Measurement and Spatial-Temporal Evolution of Industrial Carbon Emission Efficiency in Western China

Abstract

As it is an important industrial base in China, it is of great significance to improve the industrial carbon emission efficiency in the western region to promote the low-carbon sustainable development of the region. This paper selects the input–output panel data of 11 provinces in western China from 2010 to 2021, and adopts the three-stage DEA model to measure the industrial carbon emission efficiency in western China under a non-traditional geographic division at the overall and regional levels and analyze its influencing factors. The Dagum Gini coefficient, its decomposition method, and the kernel density estimation method are used to analyze the regional differences and dynamic evolution process of industrial carbon emission efficiency in the western region. The results of the study show that (1) after removing environmental and random factors, the industrial carbon emission efficiency in western China has been improved, but there are inter-regional differences, characterized by “the third region > the second region > the first region”; (2) the levels of green development, shared development, innovative development, and coordinated development have a positive impact on the improvement of industrial carbon emission efficiency in western China, while the level of industrialization has a relatively smaller influence, and economic development, government support, open development level, and energy consumption structure have not yet played a significant role; (3) the spatial differences in the efficiency of industrial carbon emissions in western China have generally increased during the sample period, with inter-regional differences being the main source; and (4) the industrial carbon emission efficiency in western China is characterized by overall improvements in time and space but with stage differences and multi-polarization of regional differences. This study has a certain reference value for improving industrial carbon emission efficiency in western China.

1. Introduction

In the context of increasingly severe global climate change and environmental challenges, the reduction of greenhouse gas emissions has become a shared responsibility and a key objective for the international community. As industrialization accelerates, carbon dioxide and other greenhouse gas emissions continue to escalate, resulting in significant consequences, such as global warming and the frequent occurrence of extreme weather events [1]. In response to this global challenge, nations have proposed and implemented measures to reduce emissions in order to achieve sustainable development goals. Given its status as one of the world’s largest developing countries and carbon emitters, China bears significant responsibility in addressing climate change. In 2015, China, a significant emitter of carbon dioxide (CO₂), made an important commitment at the Paris Climate Conference: striving to reach the peak of carbon dioxide (CO₂) emissions by 2030, and to achieve greenhouse gas (GHG) neutrality by 2060. General Secretary Xi pointed out again in the report of the 20th National Congress that Carbon Peak and Carbon Neutralization should be actively and steadily promoted. Following this, the Ministry of Industry and Information released the “14th Five-Year Plan for Green Development of Industry”, which puts forward the goal of reducing carbon emissions and energy consumption per unit of industrial added value by 13.5% and 18%, respectively, by 2025.

As the vital driving force and cornerstone of national economic development, industrial carbon emissions constitute approximately 62% of the total emissions in society, playing a crucial role in China’s carbon emissions [2]. Consequently, enhancing industrial carbon emission efficiency—that is, reducing the amount of carbon dioxide emitted per unit of output or per unit of energy consumption in industrial production processes—has become crucial for achieving the “dual carbon” goal. It directly reflects the ability and technical level of the industrial sector to control environmental impacts while pursuing economic benefits. Enhancing the efficiency of industrial carbon emissions means reducing carbon emissions while maintaining or increasing output, which is a crucial approach to achieving low-carbon industrial transformation and sustainable development.

As an important industrial base in China, the western region has attracted much attention for its industrial development and carbon emissions. For a long time, the western region has been facing the problems of high resource consumption, heavy environmental pollution, and high carbon emissions while undergoing rapid industrial development. These problems not only affect the sustainable development of the local ecological environment, but also pose a challenge to national and global carbon emission reduction targets. Therefore, enhancing industrial carbon efficiency in western China is paramount for attaining global carbon reduction objectives.

Different regions often encounter varying challenges in adopting similar approaches to achieve energy conservation and emission reduction goals. Accordingly, different regions should prioritize carbon emission reduction and enhance emission performance based on their unique characteristics. The analysis of carbon emission efficiency can provide valuable insights into regional disparities, which are essential for promoting the low-carbon transformation of industries and achieving coordinated development of regional economy, energy conservation, and emission reduction.

The potential contributions of this study are as follows, based on the aforementioned research background and purpose. Unlike previous studies, this paper focuses on a 12-year data interval spanning from 2010 to 2021, which not only encompasses the pivotal national development planning phases of the 12th Five-Year Plan and the 13th Five-Year Plan, but also extends across the critical juncture of global economic and energy structural transformation. The utilization of this extensive time series data empowers us to conduct a comprehensive and in-depth analysis of the dynamic changes in industrial carbon emission efficiency in western China, thereby unveiling long-term trends and potential underlying patterns. Secondly, as a crucial industrial hub and ecological barrier in China, enhancing the efficiency of industrial carbon emissions in the western region holds significant importance for the country’s and even the world’s low-carbon development. The scope of this paper covers 11 provinces in the western region of China which are unique in terms of geographic location, resource endowment, and level of economic development but face the common challenge of low-carbon transition and sustainable development. Therefore, employing non-traditional geographical classification criteria is more scientifically sound and reasonable for assessing and elucidating regional disparities and interrelations, providing a more refined basis for policy formulation. Thirdly, utilizing the three-stage DEA model, this study computes the industrial carbon emission efficiency of the western region as a whole and the three western regions, and efficiency decomposition is carried out to explain the driving forces of different inefficiency levels. Additionally, it examines the influence of nine environmental factors on industrial carbon emission efficiency. Fourthly, the Dagum Gini coefficient and its decomposition method, as well as the kernel density estimation method, are employed to unveil regional disparities and sources of industrial carbon emission efficiency in the western region and its three sub-regions, and to visualize the distribution pattern and evolution process of industrial carbon emission efficiency at various time points.

The remaining sections of the document are structured as follows: the literature review comprises the second section, followed by the research methodology in the third section, variable selection and data sources in the fourth section, empirical analysis in the fifth section, conclusion and policy recommendations in the sixth section, and finally, discussion is provided in the last section. The nomenclature of this thesis and the relevant variables involved in the calculations are shown in Appendix A and Appendix B, respectively.

2. Literature Review

Combing through the existing research results of scholars at home and abroad, it is found that the current research on carbon emission efficiency mainly covers the aspects of efficiency evaluation, regional differences, and influencing factors.

At present, scholars employ diverse indicators and assessment methods to quantify and analyze carbon emission efficiency. Kaya et al. [3] initially introduced the concept of carbon production efficiency, followed by subsequent proposals from scholars for carbon efficiency indicators based on various perspectives, such as carbonization index and carbon emission intensity [4,5,6]. Most of the aforementioned indicators represent “single-factor” metrics characterized by a singular proportionality relationship between total carbon emissions and inputs (or outputs). However, carbon emission efficiency is the result of the joint action of economy, energy, environment, and other factors, with the characteristics of “all factors”, which can more effectively address the relationship between economic development and carbon emission reduction [7], based on which some scholars comprehensively consider the factors of capital, energy consumption, labor force, GDP, carbon dioxide, etc., to construct carbon emission efficiency measurement indicators [8,9,10]. At present, the measurement of carbon emission efficiency mainly adopts non-parametric methods. Non-parametric models do not require the establishment of functional forms and assumptions about a priori conditions, and can effectively avoid the subjectivity of parameter weights [11]. The methods mainly include the stochastic frontier model [12,13], ZSG-DEA model [14,15], three-stage DEA model [16,17], SBM-DEA model [18], and Malmquist index method [19,20].

Scholars have conducted a wealth of research on carbon emission efficiency at different scales and in different industrial sectors. The current research scales mainly contain the international level, regional level, inter-provincial level, and city level. At the international level, Marklund and Samakolis calculated the carbon emission reduction cost of EU countries by using the distance method in the quadratic direction [21]; Zaim and Taskin [22] and Zofio and Prieto [23] conducted a study on the carbon emission efficiency of OCED countries, exploring the factors contributing to variations; Zhou et al. [24] focused on measuring the carbon emission efficiency of the 18 highest-emitting countries globally. Xiao et al. [25] conducted a global-scale investigation into the carbon emission efficiency of 136 countries. At the regional level, Liu et al. [26] assessed the carbon emission efficiency of the urban agglomeration in the Yangtze River Delta and identified spatial disparities, with higher levels observed in the east and lower levels in the west. Mi Ying et al. [27] focused on the eastern coastal region, a significant industrial cluster in China, as the research object and measured the spatial and temporal evolution characteristics of its industrial carbon emission efficiency and its influencing factors. Li Jian et al. [28] analyzed differences in carbon emission efficiencies among three major economic circles, the Yangtze River Delta, Pearl River Delta, and Beijing–Tianjin–Hebei, during the 2007–2016 period, showing relatively low overall efficiencies. At the inter-provincial level, Jiang et al. and Dalai Ma et al. [29,30] both utilized an improved SBM model to calculate industrial carbon emission efficiencies across 30 provinces in China, revealing significant provincial discrepancies. At the city level, scholars have conducted research related to carbon emission efficiency with most of the cities in China as research subjects [31,32,33,34]. Yin Jian et al. [35] explored the industrial carbon emission efficiency, spatial correlation network characteristics, and influencing factors of 49 cities in the Pearl River Basin. Wang Zhaofeng et al. [36] focused on central Hunan province as their study area, utilizing the super-efficient SBM-DEA model and Malmquist index to measure and analyze the spatial disparity of carbon emission efficiency and environmental efficiency among 14 cities (states) in Hunan province and found that most of the cities (states) in Hunan province had low carbon emission efficiency and environmental efficiency. For the analysis of carbon emission efficiency of different industrial sectors, scholars focus on pollution-intensive industries [37], such as the iron and steel industry [38], non-ferrous metal industry [39], chemical industry [40], coal production [41], etc.

In the study of factors influencing carbon emission efficiency, scholars typically consider a broad array of environmental factors impacting such efficiency. Research has identified industrial structure, energy consumption structure, and economic scale as significant determinants of carbon emission efficiency [42,43]. Further analysis by scholars has revealed that export trade contributes to enhancing China’s industrial carbon emission efficiency [44], while foreign direct investment diminishes industrial CO₂ emission efficiency but enhances it in low-emission regions [45]. Additionally, the level of scientific and technological development in provinces is linked to improved carbon emission efficiency [46], whereas resource abundance is negatively correlated with such efficiency [47]. The implementation of pilot policies for a carbon market has been shown to enhance overall emissions efficiencies [48]. Notably, comprehensive studies have examined the spatial dynamics of influential factors revealing significant long-term impacts from population size, technological progress, and economic development on carbon emissions efficiencies [49,50].

In summary, current scholarly research has extensively examined carbon emission efficiency from various perspectives. However, systematic and in-depth studies on industrial carbon emission efficiency in western China are lacking. Consequently, the spatial distribution pattern of industrial carbon efficiency in the region remains ambiguous, and the evolution law’s characteristics are unclear. This hinders the provision of detailed basic information support for green and low-carbon development in the industrial sector. To address this gap, this paper employs a three-stage DEA model to measure industrial carbon emission efficiency in western China from 2010 to 2021 at both the overall and regional levels, and analyzes the impact of nine environmental factors on industrial carbon emission efficiency. It also empirically investigates the regional disparities in the industrial carbon emission efficiency of the western region and its distributional dynamics using Dagum’s Gini coefficient and its decomposition method as well as the kernel density estimation method. Based on these findings, countermeasures are proposed to enhance industrial carbon emissions efficiency in the western region at both the general and regional levels with an aim to provide stronger support for sustainable development.

3. Methodology

3.1. Carbon Emission Efficiency Measurement Model Construction: Three-Stage DEA Model

DEA is a non-parametric model for calculating efficiency values. The conventional DEA model inadequately addresses this issue by attributing all environmental factors and statistical noise to managerial inefficiency, thereby obscuring the genuine efficiency value influenced solely by management factors and relative efficiency analysis. Various elements, including statistical noise, environmental factors, and managerial inefficiency, impact the relative efficiency of the decision-making unit (DMU). This research utilizes the three-stage DEA model proposed by Fried et al. [51] to evaluate the efficiency of industrial carbon emissions in western China. The primary strength of this model lies in its capacity to effectively exclude the influence of environmental factors, random disturbances, and management inefficiencies.

• Stage 1: Traditional DEA modeling

In the first stage, the input-oriented BCC model is chosen to calculate the initial efficiency values. The model is as follows:

$$\begin{array}{l}\min \theta -\epsilon ({\stackrel{⌢}{e}}^T{S}^{-}+e^T{S}^{+})\\ \left\{\begin{array}{l}{\displaystyle \sum _{j=1}^n{X}_j{\lambda }_j+S^{-}=\theta X_0}\hfill \\ {\displaystyle \sum _{j=1}^n{Y}_j{\lambda }_j+S^{+}=Y_0}\hfill \\ {\lambda }_j\ge 0,S^{-},S^{+}\ge 0\hfill \end{array}\right.\end{array}$$

(1)

The index j = 1, 2, …, n is used to represent the jth decision unit, X_j denotes the input value of this decision unit and Y_j represents its output value, X₀ represents the input value of the current decision unit and Y₀ represents its output value, and λ_j represents the weight of the jth decision unit relative to the current decision unit. The non-Archimedes infinitesimal is represented by ε, the residual variable by S⁺, the slack variable by S⁻, and the integrated technical efficiency by θ. The efficiency value calculated by this model is the comprehensive technical efficiency (TE), which may be further broken down into scale efficiency (SE) and pure technical efficiency (PTE) using the formula TE= SE × PTE.

• Stage 2: SFA-like regression to eliminate statistical noise and environmental influences

Given that the relative efficiency values obtained in the initial stage are influenced by environmental factors, statistical noise, and managerial inefficiency, the stochastic frontier model is used for the input-oriented SFA-like regression analysis. The formula is as follows:

$$S_{mj}=f\left(Z_j;{\beta }_m\right)+{\nu }_{mj}+{\mu }_{mj}$$

(2)

where j = 1, 2, ……., n, m = 1, 2, ……., k; S_mj represents the mth input slack value of the jth decision unit, Z_j represents the environmental variables, β_m stands for the coefficients of environmental variables; $f(Z_j;{\beta }_m)$ signifies the impact of the environmental variables on the input slack S_mj, and satisfies $f\left(Z_j;{\beta }_m\right)=Z_j{\beta }_m$; and ν_mj + μ_mj represents the integrated error term, where ν_mj represents the random disturbance term, μ_mj represents the management inefficiency term, and ν_mj and μ_mj are independent of each other.

In order to ensure the consistency of decision-making units operating in the same external environment, it is essential to optimally adjust the input variables using the following formula:

$$X_{mj}^A=X_{mj}+\left[\max \left(\mathrm{f}\left(Z_j;{\widehat{\beta }}_m\right)\right)-\mathrm{f}\left(Z_j;{\widehat{\beta }}_m\right)\right]+\left[\max \left({\nu }_{mj}\right)-{\nu }_{mj}\right]$$

(3)

where j = 1, 2, …, n and m = 1, 2, …, k; $X_{mj}^A$ represents the adjusted inputs; $X_{mj}$ represents the pre-adjusted inputs; $[\max \left(\mathrm{f}\right(Z_j;{\widehat{\beta }}_m))-\mathrm{f}(Z_j;{\widehat{\beta }}_m\left)\right]$ represents adjusting for the external environmental factors; and $[\mathit{max}\left({\nu }_{mj}\right)-{\nu }_{mj}]$ stands for placing all decision units in the same external environment.

• Stage III: Adjusted DEA model

Utilizing the optimized and adjusted input–output values in the second stage to reevaluate the efficiency of each decision-making unit can more accurately depict the industrial carbon emission efficiency level in the western region by mitigating the influence of environmental and stochastic factors.

3.2. Carbon Emission Efficiency Spatial Difference Model Construction: Dagum’s Gini Coefficient and Its Decomposition

This paper examines the regional disparities in industrial carbon emission efficiency in western China using the Dagum Gini coefficient and its decomposition approach. In comparison to the traditional Gini coefficient, the Dagum Gini coefficient offers an advantage in analyzing spatial non-equilibrium, and can not only measure the overall regional disparity, but also decompose it into intra-region disparity, inter-region disparity, and the effect of hypervariable density on the overall regional disparity, and can better measure the main sources of spatial disparity [52]. The formula of the Dagum Gini coefficient is as follows:

$$G={\displaystyle \frac{{\displaystyle \sum _{r=1}^n{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^{k_r}{\displaystyle \sum _{h=1}^{k_i}\left|y_{rj}-y_{ih}\right|}}}}}{2k^2\mu }}$$

(4)

The overall Gini coefficient is represented by G, where k represents the number of provinces and n represents the number of divided regions, y_rj(y_ih) represents the industrial carbon emission efficiency of each province in the r(i) region, k_r(k_i) denotes the number of provinces in the rth (i) region, and μ denotes the average industrial carbon emission efficiency in western China. In addition, considering that Dagum’s Gini coefficient is more convenient to calculate, before calculating the Gini coefficient, the regions need to be ranked from smallest to largest average level of industrial carbon efficiency within each region.

$${\overline{Y}}_1\le {\overline{Y}}_2\cdots \le {\overline{Y}}_h\le {\overline{Y}}_j$$

(5)

The overall Gini coefficient G can be broken down into the sum of intra-regional differences contribution G_w, inter-regional disparities contribution G_nb, and regional hypervariable density contribution G_t. In simpler terms, it can be represented as G = G_w + G_nb + G_t, where G_nb reflects the difference in distribution of industrial carbon emission efficiencies between regions r and i, while G_w represents the variation in industrial carbon emission efficiencies distribution within region r(i), and finally, G_t being the residual term of the cross-impacts on the industrial carbon emission efficiencies between the regions.

The intra-area Gini index G_rr and the contribution of intra-area variation G_w are calculated as

$$G_{rr}={\displaystyle \frac{{\displaystyle \sum _{j=1}^{k_r}{\displaystyle \sum _{h=1}^{k_i}\left|y_{rj}-y_{rh}\right|}}}{2\overline{Y_r}{k}_r^2}}$$

(6)

$$G_w={\displaystyle \sum _{r=1}^n{G}_{rr}{p}_r}{s}_r$$

(7)

G_ri and the contribution of inter-regional differences G_nb are calculated as

$$G_{\mathrm{ri}}={\displaystyle \frac{{\displaystyle \sum _{j=1}^{k_r}{\displaystyle \sum _{h=1}^{k_i}\left|y_{rj}-y_{ih}\right|}}}{k_r{k}_i(\overline{Y_r}+\overline{Y_i})}}$$

(8)

$$G_{nb}={\displaystyle \sum _{r=2}^n{\displaystyle \sum _{i=1}^{r-1}{G}_{ri}(p_r{s}_i}}+p_i{s}_r)D_{ri}$$

(9)

The contribution of the regional hypervariable density, G_t, is calculated as follows:

$$G_t={\displaystyle \sum _{r=2}^n{\displaystyle \sum _{i=1}^{r-1}{G}_{ri}}}(p_r{s}_i+p_i{s}_r)(1-D_{ri})$$

(10)

where $p_r={\displaystyle \frac{k_r}{k}}$, $s_r={\displaystyle \frac{k_r\overline{Y_r}}{k\overline{Y}}}$, r = 1, 2, 3, ……., n. D_ri denotes the relative gap in industrial carbon emission efficiency between the two regions r and i.

$$D_{ri}={\displaystyle \frac{d_{ri}-p_{ri}}{d_{ri}+p_{ri}}}$$

(11)

$$d_{ri}={\displaystyle \underset{0}{\overset{\infty }{\int }}d{F}_r}(y){\displaystyle \underset{0}{\overset{y}{\int }}(y-x)d{F}_i}(x)$$

(12)

$$p_{ri}={\displaystyle \underset{0}{\overset{\infty }{\int }}d{F}_i}(y){\displaystyle \underset{0}{\overset{y}{\int }}(y-x)d{F}_r}(x)$$

(13)

where F_r(F_i) represents the cumulative distribution function of region r(i), and d_ri denotes the disparity in industrial carbon emission efficiency contributions between regions r and i, i.e., the weighted average of all sample values in i and r for which y_rj − y_ih > 0; p_ri denotes the hypervariable first-order moment, which is also a weighted average of sample values for which y_rj − y_ih > 0.

3.3. Carbon Emission Efficiency Spatial-Temporal Evolution Model Construction: Kernel Density Estimation

As a commonly utilized non-parametric estimation method, kernel density estimation has a weak dependence on the model and effectively captures the evolutionary trend of sample distribution dynamics [53]. In this study, we adopt the non-parametric kernel density estimation method to characterize the spatial distribution of industrial carbon emission efficiency in the western region as a probability distribution, aiming to discern spatial distribution patterns and polarization phenomena of industrial carbon emission efficiency in both the western region and its three sub-regions.

Assuming that the density function of the random variable x is f(x), the probability density of the point x is

$$f(x)={\displaystyle \frac{1}{Nh}}{\displaystyle \sum _{i=1}^{N}K(\frac{X_i-x}{h}})$$

(14)

where N stands for the total number of observations; K(·) denotes the kernel density function; X_i represents the relevant observations corresponding to the independent identically distribution; x denotes the average value of the observations; and the bandwidth, denoted by h, indicates that a smaller h value leads to reduced estimation bias and increased accuracy in estimation.

Kernel function is a kind of smooth transition function and a kind of weighting function, and there are four kinds of common kernel functions; namely, the Epanechnikov kernel, Triangular kernel, Quartic kernel, and Gaussian kernel. In the research process, the Gaussian kernel is more often used, and this paper also adopts the Gaussian kernel to estimate the dynamic evolution of the distribution of industrial carbon emission efficiency in the western region, and the form of its kernel function is expressed as follows:

$$K(x)={\displaystyle \frac{1}{\sqrt{2\pi }}}\exp (-{\displaystyle \frac{x^2}{2}})$$

(15)

4. Variable Selection and Data Source

4.1. Variable Selection

4.1.1. Variables of Input and Output

(1)

Labor input. Currently, scholars commonly measure the workforce in each province by the number of employed individuals. Therefore, this paper utilizes the annual average number of employed individuals in industrial enterprises above a certain scale in each province as labor input.

(2)

Energy input. Based on the total industrial end-use consumption of raw coal, natural gas, coke, diesel fuel, gasoline, and other energy sources in each province, it is uniformly converted into standard coal as energy input.

(3)

Capital input. Based on data accessibility, this paper opts to use the total assets of large-scale industrial enterprises as a substitute for capital stock in measuring capital input.

(4)

Desired output. The gross industrial product of each province is chosen as the desired output. To eliminate the impact of price factors, the GDP deflator method is utilized to convert the nominal gross industrial product into the real gross industrial product at the base period price, using 2010 as the base period.

(5)

Non-expected output. The industrial carbon dioxide emissions of each province are selected as the non-expected output. Since this data cannot be obtained directly from the statistical yearbook, this paper selects 11 major industrial energy consumptions, such as raw coal, washed coal, coke, coke oven gas, natural gas, etc., according to the IPCC carbon emission formula published by the United Nations, and calculates to get the final industrial carbon dioxide emissions, which is given by the following formula:

$$C={{\sum }_{\mathrm{i}=1}(X}_{\mathrm{i}}\times Y_{\mathrm{i}})$$

(16)

where C denotes carbon dioxide emissions in 10,000 tons, i denotes the type of energy, X_i is the consumption of energy i in 10,000 tons of standard coal, and Y_i is the carbon emission factor of energy i. The detailed energy discount standard coal coefficients and carbon emission coefficients are shown in

Table 1. Standard coal factor and carbon emission factor for various energy sources.

	Raw Coal	Cleaned Coal	Coke	Coke Oven Gas	Natural Gas	Gasoline	Kerosene	Diesel Oil	Crude Oil	Fuel Oil	Liquefied Petroleum Gas
Standard coal conversion factors	0.713	0.900	0.971	5.714	13.300	1.471	1.471	1.457	1.428	1.428	1.714
Carbon emission factors	0.755	0.755	0.855	0.354	0.448	0.553	0.571	0.592	0.5857	0.6185	0.5042

Source: China Energy Statistics Yearbook and 2006 IPCC Guidelines for National Greenhouse.

. Since the traditional DEA cannot deal with the efficiency value of undesirable outputs, in terms of the treatment method of CO₂ emissions as non-desired outputs, there are mainly input treatment methods, such as the directional distance function method, linear data conversion method, and so on. As the relationship between the undesirable output and the inputs of labor, capital, and other factors in a particular production process cannot always be maintained in the same proportion, and as the performance value obtained by the distance function method is greatly affected by the directional vector and there is no recognized method for determining the directional vector, if the direction is not correctly selected, the performance measurement results will be inaccurate [54]. In view of this, this paper adopts the linear data conversion method proposed by Seiford and Zhu [55] to convert carbon dioxide emissions, and the specific formula is Y_i = −Y_i + B, where B denotes a vector that is large enough to be greater than all the CO₂ emission values in the panel data of the current evaluation year, so that all the transformed output data can be guaranteed to be positive; therefore, the value of B is chosen to be 1.1 times the maximum value of CO₂ emissions in the sample area, and after a linear transformation, CO₂ emissions are converted from the undesired output of the smaller the better to the desired output of the larger the better. Following this, the DEA idea can be used for research.

4.1.2. Environmental Factor Variables

External environmental variables are factors that can impact the efficiency of industrial carbon emissions, but they are not subjectively adjustable by the decision-making unit. Environmental factors have a dual effect on industrial carbon emission efficiency: positive factors contribute to higher industrial carbon emission efficiency, while negative factors have the opposite effect. The influence of external environmental factors on input slack variables needs to be considered and eliminated in the second stage of the three-stage DEA approach.

The industrial carbon emission efficiency in western China is influenced by a multitude of factors, as indicated by previous research [10,28]. Considering the specific circumstances of provincial development and data availability, this paper selects nine indicators as exogenous environmental variables affecting industrial carbon emission efficiency. These include economic development level, governmental support strength, industrialization level, energy consumption structure, innovation and development level, coordinated development level, green development level, open development level, and shared development level. The index system is presented in

Table 2. Indicator system of industrial carbon emission efficiency in western China.

Indicator Type	Indicator Name	Measurement Method
Input indicators	Industrial labor force	Average annual number of workers employed by industrial enterprises above designated size (10,000 persons)
	Industrial Energy Inputs	Industrial terminal energy consumption (10,000 tons of standard coal)
	Total industrial assets	Total assets of industrial enterprises above designated size (100 million yuan)
Desired output	Gross industrial production	Gross industrial production (100 million yuan)
Undesired output	Carbon dioxide emissions	Carbon dioxide emissions (10,000 tons)
Environment variables	Level of economic development	Per capita GDP (Yuan)
	Strength of government support	Budget expenditures as a percentage of GDP
	Industrialization level	Industrial output value as a percentage of GDP
	Energy consumption structure	Coal consumption as a percentage of total energy consumption
	Level of innovative development	Full-time equivalent of R&D personnel in industrial enterprises above designated size (person-years)
	Level of coordinated development	Proportion of urban population to total population
	Level of green development	Total investment in pollution control as a percentage of GDP
	Level of openness to development	Total utilized foreign capital as a percentage of GDP
	Level of shared development	The integration of electricity, natural gas, and LPG utilization ratios reflects a shared level of development

.

4.2. Data Source

The input–output and environmental variable data of 11 provinces in the western region of China (excluding Tibet due to data unavailability) for the years 2010–2021 are selected based on the research objectives and data accessibility. The data are sourced from the China Statistical Yearbook, China Energy Statistical Yearbook, provincial statistical yearbooks, and wind database. Economic indicators are adjusted using 2010 as the base year. Linear interpolation is applied to fill in missing data.

Meanwhile, in order to compare the differences in industrial carbon emission efficiency among regions in western China, this paper cites the research results of Lv Bin et al. [56], which divides the western region into three regions. Lv Bin et al. showed that the traditional geographic division ignores the characteristics of resource conditions, development status, and energy efficiency of each region, and lacks specificity to the problems to be solved. Therefore, using resource endowment, climatic conditions, industrial structure, energy consumption structure, and development level as a clustering index for regional division, the results of the three regions in the west are shown in

Table 3. Construction of the three western regions.

Region I	Guangxi, Chongqing, Sichuan, Guizhou, Yunnan
Region II	Inner Mongolia, Shaanxi
Region III	Gansu, Qinghai, Ningxia, Xinjiang

. From the perspective of regional construction characteristics, the provinces in the first region have strong similarities in resource conditions, development status, and industrial structure; the second region is an important energy export base in China, with more obvious resource characteristics; and the third region shares the common characteristics of backward development, abundant resources, and similar climatic conditions. Through the clustering results, it can be obtained that the first region spans a large area and does not reflect strong geographical characteristics. This shows that the way of dividing only by geographical location is not very scientific.

5. Empirical Analysis

5.1. Measurement of Industrial Carbon Emission Efficiency in the Western Region of China

5.1.1. Stage 1: Measurement of Initial Industrial Carbon Emission Efficiency in the Western Region

At this stage, the input-oriented BCC model was selected with the assistance of DEAP2.1 software to analyze the industrial carbon emission efficiency of 11 provinces in the western region from 2010 to 2021, and the results are presented in

Table 4. Industrial carbon emission efficiency in western regions in Phase I (2010–2021).

Region	Province	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	Mean Value	Ranking
Region I	Guangxi	0.928	0.891	0.86	0.848	0.907	0.936	0.936	0.808	0.826	0.848	0.769	0.736	0.8578	9
	Chongqing	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.0000	1
	Sichuan	0.911	0.896	0.932	0.954	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.9744	7
	Guizhou	0.987	0.962	0.97	0.97	0.967	0.967	0.955	0.95	1.000	1.000	1.000	1.000	0.9773	6
	Yunnan	0.956	1.000	1.000	0.997	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.9961	3
	Mean value	0.956	0.950	0.952	0.954	0.975	0.981	0.978	0.952	0.965	0.970	0.954	0.947	0.9611	—
Region II	Inner Mongolia	0.659	0.661	0.734	0.759	0.768	0.747	0.752	0.946	0.916	0.86	0.813	0.777	0.7827	11
	Shaanxi	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.945	0.937	0.944	0.9855	5
	Mean value	0.830	0.831	0.867	0.880	0.884	0.874	0.876	0.973	0.958	0.903	0.875	0.861	0.8841	—
Region III	Gansu	0.913	0.992	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.9921	4
	Qinghai	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.0000	1
	Ningxia	1.000	0.952	0.951	0.957	0.893	0.842	0.838	0.818	0.777	0.72	0.68	0.645	0.8394	10
	Xinjiang	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.946	0.874	0.819	0.796	0.9529	8
	Mean value	0.978	0.986	0.988	0.989	0.973	0.961	0.960	0.955	0.931	0.899	0.875	0.860	0.9461	—
Western region		0.941	0.941	0.950	0.953	0.958	0.954	0.953	0.957	0.951	0.932	0.911	0.900	0.9418	—

.

According to Table 4, when excluding the impact of environmental factors and random disturbances, the average efficiency values of the 11 provinces in the western region ranged from 0.900 to 0.958 during the period from 2010 to 2021. Furthermore, the average industrial carbon emissions efficiency values for the three western regions are 0.9611, 0.8841, and 0.9461, respectively, indicating that the first region has a higher efficiency than the third region, then followed by the second region. Specifically, only Guangxi province in the first region has an average value of efficiency under 0.9, and the average value of efficiency of the rest of the provinces is up to 0.95 or more, of which Chongqing Municipality is DEA effective, Sichuan, Guizhou, and Yunnan are all DEA ineffective and gradually rise to DEA effective, and Guangxi is DEA ineffective in the sample period. The efficiency means of the provinces in the second region vary widely, with Shaanxi province keeping the DEA effective in the early part of the study and becoming DEA ineffective in the later part of the study, but the efficiency values are all above 0.9. The efficiency mean value of Inner Mongolia, on the other hand, is lower, below 0.8, indicating that the efficiency of the province needs to be improved. The third region presents an uneven distribution of efficiency, with Qinghai always remaining on the efficiency frontier, Ningxia and Xinjiang provinces changing from initially DEA effective to ineffective, and Gansu province rising from a DEA inefficient to DEA efficient status. However, this measurement contains the influence of environmental factors and random disturbances, and cannot objectively and accurately reflect the industrial carbon emission efficiency of each province, so this paper will use the SFA method for the second stage of analysis.

5.1.2. Stage 2: SFA-like Regression Analysis

Utilizing the Frontier4.1 software, three input slack variables measured at the initial stage were employed as response variables, while nine environmental variables, encompassing economic development level, government support, innovation development level, open development level, industrialization level, energy consumption structure, green development level, coordinated development level, and shared development level, were utilized as independent variables for regression analysis. The findings are detailed in

Table 5. Regression results of environmental impact factors in the second stage based on SFA.

Variable	Labor Input Redundancy	Energy Input Redundancy	Capital Input Redundancy
Constant term	−14.49	−50.46	−4840.98 ***
Level of economic development	−40.84 ***	7081.64 ***	15,323.81 ***
Strength of government support	6.10	−653.24 ***	2639.51 ***
Level of innovative development	17.76 **	−5169.36 ***	−3320.48 ***
Level of openness to development	−1.13	2150.39 ***	4273.00 ***
Industrialization level	−5.04	−827.44 ***	518.23
Energy consumption structure	22.08 **	3969.06 ***	6915.79 ***
Level of green development	−2.97	−1581.78 ***	−2530.59 ***
Level of coordinated development	33.15 ***	−5182.46 ***	−9241.06 ***
Level of shared development	−2.57	−131.90 **	−717.53
σ2	224.89 **	4,618,854.20 ***	6,920,291.00 ***
γ	0.90 ***	0.80 ***	0.73 ***
Log function value	−410.061	−1120.427	−1163.294
LR value	97.156 ***	84.499 ***	57.932 ***

Note: ***, **, * indicate that the coefficient passes the test of significance at the 1%, 5% and 10% levels, respectively.

.

Table 5 shows that the one-sided errors of each input slack LR are statistically significant at the 1% level, suggesting the appropriateness of utilizing the SFA model for analysis. Additionally, most σ² and γ values for the three input slack variables (labor, energy, and capital) have passed the 1% significance test, with γ values ranging between 0.7 and 0.9. indicating that environmental factors and random factors have a more significant impact on the input redundancy of the three variables, and it is necessary to eliminate their effects.

This can be seen by further analyzing the relevant variables:

(1)

The levels of economic development and openness have a negative impact on the slack variable of labor input, while exerting a positive effect on the slack variables of energy input and capital input. This indicates that enhancing per capita GDP and promoting openness in western China will decrease labor redundancy and increase redundancy in energy and capital inputs. With the improvement of the level of economic development and open development, the labor market in the western region is becoming more efficient and flexible. Economic development has prompted industrial upgrading and structural adjustment, so enterprises are more focused on improving labor productivity and reducing reliance on inefficient labor. At the same time, the pressure of international competition brought about by open development also encourages enterprises to actively improve the quality of employees and effectively reduce labor redundancy. However, in this process, the western region’s economic growth is still significantly dependent on energy and capital. With the growth of per capita GDP and the improvement of openness, the demand for energy and capital continues to grow, but because the improvement of energy utilization efficiency and capital allocation efficiency is relatively lagging, the redundancy of energy and capital input increases.

(2)

The strength of government support has a positive impact on the slack variables for both labor and capital inputs, and is statistically significant at the 1% level for the capital slack variable. However, it exerts a negative effect on the slack variable of energy input, suggesting that increased government support leads to higher redundancy in labor and capital input slack variables while reducing redundancy in energy input. Complexities and challenges that may exist in the process of resource allocation and policy formulation by governments in western China. In order to utilize government support resources more effectively, there is a need to further improve the design of policies, strengthen supervision, increase the efficiency of policy implementation, and focus on synergies between policies to ensure efficient use of resources and reduce waste.

(3)

The level of innovation development and coordinated development in western China has a negative impact on the surplus of energy input and capital input, but a positive impact on the surplus of labor input. This suggests that the current increase in innovation development and coordinated development will reduce the excess use of energy and capital, while increasing the redundancy of labor inputs. The enhancement of innovation and development in western China has led to increased R&D investment and technological innovation, significantly enhanced production efficiency and resource utilization, and reduced energy and capital consumption per unit of output. This has resulted in a decrease in redundant energy and capital investment. The heightened level of coordinated development has fostered inter-regional economic cooperation and resource sharing, optimized resource allocation, reduced overreliance on energy and capital within a single region, and further minimized redundant inputs. However, this process has also led to surplus labor input due to a decreased dependence on labor resulting from improved production efficiency through advanced production technology and automation equipment introduction. The optimization and upgrading of the industrial structure from labor-intensive to technology-intensive have escalated the demand for high-quality talent while reducing the need for low-skilled labor, exacerbating surplus labor input.

(4)

The energy consumption structure has a favorable impact on the slack variables of labor input, energy input, and capital input. This indicates that the current energy consumption structure in western China has not yet effectively promoted the progress of industrial carbon emission efficiency. The western region may still be heavily reliant on traditional energy sources, such as coal, and the development and utilization of new and renewable energy sources are relatively lagging behind, making it slow to make progress in energy transformation and difficult to effectively reduce carbon emissions.

(5)

The degree of industrialization exerts a negative impact on the slack variables of both labor inputs and energy inputs, and a positive effect on the slack variable of capital inputs, which indicates that the current increase in the level of industrialization in the western region will reduce the redundancy of labor inputs and energy inputs, but cause an increase in the redundancy of the slack variable of capital inputs. The progress of industrialization has resulted in the rapid advancement of manufacturing, construction, service, and other industries in the western region, thereby creating more local employment opportunities and attracting a significant influx of labor. Heightened levels of industrialization have led to expanded production scale and efficiency, resulting in increased energy demands. However, during the process of industrialization, rapid technological upgrading may lead to accelerated obsolescence of old equipment and technology, thus increasing the waste of capital.

(6)

The levels of green development and shared development have a negative impact on the slack variables of labor input, energy input, and capital input. This suggests that the current increase in the levels of green development and shared development in western China will positively influence the improvement of industrial carbon emission efficiency. The enhancement of green development entails heightened focus from enterprises on energy conservation and emission reduction during the production process, achieved through the adoption of advanced production technology and equipment to minimize resource waste and pollutant emissions. The elevated level of shared development signifies a more equitable and balanced distribution of social resources, thereby reducing waste and redundancy resulting from uneven resource allocation.

5.1.3. Stage 3: Efficiency Assessment after Removing External Environmental Factors

At this stage, the industrial carbon emission efficiency of the 11 provinces in western China was re-evaluated from 2010 to 2021, using the adjusted and optimized input variables and original output variables, with the assistance of DEAP 2.1 software. The results are presented in

Table 6. Adjusted industrial carbon emissions efficiency by region (2010–2021).

Region	Province	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	Mean Value	Ranking
Region I	Guangxi	0.973	0.926	0.889	0.855	0.882	0.888	0.861	0.812	0.84	0.841	0.812	0.825	0.8670	11
	Chongqing	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.0000	1
	Sichuan	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.0000	1
	Guizhou	0.944	0.931	0.919	0.933	0.956	0.963	0.953	0.939	0.948	0.95	0.973	0.969	0.9482	8
	Yunnan	0.939	0.973	0.988	0.951	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.9876	6
	Mean value	0.971	0.966	0.959	0.948	0.968	0.970	0.963	0.950	0.958	0.958	0.957	0.959	0.9606	—
Region II	Inner Mongolia	0.851	0.882	0.902	0.909	0.943	0.917	0.930	1.000	1.000	0.979	0.949	0.894	0.9297	10
	Shaanxi	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.981	0.993	0.984	0.9965	5
	Mean value	0.926	0.941	0.951	0.955	0.972	0.959	0.965	1.000	1.000	0.980	0.971	0.939	0.9631	—
Region III	Gansu	0.994	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.9995	4
	Qinghai	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.0000	1
	Ningxia	1.000	1.000	1.000	1.000	0.986	0.968	0.959	0.933	0.936	0.907	0.86	0.832	0.9484	8
	Xinjiang	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.995	0.99	0.936	0.905	0.888	0.9762	7
	Mean value	0.999	1.000	1.000	1.000	0.997	0.992	0.990	0.982	0.982	0.961	0.941	0.930	0.9810	—
Western region		0.973	0.974	0.973	0.968	0.979	0.976	0.973	0.971	0.974	0.963	0.954	0.945	0.9685	—

.

As can be seen from the results in Table 6, after removing environmental and stochastic factors, the mean value of industrial carbon emission efficiency in western China increases from 2010 to 2021, and the range of its average value changes from [0.900, 0.958] in the first stage to [0.945, 0.979] in the third stage, which demonstrates the necessity of re-adjustment of the input variables. From the average values of the three western regions, the average values of industrial carbon emission efficiency of the three western regions increased from 0.9611, 0.8841, and 0.9461 in the first stage to 0.9606, 0.9631, and 0.981 in the third stage. The situation of “the first region > the third region > the second region” before the adjustment has changed to the situation of “the third region > the second region > the first region”, in which the efficiency value of the second region has the largest increase, indicating that the regional development environment of the second region has formed a strong constraint on the efficiency performance of the region. Combined with Figure 1a–c, which show the average value of the comprehensive efficiency of industrial carbon emissions, the average value of pure technical efficiency, and the average value of scale efficiency of the western region in the first and third phases, respectively, the following analysis can be obtained:

(1)

Comprehensive efficiency

According to Figure 1a, it can be found that the number of provinces with effective DEA increased from two before adjustment to three after adjustment, and only Guizhou and Yunnan provinces in the first region had a decrease in the average value of efficiency, while the average value of the efficiency of the remaining provinces existed unchanged or increased to different degrees, which indicated that only Guizhou and Yunnan provinces were in a favorable external environment. The average value of the combined efficiency of the first region remains unchanged overall after the adjustment. Chongqing, which remained in the efficiency frontier before the adjustment, is still in the carbon emission efficiency optimum after the third stage of adjustment. Sichuan province becomes DEA ineffective after the third stage of adjustment into the DEA frontier surface, indicating that the removal of external environmental factors after the industrial carbon emissions efficiency is more effective. Guangxi province has a lower average value of comprehensive efficiency, and is at the bottom of the average value of comprehensive efficiency of industrial carbon emission of 11 provinces in the western region after adjustment, indicating that there are deficiencies in resource allocation and management capacity, and Guangxi province should optimize the industrial structure and promote the accelerated transformation of energy structure. The average value of industrial carbon emission efficiency in the second region has improved, and the average value of comprehensive efficiency in Inner Mongolia has increased the most, with an increase of 18.77%, but the ranking of the comprehensive efficiency value is still at the bottom of the list, still DEA ineffective, which indicates that although management inefficiency will constrain the efficiency of industrial carbon emission in Inner Mongolia province, the irrationality of the inputs and outputs is the main reason for the low value of its efficiency. Shaanxi province’s industrial carbon emission efficiency value rose by a small amount, but the average efficiency value was always high, up to over 0.98, maintaining a high level. This may be due to the fact that Shaanxi province has carried out industrial restructuring and upgrading, and has invested more resources in low-carbon and high value-added industries, thus improving the overall carbon emission efficiency. The third region has the highest adjusted efficiency mean of the three western regions. Except for Ningxia province, where only the mean value of efficiency increased by a large margin, the remaining three provinces’ efficiency values changed little or remained unchanged. Qinghai province is always on the DEA efficient frontier, indicating that its inputs and outputs are reasonable and do not need to be changed. The adjusted average efficiency of Gansu province approaches the DEA frontier, and the adjusted average efficiency of Ningxia and Xinjiang provinces is improved, which is more conducive to the measurement of the real efficiency of each province after removing environmental factors.

(2)

Pure technical efficiency

According to Figure 1b, the average pure technical efficiency of industrial carbon emission in western China increased from 0.953 before adjustment to 0.984, and the number of provinces reaching the efficiency frontier increased from three before adjustment to six after adjustment. The average value of pure technical efficiency of industrial carbon emissions in the three western regions increased. After the adjustment, the situation of “the first region > the third region >the second region” changed to the situation of “the third region > the first region >the second region”. The pure technical efficiency of the first region showed a small upward trend after adjustment, with different and widely varying trends among the provinces within the region. Only Guizhou and Yunnan provinces experienced a decline in the mean value of pure technical efficiency, while the remaining nine provinces in the western region experienced either no change or a different degree of increase in the mean value of pure technical efficiency. Pure technical efficiency is realized in both Chongqing and Sichuan, provinces that are more economically developed and open to the outside world than the rest of the western region, emphasizing technological innovation and application. Guangxi and Guizhou provinces are the main reasons for pulling down the pure technical efficiency of the first region. The largest increase of 9.5 per cent in the mean value of pure technical efficiency was observed in the second region, indicating that the pure technical efficiency of industrial carbon emissions in the second region is underestimated due to environmental and stochastic factors. Shaanxi province has reached the frontier of pure technical efficiency after adjustment. Inner Mongolia province has the largest increase in the mean value of pure technical efficiency after adjustment, but the pure technical efficiency is the lowest in the western region, and there is still room for improvement, indicating that the current allocation of resources is not reasonable and that management and resource allocation capacity needs to be further strengthened. The third region has the highest adjusted mean value of pure technical efficiency among the three western regions, indicating a more efficient allocation of resources and a higher level of management in the region. Among them, Ningxia province had a larger increase in adjusted efficiency, realizing pure technical efficiency effectiveness.

(3)

Scale efficiency

According to Figure 1c, the scale efficiency of industrial carbon emissions in the western region is at a high level as a whole, and the scale efficiency of each region changes less before and after the adjustment, and the situation of “the second region > the third region > the first region” is always maintained, and the scale efficiencies of 11 provinces in the western region for one year or many years reach the scale frontier, and the overall scale efficiency average value decreases from 0.987 before the adjustment to 0.984, with a small decrease. The mean value of scale efficiency in the first region is at the bottom of the three regions, and there are large differences in scale efficiency among the provinces within the region. Chongqing and Sichuan are both on the scale frontier, indicating that these two provinces have reached the optimal scale of production. The adjusted mean value of scale efficiency decreased in Guizhou, Yunnan, and Guangxi provinces, with the largest decrease in Guangxi province, from 0.965 to 0.927, which indicates that its scale efficiency is overestimated without removing the influence of environmental and random factors, and that the scale effect in Guangxi province has not yet been formed, which restricts its carbon emission efficiency. The average value of scale efficiency in the second region is always in the first place among the three regions, indicating that the second region concentrates more resources on industrial production and has a high-scale effect, and that the industrial carbon emission reduction efforts in this region are mainly due to industrial scaling. The mean value of scale efficiencies for the third region has fluctuated slightly after adjustment, but the change is not significant. Gansu and Xinjiang provinces have reached the scale frontier for many years, with scale efficiency averages as high as 0.99, and Qinghai province’s mean value of scale efficiency is always on the frontier. However, Ningxia province is the main factor pulling down the scale efficiency in Region III. Both Ningxia and Xinjiang provinces’ scale efficiency means are lower after adjustment, but their comprehensive efficiency means are higher. For the third region, the improvement of industrial carbon emission efficiency mainly relies on its own management efficiency and the rational and effective allocation of technology, while the embodiment of the scale effect relies more on the comprehensive development environment in which it is located, and the improvement of scale efficiency is the main direction of the third region.

5.2. Analysis of Regional Differences in Industrial Carbon Emission Efficiency in Western China

According to the Dagum Gini coefficient method, the spatial and temporal differences in industrial carbon emission efficiencies and their sources in western China and the three western regions were measured from 2010 to 2021, and the contribution rates of different sources of spatial differences were explored, and the results are shown in

Table 7. Gini coefficients and contribution rates of industrial carbon emission efficiency in western China and the three regions (2010–2021).

Year	Overall Gini Coefficient	Intra-Regional Gini Coefficient			Inter-Regional Gini Coefficient			Contribution Rate (%)
		Region I	Region II	Region III	Region I − Region III	Region I − Region II	Region III − Region II	Intra- Regional Gw	Inter- Regional Gnb	Supervariable Density Gt
2010	0.021	0.015	0.04	0.001	0.014	0.039	0.039	21.49%	65.20%	13.31%
2011	0.019	0.018	0.031	0	0.017	0.031	0.03	24.06%	61.12%	14.82%
2012	0.021	0.025	0.026	0	0.021	0.027	0.025	29.00%	53.13%	17.88%
2013	0.024	0.03	0.024	0	0.027	0.03	0.023	29.00%	53.13%	17.87%
2014	0.017	0.023	0.015	0.003	0.017	0.021	0.014	33.69%	41.77%	24.54%
2015	0.018	0.022	0.022	0.006	0.016	0.025	0.021	32.85%	38.47%	28.68%
2016	0.02	0.027	0.018	0.008	0.02	0.025	0.018	35.18%	31.68%	33.14%
2017	0.024	0.037	0	0.013	0.028	0.026	0.009	38.54%	45.61%	15.85%
2018	0.021	0.031	0	0.013	0.024	0.022	0.009	38.39%	42.61%	18.99%
2019	0.025	0.031	0.001	0.022	0.029	0.024	0.02	36.52%	14.29%	49.19%
2020	0.033	0.034	0.011	0.034	0.038	0.028	0.031	35.66%	18.10%	46.24%
2021	0.037	0.032	0.024	0.041	0.041	0.036	0.037	34.53%	19.90%	45.58%

.

5.2.1. Overall Spatial Difference Analysis

The trend of the overall Gini coefficient of industrial carbon emission efficiency in western China during the sample period is depicted in Figure 2a. It is evident from Figure 2a that the overall Gini coefficient demonstrates a fluctuating upward trajectory, indicating an escalation in spatial disparities in industrial carbon emission efficiency across the western region over the sample period. The spatial disparity in industrial carbon emission efficiency generally experienced a marginal increase from 2010 to 2013, followed by a decline from 2013 to 2014, reaching a minimum level of 0.017 during the examination period. The spatial difference in industrial carbon emission efficiency in the western region once again showed an increasing trend from 2014 to 2017, and then declined again from 2017 to 2018, with a larger increase after 2018, reaching a maximum in 2021 of 0.37. In comparison with figures from 2010, there was a notable surge of 76.2% observed for spatial disparity in industrial carbon emission efficiency within the western region by year-end of 2021, equating to an average annual increase of approximately 5.3%.

5.2.2. Analysis of Spatial Variation within Regions

The Gini coefficient trends within the three regions of industrial carbon emission efficiency in western China during the sample period are depicted in Figure 2b. In terms of the mean value of the Gini coefficient, the first region has the largest intra-regional variation, with a mean value of 0.0271, followed by the third region at 0.0177, and the second region at 0.0118. Regarding trends, regions II and III show more significant changes in their intra-area Gini coefficients compared to region I. The Gini coefficient for region I shows an M-shaped trend over the sample period, with an overall slow increase, indicating that spatial disparities within region I have generally increased over the period examined. Region II’s Gini coefficient displays an initial decrease followed by an increase, showing a fluctuating downward trend from 2010 to 2017 and a substantial decline from 2016 to 2017. After stability from 2017 to 2018, it then shows an upward trend, signifying continuous reduction in spatial differences initially but subsequent potential unbalanced development later on. The overall trend for the third region’s Gini coefficient is characterized by fluctuations and significant increases, pointing towards escalating spatial disparities within this area.

5.2.3. Analysis of Spatial Differences between Regions

The trend of the Gini coefficient among the three regions of industrial carbon emission efficiency in western China during the sample period is illustrated in Figure 2c. The mean value of the Gini coefficient shows that the spatial difference between the first and second regions is most pronounced, with a mean value of 0.0278. Differences in resource endowment and industrial structure may be an important factor contributing to this spatial difference. The first region has abundant water resources and ecological resources, but relatively limited fossil energy reserves and extraction. These resource characteristics may prompt the region’s industrial development to focus more on clean energy and ecologically friendly industries, while the second region relies on abundant fossil energy, and its industrial structure favors traditional industries with high carbon emissions, which may have a greater impact on the efficiency of carbon emissions, leading to the largest spatial difference between the first and second regions. The degree of spatial variation was reduced in the order of regions I and III, and regions II and III. In terms of the trend in change, the Gini coefficient between the first and third regions exhibited a fluctuating upward trajectory over the study period, with a substantial increase indicating a significant spatial disparity growth between these two regions. The changing trend of the spatial difference between the second region and the other two regions is roughly the same, showing a W-shaped change trend during the sample period and generally showing a slight upward trend.

5.2.4. Sources and Contribution of Regional Disparities

Figure 2d illustrates the temporal evolution of the contribution of each component of the Gini coefficient to the overall Gini coefficient during the study period. It is evident from Figure 2d that inter-regional disparities make the most substantial contribution to spatial variation, followed by intra-regional differences, while hypervariable density contributes minimally. This suggests that inter-regional variations are the primary source of spatial heterogeneity in industrial carbon emission efficiency in western China. In terms of temporal trends, the contribution rate of inter-regional variance exhibits a U-shaped pattern, initially decreasing and then increasing. The contribution rate of intra-regional variance follows an inverted U-shape trend, initially rising and then declining, with alternating patterns observed for inter-regional variance contributions. The contribution from hypervariable density displays a general “W” trend over time. Therefore, efforts to reduce industrial carbon emissions in western China should focus on mitigating disparities among the three regions.

5.3. Spatial and Temporal Evolution of Industrial Carbon Emission Efficiency in Western China

The results in Figure 3 illustrate the kernel density estimation of industrial carbon emission efficiency in western China and the three western regions. Throughout the sample observation period, there is a rightward shift in the center of the industrial carbon emission efficiency kernel density curve in western China, indicating an overall improvement in industrial carbon emission efficiency in the region. In terms of wave crest morphology, there is a trend of initial increase, followed by decrease and then another increase in peak distribution of industrial carbon emission efficiency in the western region during the sample period. From 2010 to 2015, there is no significant change trend in the center of the kernel density curve while the wave peak increases, suggesting a slow increase in industrial carbon emission efficiency at this stage and a gradual reduction in regional differences. This period may be influenced by the initial economic recovery following the global financial crisis. The industrial development in the western region is still undergoing an adjustment phase, and the transformation of industrial structure has not been extensive, with the full manifestation of policy effects yet to occur. However, some preliminary policy guidance and technology introductions may have started to take effect, laying the groundwork for subsequent efficiency improvements. The peak value of the kernel density curve from 2018 to 2021 shows a clear upward trend with a significant rightward shift in its center, indicating substantial improvement in industrial carbon emission efficiency during this period. With the implementation of the “Belt and Road” initiative and the continued advancement of the western development strategy, the western region has expedited its industrial upgrading and transition towards green development. This is attributed to clearer and more robust policy incentives, leading to notable progress in technological innovation. Consequently, a multitude of energy-saving and emission-reduction technologies have been widely applied and popularized. The optimization of industrial structure has yielded remarkable results, with an increased proportion of low-carbon and environmentally friendly industries. After 2019, the peak of the right-skewed distribution tightened significantly, exhibiting a pronounced left-tail phenomenon. This suggests that while overall efficiency improved, certain provinces or industries were unable to keep pace due to technological, financial, and other constraints, resulting in relatively lower efficiency. In terms of number of wave peaks, it has been unimodal until 2019 when it became a multimodal distribution, reflecting multi-polarization trends for industrial carbon emission efficiency within that period. The variation may stem from disparities in resource endowments, economic foundations, and technological advancements across various regions and industries. Hence, when devising emission reduction policies, these distinctions should be thoroughly taken into account, and tailored strategies should be implemented to achieve a more balanced and effective remission reduction effect.

The kernel density estimation curve of industrial carbon emission efficiency in the three western regions indicates that the center of distribution of the first region shifted significantly to the right in the pre-sample period, suggesting a substantial improvement in industrial carbon emission efficiency. In contrast, there was no clear trend of change in the later period. The center of distribution in the second region does not exhibit a distinct trend, indicating slow progress in improving industrial carbon emissions efficiency. The center of the kernel density curve in the third region shows a shift to the right and then dynamic dispersion during the examination period, suggesting an improvement in industrial carbon emissions efficiency. From the wave pattern, the peak of the distribution of the first region shows fluctuating changes, the width becomes smaller in the middle and late stages of the sample, and there is a phenomenon of convergence, which indicates that the gap of the industrial carbon emission efficiency of the first region is larger in the early stage of the study, and the gap is gradually narrowed in the late stage of the study. The peak of the distribution in the second region shows a decreasing trend during the sample period, and the shape of the wave peak gradually flattens, indicating that the industrial carbon emission efficiency gap in the second region shows an increasing trend. In the third region, the right wave peak tightens significantly in the middle of the sample and there is a left-trailing phenomenon, and the wave peak disappears in the late stage of the sample, indicating that the efficiency of industrial carbon emissions in the region is further improved in the middle of the sample, but there are some provinces with lower efficiency of industrial carbon emissions, and the differences within the region increase in the late stage of the sample. From the point of view of the number of wave peaks, the first region only had lateral peaks in 2012, and the rest years were unimodal distribution, indicating that the first region had polarization in 2012, and no obvious polarization characteristics in the rest years. The kernel density curves in the second region are all unimodal distributions during the examination period, with no polarization. The third region has a distribution of side peaks in the middle of the sample, and the distance between the main peak and the side peaks is large, indicating that the industrial carbon emission efficiency of the third region is more polarized in the middle of the sample, and the polarization disappears in the later period.

6. Conclusions and Policy Implications

This study utilizes a three-stage DEA model to measure the industrial carbon emission efficiency of eleven provinces in western China from 2010 to 2021. It also examines the influence of nine environmental factors on industrial carbon emission efficiency. Empirical investigation into the regional industrial carbon emission efficiency and its distributional dynamic evolution process in western China is conducted using Dagum’s Gini coefficient, its decomposition method, and kernel density estimation. The following conclusions are drawn:

Firstly, based on the results of measuring industrial carbon emission efficiency, and after excluding environmental and stochastic factors, it is evident that the industrial carbon emission efficiency in the western region of China has shown an increase, reaching a high overall level. The industrial carbon emission efficiency among regions shows a situation of “the third region > the second region > the first region”. Comparatively speaking, the second region has the lowest pure technical efficiency and the highest scale efficiency, so further strengthening of management and resource allocation capacity is the main direction for the second region. The first region has the lowest scale efficiency, so improving scale efficiency is the main direction for the first region.

Secondly, with regard to the influencing factors of industrial carbon emission efficiency, environmental factors exert a significant impact on industrial carbon emission efficiency in western China, leading to variations in both the direction and magnitude of influence. The main significant factors influencing the improvement of industrial carbon emission efficiency in western China are the degree of shared and green development; the degree of innovative and coordinated development positively affects this improvement; the degree of industrialization has a smaller effect; and, at present, the economic development level, government support, openness to development, and energy consumption structure in western China have not yet contributed to the advancement of industrial carbon emission efficiency.

Thirdly, with regard to spatial variations in industrial carbon emission efficiency, there has been a general increase in spatial disparities in industrial carbon emission efficiency across western China during the sample period. Intra-regional differences are most pronounced in the first region and least pronounced in the second region among the three western regions. The spatial gaps between the first and third regions have significantly widened over time. The disparities between the second region and the other two regions exhibit a W-shaped trend, with a slight overall increase during the sample period. Inter-regional variances are the primary source of spatial discrepancies in industrial carbon emission efficiency in western China. The contribution of hypervariable density to overall spatial differences is minimal, displaying a W-shaped trend, while intra-regional differences show an inverted U-shaped trend.

Finally, from the perspective of spatial and temporal evolution, industrial carbon emission efficiency in western China has shown continuous improvement. In the early stage of the study, there was a gradual increase in industrial carbon emission efficiency and a reduction in intra-regional differences. However, in the later stage of the study, there was a significant increase in industrial carbon emission efficiency along with an emergence of spatial differences, leading to a phenomenon of multi-polarization. When considering the three western regions separately, it is evident that their industrial carbon emission efficiencies exhibited distinct evolutionary trends and intra-regional variations. The first region experienced a notable increase in industrial carbon emission efficiency during the initial period but remained stable thereafter, accompanied by a gradual narrowing of internal differences; meanwhile, the second region saw slow growth in industrial carbon emission efficiency coupled with widening intra-regional disparities. As for the third region, its industrial carbon emission efficiency increased over time but displayed noticeable polarization during the middle period of observation, while witnessing an expansion of intra-regional differences towards later stages.

The paper suggests the following policy recommendations for both the regional and overall levels in western China, based on the findings mentioned above.

For the regional level, comprehensive consideration should be given to adjusting regional resource allocation according to the characteristics of each region, strengthening mutual reference and cooperation between regions, integrating and coordinating regional development, and narrowing the gap between regions.

For the first region, the scale efficiency of the region is the lowest among the three western regions, with the greatest intra-regional differences. Therefore, the government should introduce corresponding policies to encourage and support enterprises with related or complementary technologies upstream and downstream of the industrial chain to actively expand their production scale through mergers and reorganizations, etc., so as to improve scale efficiency. Enterprises should actively seek policy support from national and local governments, including dedicated funds for energy conservation and emission reduction, tax incentives, and other favorable policies. By providing policy guidance and support, we aim to alleviate the costs and risks associated with energy conservation and emission reduction for enterprises. The government needs to increase its support for the backward regions, give more policies to the backward regions, provide technical support and guidance, provide financial support for the enterprises in the backward regions, and strengthen the cultivation of talent in the backward regions, so as to improve the level of their industrial carbon emission efficiency.

For the second region, its geographical development environment creates a strong constraint on efficiency performance, with the region having the lowest pure technical efficiency and the highest scale efficiency among the three western regions. Therefore, the government should strengthen infrastructure construction, improve the investment environment, optimize policy frameworks, and offer enterprises streamlined administrative approval processes and tax incentives, as well as other forms of support to attract more external resources. A dedicated fund will be established to assist enterprises in upgrading energy conservation and emission reduction technologies and promoting efficient and energy-saving technologies along with cleaner production methods. Through streamlining process flows, utilizing eco-friendly raw materials, and reinforcing waste recycling efforts, among other measures, the production process can become greener and low-carbon. The second region is encouraged to engage in technical exchanges and cooperation with the first and third regions, which have higher pure technical efficiency, to introduce advanced production technology and management experience.

For the third region, it has the highest pure technical efficiency and the highest combined efficiency of the three western regions. There is a large variation within regions in the later part of the sample. The region should maintain and improve its pure technical efficiency advantage, expand production scale and improve scale efficiency. The integration and allocation of resources should be strengthened, and the flow of resources to high-efficiency and low-energy-consumption industries and enterprises should be promoted through policy guidance and market mechanisms to ensure the efficient utilization of resources. It is necessary to optimize the industrial layout and promote the development of industrial agglomeration in order to form economies of scale and reduce operating costs. Cooperation and exchanges among regions within the third region should be strengthened, and a cooperative mechanism should be established for improving industrial carbon emission efficiency. Through the sharing of resources, technology, and experience, this will promote common progress in industrial carbon emission efficiency improvement in all regions.

At the macro level in western China, industrial enterprises in the western region should embrace a deep commitment to green development that permeates all facets of industrial progress. Reinforce collaboration among enterprises, suppliers, and customers to establish a sustainable green supply chain system that encompasses environmentally friendly raw material procurement, production, and processing, as well as product sales. Stringent environmental regulations and standards need to be established to delineate corporate environmental responsibilities and enhance penalties for non-compliance in order to ensure environmentally sustainable production. Recurrently arrange training sessions for employees to enhance their awareness of environmental protection, energy conservation, and emission reduction, thereby improving their capabilities in these areas. Establish a robust product recycling and reutilization mechanism, promote consumer engagement in product recycling initiatives, and enhance resource recycling efficiency.

Furthermore, western China should strengthen intraregional resource sharing and synergistic development, break down regional barriers by improving transportation, energy, information, and other infrastructure, and promote the free flow of resources, technology, talents, and other factors within the region in order to enhance the efficiency of overall industrial carbon emissions. Industrial cooperation and synergistic development among provinces within the western region should be promoted, and industrial planning and policy coordination should be strengthened to form a situation of complementary advantages and resource sharing. Cooperation and exchanges with the eastern region should be strengthened, advanced technology and management experience should be introduced, and enterprises from the eastern region should be encouraged to invest in the western region to promote the transfer and upgrading of industries, so as to further enhance the efficiency of industrial carbon emissions in the western region.

Finally, the government should persist in increasing its investment in innovation and research and development (R&D) for industrial enterprises in western China, particularly in the areas of clean energy, energy-efficient technologies, and the circular economy, in order to support enterprises in their technological innovation activities. Universities, research institutions, and enterprises should be encouraged to work closely together to form an integrated innovation system of industry, academia, and research to jointly promote technological innovation. Enterprises are encouraged to actively adopt advanced production technologies and equipment, such as high-efficiency motors, variable frequency speed regulation systems, waste heat recovery systems, etc. The government can set up special funds to support enterprises in introducing, digesting, and absorbing advanced low-carbon technologies and equipment at home and abroad, And could establish a comprehensive carbon emission monitoring system to enable real-time monitoring and data analysis of enterprise emissions, utilize data analysis to identify hotspots and bottlenecks in carbon emissions, and develop targeted reduction measures to drive the transition towards green and low-carbon industrial practices in the western region.

7. Discussion

In our comprehensive analysis in this paper, we have observed a significant enhancement in industrial carbon emission efficiency in western China during the sample period. However, there are notable regional disparities. This finding not only underscores the endeavors and accomplishments of the western region in addressing climate change and advancing green and low-carbon development, but also motivates us to delve deeper into the intricate driving mechanisms behind it. Comprehensive analysis reveals that the enhancement of industrial carbon emission efficiency in western China is attributed to the synergistic effect of multiple factors. Firstly, policy initiatives have emerged as the cornerstone guarantee. The thorough implementation of the strategy for developing the western region and the introduction of a series of complementary policies have injected significant momentum into regional development and provided robust support for energy conservation, emission reduction, and ecological environmental protection, and facilitated the transformation and upgrade of high-energy-consuming and high-emission industries, laying a firm groundwork for improving carbon emission efficiency. Secondly, the optimization of the industrial structure is crucial. In terms of industrial composition, the western region has successfully transitioned from traditional industries to emerging ones, enhanced the energy efficiency of traditional industries through technological upgrades and advancements, and actively fostered the clean energy sector, thereby establishing a new low-carbon and environmentally friendly industrial framework. This structural transformation fundamentally diminishes carbon emissions at their source and facilitates an enhancement in carbon emission efficiency. Finally, technological innovation and informatization serve as crucial drivers. Through independent research and development, as well as international cooperation, the western region has achieved significant breakthroughs in energy conservation and emission reduction technologies, leading to improved energy efficiency and reduced carbon emission intensity. The accelerated information construction has also provided robust support for carbon emission management, enabling the western region to monitor and manage carbon emissions more accurately.

In western China, there are notable disparities in enhancing carbon emission efficiency across different regions due to a confluence of various factors. Firstly, these discrepancies stem from variations in both resource allocation and industrial composition. The first region benefits from abundant resources and a diverse industrial framework that afford it flexibility in implementing targeted strategies for conserving energy and reducing emissions. As a major hub for China’s energy production, the second region heavily relies on fossil fuels, leading to substantial carbon emissions pressure. The third region lags behind with a predominantly singular industrial structure focused on resource extraction and primary processing, resulting in heightened carbon emission intensity. Secondly, variations in economic development levels and policy implementation intensity exist. The first region, with a higher level of economic development, can allocate more resources and technology to support energy conservation and emission reduction. In contrast, the third region faces constraints in terms of funds and technology, leading to potentially weaker policy implementation and consequently less-effective emission reduction. Despite abundant resources in the second region, its single industrial structure also hinders its economic development. Finally, variations in natural environment and climatic conditions play a significant role. The humid climate in the first region facilitates the development and utilization of clean energy, whereas the high altitude and arid areas in the third region, coupled with its limited water resources, pose constraints on the selection and implementation of energy-saving and emission-reduction technologies, thereby impacting carbon emission efficiency. Hence, it is imperative for western China to comprehensively consider and address these disparities in order to effectively enhance carbon emission efficiency.

A comprehensive examination of industrial carbon efficiency in western China not only uncovers the region’s distinctive trajectory and challenges in enhancing carbon efficiency, but also acknowledges the far-reaching implications of these findings for global industrial development and carbon governance. First, as a distinctive geographical, economic, and social entity, the endeavor to enhance industrial carbon emission efficiency in western China not only reflects the intricacy of the region but also encapsulates universal challenges in global industrial development. By conducting an in-depth analysis of western China, this study offers a unique vantage point for international scholars to observe shifts in industrial carbon emission efficiency, thereby facilitating the fusion of regional studies and global perspectives while fostering the establishment of a more comprehensive and diversified research framework. Second, in the pursuit of enhancing industrial carbon emission efficiency, western China has potentially pioneered a range of innovative and practical policy measures and technical solutions to enhance industrial carbon emission efficiency. These accomplishments not only contribute to the sustainable development of the region itself but also offer valuable insights and inspiration for global application. By sharing and disseminating these policies and technologies, we can facilitate knowledge exchange and technology transfer worldwide to collectively address pressing global challenges such as climate change and environmental pollution. Third, given the differences in economic development, industrial structure and resource endowment among regions, the investigation of industrial carbon emission efficiency in western China offers valuable insights for exploring diverse paths to reduce global carbon emissions. This will assist nations in devising more tailored strategies for carbon reduction based on their specific national circumstances.

This study is subject to certain limitations, indicating the need for further research in these specific areas. Firstly, the data sources in this paper may be somewhat limited and may not cover all the factors related to industrial carbon emission efficiency. Subsequent research could incorporate micro-level factors within enterprises and construct a more comprehensive causal relationship model through multi-level factor analysis. Secondly, this paper adopts the three-stage DEA model for efficiency measurement, which can realize the automatic empowerment of indicators and has advantages in efficiency analysis of complex production relations. However, it also has its shortcomings [17], so in future research, the three-stage DEA model can be enhanced or integrated with other methodologies, and a comparative analysis will be undertaken to select the approach that best aligns with the authors’ research requirements. Finally, this paper examines the efficiency of carbon emissions in western China as the primary focus of research, and future studies could involve comparisons with other regions or countries, particularly to investigate the mechanisms underlying the interaction of industrial carbon efficiency between central and eastern China and western China.