### 1. Introduction

_{2}emission efficiency in 32 OECD countries. Chang et al. [4] measured the CEE of different regions with a non-radial DEA model to research. In addition, SFA and MCPI methods were also applied to calculate the CEE [5, 6]. Domestic research mostly focused on the assessment of CEE and its influencing factors in nationwide provinces or several large regions [7, 8]. Different kinds of methods, such as non-radial and non-angle DEA, cross-efficiency DEA, super-efficiency DEA and SDDF models, were put forward to study the CEE and its influencing factors across the country [9–12]. Meanwhile, there is also some research using SBM and three-stage DEA models to evaluate the CEE of some special regions like Beijing-Tianjin-Hebei and coastal areas [13, 14].

### 2. Empirical Research Design

### 2.1. Methodology

#### 2.1.1. Super-efficiency DEA

*X*

*(*

_{j}*X*

*= (*

_{j}*X*

_{j}_{1},

*x*

_{j}_{2},

*x*

_{j}_{3}, ...,

*x*

*)′) and*

_{jK}*Y*

*(*

_{j}*Y*

*= (*

_{j}*y*

_{j}_{1},

*y*

_{j}_{2},

*y*

_{j}_{3}, ...,

*y*

*)′) to represent DMU j, the decision making unit. When evaluating the efficiency of the decision-making unit*

_{jM}*j*

_{0}, the specific calculation formula of the super-efficiency DEA model can be constructed as follows.

##### (1)

$$\text{min}\left\{\theta -\varepsilon \left(\sum _{i=1}^{m}{S}_{i}^{-}+\sum _{r=1}^{s}{S}_{r}^{+}\right)\right\}$$##### (2)

$$s.t.\{\begin{array}{l}\sum _{\begin{array}{l}j=1\\ j\ne {j}_{0}\end{array}}^{n}{X}_{j}{\lambda}_{j}+{s}^{-}=\theta {X}_{{j}_{0}}\hfill \\ \sum _{\begin{array}{l}j=1\\ j\ne {j}_{0}\end{array}}^{n}{Y}_{j}{\lambda}_{j}-{s}^{+}=Y\hfill \\ {\lambda}_{j}\ge 0\hspace{0.17em}(j=1,2,\dots ,n)\hfill \\ {s}^{+}\ge 0,\hspace{0.17em}{s}^{-}\ge 0\hfill \end{array}$$*θ*≥ 1, and

*s*

^{+}=

*s*

^{−}= 0, then the DMU

*j*

_{0}is said to be DEA valid; if

*θ*≥ 1, and ${s}_{i}^{-}\ne 0$ or ${s}_{r}^{+}\ne 0$, then the DMU

*j*

_{0}is said to be DEA weakly valid; if

*θ*< 1, ${s}_{i}^{-}\ne 0$ and ${s}_{r}^{+}\ne 0$, then the DMU

*j*

_{0}is represented as DEA, invalid. For the invalid evaluation unit, the super efficiency DEA and the traditional DEA efficiency value have the same evaluation results. Nevertheless, for the evaluation unit whose efficiency value reaches 1, we can compare their relative efficiency value. As shown in Fig. 1, it is assumed that point A, B, and C are all high decision making units with an efficiency value of 1, and point E represents a low production efficiency point. When calculating the efficiency value of the point B1, the point B is excluded, so that the two points A and C are used as the frontier surface, and the line segment BB

_{1}is the amplitude that the input amount can be increased. Therefore, the super-efficiency value of the point B is calculated by (

*OB*+

*BB*

_{1})/

*OB*. This value is greater than 1. The point E, which will not affect the production frontier when excluded, is the lower efficiency point. Hence, the super-efficiency DEA model has no effect on the low-efficiency evaluation subject results and can be used to compare the relative size of the high-efficiency evaluation subjects.

#### 2.1.2. Malmquist productivity index

*D*

*(*

^{t}*x*

*,*

_{t}*y*

*) and*

_{t}*D*

^{t}^{+1}(

*x*

*,*

_{t}*y*

*) are the efficiency values of decision-making unit at the period t for the reference technology at the period t and t+1. Further suppose that*

_{t}*D*

*(*

^{t}*x*

_{t}_{+1},

*y*

_{t}_{+1}) and

*D*

^{t}^{+1}(

*x*

_{t}_{+1},

*y*

_{t}_{+1}) are the efficiency values of DMU at the time t+1 for the reference technology at the time t and t+1. The MPI defines total factor productivity (TFP) as:

##### (3)

$$\begin{array}{l}TFP={\left[\frac{{D}^{t}({x}_{t+1},{y}_{t+1})}{{D}^{t}({x}_{t},{y}_{t})}\times \frac{{D}^{t+1}({x}_{t+1},{y}_{t+1})}{{D}^{t+1}\hspace{0.17em}({x}_{t},{y}_{t})}\right]}^{\frac{1}{2}}\\ =\frac{{D}^{t+1}\hspace{0.17em}({x}_{t+1},{y}_{t+1})}{{D}^{t}\hspace{0.17em}({x}_{t},{y}_{t})}\times {\left[\frac{{D}^{t}\hspace{0.17em}({x}_{t+1},{y}_{t+1})}{{D}^{t+1}({x}_{t+1},{y}_{t+1})}\times \frac{{D}^{t}\hspace{0.17em}({x}_{t},{y}_{t})}{{D}^{t+1}({x}_{t},{y}_{t})}\right]}^{\frac{1}{2}}\end{array}$$*TFP*>1, it indicates that the efficiency of the TFP is increased from time

*t*to the time

*t*+1. On the contrary, if the

*TFP*<1, indicating that the TFP is reduced during the period from

*t*to

*t*+ 1.

#### 2.1.3. Moran’s I index

##### (5)

$$I=\frac{n{\sum}_{i=1}^{n}{\sum}_{j=1}^{n}{w}_{ij}\left({x}_{i}-\overline{x}\right)\left({x}_{j}-\overline{x}\right)}{{\sum}_{i=1}^{n}{\sum}_{j=1}^{n}{w}_{ij}{\sum}_{i=1}^{n}{\left({x}_{i}-\overline{x}\right)}^{2}}$$*n*is the number of spatial units, representing the number of provinces, and

*ω*

*represents the element (*

_{ij}*i*,

*j*) of the spatial weight matrix, which is a binary virtual variable. In this paper,

*ω*

*is used to measure whether the regions are adjacent. If any two regions are adjacent, the value of*

_{ij}*ω*

*is one, otherwise zero. We all know that*

_{ij}*I*∈ [−1, 1], on the basis that the test result is significant, if

*I*∈ (0, 1], it means that the value of CEE between the regions exhibits agglomeration. Apparently, it is shown that the province with higher CEE has a higher CEE in its neighboring provinces. Similarly, when

*I*∈ [−1, 0), on the basis that the test result is significant, the province with high CEE has a lower CEE in their neighboring provinces. On the contrary, if the value equals to zero or test result is not significant, it indicates that there is no spatial correlation among the provinces. While the closer the value is to one, the stronger the spatial correlation among provinces.

### 2.2. Variable Selection and Data Source

_{2}emissions as a measure of energy-saving technology use. The higher the ratio, the less carbon dioxide produced per unit of GDP. In addition, we use Stata software to perform Stepwise Regression, the results show that all indexes should be included in the model, reflecting that there is no multicollinearity. The symbolic representation of each variable and its specific meaning are shown in Table 1.

_{2}emissions of each province are calculated according to the energy consumption carbon footprint model in the IPCC (2006) National Greenhouse Gas Inventories Guide, which estimates by primary energy consumption including raw coal, crude oil and natural gas use. The CO

_{2}emissions coefficient of various energy sources is determined as follows:

##### (6)

$${CO}_{2}=\sum _{i=1}^{n}{E}_{i}\times {NCV}_{i}\times {CEF}_{i}\times {COF}_{2}\times \frac{44}{12}$$*E*

*is the consumption of carbon-containing energy,*

_{i}*NCV*

*represents the average low calorific value,*

_{i}*CEF*

*displays the amount of carbon contained in the unit calorific value and*

_{i}*COF*

*indicates the carbon oxidation factor.*

_{i}Low (position) heat equal to 29,307 kJ of fuel, referred to as 1 kg of standard coal (1 kgce)

The first two columns of the above Table are from the General Rules for the Calculation of Comprehensive Energy Consumption (GB/T 2589-2008) (reference year is missing)

The last two columns of the Table 2 are derived from the “Guidelines for the Preparation of Provincial Greenhouse Gas Inventories” (Development and Reform Office Climate [2011] No. 1041)

##### Table 2

##### Table 3

### 3. Analysis of Empirical Results

### 3.1. Static Analysis of CEE

Firstly, the overall level of CEE in the nine western provinces is not high and the fluctuations are small. The average CEE of the nine western provinces is in the stage of diminishing returns to scale for most of the years, this is related to the lower level of economic development, excessive proportion of the secondary industry and extensive production method in the western regions, as well as the lack of technological innovation.

Secondly, there are significant inter-provincial differences in CEE among provinces. Furthermore, those provinces with more developed economies have higher CEE as a whole. From 2000 to 2015, the economic development levels of the nine western provinces, from high to low, are ranked as follow: Guangxi, Yunnan, Shaanxi, Chongqing, Inner Mongolia, Xinjiang, Gansu, Ningxia and Qinghai. This might be because in provinces with higher economic levels, the governments have greater capacity to conduct research on energy-saving technologies and advocate energy conservation and emission reduction. Therefore, companies and residents in the province have stronger awareness of ecological protection, which ultimately facilitates the improvement of carbon emission efficiency. Only the rankings’ of Inner Mongolia and Chongqing interchanged between 2008 and 2011, while the rankings’ of other provinces remained completely unchanged. Moreover, the list when the the average CEE of each province ranked from high to low is as follows; Xinjiang, Guangxi, Chongqing, Shaanxi, Yunnan, Inner Mongolia, Gansu, Ningxia and Qinghai. This depicts that showing that the provinces with higher economic development levels have higher CEE with the exception of Xinjiang. This province is sparsely-populated and located in the northwest of China and has vigorously developed its import-export trade with many countries and has kept a lower proportion of secondary industry in contrast with the other eight provinces in the last sixteen years. This is conducive to energy saving and emission reduction, thereby greatly improving the CEE.

### 3.2. Dynamic Analysis of CEE

### 3.3. Analysis of Factors Affecting CEE

*y*

_{1}) as the dependent variable and selected the industrial structure (

*x*

_{1}), urbanization (

*x*

_{2}), openness (

*x*

_{3}), energy-saving technology (

*x*

_{4}), foreign direct investment (

*x*

_{5}), fixed asset investment (

*x*

_{6}), R&D investment (

*x*

_{7}), government expenditure (

*x*

_{8}) and energy structure (

*x*

_{9}) as independent variables. Before constructing the model, the spatial auto-correlation of CEE values in the nine provinces was tested by Moran’s I index. (The specific test results can be seen from the supplementary materials; Table S1)

### 4. Conclusions and Policy Implications

The overall average level of CEE in the nine western provinces from 2000 to 2015 is not high, and the fluctuation is small. The inter-provincial differences of CEE are significant as well as the obvious differences in economic development levels, displaying that the provinces with higher levels of economic development have a higher CEE. The above conclusions can be explained mainly from two aspects. For one thing, the proportion of the secondary industry in the nine western provinces is too high and the production methods are relatively extensive, which greatly increased CO

_{2}emissions per unit of output value. For another thing, the nine western provinces lack cooperation in technological innovation, environmental governance and capital investment, and thus cannot play a synergistic effect in the development of a low-carbon economy. Among them, due to the vast territory and good regional advantages, Xinjiang has a high export trade quota and a relatively low proportion of the secondary industry. Thus, its overall average value of CEE ranks first, and the annual CEE from 2000 to 2015 is greater than 1. In contrast, Qinghai, with a higher proportion of the secondary industry and lowest level of economic development in the nine western countries, ranks last in terms of the overall average CEE, which is in a relatively serious stage of diminishing returns to scale. Therefore, it is necessary for the nine western provinces to carry out more extensive strategic cooperation in technological innovation, talent exchange, and environmental protection. This will result in greater synergy and jointly achieve the goal of low-carbon economic development and narrowing the development gap between the western, eastern and center regions.On the whole, the average value of TFP in the nine western provinces from 2000 to 2015 is greater than 1, and the overall TFP has increased by 15.5%. The growth rate gaps between provinces do not exceed 5%. In addition, the average growth rate of EC and the average growth rate of TC were 0.3% and 15.1%, respectively. The value of TFP is mainly determined by TC and has the same trend with TC. With respect to TC, the main sources are technology introduction and technological innovation. In the process of seeking higher CEE, the authorities of the nine western provinces should pay more attention to introducing supporting incentive policies so as to facilitate technology introduction and independent innovation, thereby improving the value of TFP.

The test results of global Moran’s I index imply that the CEE values of the nine western provinces are not spatially dependent, that is, there is no spatial agglomeration effect in the nine western provinces, which is totally contrary to the test results of the national or eastern regions. In addition, the regression results of Tobit model indicate that the impacts of R&D investment, energy-saving technology, urbanization and openness on CEE are significantly positive, and the degrees of influence decrease in turn. Therefore, the governments of the nine western provinces should improve CEE on the basis of following suggestions. Firstly, increasing R&D investment to promote the technological innovation and development, especially the energy-saving technology. Secondly, by promoting urbanization, high-tech industries can gain more opportunities for development. Thirdly, encouraging import and export trade so as to reduce high-emissions commercial transactions. The impacts of government expenditure, energy structure, industrial structure, fixed asset investment and foreign direct investment on CEE are significantly negative and the degrees of their influences decrease in turn. First of all, the authorities of nine western provinces should formulate a reasonable government expenditure plan and appropriately increase the proportion of environmental protection expenditures. Then, reducing the proportion of coal use and increasing the scale of clean energy use. Meanwhile, increasing the proportion of the tertiary industry and promoting the coordinated development of the three major industries. Further, reducing the proportion of fixed assets investment and strictly selecting the foreign investors to avoid excessive investment in high-energy and high-emission industries. Among them, R&D investment has the greatest positive impact on the CEE of the nine western provinces, while the government expenditure has the most negative impact on the CEE of the nine western provinces, which is worthy of more attention.

To establish the carbon emissions trading market and to make the market play an automatic adjustment role. In addition to setting strict carbon emission targets, the authorities should also be encouraged to effectively control carbon emissions through carbon emissions trading, using external markets to regulate carbon emissions. Furthermore, carbon emissions trading will encourage companies to improve the CEE by introducing technology and technological innovation, which is conductive to saving energy consumption and trading the remaining carbon emission indicators in order to obtain additional income. The income from carbon emissions trading in turn will also stimulate enterprises to increase investment in technology research and development, thus forming a virtuous cycle of technology research and development.