\beta }_1$ of the capital variable reached 3.602, indicating that the direct effect of the capital factor makes a significant contribution to the industry output. The coefficient ${\beta }_2$ of the labor variable was estimated to be −3.242 and the coefficient ${\beta }_3$ of the time variable was estimated to be −0.390, indicating that the direct effects of both the labor factor and technology do not help the industry output and may even harm it, and the suppressive effect of the labor factor is more significant. Second, the coefficients of the three squared terms ${\beta }_4$, ${\beta }_5$, and ${\beta }_6$ were estimated to be 0.099, 0.241, and 0.007, respectively, indicating that the superimposed inputs of the capital factor, labor factor, and technology are, to some extent, conducive to improving the output of the coal industry. Finally, the coefficient ${\beta }_7$ of the interaction variable between the capital factor and labor factor was estimated to be −0.375, indicating a strong substitutable relationship between them. The coefficient ${\beta }_8$ of the interaction variable between capital and time trend was estimated to be −0.034, and the coefficient ${\beta }_9$ of the interaction variable between labor and time trend was estimated to be 0.047, indicating that capital-saving technological progress occurred during the observation period; i.e., the labor factor in the input process replaced the capital factor, and so the labor factor was not fully utilized, thereby reducing the output of the coal industry to some extent.

4. Empirical Results

4.1. Temporal Evolution

According to the estimated parameters of Model 5 in Table 1, the annual TC, TE, SE, and AE of each province can be determined by calculating Equations (3)–(18) together. TFP can be obtained after these equations are summed, and then the geometric mean value can be calculated. The data and change trend of TFP and its decomposition term in the coal industry from 2010 to 2020 are shown in

Table 3. TFP and its decomposition in the coal industry from 2010 to 2020.

Year	TC	TE	SE	AE	TFP
2010–2011	0.016	−0.035	−0.029	0.043	−0.005
2011–2012	0.027	−0.035	−0.019	−0.002	−0.029
2012–2013	0.037	−0.036	−0.023	0.011	−0.011
2013–2014	0.046	−0.036	0.012	−0.007	0.015
2014–2015	0.054	−0.036	0.019	−0.004	0.033
2015–2016	0.061	−0.037	0.014	0.005	0.043
2016–2017	0.073	−0.037	0.020	0.008	0.064
2017–2018	0.087	−0.037	0.012	−0.003	0.059
2018–2019	0.093	−0.037	0.025	0.022	0.103
2019–2020	0.102	−0.037	0.014	0.009	0.087
Mean	0.060	−0.036	0.005	0.008	0.036

and Figure 2.

First, as shown in Table 3, the TC value improved from 0.016 in 2010–2011 to 0.102 in 2019–2020, showing a continuous increasing trend, with an average annual growth rate of 0.060, indicating that the technology of the coal industry is improving year by year, which has obviously become the determining factor and the main driving force of TFP growth in China’s coal industry. This is mainly attributed to the fact that China’s coal industry, which lived through the sluggish market environment after the “golden decade”, has further recognized that it is difficult to solve its own predicament and achieve sustainable development by relying extensively on factor inputs and high coal prices, so it has strengthened its emphasis on technology and innovation, introduced new materials, new technologies, and new equipment, and actively explored a new model of technological innovation and development.

Second, the annual mean value of TE is −0.036, showing a downward trend and decreasing at an increasing rate, which is consistent with the situation where $\eta$ = −0.031 < 0 in Table 1. This suggests that TE has reduced TFP growth in the coal industry by an average of 3.6% per annum. It can be seen that the negative growth trend of TE inhibits the growth rate of TFP. The main reason for this situation may be that although the development of China’s coal industry attaches great importance to the introduction of advanced technology and innovation, it does not pay enough attention to the improvement of its existing technical capabilities, resulting in the speed of technological progress far exceeding the speed of improvement of the existing technology. As a result, it has not been possible to use advanced technology as effectively as is necessary, and the inefficiency of the available technology is obvious.

Third, the SE value increased from −0.029 in 2010–2011 to 0.012 in 2013–2014, and then increased to 0.025 in 2018–2019, showing a continuous growth trend. In Figure 2, it can be seen that, with 2014 as the node, the growth in SE changed from negative to positive, indicating that the SE, like TE, was the main factor reducing TFP growth before 2014. However, after 2014, SE increased steadily, which played a positive role in promoting the growth of TFP. However, the annual average value of SE in 2010–2020 was only 0.005, indicating that its contribution to TFP growth was very weak. In addition, according to the calculation theory of SE, the main factors affecting SE include the factor output elasticity and factor input growth rate.

Table 4. Factor output elasticity of the coal industry from 2010 to 2020.

Year	Capital	Labor	RTS	Scale Effect
2010	0.156	0.564	0.720	drs 1
2011	0.155	0.561	0.716	drs
2012	0.139	0.569	0.707	drs
2013	0.135	0.560	0.695	drs
2014	0.138	0.556	0.693	drs
2015	0.153	0.541	0.695	drs
2016	0.180	0.506	0.686	drs
2017	0.174	0.533	0.707	drs
2018	0.155	0.579	0.733	drs
2019	0.197	0.543	0.740	drs
2020	0.212	0.533	0.745	drs
Mean	0.163	0.550	0.713	drs

¹ drs is an abbreviation for decrease.

shows the factor output elasticity of the coal industry from 2010 to 2020. The annual average value of the output elasticity of capital factor is 0.163, indicating that, for every 1% increase in capital input in the production process, the output will increase by 0.16%; meanwhile, the annual average output elasticity of the labor factor is 0.550, indicating that, for every 1% increase in labor input, the output will increase by 0.55%. Therefore, the labor factor is relatively scarce, and the capital factor is relatively abundant, which also explains the capital-saving technological progress in the analysis above. It is worth noting that the total RTS value of the factor output elasticity in each year from 2010 to 2020 is less than 1, so it is inferred that the coal industry has diminishing returns to scale, and expanding the factor input restricts the growth of TFP. There are inefficient factor inputs and scale expansion in the production process of the coal industry.

Fourth, in accordance with Figure 2, the AE curve revolves around the horizontal axis of the 0-value coordinate for a long time, showing a fluctuating state that alternates up and down. The value decreased from 0.043 in 2010–2011 to −0.007 in 2013–2014, and then rose to 0.022 in 2018–2019, which shows that the AE increased and decreased frequently. It is worth noting that the AE curve lies above the SE curve and the TFP curve until 2014, indicating that the AE contributed more to TFP growth than the SE during this time period. After this, the opposite trend occurred. From the principle of measurement in this paper, AE can be further decomposed into capital factor allocation efficiency (KAE) and labor factor allocation efficiency (LAE), shown as Figure 3. It can be seen that, except for 2014–2015 and 2019–2020, the KAE curve is above the LAE curve for most of the time period, indicating that KAE contributes more to AE. Numerically, the average annual growth of KAE is 0.007, while the average annual growth of LAE is only 0.001, again indicating that KAE growth is the main cause of AE growth.

Fifth, TFP growth in the coal industry shows an upward trend from 2010 to 2020, with an average annual growth rate of 0.036, indicating that the contribution of TFP to the output growth of the coal industry is increasing, which plays a good role in promoting the production development of the coal industry. Specifically, with 2014 as the node, TFP growth has gone through two stages. The first stage is the reversal period from 2010–2014, which improved from −0.005 to 0.015, indicating that TFP in the coal industry changed from negative to positive growth in this period and has started to play a positive role in production. The second stage is the period of fluctuating growth from 2014–2020, from 0.005 to 0.087, and despite the decrease in individual years, the average annual growth rate is relatively stable, reflecting the increasingly important role played by TFP growth in the production of the coal industry.

To sum up, the increase in TFP in the coal industry is mainly because the increase in TC (0.060) compensated for the negative impact of the decrease in TE (−0.036) on an annual average of 0.024, while SE and AE also increased on average by 0.005 and 0.008, respectively. It can be concluded that TC growth is the key factor for TFP growth, and SE growth and AE growth also played a weak role in promoting this, while the decrease in TE inhibited TFP growth in China’s coal industry.

4.2. Spatial Feature

There are regional differences in the distribution of coal resources in China and the development of this industry remains unbalanced. Therefore, to portray its temporal evolution, it is necessary to continue to discuss its spatial features during the study period to understand the regional development characteristics of China’s coal industry. Considering the regional division criteria above,

Table 5. TFP and its decomposition terms by region and province in 2010–2020.

Region	Province	TC	TE	SE	AE	TFP
	Hebei	0.066	−0.067	0.020	−0.004	0.015
	Jiangsu	0.039	−0.091	0.022	0.018	−0.013
East	Fujian	0.077	−0.076	0.004	0.008	0.013
	Shandong	0.071	−0.062	0.039	−0.021	0.027
	Mean	0.063	−0.074	0.021	0.000 1	0.011
	Shanxi	0.073	−0.021	0.020	−0.057	0.015
	Anhui	0.056	−0.057	0.027	−0.005	0.021
	Jiangxi	0.071	−0.085	0.016	−0.005	−0.002
Central	Henan	0.079	−0.065	0.029	−0.030	0.013
	Hubei	0.056	−0.079	−0.016	0.064	0.025
	Hunan	0.088	−0.091	0.021	−0.012	0.005
	Mean	0.071	−0.066	0.016	−0.007	0.013
West	Inner Mongolia	0.031	−0.002	−0.009	0.015	0.035
	Guangxi	0.054	−0.069	−0.002	0.032	0.015
	Chongqing	0.075	−0.083	0.026	−0.015	0.003
	Sichuan	0.089	−0.076	0.030	−0.034	0.010
	Guizhou	0.073	−0.051	0.010	−0.020	0.012
	Yunnan	0.073	−0.060	0.016	−0.017	0.011
	Shaanxi	0.040	−0.014	−0.026	0.011	0.011
	Gansu	0.052	−0.062	−0.017	0.046	0.018
	Qinghai	0.014	−0.055	−0.009	0.051	0.002
	Ningxia	0.008	−0.058	−0.119	0.155	−0.014
	Xinjiang	0.027	−0.025	−0.031	0.056	0.026
	Mean	0.049	−0.050	−0.012	0.025	0.012
Northeast	Liaoning	0.070	−0.074	0.020	−0.008	0.008
	Jilin	0.058	−0.079	0.019	−0.003	−0.004
	Heilongjiang	0.088	−0.072	0.022	−0.028	0.010
	Mean	0.072	−0.075	0.020	−0.013	0.004

¹ The value of 0.000 is because the value in the table is only reserved to 3 decimal places.

and Figure 4 present the annual average values of TFP and decomposition terms for 24 sample provinces in four regions of China from 2010 to 2020.

By region, in order of growth rate, from high to low, the TFP growth trend is central (0.013) > west (0.012) > east (0.011) > northeast (0.004), which may be caused by the gradual shift in focus from the northeast and east to central and west in recent years due to the national layout optimization of the coal industry. The TC presents as northeast (0.072) > central (0.071) > east (0.063) > west (0.049), with the highest growth in the northeast, similar to the previous research results [31]. TE, on the other hand, shows as west (−0.050) > central (−0.066) > east (−0.074) > northeast (−0.075), which may be due to the fact that the central and western regions have a weak technical foundation in the early stages, but under the effect of the policy dividend, they can implement new technology and new equipment faster and better to transform science and technology applications. The SE performance is in the order east (0.021) > northeast (0.020) > central (0.016) > west (−0.012), with better socio-economic development and a higher degree of openness in the central and eastern regions, as well as a higher level of foreign investment utilization and management refinement, making their SE growth much greater than that of the west region. AE performance is in the order west (0.025) > east (0.000) > central (−0.007) > northeast (−0.013), with the western region benefiting from the impact of a series of policy dividends implemented by the country. The investment environment has improved and the efficiency of resource allocation has continuously enhanced, which is significantly better than other regions.

Specifically, TFP increased by an average of 0.011 in the east, and while TC increased by an average of 0.063, TE decreased by an average of 0.074, offsetting the increase from TC growth. With AE remaining essentially unchanged, the eastern region benefited from an average SE increase of 0.021, which eventually compensated for the negative effect of the lower TE. The average TFP in the central region increased by 0.013, of which the average TC increase of 0.071 completely compensated for the average TE decrease of 0.066. At the same time, the average SE growth of 0.016 also completely compensated for the average AE decrease of 0.007, which ultimately led to the improvement of TFP. In the western region, the average TC increased by 0.049, and the average TE decreased by 0.050. The negative effect of the latter completely offset the positive effect of the former, resulting in an average decrease of 0.001 in TFP. However, the average AE increase, by 0.025, is much larger than the average SE decrease, 0.012, which ultimately resulted in the average TFP increase of 0.012. TFP in northeast China increased by 0.004 on average, showing a weak improvement. Although the average TC increase of 0.072 is not enough to make up for the obstruction caused by the average TE decrease (0.075), the average SE increase of 0.020 made up for the average AE decrease (0.013) and the rest of the negative effect caused by the decrease in TE.

By province, TFP growth and the decomposition of the coal industry in different provinces within the same region also varied slightly. In the eastern region, except for Jiangsu, the TFP of the coal industry in three provinces—Hebei, Fujian, and Shandong—showed improvement, but the reasons for this improvement are different. Jiangsu is the province with the lowest average TC growth (0.039) but the largest average TE decline (−0.091) among the four eastern provinces. It can be seen that the decline in TFP in Jiangsu’s coal industry was mainly caused by the slow TC growth and the rapid decline in TE. The situations of Hebei and Fujian are similar, where the average TFP growth values in the coal industry both reached 0.001 only due to the combined effect of TC growth and the decrease in TE. However, the difference is that the average SE growth in Hebei (0.020) compensated for the average decrease in AE (−0.004), while the SE (0.004) and AE (0.008) both weakly increased in Fujian. Unlike the three provinces mentioned above, the increase in TC in Shandong (0.071) fully compensates for the decrease in TE (−0.062), and the increase in SE (0.039) fully compensates for the decrease in AE (−0.021). All provinces in the central region show improvements in TFP except for Jiangxi (−0.002), which shows a small decrease. Among them, Hubei province has the largest average TFP increase (0.025), and although its SE is the only decrease (−0.016) in the region, its AE is the only increase (0.064) and performs much better than other provinces. Shanxi and Henan, the major coal provinces in the central region, perform similarly, relying mainly on TC growth to compensate for the negative effect of the lower AE. Anhui, Jiangxi, and Hunan provinces have similar performances, with their lower TE fully offsetting TC growth.

Among the western regions, Inner Mongolia and Xinjiang rank in the top two in terms of average TFP growth, reaching 0.035 and 0.026, respectively, but the reasons for their growth differ. The average TC growth in Inner Mongolia (0.031) is the key factor for its TFP growth, while the TFP growth in Xinjiang is mainly driven by the average AE growth (0.056). Sichuan and Chongqing rank above other provinces in the region in terms of average TC growth, but they also show the largest decreases in AE, which is why the TFP growth in both provinces is not high overall. TFP growth in Guangxi, Shaanxi, Gansu, and Qinghai is mainly driven by the growth of TC and AE, while the decreases in TE and SE have a negative effect. The TFP of the coal industry in Chongqing, Guizhou, and Yunnan benefits from the growth brought on the increase in SE as well as TC growth. It is clear that advanced technology is the main driver of the coal industry in the western region, while “soft factors”, such as the production management system, hinder the improvement of the coal industry. The long history of coal mining in northeast China has led to serious resource depletion and a series of economic and social problems, which are not conducive to the improvement of TFP in the coal industry. This situation is similar to those of Heilongjiang and Liaoning, where the average TFP growth is not high, and Jilin even shows negative growth. An analysis of Table 5 shows that the main hindering force comes from the decreases in TE and AE, which indicates that the management system and mechanism of the coal industry in northeast China may still have many unreasonable aspects and may not been able to keep up with the requirements of industry development.

5. Discussion

The high-quality development of the coal industry is desired for industry in the new era, and TFP growth is the fundamental way for the coal industry to achieve this. We measured and decomposed the TFP of the coal industry in China’s major coal-producing provinces by constructing a model, and conducted a spatio-temporal analysis on this basis.

Apparently, TFP growth of the coal industry played a significant role in promoting industrial output. Notably, it turned from negative to positive in 2014 because the Chinese government put forward the energy revolution strategy in the same year. The development of the coal industry has also benefited from innovations in consumption, supply, technology, and system and international cooperation, thus realizing the transformation of high-quality development, which is consistent with Zhang’s research results [45]. Therefore, the measurement results of total factor productivity growth of the coal industry show the overall status quo of the development of China’s coal industry, and support the correctness and effectiveness of relevant policies, including the strategy of energy revolution, and strengthen the confidence in continuing to promote and deepen the reform. During the study period, 10 key tasks, such as mergers, reorganization, and increasing technological innovation, proposed by the coal industry have promoted the development and expansion of the coal industry, and also make it possible to introduce advanced technologies and large-scale modern equipment. The nationwide investment in innovation (including capital, talent, and equipment, etc.) further enhanced the advancement of technology, which may be the main reason for the TC growth. However, this has also brought new problems, such as the slow integration of new technologies, issues with the organization’s internal structure and personnel redundancy, the distortion of resource allocation, etc., accompanied by the increase in the organizational cost and the decline of management. All of these may be the reasons for the insignificant increase in SE and AE and the decrease in TE. The findings of Cai [33] and Zhao [4] are similar to those found in this paper. The multiple decomposition of total factor productivity growth clearly and accurately identifies the advantages and disadvantages of the development of China’s coal industry, and points out the direction and focus for industry reform.

Affected by the unbalanced endowment of coal resources and development conditions in China, the growth of TFP in China’s coal industry is also uneven across regions. Similar to Cai’s research results, the authors of this paper also believe that the “policy dividend” of the strategy of developing the western region and the rise of the central region have largely yielded favorable production factors, improving coal industry development. However, the management and system have not been able to match the speed of industry development. Although the eastern and northeastern regions have a good technical foundation, due to the exhaustion of coal resources and the high cost of deep mining, the production scale can only be gradually reduced. The development of total factor productivity growth varies in different provinces within the same region. However, most of the provinces with fast TFP growth also rank high in terms of raw coal production, and highly overlap with the regions where large bases for coal production are located. It can be seen that resource endowment and industrial agglomeration play a significant role in promoting the high-quality development of the coal industry through scale optimization and factor resetting. The identification of obvious regional differences in industry development provides a practical reference for the country to grasp industry development laws and for each region and province to identify its own progress barriers.

Despite the research results, this paper still has some shortcomings. First, the TFP growth measurement model, the BC92 model, cannot distinguish between technical inefficiency and sample heterogeneity. We will choose more models [46] (such as the BC95 model, etc.) for comparison in future research to explore heterogeneity in depth. Second, due to the limitation of data availability, the input factors do not include energy, data, and technology, etc., which will also be addressed in later studies. Third, our future research still needs to work on the influencing factors that cause individual efficiency changes.

6. Conclusions and Policy Implications

To accurately determine the actual development status and driving force behind the development of China’s coal industry, we constructed a stochastic frontier analysis function model based on the translog function form and measured the TFP growth of China’s coal industry using panel data from the coal mining and washing industry in 24 major coal-producing provinces in China from 2010 to 2020. Then, we analytically presented the development characteristics in spatial and temporal dimensions based on its decomposition into TC, TE, SE, and AE. The main findings are as follows. First, TFP growth in China’s coal industry experienced an upward trend, the transition from negative to positive growth was achieved with 2014 as the node, and its annual average growth rate was 0.036. Second, TC growth was the main driver of TFP growth in China’s coal industry during the study period, and SE growth and AE growth had limited contributions, while the decrease in TE hindered TFP growth. Third, the growth of TFP in China’s coal industry is also uneven across regions, with the central region ranking first, the northeast region ranking last, and the western and eastern regions ranking in the middle in that order. Additionally, there are also differences in the sources of growth in the four regions. Fourth, the reasons for TFP growth in the coal industry vary from province to province. In addition to TC growth, SE growth in Jiangsu, Shandong, Anhui, Sichuan, and Henan contributes a relatively high percentage of TFP growth, while AE growth in Hubei, Gansu, Qinghai, Inner Mongolia, and Xinjiang has become the second driver to the increase in TFP.

In light of the findings of this study, the following policy implications are presented: first, we should continue to enhance the role of TFP growth in promoting the development of the coal industry, and abandon the traditional method of increasing industry output by increasing input of production factors. The country needs to continue to promote the energy production and consumption revolution to optimize the coal industry development system. Second, it is very important to continuously improve the leading ability of scientific and technological innovation in the coal industry to raise its technological progress efficiency, gradually improve the management system and mechanisms of the coal industry to enhance its technical efficiency, accelerate the optimization of the intensive development layout of the coal industry to highlight its scale efficiency, and steadily promote the market-oriented reform of the coal industry to tap its factor allocation efficiency. Third, we should pay more attention to coordinated regional development while striving for TFP growth in the coal industry at the national level. The central region needs to focus more on scale optimization, the western region should strengthen the introduction of advanced technology and the improvement of the management level, while the eastern and northeastern regions need to focus on deep mining technology and effective factor allocation, respectively. Fourth, each province needs to explore its development advantages and complement its development shortcomings to formulate development plans for the coal industry in a targeted manner. For instance, Inner Mongolia, Xinjiang, and Shaanxi need to speed up industrial agglomeration to achieve scale optimization, while Shanxi, Henan, and Shandong need to promote the market-based allocation of factor production to achieve the optimal representation of the value of production factors.