1 Introduction

Since mainland China’s economic reform and opening policy started in 1978, China’s economy has developed rapidly and it became the world’s second-largest economy in 2010 [4]. According to the National Bureau of Statistics of China (NBSC), China’s real GDP has grown by a factor of about 110 comparing 2010 with 1978. With such astonishing economic expansion, China’s energy consumption is also growing rapidly. In 2010, China consumed 3.48 billion tons of standard coal, while in 1978 it was 571 million tons. By 2007, China had already overtaken the United States to become the world’s largest energy consumer [35]. However, after the rapid growth of China’s economy in the past three decades, it has become clear that the increasing energy consumption and environmental pollution are currently hindering the sustainability of China’s economic growth. An increasing number of scholars are focusing on efficiency evaluation in terms of the energy and environment, which is considered a crucial step in any approach to energy saving and emission reduction.

The transportation sector is one of the high energy consumption and high pollution sectors worldwide [19, 23]. According to National Bureau of Statistics of China, in 2012, China’s transportation energy consumption volume was 302 million tons of standard coal and the transportation sector was one of the few sectors whose consumption increase rate was more than 7.2 % annually in the previous decade, which means it is growing faster than the average annual increase rate of energy production, which is \(<\)6 % [11]. China’s transportation energy consumption is overwhelmingly dominated by fossil fuels, whose use produces large quantities of undesirable gases like carbon dioxide (CO\(_{2}),\) making the use of fossil fuels responsible for China’s current high levels of pollution. Huge transportation demand will stimulate more demand for infrastructure investment and energy consumption. Thus, the public should pay great attention to the energy utilization problem of the transportation industry. Environmental problems caused by large amounts of energy consumption, such as air pollution, should also be taken seriously enough. It is very important for scholars to do research on energy efficiency and environmental pollution problems related to the transportation sector.

Current indices of energy or environmental performance are constructed in the form of mathematical programming methods such as data envelopment analysis (DEA). As a nonparametric approach to evaluate the relative efficiency of a set of comparable decision making units (DMUs), DEA, which was developed by Charnes et al. [6], has been widely investigated and popularly applied to many fields such as universities [4, 20], health services [33], and banks [2, 9]. In this paper, we apply DEA method to evaluate the energy and environmental efficiency of China’s transportation sector.

Research on energy and environmental issues has a long history. Zhou et al. [40] summarized more than 100 studies on the application of DEA to environmental and energy policy. In terms of energy efficiency, Hu and Wang [18] proposed an index of total factor energy efficiency to analyze energy efficiencies of 29 administrative regions in China for the period 1995–2002. However, in their research GDP was the single output while undesirable outputs were neglected. This may be unreasonable in real production, as the utilization of fossil fuels always produces pollutants. Zhou and Ang [39] also presented several DEA-type models and calculated the impacts on energy efficiency of changes in energy mix. More recent approaches in handling undesirable outputs for the DEA framework are the slacks-based measurement model [10, 22] and non-radial DEA models [44]. Hernández-Sancho et al. [17] used a non-radial DEA to measure the energy efficiency of 177 waste water treatment plants in Spain. In terms of environmental efficiency, Zhou et al. [41] measured the carbon emission performance of eight world regions using DEA techniques, and divided outputs into desirable and undesirable outputs without considering non-energy inputs. Song and Wang [30] calculated China’s regional environmental efficiency scores from the perspectives of technological progress and government regulation by applying a DEA decomposition method. Xie et al. [36] proposed a dynamic environmental efficiency evaluation of electric power industries in BRIC countries (Brazil, Russia, India, and China) by using the environmental Malmquist index. Based on an environmental super-efficiency data envelopment analysis (SEDEA) model, Yang et al. [37] evaluated the environmental efficiency of 30 provinces in China during the period of 2000–2010. Shabani et al. [27] proposed using DEA in the optimization of energy consumption of carnation production.

In addition, there are also some published studies that directly address energy and environmental efficiency evaluation of transportation sectors in various parts of the world. Ramanathan [24] used DEA to measure the energy efficiency of alternative transportation modes in India and found out a gradual improvement in energy efficiency of rail transport. Tongzon [32] assessed the efficiency of four Australian and twelve international container ports based on DEA. Advenier et al. [1] analyzed the energy efficiency of road transportation with different technologies and different fuels, and his results showed that natural gas had the highest efficiency. Ediger and Camdali [13] examined energy and energy efficiencies in the Turkish transportation sector from 1988 to 2004, the results showing that the overall efficiency patterns were basically controlled by the fuel consumption in airlines. Chang et al. [7] also proposed a non-radial DEA model with the slacks-based measure (SBM) to analyze the environmental efficiency of China’s transportation sector, which contributes to reducing energy consumption and environmental pollution. Zhou et al. [43] not only examines the energy efficiency performance of China’s transportation sector from 2003 to 2009, but also maximizes energy-saving potential of the transportation sector of 30 Chinese administrative regions by a DEA approach considering undesirable outputs. A new model, three-stage virtual frontier DEA, was proposed by Cui et al. [11] to evaluate transportation energy efficiencies. They also applied their method to the case of 30 Chinese provincial administrative regions from 2003 to 2012 to verify its rationality. Egilmez et al. [14] utilized a two-step hierarchical methodology to quantify the transportation-related carbon, energy, and water footprint of any nation’s manufacturing sectors and evaluate the environmental vs. economic performance based on eco-efficiency scores. A non-radial DEA model that considers multidirectional efficiency analysis (MEA) involving undesirable outputs was presented by Bi et al. [5] for the measurement of regional energy and environmental efficiency of China’s transportation sector during the period 2006–2010.

However, the literature lacks a comprehensive consideration of transportation sectors from the aspect of saving energy and reducing pollution at the same time. In this paper, we develop a slack-based DEA model to measure the total factor energy and environmental efficiency of China’s regional transportation sectors considering energy saving and CO\(_{2}\) emission reduction. Our model considers a joint production framework of both non-energy inputs and energy inputs, as well as desirable outputs and undesirable outputs and can better reflect China’s transportation sector performance.

The rest of this paper is organized as follows. In Sect. 2, we give a suitable model for evaluating the transportation sectors. Section 3 shows the empirical study of energy and environmental efficiency analysis of China’s 30 regional transportation sector. Finally, conclusions and further research directions are given in Sect. 4.

2 Methodology

The aim of this paper is to develop a framework for measuring energy and environmental efficiency in 30 of China’s regional transportation sectors considering energy consumption and CO\(_{2}\) emissions. More specifically, we estimate the total factor energy and environmental efficiency using a joint production framework of both non-energy inputs and energy inputs, as well as desirable outputs and undesirable outputs.

Since Koopmans [21] make the first attempt to evaluate the production efficiency with undesirable outputs, there have been a variety of approaches based upon it. Song et al. [29] and Chen and Delmas [8] divided DEA models addressing undesirable outputs into three categories. The first category is taking the undesirable outputs as inputs [28, 34]. The second category is conducting data transformation to undesirable outputs [25, 26]. The first two categories assume that undesirable outputs are strongly disposable, meaning that the disposal of any undesirable output can be generated without incurring damage from other undesirable outputs. The third category assumes the weak disposability of undesirable outputs in a non-parametric DEA model [15, 42]. Because of the prevalence of the strong disposability assumption on undesirable outputs in DEA literature, it is chosen in this paper for treating the undesirable outputs.

Suppose that there are n regions denoted by DMU\(_{j}\) (\(j=1,\ldots ,n\)), and each of them consumes m different non-energy inputs and d different energy inputs to produce s different desirable outputs along with p different undesirable outputs. Define \(x_{ij} =(x_{1j} ,x_{2j} ,\ldots ,x_{mj} )^T\), \(e_{kj} =(e_{1j} ,e_{2j} ,\ldots ,e_{dj} )^T\), \(y_{rj} =(y_{1j} ,y_{2j} ,\ldots ,y_{sj} )^T\), and \(b_{gj} =(b_{1j} ,b_{2j} ,\cdots ,b_{kj} )^T\) as the non-energy input, energy input, desirable output, and undesirable output vectors of DMU\(_{j}\), respectively. The corresponding production possibility set assuming variable returns to scale (VRS) [3] can be described as follows.

$$\begin{aligned} \begin{array}{ll} T=\Big \{{\left( x_i ,e_k ,y_r ,b_g\right) \vert } &{} \sum \limits _{j=1}^n {\lambda _j x_{ij} +s_i ^{x-}=x_i ,}\quad i=1,\ldots ,m \\ &{}\sum \limits _{j=1}^n {\lambda _j e_{kj} +s_k ^{e-}=e_k ,}\quad k=1,\ldots ,d \\ &{}\sum \limits _{j=1}^n {\lambda _j y_{rj} -s_r ^{y+}=y_r ,}\quad r=1,\ldots ,s \\ &{}\sum \limits _{j=1}^n {\lambda _j b_{gj} +s_g ^{b-}=b_g ,}\quad g=1,\ldots ,p \\ &{}\sum \limits _{j=1}^n {\lambda _j =1,}\\ &{}\lambda _j ,s_i ^{x-},s_k ^{e-},s_r ^{y+},s_g ^{b-}\ge 0,\quad \forall j,i,k,r,g \Big \} \\ \end{array} \end{aligned}$$
(1)

In model (1), \(\lambda _j ,(j=1,\ldots ,n)\) are intensity variables for connecting inputs and outputs by a convex combination associated with each DMU\(_{j}\). \(s_i ^{x-}\), \((i=1,\ldots ,m)\), \(s_k ^{e-}\), (\(k=1,\ldots ,d)\), \(s_r ^{y+}\), \((r=1,\ldots ,s)\), and \(s_g ^{b-}\), \((g=1,\ldots ,p)\) are slack variables for non-energy, energy, desirable outputs, and undesirable outputs. In the transportation sector, each DMU likes to produce desirable outputs as much as possible, while at the same time emitting undesirable outputs and consuming non-energy and energy resources as little as possible.

We present our DEA framework based on the SBM developed by Tone [31]. The SBM–DEA model in this study extends prior SBM–DEA models by adding the undesirable output into both the objective function and constraints function. Since our paper mainly focuses on efficiency evaluation considering energy saving and undesirable outputs reduction, our approach mainly focuses on the slack variables of energy inputs and undesirable outputs. In other words, this paper differs from others in that we evaluate efficiency considering both energy and environmental factors.

Using Tone’s [31] SMB model and considering energy inputs and undesirable outputs, the corresponding SMB–DEA model can be written as the following model (2).

$$\begin{aligned} \begin{array}{ll} Min&{} \theta _0 =\frac{1-\frac{1}{d}\sum \nolimits _{k=1}^d {\frac{s_k ^{e-}}{e_{k0} }} }{1+\frac{1}{p}\sum \nolimits _{g=1}^p {\frac{s_g ^{b-}}{b_{g0} }} } \\ &{}s.t. \sum \limits _{j=1}^n {\lambda _j x_{ij} +s_i ^{x-}=x_{i0},}\quad i=1,\ldots ,m \\ &{}\sum \limits _{j=1}^n {\lambda _j e_{kj} +s_k ^{e-}=e_{k0} ,}\quad k=1,\ldots ,d \\ &{}\sum \limits _{j=1}^n {\lambda _j y_{rj} -s_r ^{y+}=y_{r0} ,}\quad r=1,\ldots ,s \\ &{}\sum \limits _{j=1}^n {\lambda _j b_{gj} +s_g ^{b-}=b_{g0} ,}\quad g=1,\cdots ,p \\ &{}\sum \limits _{j=1}^n {\lambda _j =1,}\\ &{}\lambda _j ,s_i ^{x-},s_k ^{e-},s_r ^{y+},s_g ^{b-}\ge 0,\quad \forall j,i,k,r,g \\ \end{array} \end{aligned}$$
(2)

The subscript 0 denotes the DMU whose energy and environmental efficiency is being measured. Obviously, the index \(\theta _{0}\) for energy and environmental efficiency is between 0 and 1. The larger the index, the better the corresponding region performs both in saving energy and protecting the environment. The DMU is efficient in the presence of energy inputs and undesirable outputs if \(\theta _{0} ^*=1\), indicating that all the energy and undesirable output slacks variable are 0 (\(s_k ^{e-}=s_g ^{b-}=0\)).

However, model (2) is a nonlinear program, and we need to transform it into a standard linear program by using the transformation suggested by Tone [31]. Let \(1+\sum \nolimits _{g=1}^p {\frac{s_g^{b-}}{b_{g0}}} =\frac{1}{t}\), \({\lambda }^{\prime }_{j}=t\lambda _{j} ,{s}_{i}^{\prime x-}=ts_{i}^{x-},{s}_{k} ^{\prime e-}=ts_{k}^{e-},{s}_{r}^{\prime y+}=ts_{r}^{y+},{s}_{g}^{\prime b-}=ts_{g}^{b-}\ge 0,\forall j,i,k,r,g\). Then model (2) can be transformed into following linear model (3).

$$\begin{aligned} \begin{array}{ll} Min&{} \theta _0 =t-\frac{1}{d}\sum \nolimits _{k=1}^d {\frac{{s}_k ^{\prime e-}}{e_{k0} }} \\ &{}s.t. \sum \limits _{j=1}^n {{\lambda }_j x_{\prime ij} +{s}_i ^{\prime x-}=tx_{i0} ,}\quad i=1,\ldots ,m \\ &{}\sum \limits _{j=1}^n {{\lambda }_j e_{\prime kj} +{s}_k ^{\prime e-}=te_{k0} ,} \quad k=1,\ldots ,d \\ &{}\sum \limits _{j=1}^n {{\lambda }_j y_{\prime rj} -{s}_r ^{\prime y+}=ty_{r0} ,} \quad r=1,\ldots ,s(3) \\ &{}\sum \limits _{j=1}^n {{\lambda }_j b_{\prime gj} +{s}_g ^{\prime b-}=tb_{g0} ,} \quad g=1,\ldots ,p \\ &{}t+\frac{1}{p}\sum \nolimits _{g=1}^p {\frac{{s}_g ^{\prime b-}}{b_{g0} }} =1 \\ &{}\sum \limits _{j=1}^n {{\lambda }\prime _j =t,}\\ &{}{\lambda }^{\prime }_j ,{s}_i ^{\prime x-},{s}_k ^{\prime e-},{s}_r ^{\prime y+},{s}_g ^{\prime b-},t\ge 0,\quad \forall j,i,k,r,g \\ \end{array} \end{aligned}$$
(3)

3 Empirical study

3.1 Input and output indicators

In this section, we examine the energy and environmental efficiency in the transportation sectors of 30 provinces in mainland China in 2011. We excluding Tibet due to the absence of relevant data on energy and undesirable output for that area. The transportation sector in China is defined to consist of transport, storage, and post according to China’s Statistical Yearbooks, so we follow this definition to collect the relevant data in China. As Golany and Roll [16] indicated, the number of evaluated DMUs should be more than five times the total selected number of inputs and outputs, otherwise the validity and credibility of the results will be seriously compromised. Hence, following many studies [5, 7, 12, 38], our study selects two non-energy inputs, one energy input, one desirable output, and one undesirable output considering the production process of transportation sector. Therefore, labor and investment of fixed assets (namely capital) are used as two non-energy inputs, the volume of energy consumed in the transportation sector in the energy input, a value-added amount in the transportation sector is the only desirable output, and the volume of CO\(_{2}\) emissions related to fuel used in the sector is the only undesirable output. The total energy consumption includes all types of energy, such as coal, oil, natural gas, and electricity, but we convert these energies to the ton coal equivalent (tce). The input–output measures that are used in this process are summarized in Table 1.

Table 1 Variables of inputs and outputs
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The data related to non-energy inputs, energy input, and desirable output are collected from “China Statistical Yearbook 2012”, “China City Statistical Yearbook 2012”, and “China Energy Statistical Yearbook 2012”. Unfortunately, there are no official statistics yet on provincial CO\(_{2}\) emission in China. Therefore, following Bi et al. [5] and Chang et al. [7], we estimate the CO\(_{2}\) emissions in the regional transportation sectors for the year of 2011 by using a fuel-based carbon footprint model. After collecting the related data on the inputs and outputs, a data set encompassing 30 provinces in 2011 is prepared for analysis in Table 2.

Table 2 Raw data on 30 provincial transportation sectors of China
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3.2 Results of our approach and analysis

We use the proposed model to evaluate the energy and environmental efficiency of 30 Chinese regional transportation sectors. The evaluation results are listed in the following Table 3. Along with the efficiencies, we also provide the potential reduction of energy and CO\(_{2}\) emissions (which are measured by the slack variables \(s_l^{e-} \) and \(s_k^{b-} \) respectively) for the sectors.

Table 3 Efficiency evaluation results
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In the results, several conclusions can be drawn. Firstly, we can see that only 6 of the 30 regional transportation sectors are evaluated as efficient. They are Hebei, Jiangsu, Shandong, Hainan, Qingdao, and Ningxia. They all get the efficiency scores 1. Transportation sectors in these regions perform well mainly because in recent years these regions have made great progress in many aspects, such as the implementation of technology innovation policies, to improve energy and environmental efficiencies in their transportation sectors. Also, we can see from the results that there is no need for these transportation sectors in these regions to reduce their energy consumptions or CO\(_{2}\) emissions.

Secondly, the efficiency scores of the inefficient transportation sectors are generally low. Among them the transportation sector with the highest efficiency (0.7543) is Zhejiang and that with the lowest efficiency (0.1078) is Yunnan. Twenty-three of the inefficient transportation sectors’ efficiency scores are smaller than 0.6. This shows that China has bad performance in energy saving and CO\(_{2}\) emissions reduction in its transportation industry. In the recent past, China’s regional transportation sectors have experienced a huge expansion. In order to meet the needs of economic development, massive amounts of input resources are used in transportation systems. But the output is far less than the ideal targets. Therefore, there is great potential for these inefficient regions to reduce energy consumption and CO\(_{2}\) emission.

Thirdly, we see that there exist potential reductions in energy consumption and CO\(_{2}\) emissions of the transportation sectors in the regions. Table 3 shows that except for the 6 efficient regions, the other regions all need to reduce their energy consumption and CO\(_{2}\) emission. Among the inefficient regions, Guangdong can reduce largest amount of energy consumption, with potential for saving 955.95 thousand TECs. Tianjin could reduce only 88.71 TECs in energy consumption, which is the smallest reduction among these inefficient regions. The potential in the reductions of CO\(_{2}\) emissions are also very great among the inefficient DMUs. These reductions range from 1953225.3 tons in Gansu to 20,257,513 t in Guangdong. From a whole system point of view, China has great potential for energy saving and CO\(_{2}\) emissions reduction in its transportation system. The data indicate that China has the potential to save a total amount of 7906.14 thousand TECs and to reduce a total amount of 168,257,417.90 t of CO\(_{2}\) emissions to achieve a better energy and environmental efficiency. This is bad news as well as good news for China. It is bad news because this result indicates that China has very bad performance in energy saving and CO\(_{2}\) emissions abatement in its transportation systems. The reason that we call it good news can be explained as the follows. The large potential for reductions in energy consumption and CO\(_{2}\) emissions indicate not only that China can improve its energy and environmental efficiency through energy saving and CO\(_{2}\) emissions abatement but also that theoretically China can fulfill its promise to the world about saving energy and making CO\(_{2}\) emissions abatement without reducing its current desirable outputs.

Finally, we divide the 30 regions into 6 bigger areas as shown in Table 4. Then, we calculate the areas’ average efficiencies as well as average amounts of energy saving and CO\(_{2}\) emissions abatement. The results are listed in the following Table 5.

Table 4 Six bigger areas
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Table 5 Calculation results of the six areas
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From the results in Table 5, it is interesting to find that the average efficiencies of East China (0.6032) and Northwest China (0.5657) are higher than those of the other areas. In addition we can see that the average reductions in energy consumption and CO\(_{2}\) emissions in these two areas are generally smaller than those of the other areas. This phenomenon may be explained by two reasons. Firstly, the developed provinces with better economic development level will invest more capital to incorporate advanced technologies for production in transportation sectors, which will result in the situation that more energy is saved and less emissions are produced. Secondly, better economic levels in the relatively more developed areas will attract more skilled labor. The skilled laborers work more effectively in the production, so high efficiency scores are generated.

4 Conclusions

In this paper, we aim at analyzing the energy and environmental efficiency of China’s regional transportation sectors. Firstly, we develop a framework for measuring energy and environmental efficiency of any transportation sector considering energy consumption and CO\(_{2}\) emissions based on an SBM–DEA model. The proposed model can not only be used for evaluating the energy and environmental efficiency for the transportation sectors but also it can effectively identify the potential amount of reductions in both energy consumption and CO\(_{2}\) emissions for those sectors. Our model differs from the other current models mainly in that we consider reductions in both energy consumption and CO\(_{2}\) emissions when evaluating the transportation sectors.

The results of our empirical study show that most of the regional transportation sectors in China have low energy and environmental efficiencies. China has not performed eco-efficiently in its transportation industry, and it has great potential in reducing its energy consumption and CO\(_{2}\) emissions. From a whole system point of view, China has the potential to save a total of 7906.14 thousand TECs and to eliminate a total of 168,257,417.90 t of CO\(_{2}\) emissions to achieve better energy and environmental efficiency. In addition, we find that the average efficiencies of East China (0.6032) and Northwest China (0.5657) are higher than those of the North China, Northeast China, Central South China, and Southwest China.

Two further research directions can be drawn from our study. Firstly, we analyze the energy and environmental efficiency of China’s regional sectors using only the data of 2010. Data of more years could be incorporated to do a dynamic analysis for the transportation sectors. Secondly, our model can be extended under the assumptions of other types of returns to scale, i.e., constant returns to scale, increasing returns to scale, and decreasing returns to scale.