Research on Energy Efficiency Evaluation of Provinces along the Belt and Road under Carbon Emission Constraints: Based on Super-Efficient SBM and Malmquist Index Model

Abstract

About 50% of China’s total energy consumption is generated by the Belt and Road regions, which mainly involves 18 provinces, municipalities, and autonomous regions. To complement each other, the focus on total factor energy efficiency in key regions cannot be ignored. This paper selects the key domestic areas of the Belt and Road as the research object, follows the research ideas of static measurement and dynamic decomposition, and considers the constraints of carbon emissions. The super-efficiency SBM model can measure the energy efficiency statically and include all factors of each province and city from 2015 to 2019, and the Malmquist productivity index model is able to decompose the variation in total factor energy efficiency. The research results show that (1) there are apparent differences in energy efficiency among the provinces along the Belt and Road for the average total factor energy efficiency of the 21st-Century Maritime Silk Road region is 1.03, which is significantly higher than that of the 12 provinces along the Silk Road Economic Belt; (2) from the perspective of time, the provinces along the Belt and Road’s total factor energy efficiency shows a fluctuating upward trend, which is deeply affected by technological progress; (3) from the perspective of index decomposition, the main reason for the low energy efficiency of the provinces in the Silk Road Economic Belt region is low technical efficiency, and the main factor supporting the improvement of the 21st-Century Maritime Silk Road region energy efficiency is technological progress.

1. Introduction

Facing the increasingly severe pressure of energy resource security and ecological environmental protection, changing the mode of economic development and further promoting energy conservation and energy efficiency improvement have become an important path to achieve economic decarbonization growth and promote high-quality development [1]. As the low-carbon economy increasingly becomes the inevitable trend of future economic development [2], coordinating the relationship among energy, carbon emission, and economic growth is the key to realize decarbonization growth and maintain sustainable development of economy [3]. Therefore in 2020, China had clearly advanced the goals and tasks of achieving carbon peaks by 2030 and carbon neutrality by 2060, which provided a stronger impetus to comprehensively and collaboratively promote the transformation of China’s production, lifestyle, and energy consumption, and further promote sustainable economic development. The key to sustainable economic development under the constraints of low-carbon resources is the efficient utilization of resources [4]. To this end, the implementation of control of energy consumption to reduce energy consumption intensity and comprehensively improve the energy utilization efficiency, as well as to effectively obtain control of the total amount of energy consumption is the key point for solving environmental problems and is also the key support for achieving goals as scheduled.

In order to achieve sustainable development of economy, China has introduced the proposal of the Belt and Road in 2013. The Belt and Road is the abbreviation of the Silk Road Economic Belt and the 21st-Century Maritime Silk Road. The proposal of the Belt and Road is aimed at promoting the joint development of all nations, achieve win–win cooperation, jointly build a community of interests and shared destiny, and build a community of responsibilities with economic integration and cultural inclusiveness. Through the joint construction of the Belt and Road, it not only promotes economic and social development of partner countries but also significantly improves the level of openness and the quality of economic development in the provinces along the route in China. How to break the development constraints caused by rigid energy demand and environmental pollution also has become an essential topic of the Belt and Road construction [5].

So, what is the current status of energy efficiency in the provinces along the Belt and Road under the constraints of carbon emissions? Under the background of energy saving and carbon reduction, how does this proposal plan to effectively improve the energy efficiency of these provinces along the Belt and Road to attain the concerted efforts of economic development and environment protection? To this end, it is necessary to evaluate the energy efficiency of the provinces objectively and accurately along the Belt and Road under the constraints of carbon emissions, which is of great significance to promoting the energy efficiency of the provinces along the Belt and Road.

2. Research Reviews

The concept of sustainable development was formally proposed in 1980. “The World Conservation Strategy” clearly states that it is necessary to study the fundamental relationships among natural, social, ecological, and economic resources, as well as the utilization of natural resources in order to ensure global sustainable development [6]. Sustainable development should follow the principles of fairness, continuity, and commonality [7]. With the increasingly severe challenges faced by the world’s energy supply, energy environment, energy allocation, and energy efficiency [8], the General Assembly of the United Nations adopted “the 2030 Agenda for Sustainable Development” in 2015, in which Goal 7 clearly stated that energy efficiency should be improved [9]. For China, it is imperative to improve energy efficiency. On one hand, research shows that carbon emissions are the main factor affecting China’s sustainable development [10,11], and there are significant differences in carbon emissions among provinces in China [12]. One of the best measures to reduce carbon emissions is to improve energy efficiency [13]. On the other hand, in order to achieve sustainable economic development, the rate of technological progress must be greater than the growth rate of social final output and consumption [14], because depletable energy will have a negative impact on sustainable economic development [15]. To reduce this negative impact, energy efficiency also needs to be improved.

For the past few years, scholars have performed numerous studies on energy efficiency and achieved many valuable results. For example, some scholars performed DEA decomposition based on provincial data and calculated energy efficiency under the condition of total factor productivity [16]; they also studied the energy efficiency of nearly 30 provinces in China through the DEA method [17]. Scholars also studied energy efficiency in 30 administrative regions of China from three aspects, which are comprehensive input, technical efficiency, and effective output, through the DEA method [18]. The DEA method modified by Bootstrap was used to evaluate the efficiency of energy in central, western, and eastern China and to analyze the differences in the efficiency between these regions [19]. A DEA model was constructed to study the level of energy efficiency in the western area of China [20]. The BCC and Malmquist models [21] measured the total factor energy efficiency of China and conducted a comparative analysis on the differences between coastal, northeastern, central, and western regions [22]. The BCC model measured and analyzed the total factor productivity of China’s coastal areas. The SBM model in the nonradial DEA model was used to study various provinces’ energy efficiency in China [23]. In addition, some scholars have studied energy efficiency under carbon emission constraints. For example, the super-efficiency VRS-DEA model was used to assess the total factor energy efficiency of China’s coastal areas under carbon emission constraints [24]. The super-efficiency SBM-DEA method [25] made a comparative analysis of energy efficiency in the two cases whether carbon emission constraint was included or not. The Malmquist–Luenberger index was used to study the total factor energy efficiency of agriculture under the constraint of carbon emissions in the eastern, western, and central regions of China [26]. The multimodel of DEA was used to obtain the overall situation of energy consumption efficiency in China’s provinces and cities and the differences in energy consumption efficiency between regions under environmental constraints [27].

Through the above systematic review of energy efficiency research, some deficiencies can be found. Firstly, in terms of research objects, the existing research is mostly based on a province or a specific area, such as the northwest, east, coast, and other regions, to measure energy efficiency, while the research on energy efficiency of provinces, which are included in the Belt and Road, is still insufficient. Secondly, from the perspective of research, most scholars’ research on energy efficiency does not consider the important factor of carbon emission constraints. Although some scholars have considered carbon emission constraints in energy efficiency research, most of them focus on static analysis (such as super-efficiency SBM model) or dynamic analysis (such as Malmquist index analysis), and there are still some weak points in studies combining dynamic analysis and static analysis.

Based on the above research status, using the backdrop of green emission reduction, this paper selects the provinces included in the Belt and Road as the object to be studied and use the super-efficiency SBM model of unexpected excess and the global reference Malmquist index decomposition method to measure and evaluate the energy efficiency of provinces included in the Belt and Road under carbon emission constraints.

3. Model Construction and Indicator Selection

3.1. Model Construction

The DEA method, which is called data envelopment analysis, has been extensively used in the research on the evaluation and calculation of the multi-output and multi-input efficiency for the same kind of decision-making unit, and it is constantly developing and improving. Traditional DEA models include CCR and BCC for radial distances. That is, the measure of efficiency allows all inputs to decrease in the same proportion or all outputs to increase in the same proportion [28]. However, when a nonzero slack exists in either input or output, the improvement of slack variables is not reflected in the measure of efficiency value. It may result in an efficiency value overestimation of the decision unit. To solve this problem, a nonradial SBM model was proposed under standard efficiency [29], which solves the problem of ignoring the slack variable in the evaluation process of efficiency by the abovementioned model. However, in the case that multiple decision-making units appearing at the same time are completely effective, the above three standard efficiency models cannot make further comparisons to these decision-making units. The super-efficient SBM model proposed by [30] solves this problem well and has been extensively used. In addition, different from the efficiency evaluation of the general standard model, the energy consumption efficiency evaluation of the provinces along the Belt and Road should consider not only the expected output, such as GDP, but also the unexpected output, which include environmental pollution factors, such as carbon emissions.

Due to the above factors, the authors of this paper studied the super-efficiency SBM model as well as the Malmquist productivity index model to analyze the panel data of energy input and output in 17 provinces included in the Belt and Road, which makes the static calculation results of energy efficiency more accurate. At the same time, it makes up for the shortage of the super-efficiency SBM model in the dynamic efficiency analysis of time series data. The model construction process is as follows.

3.1.1. Super-Efficient SBM Model Considering Undesired Output

As mentioned above in the actual production process, in addition to “good” outputs, such as GDP, there are often many “bad” outputs, such as pollutants and waste. To measure whether DMU is effective in the presence of undesired outputs, ref. [31] further improved SBM and proposed an SBM model with unexpected output. Drawing on its practice, this study used the super-efficiency-SBM model with undesired output, which combines the super-efficiency SBM model with the SBM model, including undesired output, to measure the energy efficiency of 17 provinces along the Belt and Road. Specifically, for each province, three vectors (input, expected output, and undesired output) are included, which are expressed as follows:

$$X=[x_1,\cdot \cdot \cdot ,x_n]\in R^{m\times n}>0$$

(1)

$$Y^g=[y_1^g,\cdot \cdot \cdot ,y_n^g]\in R^{s_1\times n}>0$$

(2)

$$Y^{\mathrm{b}}=[y_1^b,\cdot \cdot \cdot ,y_n^b]\in R^{s_2\times n}>0$$

(3)

The production possibility set based on the above assumptions is:

$$P=\left\{\left(x,y^g,y^b\right)|x\ge X\lambda ,y^g\le Y^g\lambda ,y^b\ge Y^b\lambda ,\lambda \ge 0\right\}$$

(4)

Then, the constructed super-efficiency-SBM model with unexpected output is expressed as follows:

$$\rho ={\min }_{\lambda ,s^{-},s^g,s^b}\frac{1+\frac{1}{m}{\displaystyle \sum _{i=1}^m{s}_i/x_{ik}}}{1-\frac{1}{s_1+s_2}\left({\displaystyle \sum _{r=1}^{s_1}\frac{s_r^g}{y_{rk}^g}+{\displaystyle \sum _{l=1}^{s_2}\frac{s_l^b}{y_{lk}^b}}}\right)}$$

$$s.t.\{\begin{array}{l}{\displaystyle \sum _{j=1,j\ne k}^n{x}_{ij}{\lambda }_j-s_i^{-}\le x_{ik}}\hfill \\ {\displaystyle \sum _{j=1,j\ne k}^n{y}_{rj}^g{\lambda }_j+s_r^g\ge y_r^g}\hfill \\ {\displaystyle \sum _{j=1,j\ne k}^n{y}_{lj}^b-s_l^b\le y_l^b}\hfill \\ {\displaystyle \sum _{i=1}^n{\lambda }_i=1}\hfill \\ 1-\frac{1}{s_1+s_2}({\displaystyle \sum _{r=1}^{s_1}\frac{s_r^g}{y_{rk}^g}+{\displaystyle \sum _{l=1}^{s_2}\frac{s_l^b}{y_{lk}^b}}})\ge \epsilon \hfill \\ \lambda ,s^{-},s^g,s^b\ge 0,1\le e\lambda \le u\hfill \\ i=1,2,\cdot \cdot \cdot ,m;r=1,2,\cdot \cdot \cdot ,s;j=1,2,\cdot \cdot \cdot ,n(j\ne k)\hfill \end{array}$$

(5)

where $\rho$ is the efficiency value, $\lambda$ is the weight vector, $X$ is the input vector, $y^g$ and $y^b$ are the expected and undesired outputs, $s^{-}$ is the input slack variable, and $s^g$ and $s^b$ are the expected and undesired output slack variables. Then, we used the Charnes-Cooper transformation method to transform the above model into an equivalent linear programming model [32]. The specific method is to introduce a new variable $\theta$ whose expression is:

$$\theta \left[1-\frac{1}{s_1+s_2}\left({\displaystyle \sum _{r=1}^{s_1}\frac{s_r^g}{y_{rk}^g}+{\displaystyle \sum _{l=1}^{s_2}\frac{s_l^b}{y_{lk}^b}}}\right)\right]=1$$

(6)

The equivalent linear programming model can be written as Equation (7). Solving the linear programming of Equation (7) can obtain the optimal solution ${\rho }^{*}={\tau }^{*}, {\lambda }^{*}=\frac{{\Lambda }^{*}}{{\theta }^{*}}, s^{-*}=\frac{S^{-*}}{{\theta }^{*}},s^{g *}=\frac{S^{g *}}{{\theta }^{*}},s^{b *}=S^{b *}/{\theta }^{*}$.

$$\tau ={\min }_{\wedge ,s^{-},s^g,s^b}\left(\theta +\frac{1}{m}{\displaystyle \sum _{i=1}^m\frac{s_i^{-}}{x_{ik}}}\right)$$

$$s.t.\{\begin{array}{l}1=\theta -\frac{1}{s_1+s_2}\left({\displaystyle \sum _{r=1}^{s_1}\frac{s_r^g}{y_{rk}^g}+{\displaystyle \sum _{l=1}^{s_2}\frac{s_l^b}{y_{lk}^b}}}\right)\hfill \\ {\displaystyle \sum _{j=1,j\ne k}^n{\wedge }_j{x}_{ij}-s_i^{-}\le \theta x_{ik}}\hfill \\ {\displaystyle \sum _{j=1,j\ne k}^n{\wedge }_j{y}_{rj}^g+s_r^g\ge \theta y_r^g}\hfill \\ {\displaystyle \sum _{j=1,j\ne k}^n{\wedge }_j{y}_{lj}^b-s_l^b\le \theta y_l^b}\hfill \\ s_i^{-}\ge 0,s_r^g\ge 0,s_l^b\ge 0,\theta l\le e\wedge \le \theta u,{\wedge }_j\ge 0\hfill \end{array}$$

(7)

3.1.2. Non-Radial, Non-Angular Malmquist Productivity Index

In a nonparametric framework, MPI, which means the Malmquist Productivity Index, is an index that represents the growth of DMU Total Factor Productivity (TFP) to evaluate intertemporal changes in efficiency. Based on the previous super-efficient SBM model with undesired output, we construct a nonradial and nonangular MPI.

$$\begin{array}{ll}MP{I}_0(x^{t+1},y^{t+1},x^t,y^t)& ={\left[\frac{d^t(x^{t+1},y^{t+1})}{d^t(x^t,y^t)}\times \frac{d^{t+1}(x^{t+1},y^{t+1})}{d^{t+1}(x^t,y^t)}\right]}^{\frac{1}{2}}\\ & =\mathrm{EFFCH}\times \mathrm{TECH}\end{array}$$

(8)

where

$$\mathrm{EFFCH}=\frac{D_{}^{t+1}(x^{t+1},y^{t+1})}{D^t(x^t,y^t)}$$

(9)

$$\mathrm{TECH}=\frac{D^t(x^{t+1},y^{t+1})}{D^{t+1}(x^{t+1},y^{t+1})}\times \frac{D^t(x^t,y^t)}{D^{t+1}(x^t,y^t)}$$

(10)

In Formula (8), $\left(x^t,y^t\right)$ and $\left(x^{t+1},y^{t+1}\right)$ represent the input and output of period $t$ and period $t+1$, respectively, $M\left(x^{t+1},y^{t+1},x^t,y^t\right)$ is the global reference Malmquist index, $D^t\left(x^t,y^t\right)$ and $D^{t+1}\left(x^{t+1},y^{t+1}\right)$ represent the comprehensive efficiency levels of the frontier in the $t$ period and the $t+1$ period, respectively, and the ratio of the two is expressed as the change in the overall efficiency level. When $M>1$, it indicates that the efficiency is improved; when $M<1$, it indicates that the efficiency is reduced. Additionally, the $M$ index can be further decomposed into $\mathrm{TFPCH}, \mathrm{EFFCH}, \mathrm{and} \mathrm{TECH}$, representing total factor productivity, comprehensive efficiency (or technical efficiency), and technological progress, respectively. The comprehensive efficiency $\left(\mathrm{EFFCH}\right)$ can be further decomposed into scale efficiency $\left(\mathrm{SEC}\mathrm{H}\right)$ and pure technical efficiency $\left(\mathrm{PTECH}\right)$, and the relationship between variables is expressed as:

$$\begin{array}{ll}\mathrm{TEPCH}& =\mathrm{EFFCH}\times \mathrm{TECH}\\ & =(\mathrm{PTECH}\times \mathrm{SECH})\times \mathrm{TECH}\end{array}$$

(11)

EFFCH refers to efficiency change, which measures the change in technical efficiency of ${\mathrm{DMU}}_0$ from period T to period T + 1. If $\mathrm{EFFCH}>1$, it means that the efficiency from T period to T + 1 period has improved; if $\mathrm{EFFCH}<1$, it means that the efficiency from T period to T + 1 period has decreased; if $\mathrm{EFFCH}=1$, it means that from the efficiency from T period to T + 1 period remains the same. TECHC refers to technological change, which measures the transformation of ${\mathrm{DMU}}_0$ from period T to period T + 1 technological frontier, that is, technological progress. If $\mathrm{TECHC}>1$, it means the technological progress of ${\mathrm{DMU}}_0$ from T period to T + 1 period; if $\mathrm{TECHC}<1$, it means the technological regression of ${\mathrm{DMU}}_0$ from T period to T + 1 period; if $\mathrm{TECHC}<1$, it means the technical level of ${\mathrm{DMU}}_0$ remains unchanged from T period to T + 1 period.

3.2. Indicator Selection

This study measures and evaluates the energy efficiency of provinces along the Belt and Road from the perspective of carbon emission constraint. Under the premise of following the construction principles of feasibility, rationality, and availability, combining with actual production activities, and referring to previous studies, we select five representative indicators from three aspects of input, expected output, and unexpected output [28,29,30].

3.2.1. Input Indicators

Labor input, as an essential input variable for labor factor, is widely used in other similar studies. Not considering the difference in quality of labor, labor hours, and labor types, we take the average employment number at the beginning and end of the year in each province and city as the labor input [18,23,33,34]. The method is to use the average number of people employed in both previous and current years as the number of people employed that year.

Total energy consumption reflects the level of energy consumption and the situation of energy conservation and consumption reduction, including the consumption of coal, oil, and natural gas. This paper refers to the national unified conversion standard coal coefficient. The energy consumption of each province in total is selected as an indicator of measure. [33,35,36,37,38]. The unit is tons of standard coal.

Capital stock of a single province in 2000 was assessed through the method, which is actual gross capital formation of each province in 2001 to the sum of the depreciation rate and the average value, which is fixed asset investment growth rate from 2001 to 2005, and then take it as the base period, using the method of perpetual inventory to estimate the capital stock of every province during 2015–2019 [34,39,40]. The calculation formula is:

$$K_t=I_t+(1-\delta )K_{t-1}$$

(12)

K_t is the capital stock in period t, I_t is the investment amount in period t, δ is the depreciation rate, and the value is 10.90%.

3.2.2. Output Indicators

Output indicators mainly include expected output and unexpected output.

For expected output, resource input will bring economic growth, and at the same time, it is related to China’s carbon intensity target management. Therefore, the regional GDP of each province and city is selected as the expected output [19,33,35].

For unexpected output, as the main component of greenhouse gas, the small change of carbon dioxide concentration that has an important impact on global temperature, and it is also the main monitoring indicator of energy conservation and emission reduction in various countries. In order to achieve the “dual carbon” target as scheduled and embark on the road to green and sustainable development, it is imperative to control carbon dioxide emissions reasonably. Therefore, we chose CO₂ emissions as the measurement index of undesired output. Because there is no relevant data on the CO₂ emissions of each province in the statistical yearbooks over the years, this study uses the consumption of fossil energy to measure the CO₂ emissions of the provinces included in the Belt and Road [36,41]. The calculation formula uses the carbon energy consumption multiplied by the carbon conversion coefficient and then multiplied by the CO₂ gasification coefficient as the CO₂ emission.

Carbon-containing energy consumption refers to the CO₂ released by coal, oil, and natural gas in the process of consumption. The carbon conversion coefficient adopts the coefficient specified by the Energy Research Institute of the National Development and Reform Commission. The value is 0.67. CO₂ gasification coefficient refers to the mass ratio before and after carbon is completely oxidized to CO₂, which is 44/12. The value in this paper is 3.67. The constructed energy efficiency evaluation indicators are revealed in

Table 1. Energy efficiency evaluation indicators.

First-Level Indicators	Second-Level Indicators	Third-Level Indicators	Value
Input Indicators	Labor	Total Number of Employees	10,000 persons
	Energy Consumption	Total Energy Consumption	10,000 tons
	Capital Stock	perpetual inventory method to estimate the capital stock	100 million yuan
Output Indicators	Expected Output	Actual GDP	100 million yuan
	Unexpected Output	CO2 Emissions	10,000 tons

.

4. Empirical Research

This paper selects 17 provinces included in the Belt and Road as research objects. Because of lacking data, the Tibet Autonomous Region is not considered, and uses MaxDEA Ultra 6.9 to evaluate the energy efficiency of relevant provinces from 2015 to 2019. Relevant data sources are obtained through calculation and arrangement according to the “Statistical Yearbook”, “China Energy Statistical Yearbook”, as well as “China Statistical Yearbook” of every province. It should be noted that when using MaxDEA Ultra software for data processing, the efficiency frontier is constructed based on all cross-section data from 2015 to 2019, and the global reference MPI index is used to dynamically evaluate the energy efficiency of every decision-making unit in each period. The flowchart of the analytical process is shown in Figure 1.

4.1. Result Analysis of Super-Efficiency SBM Model

The energy efficiency of 17 provinces along the Belt and Road are measured based on the condition of constant return to scale (CRS) and the input-oriented super-efficiency SBM model. The results are revealed in

Table 2. The total factor energy efficiency values of provinces included in the Belt and Road from 2015 to 2019.

Province	2015	Rank	2016	Rank	2017	Rank	2018	Rank	2019	Rank
Inner Mongolia	0.741	10	0.739	9	0.592	14	0.656	12	0.870	5
Heilong jiang	0.619	14	0.664	11	0.658	11	0.631	13	0.683	9
Jilin	0.778	9	0.770	8	0.735	8	0.706	9	0.641	13
Liaoning	0.886	5	0.717	10	0.694	9	0.747	8	0.629	14
Shaanxi	0.573	16	0.581	16	0.614	13	0.579	16	0.668	10
Gansu	0.608	15	0.602	15	0.553	15	0.630	14	0.575	16
Ningxia	0.510	17	0.502	17	0.462	17	0.591	15	0.593	15
Qinghai	0.631	13	0.608	14	0.524	16	0.540	17	0.500	17
Chongqing	0.807	6	0.794	7	0.832	6	0.806	6	0.794	7
Guangxi	0.806	7	0.863	5	0.766	7	0.763	7	0.667	11
Yunnan	0.649	11	0.654	12	0.667	10	0.677	10	0.795	6
Xinjiang	0.646	12	0.620	13	0.633	12	0.667	11	0.658	12
the Silk Road Economic Belt	0.689		0.676		0.703		0.742		0.673
Shanghai	0.943	4	1.012	3	1.013	3	1.016	3	1.077	1
Zhejiang	1.001	3	1.003	4	1.009	4	1.019	2	1.012	2
Fujian	1.040	2	1.017	2	1.023	2	0.842	4	1.009	3
Guangdong	1.061	1	1.046	1	1.029	1	1.021	1	0.931	4
Hainan	0.783	8	0.831	6	0.847	5	0.834	5	0.776	8
the 21st-Century Maritime Silk Road	0.967		0.982		0.984		0.946		0.961

.

According to the analysis results in Table 2, the average energy efficiency and historical efficiency values of the relevant provinces of the 21st-Century Maritime Silk Road were significantly higher than those of 12 provinces along the Silk Road Economic Belt from 2015 to 2019. Among the provinces related to the Silk Road Economic Belt, Energy efficiency in Chongqing and Guangxi is at the forefront of the Silk Road Economic Belt region from 2015 to 2019. The energy efficiency of Shaanxi, Gansu, Ningxia, and Qinghai are at the regional downstream level, and the overall energy efficiency in three provinces in northeastern China are relatively low. It should also be noted that the energy efficiency of Jilin and Liaoning provinces was in decline from 2015 to 2019, and there is a further downward trend. The ranking of energy efficiency values in Inner Mongolia fluctuates greatly, with the lowest rising from the 14th place in 2017 to the 5th place in 2019. This may be related to the narrowing of the internal gap in energy efficiency in the tested area from 2015 to 2019. The energy efficiency of five provinces along the 21st-Century Maritime Silk Road is at the Belt and Road Regional Frontier from 2015 to 2019. The four provinces of Shanghai, Zhejiang, Fujian, and Guangdong have been at the forefront of overall energy efficiency over the years, while the energy efficiency of Hainan province is relatively lower than the regional average, and there is a possibility that the difference will further expand. In general, the energy efficiency of these 17 provinces covered by the Belt and Road under the super-efficiency SBM model, which considers unexpected output, shows remarkable characteristics. The specific performance in the Silk Road Economic Belt and the 21st-Century Maritime Silk Road regions shows obvious external regional differences and internal consistency, and the differences between regions show the characteristics of fluctuation and convergence in 2015–2018.

4.2. Malmquist Index Results Analysis

Under the conditions of variable returns to scale (VRS) and constant returns to scale (CRS), the total factor energy efficiency of provinces is not very different. Therefore, the returns to scale are still assumed to remain unchanged and measure the changes and decomposition of Malmquist total factor energy efficiency over the years of the provinces included in the Belt and Road under the unexpected output. The results are presented in

Table 3. Total factor energy efficiency and decomposition of provinces along the Belt and Road.

Province	Overall Efficiency	Technological Progress	Pure Technical Efficiency	Scale Efficiency	Total Factor Energy Efficiency
Inner Mongolia	1.058	0.922	1.104	0.969	0.953
Heilong jiang	0.889	1.002	0.922	0.957	0.876
Jilin	0.894	1.030	0.899	0.991	0.915
Liaoning	0.924	1.016	0.902	1.032	0.936
Shaanxi	0.961	1.001	0.970	0.988	0.957
Gansu	0.990	1.020	0.990	0.999	1.008
Ningxia	1.047	0.971	1.096	0.965	1.011
Qinghai	0.946	1.003	0.971	0.975	0.946
Chongqing	0.997	1.029	0.990	1.007	1.027
Guangxi	0.957	1.025	0.955	1.002	0.977
Yunnan	1.054	1.006	1.068	0.991	1.062
Xinjiang	1.157	0.905	1.137	1.016	1.024
the Silk Road Economic Belt	0.990	0.994	1.000	0.991	0.974
Shanghai	1.034	1.029	1.031	1.003	1.065
Zhejiang	1.002	1.062	1.003	0.999	1.065
Fujian	1.001	1.012	1.002	0.999	1.015
Guangdong	0.969	1.044	0.979	0.990	1.009
Hainan	0.999	1.029	1.003	0.997	1.025
the 21st-Century Maritime Silk Road	1.001	1.035	1.004	0.998	1.036
Average	0.993	1.125	1.001	0.993	0.992

and

Table 4. Changes and analysis of total factor energy efficiency in two regions of the Belt and Road over the years.

Years	12 Provinces Included in the Silk Road Economic Belt			5 Provinces Included in the 21st-Century Maritime Silk Road
	EFFCH	TECH	TFPCH	EFFCH	TECH	TFPCH
2015–2016	1.020	0.959	0.979	0.993	0.978	0.957
2016–2017	0.932	1.021	0.951	1.003	1.019	1.022
2017–2018	1.077	0.975	1.050	0.963	1.036	0.995
2018–2019	0.969	1.017	0.951	1.019	1.126	1.146
Mean Value	0.999	0.993	0.983	0.995	1.040	1.030

Note: EFFCH is the variation in technical efficiency, TECH is the variation in technological progress, and TFPCH is the variation in total factor energy efficiency.

.

4.2.1. Based on Spatial Dimension

According to the measured results in Table 3, the average total factor energy efficiency of these 17 provinces covered by the Belt and Road from 2015 to 2019 was 0.992, and in addition the average growth rate was −0.11% [42]. Except for Gansu, Ningxia, Chongqing, Yunnan, and Xinjiang, the average growth rate of total factor energy efficiency in the other seven provinces along the Silk Road Economic Belt region are negative. This is mainly due to the generally low average overall efficiency of the measured areas. The total factor energy efficiency of all areas in the 21st-Century Maritime Silk Road region is positive, as the average growth rate is 3.6%, and the value is at the forefront of overall efficiency. The average growth rate of total factor energy efficiency between the 12 provinces included in the Silk Road Economic Belt and the five other provinces included in the 21st-Century Maritime Silk Road differs by 6.2%. The regional difference is obvious.

The average energy efficiency of 12 provinces along the Silk Road Economic Belt was 0.974 during the measurement period, and the average growth rate was −2.6%. Within the region, except for the five provinces and cities of Gansu (1.008), Ningxia (1.011), Chongqing (1.027), Yunnan (1.062), and Xinjiang (1.024), the remaining seven provinces are far below the frontier of efficiency. The total factor energy efficiency of the six provinces that are Inner Mongolia, Heilongjiang, Jilin, Liaoning, Shaanxi, and Qinghai is below the regional average. The total factor energy efficiency in three northeastern provinces and Qinghai are the lowest in the region; in addition, average growth rate of these provinces reaches a level of −5% or even lower (Heilongjiang reached −12.4%). Further investigation of the reasons for the decline in total factor energy efficiency in the relevant provinces of the Silk Road Economic Belt indicates that the main reason for the decline in total factor energy efficiency in Heilongjiang, Jilin, Shaanxi, and Qinghai provinces is the decline in scale and pure technical efficiency. The growth in total factor energy efficiency is hindered by the decline in pure technical efficiency in Liaoning and Guangxi provinces. Inner Mongolia is primarily negatively affected by scale efficiency. In summary, the improvement of total factor energy efficiency in the studied region generally comes from the pulling effect of technological progress. However, the decline in overall efficiency is also a common problem faced by the provinces in this region.

The total factor energy efficiency of the five provinces included in the 21st-Century Maritime Silk Road is greater than 1, and the average growth rate is 3.6%. Overall performance is good. The growth in total factor energy efficiency in the region is chiefly pulled by the progress of technology. The energy efficiency of Shanghai (1.065) and Zhejiang (1.065) is higher than the efficiency value in average, and they are at the frontier of efficiency. However, it should be considered that the value of scale efficiency index is relatively small in the decomposition index, indicating that the low technical efficiency caused by the scale efficiency decline generally indicates the growth in overall energy efficiency in the region. This also reflects that the development of green emission reduction technology has indeed improved the energy efficiency level in the region to a certain degree, but the unreasonable defects of factor allocation and production scale still exist.

4.2.2. Based on Time Dimension

Table 4 shows the total factor energy efficiency value of the 12 provinces along the Silk Road Economic Belt fluctuated between 0.951 and 1.05 from 2015 to 2019, and the rate of average growth is 1.7%. Fluctuation is obvious. In addition, the total factor energy efficiency value of the other five provinces included in the 21st-Century Maritime Silk Road fluctuates between 0.957 and 1.146, and the average growth rate is 3%. It shows an upward trend of fluctuation. Overall, the two key regions’ total factor energy efficiency showed high volatility during the measured period.

The average growth rate of total factor energy efficiency in 12 provinces included in the Silk Road Economic Belt region only showed positive growth (5%) from 2017 to 2018, and the rest of the years had different degrees of decline. Specifically, in 2016–2017 and 2018–2019, the overall efficiency had negative influence of different degrees on total factor energy efficiency. The overall efficiency dropped the most between 2016 and 2017, reaching 6.8%. Technological progress also fluctuated considerably during the measured period. The technological progress between 2015–2016 and 2017–2018 declined in different degrees, with a drop of more than 2.5%. The relevant provinces along the Silk Road Economic Belt should show an increase in the investment in green emission reduction technologies and strengthen the pulling effect of progressing technology on total factor energy efficiency.

From 2015 to 2019, the average growth rate of total factor energy efficiency in those five provinces along the 21st-Century Maritime Silk Road was 3%. The average growth rate of total factor energy efficiency reached 14.6% between 2018 and 2019. The change in total factor energy efficiency was the smallest between 2017 and 2018, and there was a decrease in energy efficiency by 0.5%. Overall, the improvement of energy efficiency in this region is mainly advanced by progressing technology. The speed of technological progress showed an upward trend from 2015 to 2019, and the average growth rate is 4%. However, it should be noted that the overall efficiency of this region declined in different degrees in 2015–2016 and 2017–2018. Therefore, the efficiency of resource allocation should be further improved in the future.

4.2.3. From the Point of View of Exponential Decomposition

Figure 2 shows technical efficiency can be divided into scale efficiency and pure technical efficiency, and the regional fluctuations of technical efficiency and pure technical efficiency are found to be highly consistent. There are small differences in scale efficiency. The regional difference of pure technical efficiency is the main factor that affect the fluctuation of technical efficiency. The improvement of technical efficiency comes from the positive impact of pure technical efficiency of some provinces, such as Heilongjiang, Inner Mongolia, Ningxia, and Qinghai. Some are driven by the improvement of scale efficiency, such as Liaoning, Chongqing, and Guangxi.

According to Figure 2, if it falls within the circle where the technical efficiency is exactly 1, then the technical efficiency is lower than 1. It indicates that the technical efficiency needs to be improved. Specifically, the pure technical efficiency of those five provinces, including Heilongjiang, Jilin, Liaoning, Qinghai, and Guangxi, was relatively low during the measured period. In the future, we should focus on improving the level of pure technical efficiency. The scale efficiency of those three provinces, including Heilongjiang, Ningxia, and Inner Mongolia, has not reached the average level. The improvement of technical efficiency is negatively influenced by the scale factor, and the scale factor is also the direction that should be improved in the future.

5. Conclusions and Recommendations

Due to the super-efficiency SBM model of unexpected output and the Malmquist index decomposition model, this study measures and evaluates the energy efficiency values of 17 provinces included in the Belt and Road from 2015 to 2019, and draws the following conclusions:

• Apparent differences in energy efficiency exist among the 17 provinces included in the Belt and Road. Specifically, the energy efficiency of 12 provinces included in the Silk Road Economic Belt region is generally low. There is little difference within the region. Mean is 0.983. The five provinces in the 21st-Century Maritime Silk Road area have high energy efficiency, with an average value of 1.03, which is at the forefront of the Belt and Road regional efficiency.
• From the perspective of time, the total factor energy efficiency of provinces included in the Belt and Road shows a fluctuating upward trend. This upward trend is chiefly driven by technological progress, and the improvement of energy efficiency is negatively influenced by technical efficiency.
• The main reason for the low energy efficiency of the provinces along the Silk Road Economic Belt region is low technical efficiency. The main factor supporting the improvement of energy efficiency in the provinces of the 21st-Century Maritime Silk Road is technological development. Specifically, scale efficiency and pure technical efficiency of Heilongjiang, Shaanxi, and Qinghai are all below the regional average. The pure technical efficiency of Jilin, Liaoning, Gansu, and Guangxi provinces is low. The future improvement direction of Inner Mongolia and Ningxia is to improve technology and improve scale efficiency.

Based on the above conclusions, this paper highlights the following policy recommendations for improving energy efficiency in the Belt and Road region.

• The improvement of total factor energy efficiency of provinces included in the Silk Road Economic Belt is the focus of the next step. The energy efficiency of provinces included in the Silk Road Economic Belt region is relatively low, which especially shows a development situation with low levels of scale efficiency and pure technical efficiency. On one hand, the market exit mechanism should be improved, and environmental constraints on industries that have high energy consumption and high pollution should be strengthened. On the other hand, it is necessary to explore the implementation of fiscal and taxation promotion policies and supporting systems according to local conditions, mobilize the enthusiasm of market players to achieve green technology progress, and guide enterprises to develop intensively, greenly, and sustainably.
• To optimize and improve the scale efficiency of the areas included in the 21st Century Maritime Silk Road, the low scale efficiency mainly limits the improvement of energy efficiency in the 21st-Century Maritime Silk Road region. It is necessary to accelerate the exploration of energy marketization reform and strengthen the decisive role of the market in the allocation of resource elements. The transformation of government functions should be accelerated to transform role from the rule maker to the market supervisor and service provider and build the region into a high-quality development demonstration area.
• In response to the obvious regional differences in energy efficiency between the Silk Road Economic Belt region and the 21st-Century Maritime Silk Road region, the establishment of a joint cooperation in the region for green and low-carbon development can be taken into consideration, as well as forming a green alliance for ecological civilization construction. Due to strong external correlations, inter-regional development is bound to have indirect effects on neighboring regions. Therefore, the regional co-construction mechanism should be actively explored. Through joint planning and implementation of programs aiming at emission reduction and energy saving, the minimization of individual emission-reduction costs within the region can be achieved under the environmental constraints of overall energy saving and emission reduction and promoting the region to step into the goal of ecological civilization and green development.
• In terms of energy conservation and emission reduction, it is necessary to further optimize the energy consumption structure, improve the energy price system and emission trading market, effectively control emissions of nondesired output, such CO₂, and promote sustainable low-carbon economic development. At the same time, we should promote a clean and low-carbon green economic development model and gradually reduce the proportion of fossil energy consumption. In addition, it is necessary to significantly increase the intensity and scale of clean energy development, promote the development and utilization of renewable energy, such as solar, wind, biomass, and geothermal energy, and actively promote green GDP in order to fully meet the needs of sustainable economic development.