An Analysis of Low-Carbon Economy Efficiency in 30 Provinces of China Based on the Multi-Directional Efficiency Method

Abstract

In light of the increasing focus on global climate change and environmental issues, countries around the world are collaboratively working towards the establishment of a low-carbon economy (LCE). As the most populous developing nation, China is proactively advocating for low-carbon economic development as a means to achieve sustainable growth. Nevertheless, the efficiency of the low-carbon economy (LCEE) exhibits considerable variation across different regions within China. This article seeks to explore the regional disparities in LCEE throughout the country and to identify the factors that contribute to these variations. Firstly, this paper examines the advancements in LCEE research, concentrating on an analysis of 30 Chinese provinces. Employing the Multi-directional Efficiency Analysis (MEA) framework alongside the global Malmquist (GM) index, this study evaluates the efficiency of the low-carbon economy across the 30 provinces from 2010 to 2021. Secondly, by integrating spatial autocorrelation analysis techniques, the research encompasses a multifaceted examination, including spatiotemporal analysis, regional disparities, driving factors, and potential for improvement. The findings indicate significant discrepancies in LCEE among various provinces in China. Notably, LCEE tends to be higher in the eastern coastal regions, attributed to their advanced economic development, whereas the western inland areas generally exhibit lower efficiency levels due to comparatively limited economic progress. Thirdly, LCEE exhibits significant spatial heterogeneity, with clear high–high and low–low clustering patterns, revealing systemic coordination gaps between eastern coastal and central/western regions. Fourthly, from the decomposition results of the global Malmquist index, it can be seen that efficiency change (EC) is less than 1 and technology change (TC) is greater than 1, which promotes the improvement of LCEE. Technical efficiency is the main factor affecting the improvement of LCEE.

1. Introduction

Since the initiation of reform and opening up, China has experienced considerable economic advancement; however, this progress has been accompanied by an excessive focus on GDP growth, resulting in the neglect of environmental pollution. The prolonged and extensive reliance on traditional fossil fuels has caused significant pollution and degradation of the ecological environment [1]. Consequently, to establish a resource-efficient and environmentally sustainable society, China must confront two critical challenges: first, the issue of resource wastage, and second, the environmental pollution and excessive carbon dioxide emissions that have arisen from an unbalanced emphasis on GDP growth during the economic development process.

It is imperative to transform the development model and promote the transition towards green, low-carbon, and sustainable practices in production and lifestyle in order to mitigate environmental pollution and foster a harmonious relationship between economic growth and environmental conservation. Analyzing LCEE across various provinces and advancing its implementation not only addresses the environmental and resource challenges encountered in the current phase of development but also aligns with the global initiative to promote sustainable development. This endeavor holds significant importance for China as it strives to establish a modern nation. LCEE serves as a comprehensive evaluative metric that not only reflects the quality and efficiency of economic development but also illustrates the effective utilization of resources and the safeguarding of the environment [2]. Research on low-carbon economy efficiency (LCEE) in China holds significant academic and practical value, as it contributes to the development of environmentally friendly economic systems, enhances resource allocation efficiency, facilitates regional coordination, stimulates green technology innovation, accelerates the transition to sustainable development models, and provides technical support for low-carbon economy progress.

This article first examines the advancements in research pertaining to low-carbon economic efficiency, subsequently focusing on a selection of 30 provinces in China as the subjects of study. Utilizing the Multi-Directional Efficiency Analysis (MEA) model alongside the global Malmquist index, the study calculates the low-carbon economic efficiency of these provinces from 2010 to 2021. The analysis incorporates spatial autocorrelation to explore various dimensions, including spatiotemporal trends, regional disparities, driving factors, and potential pathways for improvement. Ultimately, the article proposes optimization strategies aimed at enhancing low-carbon economic efficiency in China and synthesizes experiences of high-quality development within the low-carbon economy, offering exemplary cases for consideration in the low-carbon economic development of other regions. The research connects ecological modernization theory with practical decarbonization solutions.

2. Literature Review

2.1. Research on Efficiency Theory of Low-Carbon Economy

The notion of a “low-carbon economy” was initially articulated in the publication “Our Future Energy: Creating a Low Carbon Economy.” This concept emphasizes the role of innovation in minimizing energy and resource consumption, as well as reducing greenhouse gas and pollutant emissions, thereby facilitating sustainable economic and social development without compromising economic growth [3]. Over time, as the ratio of material and energy inputs to economic output diminishes, the self-reinforcing mechanisms of the LCE are expected to experience significant enhancement. As the LCE increasingly becomes the predominant strategy for economic development, it draws upon principles of ecological economics, improves environmental quality through effective resource allocation, addresses both economic and environmental challenges, and creates new avenues for economic advancement.

Since the UK government first proposed the concept of a low-carbon economy in 2003, it has gained global recognition, with many countries adopting carbon reduction targets [3]. China pledged to reduce its CO₂ emission intensity per unit of GDP by 40–45% by 2020 compared to 2005 levels. At the Ninth Central Financial and Economic Affairs Commission meeting, China further committed to peaking carbon emissions by 2030 and achieving carbon neutrality by 2060—a strategic decision integral to sustainable development and the vision of a shared future for humanity [4]. These goals align with China’s pursuit of eco-conscious, green, and low-carbon high-quality development [5], embedding carbon peaking and neutrality into its broader ecological civilization framework. Policy measures include strict controls on coal-fired power projects, capping coal consumption growth during the 14th Five-Year Plan (2021–2025), and phased reductions thereafter. Additionally, China’s acceptance of the Kigali Amendment to the Montreal Protocol strengthens non-CO₂ greenhouse gas regulation, while its national carbon market facilitates emissions trading. Against this backdrop, low-carbon economic efficiency (LCEE), which evaluates input–output performance [6], has emerged as a critical metric for global policy formulation.

2.2. Research on Low-Carbon Economy Efficiency

The primary principle underlying the LCE is the efficiency theory, which emphasizes the improvement of existing ecological conditions through the implementation of LCE initiatives. This approach aims to optimize energy efficiency in economic production while simultaneously reducing pollutant emissions.

From a methodological perspective, scholars predominantly employ Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) for efficiency assessment. Wu et al. [7] pioneered the Super-PEBM model integrated with DEA techniques to dynamically evaluate energy and environmental efficiency across China’s 29 provincial-level regions, revealing spatiotemporal evolution patterns of regional efficiency. Dellnitz et al. [8] advanced environmental DEA methodology by developing a Pearson correlation-based EBM optimization model, which enhances robustness in handling outliers through median-based algorithms. Ren et al. [9] adopted a super-SBM model to analyze three waves of nationally representative longitudinal survey data. By integrating maximum likelihood structural equation modeling (ML-SEM) with dynamic panel data analysis, their research systematically investigated the complex dynamic relationships among household income, consumption propensity, and resource efficiency. The findings demonstrate an overall declining trend in household resource efficiency alongside converging inter-household disparities, while revealing a non-linear U-shaped relationship between income levels and efficiency performance. For macro-level analysis, Zhang et al. [10] implemented SFA to empirically investigate the carbon emission efficiency during industrialization and urbanization processes in the Yangtze River Economic Belt, systematically elucidating the relationship between economic development and carbon efficiency.

The recent academic literature indicates that DEA is the most commonly used method for studying low-carbon economic efficiency. Zhou et al. [11] developed a comprehensive indicator to assess the level of digital development, utilizing panel data from 264 cities in China spanning the years 2008 to 2020, and employed the Super-SBM model to quantify LCEE. In a separate study [12], a DEA model was utilized to evaluate LCEE across 94 provincial-level regions in China, Japan, and South Korea from 2013 to 2019. Following this, researchers implemented a cross-validated grid search methodology to determine the most effective predictive model among ten widely recognized machine learning algorithms. Additionally, Jin and colleagues [13] conducted an extensive evaluation of the effectiveness of technological innovation, low-carbon economic growth, and productivity across 35 industrial subsectors in China. Their approach integrated a dual-phase DEA framework with sliding window analysis to monitor performance trends over time.

They found that the technological innovation of Chinese industry is not coordinated with the development of a low-carbon economy. Yao and his research team [14] conducted a comprehensive empirical investigation into the correlation between LCEE and the development of digital finance across 100 urban centers in the Yangtze River Economic Zone of China. Employing the entropy weighting method alongside a coupling coordination framework, they systematically examined the interactions between these variables and identified the key factors influencing their relationship. Luo and Lin [15] developed an improved DEA model with projection analysis to examine Zhejiang Province’s municipal-level LCEE, identifying inefficiency sources and revealing a U-shaped efficiency trajectory. Yang et al. [16] pioneered the integration of SBM-DEA with discordant coupling models to analyze LCEE-STDL interactions (2008–2017), supplemented by panel VAR to quantify bidirectional effects. Their follow-up work [17] employed SBM-DEA and Tobit regression on 2005–2019 data, systematically disentangling spatially heterogeneous drivers of provincial LCEE variations. These studies collectively demonstrate the value of hybrid models (DEA + projection/coupling/Tobit) for efficiency diagnostics, consistent spatial–temporal divergence patterns in Chinese LCEE evolution, and the critical role of technological factors in efficiency transitions.

DEA is widely recognized as the predominant methodology within academic circles for assessing LCEE. Prominent analytical models in this domain include the super-efficiency SBM [18], the Super-SBM [19], and the SBM–Dynamic Data Envelopment Framework (DDF) integrated with the global Malmquist index [20]. It is apparent that there is a growing trend among researchers to utilize the SBM framework, which is a traditional benchmarking model. However, when this model is employed for calculations, it tends to yield results that indicate a continuous upward trend, which is not a plausible representation of variations in LCEE. In contrast, the application of the MEA model reveals a “U”-shaped trajectory, which aligns better with the timing of our country’s implementation of policy that focuses on saving energy and protecting the environment.

The research undertaken by pertinent experts and scholars predominantly centers on the factors that affect LCEE, as well as strategies for advancing the LCE and improving its efficiency. Some of the models employed in these investigations are regarded as outdated. In recent years, China has actively pursued the development of an LCE, consistently accelerating the transition towards a low-carbon economic framework and innovating methodological approaches to address research challenges. In light of this context, the present article focuses on an analysis of 30 Chinese provinces, utilizing the MEA model to assess the levels of LCEE development and to conduct spatial analysis.

2.3. Development of Multi-Directional Efficiency Analysis

Most studies focused on low-carbon economic efficiency primarily utilize conventional DEA techniques, which limit the assessed Decision-Making Units (DMUs) to either a uniform radial reduction in all input variables or a uniform radial increase in all output variables. This assumption may be insufficient for a comprehensive evaluation of efficiency, as it fails to consider the potential for different input or output variables to be modified in varying proportions, thereby providing more accurate and contextually relevant efficiency measurements.

The MEA method is regarded as a viable alternative to conventional DEA techniques [21]. This method facilitates the selection of benchmarks that allow for the independent consideration of the improvement potential of each input or output variable. As a result, a reduction in inputs or the enhancement of outputs is carried out in accordance with the identified potential for efficiency improvement. This feature makes MEA particularly effective for analyzing the efficiency profiles of individual DMUs in a standalone manner. By assessing the improvement potential of each variable independently, MEA permits each DMU to simultaneously reduce the consumption of certain inputs while increasing the production of specific outputs, without the need to establish predetermined priorities among the variables.

Table 1. Development history of MEA.

Ref.	Year	Method Model Theory	Contribution	Constraint
[21]	1999	Efficiency assessment	The article axiomatizes the implicit Farrell selection used in DEA, separating the reference plan selection in decision unit efficiency evaluation from performance slack measurement, and proposing the MEA method.	Mixing the selection of reference schemes with performance relaxation measurements may lead to bias and inaccuracy in the evaluation results.
[22]	2004	Super-efficiency evaluation, potential improvement methods, super-efficiency indicators, Farrell’s super-efficiency indicators, convex hull technology	The article introduces super-efficiency evaluation and defines reference selection and related super-efficiency indicators, expanding the methodology of super-efficiency analysis.	The lack of empirical data support in comparing different super-efficiency indicators in the paper may lead to insufficient reliability of the results.
[23]	2010	MEA, Range Direction Model (RDM), Variable Return to Scale (VRS)	The article extends the MEA model and scope-oriented model to address directional and non-directional technical inefficiencies, and analyzes them under variable and constant scale returns.	The paper failed to clarify the effectiveness and limitations of the new model in real-world problems.
[24]	2012	DEA, MEA	Based on data from joint stock banks and state-owned banks in China, the efficiency differences and influencing factors were studied using the MEA method.	The study failed to consider the impact of external environmental factors on bank efficiency.
[25]	2021	MEA	The article observed the efficiency patterns of each input and output during three periods of common agricultural policies and analyzed the regional efficiency of agricultural resources.	This study may have hypothesized CRS, but this may not be applicable to all agricultural regions.

briefly introduces the development history of MEA, which was first proposed in [21], further developed in [22,23], and used in [24,25]. The advantages of employing MEA include (1) the ability to derive potential improvement metrics grounded in specific input and output data, resulting in findings that are more applicable; (2) the capacity to assess the individual efficiency values of each evaluation unit across various stages, thereby facilitating both the identification of the efficiency status of different units and the discernment of diverse efficiency patterns; (3) the integration of unexpected output variables into the MEA framework, yielding more comprehensive analytical results; and (4) the avoidance of proportional improvements inherent in radial models, thereby enhancing the accuracy of the results. In summary, MEA selects benchmarks for input reduction and output expansion based on the specified improvement potential associated with each variable, thereby enabling targeted investigations into efficiency patterns.

3. Research Methodology

3.1. Overview of Multi-Directional Efficiency Analysis Methods

Currently, the predominant research methodologies employed for measuring efficiency within the academic community are DEA [26,27,28,29] and Stochastic Frontier Analysis (SFA) [30,31]. The key distinction between these two approaches lies in the fact that DEA does not necessitate a predetermined production function, whereas SFA is capable of accounting for the influence of random errors [32].

The MEA method, as a supplement and extension of the DEA method, originated from the initial proposal by Bogetoft and Hougaard [21]. This study employs an MEA approach to determine the LCEE for 30 provinces in China over the period from 2010 to 2021. The current literature indicates that the MEA method has been extensively utilized across various domains, including energy [33], agriculture [25], transportation [34], and banking [35]. The MEA model employs linear programming techniques to initially ascertain the optimal enhancement values for each variable within the evaluation unit, subsequently establish an ideal reference point, and ultimately compute the efficiency of each variable. This study employs an MEA model that accounts for unexpected outputs to evaluate and analyze the LCEE of 30 provincial-level regions [36]. A comprehensive description of the model is provided in the following sections.

• ${\mathrm{mind}}_{\mathrm{io}}$

$$\mathrm{s}.\mathrm{t}. \left\{\begin{array}{l}{\displaystyle \sum _{j=1}^n{\lambda }_j}{x}_{ij}\le d_{io}\hfill \\ {\displaystyle \sum _{j=1}^n{\lambda }_j}{x}_{-ij}\le x_{-io},-i=1,\dots ,i-1,i+1,\dots m\hfill \\ {\displaystyle \sum _{j=1}^n{\lambda }_j}{y}_{rj}\ge y_{ro},r=1,\dots ,s_1\hfill \\ {\displaystyle \sum _{j=1}^n{\lambda }_{\mathrm{j}}}{c}_{kj}=c_{ko},k=1,\dots ,s_2\hfill \\ {\lambda }_j\ge 0,j=1,\dots ,n\hfill \end{array}\right.$$

(1)

• $\min {\delta }_{\mathrm{ro}}$

$$\mathrm{s}.\mathrm{t}. \left\{\begin{array}{l}{\displaystyle \sum _{j=1}^n{\lambda }_j}{y}_{rj}\ge {\delta }_{ro}\hfill \\ {\displaystyle \sum _{j=1}^n{\lambda }_j}{y}_{-rj}\ge y_{-ro},-r=1,\dots ,r-1,r+1,\dots ,s_1\hfill \\ {\displaystyle \sum _{j=1}^n{\lambda }_j}{x}_{ij}\le x_{io},i=1,\dots ,m\hfill \\ {\displaystyle \sum _{j=1}^n{\lambda }_j}{c}_{kj}=c_{ko},k=1,\dots ,s_2\hfill \\ {\lambda }_j\ge 0,j=1,\dots ,n\hfill \end{array}\right.$$

(2)

• $\min {\varphi }_{\mathrm{ko}}$

$$\mathrm{s}.\mathrm{t}. \left\{\begin{array}{l}{\displaystyle \sum _{j=1}^n{\lambda }_j}{c}_{kj}={\varphi }_{ko}\hfill \\ {\displaystyle \sum _{j=1}^n{\lambda }_j}{c}_{-kj}=c_{-ko},-k=1,\dots ,k-1,k+1,\dots ,s_2\hfill \\ {\displaystyle \sum _{j=1}^n{\lambda }_j}{x}_{ij}\le x_{io},i=1,\dots ,m\hfill \\ {\displaystyle \sum _{j=1}^n{\lambda }_j}{y}_{rj}\ge y_{ro},r=1,\dots ,s_1\hfill \\ {\lambda }_j\ge 0,j=1,\dots ,n\hfill \end{array}\right.$$

(3)

Equations (1)–(3) function as ideal benchmarks for the input variables, expected output variables, and unexpected output variables, respectively. In these equations, “n” stands for the quantity of evaluation units; “m” denotes the quantity of input variables “x”; “S1” denotes the quantity of anticipated outputs “y”; and “S2” denotes the quantity of unanticipated outputs “c”. We can obtain the perfect point of reference (optimal solution) for the evaluation units.

• $\max {\beta }_{io}+{\beta }_{ro}+{\beta }_{ko}$

$$\mathrm{s}.\mathrm{t}. \left\{\begin{array}{c}{\displaystyle \sum _{j=1}^n{\lambda }_j}{x}_{ij}\le x_{io}-{\beta }_{io}\left(x_{io}-d_{io}^{*}\right),i=1,\dots ,m\\ {\displaystyle \sum _{j=1}^n{\lambda }_j}{y}_{rj}\ge y_{ro}+{\beta }_{ro}\left({\delta }_{ro}^{*}-y_{ro}\right),r=1,\dots ,s_1\\ {\displaystyle \sum _{j=1}^n{\lambda }_j}{c}_{kj}=c_{ko}-{\beta }_{ko}\left(c_{ko}-{\varphi }_{ko}^{*}\right),k=1,\dots ,s_1\\ {\lambda }_j\ge 0,j=1,\dots ,n\end{array}\right.$$

(4)

The linear programming model (4) is capable of determining the MEA efficiency for each variable within the evaluation unit. Notably, $\left({\lambda }_j^{*},{\beta }_{io}^{*},{\beta }_{ro}^{*},{\beta }_{ko}^{*}\right)$ represents the optimal solution derived from model (4). So the MEA efficiency value for each variable of $\left(x_{io},y_{io},c_{ko}\right)$ can be defined [37].

For every input variable $x_{io}$, the MEA efficiency value for each variable can be articulated as follows:

$${\theta }_i={\displaystyle \frac{x_{io}-{\beta }_{io}^{*}\left(x_{io}-d_{io}^{*}\right)}{x_{io}}}$$

(5)

For each expected output variable, the efficiency value of each variable in the MEA can be defined as

$${\theta }_r={\displaystyle \frac{y_{r\mathrm{o}}}{y_{r\mathrm{o}}+{\beta }_{r\mathrm{o}}^{*}\left({\delta }_{r\mathrm{o}}^{*}-y_{r\mathrm{o}}\right)}}$$

(6)

For each unexpected output variable, the MEA efficiency value of each variable can be defined as

$${\theta }_k={\displaystyle \frac{c_{k\mathrm{o}}-{\beta }_{ko}^{*}\left(c_{k\mathrm{o}}-{\varphi }_{k\mathrm{o}}^{*}\right)}{c_{k\mathrm{o}}}}$$

(7)

This study strictly follows the modeling paradigm of the classic MEA literature (Bogetoft&Hougaard, 1999 [21]) and adopts the assumption of a constant return to scale (CRS).

3.2. Global Malmquist

The Malmquist index serves as a widely recognized metric for assessing variations in productivity, enabling the evaluation of productivity shifts across two distinct timeframes. The DEA-based Malmquist index can be further disaggregated into two constituent elements: technical efficiency change (EC) and technical change (TC). This study employs the MEA methodology proposed by Bogetoft and Hougaard [21] and Asmild [34] as a substitute for DEA in the assessment of efficiency.

The Malmquist model is a method for calculating the Malmquist index, which was introduced by Pastor and Lovell [37].

$$S^g=S^1\cup S^2\cup \dots \cup S^p=\left\{\left(x_j^1,y_j^1\right)\right\}\cup \left\{\left(x_j^2,y_j^2\right)\right\}\cup \dots \left\{\left(x_j^p,y_j^p\right)\right\}$$

(8)

Because the same frontier is referenced in each period, one Malmquist index is computed.

$$M_g\left(x^{t+1},y^{t+1},x^t,y^t\right)={\displaystyle \frac{E^g\left(x^{t+1},y^{t+1}\right)}{E^g\left(x^t,y^t\right)}}$$

(9)

Although the adjacent two periods refer to the same global frontier when calculating the Malmquist index, the efficiency changes still use their respective frontiers:

$$EC={\displaystyle \frac{E^{t+1}\left(x^{t+1},y^{t+1}\right)}{E^t\left(x^t,y^t\right)}}$$

(10)

The degree of closeness between frontier t + 1 and the global frontier can be represented by ${\displaystyle \frac{E^g\left(x^{t+1},y^{t+1}\right)}{E^{t+1}\left(x^{t+1},y^{t+1}\right)}}$; the larger the ratio is, the closer frontier t+1 is to the global frontier. The degree of closeness between frontier t and the global frontier can be represented by ${\displaystyle \frac{E^g\left(x^t,y^t\right)}{E^t\left(x^t,y^t\right)}}$; the larger the ratio is, the closer frontier t is to the global frontier. The changes between frontier t + 1 and frontier t can be represented by the ratio of the two ratios.

$$T{C}_g={\displaystyle \frac{E^g\left(x^{t+1},y^{t+1}\right)}{E^{t+1}\left(x^{t+1},y^{t+1}\right)}}{\displaystyle \frac{E^t\left(x^t,y^t\right)}{E^g\left(x^t,y^t\right)}}$$

(11)

The Malmquist index can be decomposed into technical efficiency (EC) and technical progress (TC):

$$\begin{array}{ll}{M}_g\left(x^{t+1},y^{t+1},x^t,y^t\right)& ={\displaystyle \frac{E^g\left(x^{t+1},y^{t+1}\right)}{E^g\left(x^t,y^t\right)}}\\ & =EC\times T{C}_g\end{array}$$

(12)

3.3. Analysis of Spatial Autocorrelation

3.3.1. Global Moran Index

Global Moran’s I (range: [−1, 1]) quantifies spatial clustering, with positive/negative values indicating correlation/dispersion. The formula is calculated as follows:

$${\mathrm{Moran}’\mathrm{s} \mathrm{I}}_{\mathrm{G}}={\displaystyle \frac{1}{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{W}}_{\mathrm{ij}}}}}}\times {\displaystyle \frac{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{W}}_{\mathrm{ij}}}}\left({\mathrm{x}}_{\mathrm{i}}- \overline{\mathrm{x}}\right)\left({\mathrm{x}}_{\mathrm{j}}- \overline{\mathrm{x}}\right)}{{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}}- \overline{\mathrm{x}}\right)}^2}/\mathrm{n}}}$$

(13)

This comprises the spatial weight matrix, regional sample values for i and j, and the total region count.

3.3.2. Local Moreland Index

Local spatial autocorrelation is typically illustrated through the use of Moran scatter plots [38]. A Moran’s I value exceeding zero indicates a propensity for similar units in proximity to cluster together, whereas a value below zero suggests a tendency for them to disperse. A value of zero signifies a random distribution of the units in question [39]. The formula for calculating this measure is provided below.

$${\mathrm{Moran}’\mathrm{s} \mathrm{I}}_{\mathrm{L}}={\displaystyle \frac{\left({\mathrm{x}}_{\mathrm{i}}- \overline{\mathrm{x}}\right){\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{ij}}}\left({\mathrm{x}}_{\mathrm{j}}- \overline{\mathrm{x}}\right)}{{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}}- \overline{\mathrm{x}}\right)}^2}/\mathrm{n}}}$$

(14)

The Moran scatter plot is divided into four quadrants, each illustrating distinct forms of spatial autocorrelation. The first quadrant (H-H) and the third quadrant (L-L) signify areas of high and low values, respectively, that are surrounded by similar values, thereby indicating a positive correlation. The second quadrant (L-H) and fourth quadrant (H-L) display low and high values surrounded by opposite values, indicating a negative correlation [40].

4. Variables and Data Description

Drawing from the relevant literature and the theoretical framework of the “energy economy environment”, this study identifies energy consumption, fixed assets, and labor force as the input variables, with regional GDP designated as the expected output variable. Additionally, carbon dioxide emissions are considered as an unintended output. The specific indicators are detailed in

Table 2. LCEE index system.

Index Level	Representational Index
Input	Number of employees at the end of the year
	Capital stock
	Total energy consumption
Expected output	Gross regional product
Undesirable output	Carbon dioxide

.

The selection of variables in this study is based on the following rationale: (1) GDP serves as the expected output since the pursuit of a low-carbon economy aims to achieve optimal economic benefits with minimal input factors while reducing carbon emissions and energy consumption. (2) Carbon dioxide emissions are treated as the undesirable output because low-carbon economic efficiency originates from sustainable development principles that require simultaneous GDP growth and greenhouse gas reduction, with CO₂ being selected due to its significant policy attention and data availability among greenhouse gases. (3) Following the Solow growth model (Y=F (K, AL)), labor input is represented by year-end employment figures, as standardized labor intensity data are unavailable for China. (4) Capital stock is used as the capital investment indicator. (5) Energy is the fundamental production factor for economic growth. In classical production functions such as the Cobb–Douglas model, energy, labor, and capital jointly determine the level of output. The research on low-carbon economic efficiency needs to include energy input to reflect the real production costs.

To analyze LCEE and its characteristics in 30 provinces (The raw data can be found in Appendix A), this study collected and organized panel data from 2010 to 2021 for the 30 provincial regions. The descriptive statistics, which include a total of five indicators, are presented in

Table 3. Descriptive statistics of variables for 2010–2021.

	Variable	Mean Value	Standard Deviation	Maximum Value	Minimum Value
Input index	Number of employees	25.654	16.337	70.720	2.770
	Capital stock	6.748	4.807	23.973	0.307
	Energy consumption	105.030	62.271	335.206	11.488
Expected output	Gross regional product	2.381	1.912	10.022	0.135
Undesirable output	Carbon dioxide emissions	3.371	2.182	9.472	0.289

.

(1)

Labor input: Labor input is represented by the number of employees per unit at the end of the year. The data is sourced from the Statistical Yearbooks of Chinese Provinces from 2010 to 2021.

(2)

Capital investment: Capital stock is considered a capital input. Due to the absence of specific data in the statistical yearbooks, this research utilizes the perpetual inventory method to estimate capital stock across 30 provinces in China. A depreciation rate of 9.6% is applied to the capital. Furthermore, the “investment goods price index” is replaced by the fixed capital investment price index, and the total investment in fixed assets by society is treated as the annual aggregate of fixed asset investments. To ensure data integrity, the total fixed asset investment figures for all years are standardized, using 2010 as the base year for comparison. The data is sourced from provincial Statistical Yearbooks (2010–2021) and individual provinces’ Annual Statistical Yearbooks.

(3)

Energy consumption: Total energy expenditure at the prefectural city level serves as the metric for energy consumption assessment. According to the National Eleventh Five-Year Plan outline, the energy usage per GDP unit is an essential indicator for evaluating energy efficiency. It can be utilized to compare energy consumption levels among different cities. The data from 2000 to 2019 is sourced from the China Energy Statistical Yearbook. After 2020, the data energy yearbook was updated, and some provinces and cities did not disclose their total energy consumption, which was calculated using Formula (15). The data in the formula comes from the Annual Statistical Yearbook of each province from 2010 to 2021.

Total energy consumption = energy consumption per unit of GDP × regional GDP

(15)

(4)

Expected output: The regional gross domestic product (GDP) is utilized as a measure of expected output. This metric reflects the economic benefits derived from the economic activities of resident units within a region, accounting for the contributions of energy, labor, capital, and environmental pollution to economic value. To ensure consistency with the capital stock measurement, the GDP is adjusted to reflect constant prices, using 2010 as the base year. GDP data comes from the China Statistical Yearbook (2010–2021).

(5)

Undesirable output: Undesirable output is expressed in terms of carbon dioxide emissions. Carbon dioxide emissions data for the 30 provinces are derived from the CEADS database, with the carbon emission inventory consistently computed by the CEADS team [41,42].

Utilizing the aforementioned methodology and dataset, the empirical research section of this article aims to analyze the LCEE in 30 provinces of China. In particular, the practical procedure is depicted in Figure 1.

5. Efficiency Analysis of Low-Carbon Economy in China

5.1. Efficiency Measurement of Low-Carbon Economy in China

Based on the construction of a non-radial MEA model considering unexpected outputs, a global frontier plan is established. This article uses the planning and solving module in Office and the Excel Solver tool to solve data problems. The results of measuring the LCEE of 30 provincial-level administrative regions are presented in Figure 2.

The average LCEE across the 30 provinces of China is recorded at 0.631. An analysis of the period from 2010 to 2021 reveals a U-shaped trajectory in efficiency, characterized by an initial decline followed by a subsequent increase. Specifically, efficiency experienced a gradual decrease from 2010 to 2016, coinciding with a resurgence of large-scale industrial activities following the Olympic Games, which resulted in heightened industrial emissions and carbon dioxide output. Notably, LCEE peaked between 2010 and 2011, a period marked by China’s rapid economic recovery from the global financial crisis, bolstered by the implementation of a two-year “four trillion yuan” economic stimulus plan that yielded favorable outcomes [43]. However, from 2011 to 2015, efficiency began to decline, reaching a nadir as the Chinese economy shifted towards altered growth paradigms, resulting in a significant deceleration of the annual real GDP growth rate. The decline persisted from 2015 to 2016, during which the level of technological advancement fell short of the optimal output associated with economies of scale. The low capacity for technology transformation and absorption has not fully utilized the green growth potential driven by the scale effect of technology, resulting in low LCEE. It was not until 2016 that carbon dioxide emissions began to rise gradually, a trend attributed to the implementation of stricter environmental regulations and enhanced oversight, which have effectively reduced CO₂ emissions through the promotion of energy efficiency and pollution control initiatives [44].

From a regional perspective (Figure 3), a comparison is made between the eastern, central, and western parts of China. From 2010 to 2017, the average LCEE in China showed a decreasing trend from east to west, with the eastern region above the national average and the central and western regions below it. Comparing the trends of LCEE in the three major regions, it can be observed that the overall trend in the eastern region is similar to those in the central and western regions, all of which closely follow the changes in the national average LCEE, generally presenting a “U” shape [45].

LCEE varies significantly across provinces, ranging from 0.478 to 0.9, which highlights the considerable disparities in development levels among them. The distribution of LCEE resembles an olive shape, characterized by a narrower range at both ends and a broader central segment. The top five provinces exhibit high LCEE values and have achieved the effective frontier, suggesting that they have successfully balanced resource conservation and environmental protection within their economic development strategies, comprehensively accounting for both resource and environmental factors [17]. Conversely, among the 26 provinces and cities with low LCEE, 6, including Tianjin, report values exceeding the national average. This indicates that while their green economic development aligns with the principles of ecological civilization, there remains a lack of adequate investment in harmonizing economic growth with environmental sustainability. The remaining 19 provinces and cities demonstrate relatively low LCEE performance. To improve LCEE, it is imperative to enhance investments in resource utilization, environmental pollution management, and industrial restructuring [46].

5.2. Dynamic Evolution and Driving Mechanism Analysis of LCEE

The examination of the progressive changes in LCEE can assist in recognizing the developmental patterns and influential factors affecting efficiency across the 30 provinces. The global Malmquist index can be decomposed into efficiency change (EC) and technology change (TC). The underlying factors that influence shifts in LCEE are examined through an analysis of intrinsic driving forces. When the GM is less than 1, it indicates a downward trend in LCEE during that stage. When the GM index exceeds a value of 1, it indicates an upward trend in LCEE during that time. A higher GM index value indicates a more rapid rise in LCEE during that period [47].

Between 2010 and 2021, an analysis of the GM index of LCEE across 30 provinces in China reveals that over half of these provinces exhibited a general improvement in efficiency. The period from 2020 to 2021 marked the most pronounced increase in efficiency among the 30 provinces. The GM index recorded values consistently below 1 from 2011 to 2016, signifying a substantial decline in efficiency. Conversely, from 2016 to 2021, the index demonstrated a positive upward trajectory.

Figure 4 demonstrates that both the GM and TC indices generally show rising trends with fluctuations, whereas the TC index alone displays a variable pattern. EC and TC exhibited a reverse trend from 2014 to 2018, whereas GM demonstrated an increasing pattern. From 2018 to 2021, EC and TC displayed co-directional changes, but the GM index showed an overall downward trend.

Due to the varying development statuses of different provinces and cities, their heterogeneity is analyzed at the provincial level, and the results are illustrated in Table 3. An examination of the GM index from 2010 to 2021 revealed that the GM indexes for 30 provinces and cities could be categorized into two groups: those exceeding 1 and those falling below 1. Of the overall sample, 60% exhibited a GM index greater than 1. Among these, 11 provinces, including Inner Mongolia and Ningxia, reported an EC of less than 1, indicating that these regions rely exclusively on TC to enhance total factor productivity. As a result, the primary objective for these urban areas in the forthcoming years will be to improve technological efficiency in order to boost overall productivity. Conversely, all provinces with a GM index below 1 are influenced by both EC and TC and have experienced a decline in their GM index. These provinces represent critical areas for future environmental enhancements. It is essential to recognize TC and efficiency improvements as dual drivers for enhancing total factor efficiency, and efforts to promote these aspects should be undertaken concurrently.

The decomposition of the global Malmquist index provides predictive insights into future LCEE trends. Provinces with persistent technological progress (TC > 1) (e.g., Shanghai, Jiangsu, Shandong in

Table 4. GM index and its breakdown for 30 Chinese provinces from 2010 to 2021.

Serial Number	Province	GM	EC	TC	Overall Trend
1	Beijing	1.011	1.000	1.011	Rising
2	Tianjin	1.057	1.017	1.043	Rising
3	Hebei	0.999	0.989	1.012	Descending
4	Shanxi	1.012	1.018	0.994	Rising
5	Inner Mongolia	1.031	0.997	1.034	Rising
6	Liaoning	1.030	1.004	1.027	Rising
7	Jilin	1.023	1.027	0.998	Rising
8	Heilongjiang	0.994	0.985	1.012	Descending
9	Shanghai	1.035	1.000	1.035	Rising
10	Jiangsu	1.012	0.993	1.019	Rising
11	Zhejiang	0.995	0.986	1.017	Descending
12	Anhui	0.998	0.989	1.010	Descending
13	Fujian	0.984	0.982	1.003	Descending
14	Jiangxi	1.015	0.993	1.026	Rising
15	Shandong	1.024	0.997	1.035	Rising
16	Henan	1.013	0.994	1.021	Rising
17	Hubei	0.988	0.989	0.998	Descending
18	Hunan	1.004	0.999	1.006	Rising
19	Guangdong	0.969	0.966	1.007	Descending
20	Guangxi	1.013	0.997	1.017	Rising
21	Hainan	0.991	0.982	1.010	Descending
22	Chongqing	1.006	1.001	1.006	Rising
23	Sichuan	1.005	0.999	1.007	Rising
24	Guizhou	0.971	0.970	1.005	Descending
25	Yunnan	0.992	0.987	1.005	Descending
26	Shanxi	1.014	0.996	1.021	Rising
27	Gansu	1.016	0.988	1.031	Rising
28	Qinghai	0.973	0.976	0.996	Descending
29	Ningxia	1.028	0.997	1.030	Rising
30	Xinjiang	0.975	1.001	0.988	Descending
	Mean value	1.006	0.994	1.014	Rising

) are likely to maintain LCEE growth, as their productivity gains are driven by innovation rather than temporary efficiency adjustments. Conversely, provinces with EC < 1 (e.g., Inner Mongolia, Ningxia) face structural inefficiencies in resource allocation, implying that without institutional reforms (e.g., carbon pricing, industrial upgrading), their LCEE may stagnate.

5.3. Improvement Potential and Path Analysis

Further exploration of the reasons for the differences, including the sources of inefficiency and variations in efficiency models, as well as an analysis of potential production improvements, can lead to more effective policy recommendations. Therefore, based on Formulas (5)–(7), a total of 1800 efficiency values were calculated for five variables shown in

Table 5. Efficiency value of each variable in 30 provincial regions of China.

Province	Employment MEA Efficiency Value	Energy Consumption MEA Efficiency Value	MEA Efficiency Value of Capital Stock	GDP-MEA Efficiency Value	CO2 MEA Efficiency Value	Combined MEA Efficiency Value
Beijing	0.940	0.981	0.956	0.989	0.821	0.893
Tianjin	0.925	0.946	0.952	0.809	0.510	0.720
Hebei	1.000	1.000	1.000	0.665	0.365	0.637
Shanxi	0.886	0.936	0.955	0.659	0.236	0.571
Inner Mongolia	0.984	0.972	0.980	0.717	0.152	0.594
Liaoning	0.557	0.672	0.748	0.901	0.170	0.536
Jilin	0.619	0.684	0.818	0.793	0.267	0.527
Heilongjiang	0.754	0.880	0.872	0.830	0.326	0.618
Shanghai	1.000	1.000	1.000	0.989	0.723	0.883
Jiangsu	1.000	1.000	1.000	0.811	0.407	0.707
Zhejiang	1.000	1.000	1.000	0.856	0.525	0.757
Anhui	0.784	0.933	0.955	0.817	0.518	0.687
Fujian	0.931	0.966	0.959	0.834	0.510	0.723
Jiangxi	0.649	0.878	0.876	0.946	0.309	0.638
Shandong	0.779	0.903	0.888	0.880	0.288	0.637
Henan	0.525	0.705	0.825	0.903	0.259	0.558
Hubei	0.637	0.811	0.788	0.955	0.347	0.626
Hunan	0.570	0.789	0.754	1.000	0.257	0.600
Guangdong	0.980	0.994	0.980	0.974	0.801	0.900
Guangxi	0.351	0.537	0.714	1.000	0.196	0.514
Hainan	0.472	0.696	0.685	1.000	0.260	0.563
Chongqing	0.587	0.813	0.731	1.000	0.314	0.615
Sichuan	0.597	0.827	0.740	1.000	0.263	0.609
Guizhou	0.595	0.766	0.851	0.927	0.227	0.587
Yunnan	0.333	0.568	0.666	1.000	0.204	0.510
Shanxi	0.503	0.698	0.808	0.934	0.196	0.550
Gansu	0.554	0.799	0.797	0.922	0.325	0.597
Qinghai	0.389	0.504	0.483	0.989	0.181	0.478
Ningxia	0.780	0.757	0.820	0.798	0.127	0.533
Xinjiang	0.784	0.861	0.893	0.759	0.220	0.573

, including input, expected output, and unexpected output, in 30 provinces from 2010 to 2021.

5.3.1. Analysis of the Average Efficiency of Provincial MEA and Its Improvement Approach

A study was carried out on the mean efficiency values of provinces from 2010 to 2021. Since this article primarily examines LCEE, it emphasizes choosing energy consumption MEA efficiency metrics and carbon dioxide MEA efficiency metrics to evaluate the possible enhancement of overall MEA efficiency in various provinces.

Energy consumption MEA efficiency is 1 when a province’s overall MEA efficiency is low in terms of energy input, but GDP-MEA efficiency and carbon dioxide MEA efficiency are both less than 1. This indicates that the provinces and cities are demonstrating productivity levels that fall short of expectations in their overall performance, alongside an excessive generation of unexpected outputs relative to the current technological capabilities. The potential for enhancement in output, particularly in terms of unexpected outputs, surpasses that for input improvements, resulting in suboptimal overall output. Provinces such as Hebei and Shanghai are identified as key areas where future strategies to improve overall MEA efficiency should focus on reducing unexpected outputs. This will require advancements in production processes, the upgrading of industrial technologies, and an increase in expected output, all while maintaining a constant level of overall energy consumption within these urban areas. Conversely, other provinces and cities are characterized by excessive energy input, a surplus of unexpected output, and a deficiency in expected output.

5.3.2. Improvement Potential Analysis

This section presents the energy MEA efficiency, labor MEA efficiency, capital MEA efficiency, GDP MEA efficiency, and carbon dioxide MEA emission efficiency for the year 2021. The efficiency values provided are not absolute measures; rather, they are relative efficiency values derived from a common frontier established using 30 provinces as evaluation units. These values do not reflect actual efficiency but rather indicate the ratio of distance to the frontier under specific technical conditions, thereby highlighting potential areas for enhancement and outlining a pathway for future progress. The overall efficiency scores for MEA in Beijing, Tianjin, and Shanghai are each recorded as 1, signifying the effectiveness of MEA in these regions. The efficiency output of GDP MEA in 14 provinces, including Hebei and Fujian, is insufficient, leaving room for improvement. Other provinces and cities have redundant inputs and insufficient output.

From the standpoint of input–output factors, the provinces of Hubei, Guangdong, and Sichuan demonstrate the highest levels of inefficiency in total energy consumption. The regions experiencing significant capital investment waste are identified as Yunnan, Hubei, and Guangxi. Additionally, the cities exhibiting the most pronounced redundancy in labor input include Jincheng, Sichuan, Yunnan, and Hubei. In summary, the total surplus in energy consumption is the most substantial, followed by comparatively lower levels of capital investment and labor waste. Hubei Province emerges as the area with the most severe waste of input factors. Regarding unexpected output factors, the provinces and cities with carbon dioxide emissions exceeding 50% are Beijing, Tianjin, Shanghai, and Anhui.

According to the analysis of the input–output capacity in 2021, Beijing, Tianjin, and Shanghai have emerged as the leading regions among the 30 provinces studied from 2010 to 2021, showing no further potential for improvement. However, this does not imply that these three cities are devoid of the need for improvement or that all resources have been utilized at their maximum efficiency. Over time, as technological advancements progress and production boundaries expand, new opportunities for enhancement will arise, facilitating the achievement of an optimal input–output ratio. As illustrated in Figure 5 and Figure 6, the primary factor contributing to the low efficiency observed is the inadequate performance of the unforeseen output MEA in various other cities.

Through the analysis of input–output potential, specific directions for enhancing input–output efficiency have been identified. This information is advantageous for decision-makers, as it elucidates the potential improvements in input factors, their respective proportions, and the degree of inefficiency associated with each factor. Key areas for enhancement include minimizing waste in resource inputs, maximizing effective outputs, and reducing carbon dioxide emissions. It is important to emphasize that the aforementioned analysis, which focuses on reducing inputs, increasing expected outputs, and minimizing unexpected outputs, serves primarily to identify the causes of low efficiency and to highlight potential avenues for improvement. However, it does not reflect actual adjustments in input and output, as it represents an optimal state within a mathematical model. In practice, adjustments are constrained by existing technological conditions, making it impractical to modify one or more factors in isolation to achieve optimal outcomes. Consequently, the potential for improvement is fundamentally linked to enhancing the technological and managerial capabilities associated with ineffective factors, thereby reducing the potential for improvement in these areas. Provinces exhibiting low efficiency can be benchmarked against those with optimal efficiency, facilitating the enhancement of their technical and managerial standards and progressively narrowing the efficiency gap. This approach ultimately aims to achieve improvements in relative efficiency.

6. Spatial Analysis of Efficiency of Low-Carbon Economy in China

6.1. Spatial Autocorrelation Analysis

6.1.1. Global Autocorrelation Analysis

Further exploring the spatial correlation of LCEE in 30 provinces, the study applies Moran’s I to perform a comprehensive assessment of spatial autocorrelation. The findings are presented in

Table 6. Global Moran’s I for LCEE.

Year	Global Moran’s I	E(I)	sd(I)	z	p-Value
2010	0.069	−0.034	0.049	2.088	0.037
2011	0.074	−0.034	0.05	2.192	0.028
2012	0.082	−0.034	0.05	2.339	0.019
2013	0.168	−0.034	0.049	4.112	0.000
2014	0.166	−0.034	0.049	4.082	0.000
2015	0.187	−0.034	0.048	4.600	0.000
2016	0.153	−0.034	0.048	3.925	0.000
2017	0.199	−0.034	0.05	4.674	0.000
2018	0.212	−0.034	0.05	4.922	0.000
2019	0.217	−0.034	0.049	5.176	0.000
2020	0.217	−0.034	0.049	5.113	0.000
2021	0.223	−0.034	0.048	5.321	0.000

.

The LCEE has exhibited notable clustering characteristics, transitioning from an initially irregular distribution to a more pronounced clustering pattern. Between 2010 and 2012, Moran’s I statistic achieved a significance level of 5%, while from 2013 to 2021, it attained a significance level of 1%, thereby indicating a robust positive spatial correlation [48]. Furthermore, the Moran index demonstrated an increase from 0.069 in 2010 to 0.223 in 2021, reflecting a distinct upward trend that signifies a rapid agglomeration of LCEE across provinces.

6.1.2. Local Autocorrelation Analysis

To delve deeper into the local spatial features of LCEE in 30 provinces of China, this study employed Stata17 software to generate Moran scatter plots illustrating LCEE for 2010, 2014, 2017, and 2021, as shown in Figure 7. These plots can offer a more precise depiction of the trends and evolutionary characteristics of spatial agglomeration. The data from 2010 indicates that the majority of provinces display (L-L) and (H-L) distribution patterns, as illustrated in the accompanying graph. The disparity in spatial correlation between provinces exhibiting negative and positive spatial correlations in that year is minimal. The overall level of dispersion among the 30 provinces experienced a significant increase in both 2014 and 2021, indicating a transition from (L-L) and (H-L) clusters to (H-H) and (L-L) clusters. The local Moran scatter plot from 2010 to 2021 illustrates a clear trend of clustering among the 30 provinces, highlighting a positive spatial correlation and a propensity for the formation of (H-H) and (L-L) distributions.

The findings suggest that the LCEE values of many provinces are approaching those of neighboring provinces, and the local spatial differences are decreasing. In 2021, provinces situated in the first quadrant, including Beijing, Tianjin, and Inner Mongolia, demonstrate a clustering of high LCEE (H-H). Conversely, in the third quadrant, areas such as Shanxi, Jilin, Heilongjiang, and Henan display limited radiative driving effects on development, reflecting a clustering of low LCEE (L-L) and a pronounced imbalance between economic growth and environmental sustainability. Consequently, a transformation and development strategy is essential.

6.2. Examination of Spatial Distribution Traits

6.2.1. Spatial Evolution of Interprovincial MEA Efficiency

The spatial distribution maps of MEA efficiency in provinces in 2010, 2014, 2017, and 2021 were plotted using ArcGIS 10.8, as shown in Figure 8, which more intuitively expresses the non-equilibrium of spatial distribution and displays the spatial evolution process.

Between 2010 and 2021, the differences in MEA efficiency among provinces progressively diminished, with a notable shift from the western and eastern regions towards the central region. As there has been an increasing focus on green development in the central and eastern areas, the relative advantages of the western region have correspondingly diminished.

Overall, the MEA efficiency of Xinjiang and Guizhou declined from relatively high levels in 2010 to relatively low levels in 2021, with significant fluctuations in green economic efficiency, indicating decreasing coordination between economic development and environmental sustainability. In contrast, other provinces experienced varying degrees of efficiency fluctuations. From 2010 to 2014, MEA efficiency generally declined across most provinces. However, between 2014 and 2017, many regions—particularly in central China—showed significant improvements. Spatially, MEA efficiency remained relatively high in the Beijing–Tianjin region and southern coastal provinces. Central China, including Henan, Shaanxi, Hubei, and Hunan, formed a medium-efficiency zone, while western regions such as Xinjiang, Qinghai, and Yunnan exhibited persistently low efficiency. The low MEA efficiency in these provinces may be attributed to multiple factors, including inefficient energy utilization, heavy industrial structures, suboptimal energy consumption patterns, insufficient technological innovation, weak environmental policy enforcement, and regional development imbalances. Many underperforming provinces also rank in the lower–middle tier economically and demonstrate poor efficiency.

6.2.2. Spatial Evolution of GDP-MEA Efficiency

The spatial distribution map of GDP-MEA efficiency was plotted using ArcGIS 10.8, as shown in Figure 9, which more intuitively expresses the spatial evolution and trend of GDP-MEA efficiency in 30 provinces of China in 2010, 2014, 2017, and 2021.

In 2010, sixteen provinces and municipalities in China attained a GDP-MEA efficiency score of 1, categorizing them as GDP-MEA efficient regions. Comparative analysis indicates that Ningxia, Inner Mongolia, and Shanxi exhibit comparatively low GDP-MEA efficiency, which may be attributed to their industrial structures that are predominantly traditional or resource-based. This reliance on conventional industries correlates with a diminished presence of green and high-tech sectors, resulting in suboptimal resource utilization and inadequate responses to environmental pollution challenges. By 2014, Xinjiang and Guizhou had transitioned from being classified as GDP-MEA efficient provinces to relatively inefficient ones. Additionally, six provinces, including Gansu and Liaoning, experienced notable declines in efficiency, while Qinghai and Heilongjiang improved their standings to become GDP-MEA efficient. The year 2017 marked a gradual increase in the number of provinces achieving GDP-MEA efficiency, with significant improvements noted in Inner Mongolia, Gansu, Guizhou, and Anhui, culminating in a total of nineteen provinces recognized as GDP-MEA efficient by that year.

However, Jilin and Shanxi continued to demonstrate low GDP-MEA efficiency, potentially due to limited technological innovation and a lower proportion of clean energy utilization. In 2021, a decline in GDP-MEA efficiency was observed across numerous provinces and municipalities. Central provinces such as Shaanxi, Shanxi, and Henan shifted from high efficiency to a medium-efficiency classification. The period from 2017 to 2021 revealed an overall downward trend in GDP-MEA efficiency, accompanied by pronounced regional disparities. Provinces like Shanxi, Hebei, and Zhejiang maintained persistently low efficiency levels, likely due to insufficient enforcement of environmental regulations, which has led to ineffective pollution control measures. This situation may result in excessive resource consumption and severe environmental degradation, thereby hindering advancements in LCEE. Conversely, provinces such as Sichuan, Hunan, and Chongqing consistently ranked among the highest in GDP-MEA efficiency, indicating a more rational energy consumption structure characterized by a significant reliance on clean energy and a relatively advanced state of green technology research and application.

6.2.3. Spatial Evolution of CO₂ MEA Efficiency

A spatial distribution map of carbon dioxide emission efficiency (CO₂-MEA efficiency) was created using ArcGIS10.8, as shown in Figure 10, to visually represent the spatial evolution and trends of CO₂-MEA efficiency in 30 provinces of China.

The trend observed from northwest to southeast suggests that provinces and cities in the southeastern region are increasingly prioritizing low-carbon development initiatives. In 2010, Guangdong and Fujian were identified as provinces exhibiting high carbon dioxide MEA efficiency, while Beijing, Zhejiang, Heilongjiang, and six additional provinces and cities also demonstrated relatively high levels of carbon dioxide MEA efficiency. These regions emphasize energy efficiency and the utilization of clean energy sources, reflecting more rational industrial and energy structures. Carbon dioxide emissions in these areas primarily stem from industrial production and energy consumption, whereas many provinces characterized by lower carbon dioxide emissions are often dominated by heavy industries. This industrial focus contributes to elevated energy consumption and emissions, resulting in higher carbon dioxide emissions and diminished MEA efficiency.

In 2014, Beijing and Shanghai emerged as the municipalities exhibiting the highest efficiency in carbon dioxide MEA. Conversely, the carbon dioxide MEA efficiency in eight provinces and municipalities, including Qinghai, Heilongjiang, Fujian, and Yunnan, experienced a decline of one to two levels. In contrast, improvements in efficiency were noted in Xinjiang, Gansu, and Guizhou. In 2017, there was a general decrease in the carbon dioxide MEA efficiency across all provinces in China. However, from 2017 to 2021, a notable upward trend in overall carbon dioxide MEA efficiency was observed, with Beijing, Tianjin, and Shanghai maintaining higher levels of efficiency. The development status of provinces such as Gansu, Henan, and Shaanxi has also seen enhancements. Nevertheless, regions such as Inner Mongolia, Xinjiang, and Guizhou continue to exhibit relatively low carbon dioxide MEA efficiency. This situation may be attributed to several factors, including delayed transitions in the energy system, prevailing industrial structures, widespread economic growth models, and a lack of sufficient environmental awareness and proactive measures.

6.3. Regional Heterogeneity Analysis

The analysis presented in the preceding chapters indicates that, in 2021, the spatial distribution of provincial MEA efficiency and unexpected output MEA efficiency values, specifically concerning carbon dioxide MEA efficiency, exhibited notable consistency. These efficiency values were primarily concentrated in the northern and southeastern regions of China, with particular emphasis on the areas surrounding Beijing and Tianjin. Over the course of the study, these regions have demonstrated a progressive enhancement in their MEA efficiency values. The disparities in unexpected output MEA efficiency values across various provinces can be attributed to differing technological levels, as determined by MEA principles. The potential for improvement is guided by an optimal direction vector based on a singular indicator, which evolves in accordance with technological boundaries. Consequently, the efficiency values of provinces vary over time, leading to distinct spatial distribution characteristics across different periods.

In 2021, the regions of Beijing, Shanghai, and Guangzhou demonstrated the highest levels of MEA efficiency, a phenomenon likely linked to their sophisticated technological infrastructure, strong economic growth, efficient resource management, and proactive engagement in the research and implementation of low-carbon technologies, as well as the enforcement of low-carbon policies. These provinces have positioned themselves as frontrunners in the establishment of zones with low-carbon development advantages, resulting in continuous improvements in environmental efficiency. This advancement is supported by the integration of cutting-edge clean technologies and the enhancement of carbon market mechanisms, which together facilitate energy utilization efficiency approaching the production possibility frontier. Furthermore, the growth of modern service sectors and strategically emerging industries has markedly decreased carbon emission intensity per unit of GDP.

In contrast, provinces such as Hubei, Henan, and Shaanxi, which are characterized by relatively low economic levels and small scales of industrial production, have undergone shorter cycles of industrial structural adjustment, resulting in favorable outcomes. Conversely, the low-carbon transformation in central and western provinces exhibits distinct characteristics. For example, Hubei and Henan have actively engaged in the new energy sector, achieving significant progress in the low-carbon restructuring of their industrial frameworks. However, provinces with lower Multi-Factor Efficiency (MEA), such as Shanxi, Hebei, and Guizhou, are facing considerable challenges in transitioning from traditional high-carbon industries. Their energy structures, which are heavily dependent on coal and the heavy chemical industry, pose substantial obstacles to low-carbon development. This regional heterogeneity fundamentally reflects the structural contradictions inherent in China’s low-carbon economic transformation process. Advanced regions have advanced to an innovation-driven low-carbon development stage, while less developed areas remain trapped in resource-dependent development models.

7. Conclusions and Policy Implications

7.1. Main Conclusions

Over the last ten years, China has shifted from rapid expansion to focusing on improving the quality of development, with the advancement of LCEE becoming a key catalyst in this evolution. Analyzing the LCEE data from 30 Chinese provinces between 2010 and 2021 leads to the following conclusions:

1. Over the duration of the study, the LCEE of China exhibited a roughly U-shaped trend of “first decreasing, then increasing”. The national LCEE decreased from 0.64 (2010) to 0.605 (2016) and then recovered to 0.668 (2021). The initial drop reflected energy-intensive industrial expansion during rapid urbanization, while post-2016 improvement stemmed from environmental policies like the “Ten Measures for Air Quality” and clean energy adoption, yielding 4% efficiency gains. Beijing, Shanghai, and Guangdong emerged as leaders (average efficiency > 0.85), while Qinghai, Guangxi, and Yunnan showed the lowest performance. There is still great potential to improve China’s overall LCEE.

2. There are regional disparities in the LCEE of China. Despite an overall enhancement in LCEE, substantial differences persist among provinces. LCEE exhibits a gradual decline from the eastern to western regions, with the eastern region demonstrating a higher level of efficiency relative to the other two regions. Specifically, the average LCEE in the eastern coastal provinces, such as Beijing and Shanghai, exceeds 0.72, which is markedly higher than the averages of 0.6 in the central region and 0.57 in the western region, indicating pronounced regional differences. In the eastern region, advantageous geographic characteristics, a robust economy, and significant integration with the global community have facilitated its development. The central region exhibits a moderate level of efficiency. As industries have been relocated from the eastern region, these areas face the challenge of increasing resource and environmental pressures. Conversely, the western region demonstrates relatively low efficiency, attributed to its remote location and underdeveloped economic conditions.

3. The findings from the spatial analysis (refer to Table 6) indicate a notable presence of spatial autocorrelation in the provincial-level LCEE of China, as evidenced by the increase in the Global Moran’s I from 0.069 in 2010 to 0.223 in 2021. The LCEE gradually exhibits clear patterns of high–high clustering and low–low clustering, with significant spatial heterogeneity. Notably, regions exhibiting high efficiency are primarily concentrated in the Beijing–Tianjin–Hebei, Yangtze River Delta, and Pearl River Delta areas. These regions have effectively decoupled economic growth from carbon emissions, a process supported by rigorous environmental regulations and improvements in industrial practices, as depicted in Figure 9, where the GDP-MEA efficiency consistently surpasses 0.85. In contrast, regions with low efficiency are mainly located in western energy provinces, such as Ningxia and Xinjiang, which show a CO₂-MEA efficiency of less than 0.3 (refer to Figure 10), highlighting a pronounced carbon lock-in effect.

4. The decomposition of the global Malmquist index shows that technical efficiency (EC) remains below 1 in most years, while technical progress (TC) remains above 1 in most years, and technology is the main driving force for LCEE improvement. This pattern aligns with China’s phased policy interventions. For instance, the post-2013 acceleration in TC correlates with the implementation of the Air Pollution Prevention and Control Action Plan (2013), which enforced stricter emissions standards and incentivized clean technology adoption. Similarly, the “13th Five-Year Plan” (2016–2020) prioritized industrial upgrading and energy structure optimization, further amplifying TC’s role. However, the lagging EC values reflect systemic inefficiencies in resource allocation and regional disparities in policy execution, particularly in central and western provinces. These findings underscore that while exogenous policy shocks (e.g., carbon neutrality pledges) catalyze technological leaps, endogenous structural reforms are critical to translating innovation into sustained efficiency gains.

7.2. Policy Implications

• Strengthen regional coordinated development and optimize resource allocation. The findings of the experiment indicate that the LCEE in the coastal provinces of eastern China, including Beijing, Shanghai, and Guangdong, is markedly superior to that in the central and western regions. This disparity is particularly pronounced in the western provinces, such as Qinghai and Xinjiang, which exhibit lower efficiency levels. The observed regional variation can primarily be attributed to the unequal distribution of economic development, technological capabilities, and resource allocation. In light of the pronounced regional disparities, it is imperative for the central region to prioritize the establishment of a balance between fostering economic development and environmental protection while striving to create an LCE. Additionally, there is a need to promote the enhancement and modernization of industrial infrastructure. The western region must bolster policy support and attract further resources and funding to facilitate investments in green economic development. Meanwhile, coastal provinces that are already developed should concentrate on adjusting and optimizing their industrial structures, as well as increasing the research and application of green technologies in the pursuit of advancing an LCE. Furthermore, inland provinces should capitalize on their resource advantages to achieve significant progress in the development of a low-carbon economy [49].
• Promote technological innovation and improve technical efficiency. An analysis of the global Malmquist index decomposition reveals that EC is the primary constraint on the enhancement of low-carbon economic efficiency, whereas TC contributes positively to its advancement. Consequently, it is imperative that policy initiatives prioritize the promotion of green technology innovation, particularly in the central and western regions, where EC remains comparatively low. To optimize the advantages of local resources and identify opportunities for improving energy efficiency across various regions, it is imperative to prioritize technological innovation. The economic structure of China is significantly influenced by the distinctive contributions of its eastern, central, and western regions. The eastern region is at the forefront of technological innovation and is increasing investments in research and development of green technologies. The central region, characterized by its unique geographic location and resource abundance, serves as a crucial intermediary between the eastern and western regions. It can capitalize on its geographical position to facilitate the sustainable management of agricultural resources. Meanwhile, the western region, endowed with rich natural resources and extensive land, has the potential to actively advance the development of clean energy and green industries, enhance ecological protection and environmental governance, and improve the stability and functional services of its ecosystems.
• Promote interregional collaboration to enhance spatial spillover effects. From a spatial analysis perspective, LCEE exhibits distinct spatial distribution characteristics and significant clustering effects. To address these spatial disparities and leverage clustering effects, policymakers should adopt a multi-pronged approach. First, interregional collaboration should be strengthened to enhance spatial spillovers, such as promoting technology transfer from high-efficiency provinces to neighboring low-efficiency regions and expanding cross-provincial carbon trading mechanisms. Second, differentiated low-carbon policies should be implemented based on regional clustering characteristics—high-efficiency clusters should focus on maintaining technological leadership through green innovation, while low-efficiency clusters require targeted industrial restructuring and energy transition strategies to break the “low–low” lock-in effect. Finally, spatial planning should be integrated into national low-carbon strategies, optimizing infrastructure investments and providing spatially targeted fiscal incentives to support lagging regions. By leveraging these spatial dynamics, China can achieve more balanced and sustainable low-carbon development across all provinces.