The evaluation of transportation energy efficiency: An application of three-stage virtual frontier DEA

Transportation Research Part D 29 (2014) 1–11

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Transportation Research Part D journal homepage: www.elsevier.com/locate/trd

The evaluation of transportation energy efficiency: An application of three-stage virtual frontier DEA Qiang Cui a,⇑, Ye Li b a b

Transportation Management College, Dalian Maritime University, No. 1 Linghai Road, Dalian City 116026, China Faculty of Management and Economics, Dalian University of Technology, No. 2 Linggong Road, Dalian City 116024, China

a r t i c l e

i n f o

Keywords: Transportation energy efficiency Three-stage virtual frontier DEA Evaluation Provincial administrative regions

a b s t r a c t In this paper, transportation energy efficiency is newly defined and its inputs and outputs are obtained through literature review. Labor input, capital input and energy input are selected as the inputs, passenger turnover volume and freight turnover volume are defined as the outputs. A new model—three-stage virtual frontier DEA (three-stage virtual frontier Data Envelopment Analysis) is proposed to evaluate transportation energy efficiencies. The case of thirty Chinese PARs (provincial administrative regions) from 2003 to 2012 is applied to verify its rationality. In the three-stage virtual frontier DEA, the reference DMU (decision-making unit) set and the evaluated DMU set are two different sets so that it can distinguish the DEA efficient DMUs. And in the evaluating process, the reference DMU set remains unchanged to assure its results more reasonable than Super DEA model. The results show that transport structure and management measures have important impacts on transportation energy efficiency. Ó 2014 Elsevier Ltd. All rights reserved.

Introduction In recent years, the rapid economic growth of China has resulted in the extrusive contradiction between energy supply and demand. According to National Bureau of Statistics of China, in 2012, transportation sector’s energy consumption volume is 302 million tons standard coal and is one of the few sectors whose consumption increase rate are more than 7.2% in the past 10 years. However, the average increase rate of energy production in the past 10 years is less than 6%. The contradiction between energy supply and demand is becoming more and more apparently. Meanwhile, the passenger transport volume is 37.9 billion person-times and the freight transport volume is 41.2 billion tons. The average increase rate of passenger transport volume in the past 10 years is 7.6% and that of freight transport volume is 11.5%. More infrastructure investment and energy consumption will be stimulated by the huge transportation demand. Great public attentions have been drawn on the energy utilization problem of transportation industry. Energy efficiency is defined to reflect whether the energy has been used efficiently (Clinch et al., 2001; Shi et al., 2008; Blomberg et al., 2012). For the past few years, a small number of papers had focused on the energy efficiency of transportation sector. Greene and Fan (1994) used Divisia method to calculate transportation energy efficiency trends in U.S. from 1972 to 1992, the results showed that passenger transportation’s energy efficiency had increased from 1972 to 1977 but decreased from 1977 to 1992, freight transportation’s energy efficiency had varied extremely from 1972 to 1992. Vanek and Morlok (2000) analyzed

⇑ Corresponding author. Tel.: +86 411 84728486; fax: +86 411 84726939. E-mail address: [email protected] (Q. Cui). http://dx.doi.org/10.1016/j.trd.2014.03.007 1361-9209/Ó 2014 Elsevier Ltd. All rights reserved.

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Q. Cui, Y. Li / Transportation Research Part D 29 (2014) 1–11

the freight energy efficiency of U.S. through commodity-based analysis and commodity groups varied widely in the ratio of energy use in production to energy use in transport. Ahman (2001) considered the technical potential concerning the energy efficiency attainable for vehicles with alternative power trains within 10–20 years, the results showed that there was potential for doubling the primary energy efficiency using alternative power trains in vehicles. Advenier et al. (2002) analyzed the energy efficiency of road transportation with different technologies and different fuels, the results showed that natural gas had the highest efficiency. Ji and Chen (2006) assessed energy efficiencies of Chinese transport sector from 1978 to 2002, waterways transport was proved the most effective one, followed by railways, highways and civil aviation in that order. Utlu and Hepbasli (2006) compared the energy and exergy utilization efficiencies in the Turkish transportation sector with other countries from 2000 to 2020, roadway appeared to be the most efficient mode when compared with railway, air and seaway. Ediger and Camdali (2007) examined energy and exergy efficiencies in Turkish transportation sector from 1988 to 2004, the results showed that the overall efficiency patterns were basically controlled by the fuel consumption in airways. Saidur et al. (2007) calculated the energy and exergy efficiencies of transportation sector in Malaysia from 1995 to 2003. The results showed that road sub-sector had appeared to be the most efficient one compared to the air and marine sub-sectors. Jaber et al. (2008) presented energy analysis and exergy utilization in the transportation sector of Jordan and the average estimated overall energy efficiency was found as 23.2%. Ji et al. (2009) used time series analyses for the emission exergy and emission exergy intensity of the whole Chinese transportation as well as for its four sectors of highways, railways, waterways and civil aviation from 1978 to 2004. However, transportation energy efficiencies in above papers are defined as the heat amount released at certain temperature and certain pressure. It cannot reflect the relationship between transportation inputs and its outputs. In this paper, transportation energy efficiency is defined as an efficiency, which is calculated through comparing the relationship between the outputs and the inputs. Transportation energy efficiency evaluates the effects of the inputs, which is vital to the energy usage performance of transportation sector. The selection of inputs and outputs According to the above literature review, few literatures define transportation energy efficiency as the relationship of transportation inputs and its outputs. So this paper will summarize existing energy efficiency papers to lay theoretical foundation for building reasonable index system of transportation energy efficiency. The inputs and outputs in some studies are shown in Table 1. From Table 1, it can be concluded that labor input, capital input and energy input are defined as the inputs in most papers. For outputs, most papers’ energy efficiencies contain added value. In this paper, according to the common aspects of transportation energy efficiency and other energy efficiencies, the inputs of transportation energy efficiency are chosen from the aspects of labor input, capital input and energy input. The outputs are chosen from the aspects of passenger transport performance and freight transport performance. According to the literature review and the reality of transportation industry, this paper selects the inputs and outputs for transportation energy efficiency. Three measurable variables are selected as the inputs: labor input (number of staffs working in transportation industry), capital input (transportation fixed assets investment) and energy input (transportation Table 1 The inputs and outputs in some energy efficiency papers. Papers

Inputs

Outputs

Boyd and Pang (2000) Clinch et al. (2001) Ramanathan (2005)

Electric, fuel Labor input, cost input, energy input CO2 emissions per capita, Fossil fuel energy consumption

Onut and Soner (2006)

Number of employees, annual electricity consumption, annual water consumption, annual liquefied petroleum gas consumption Final consumption of electricity, thermal aggregation of all fossil fuels final consumptions Labor input, capital input, energy input Industrial capital stock, industrial labor force, industrial energy consumption Labor, capital, energy, materials Capital, labor, energy, materials, services Annual data on industrial investment in fixed assets, Industrial energy consumption, industrial labor Capital input, labor input, energy input Capital stock, labor force Labor, energy, capital, materials

Add value Energy benefit, environmental benefits Gross domestic product per capita, non-fossil fuel energy consumption Occupancy rate, annual total revenue, total number of guests Gross output, value added from both categories

Azadeh et al. (2007) Hu and Kao (2007) Wei et al. (2007) Mukherjee (2008a) Mukherjee (2008b) Shi et al. (2008) Wang and Zhou (2008) Zhou and Ang (2008) Martínez et al. (2010) Blomberg et al. (2012) Tao et al. (2012) Cui et al. (2014)

Labor, electricity, oil Number of employees, energy consumption, capital stock Number of employees in energy industry, energy consumption amount, energy services amount

Gross domestic product Industrial value added, industrial CO2 emissions Gross value of manufacturing production Gross output Industrial added value, volume of industrial waste gas from the process of fuel burning The gross product value of industrial enterprises Gross domestic product, CO2 emissions The gross value of manufacturing deflated by the wholesale price index Pulp or paper Gross industry output, carbon dioxide emissions CO2 emissions per capita, industrial profit amount

Q. Cui, Y. Li / Transportation Research Part D 29 (2014) 1–11

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energy consumption volume). Two measurable variables are selected as the outputs: freight turnover volume and passenger turnover volume. Methodology Traditional three-stage Data Envelopment Analysis Data Envelopment Analysis (Charnes et al., 1978; Zhou et al., 2008) is a data planning method to evaluate the relative efficiencies of DMUs (decision-making units) with multi-inputs and multi-outputs. It has been applied to theory innovation, model development and practical application. The detailed introductions of DEA (Data Envelopment Analysis) are shown in Appendix A. Traditional three-stage Data Envelopment Analysis was proposed by Fried in 2002 (Fried et al., 2002). It can eliminate the effects of non-operational factors, such as external environment and random error. Three-stage DEA is superior to traditional DEA method in reflecting the operational level of decision-making units (Hsu and Hsueh, 2009; Estelle et al., 2010). It has three main steps: 1. Run traditional DEA model. The traditional DEA model can reflect the validity of decision-making units under the assumption of VRS (Variable Returns Scale). 2. Conduct SFA (Stochastic Frontier Analysis). The model can observe the influence of environmental factors and random factors on the slack variables of the inputs in DEA model, which can get the input redundancy caused by external factors. Then SFA model is applied to adjust the inputs so that the effects of environmental factors and random factors can be eliminated. 3. Run DEA model again. The original inputs are replaced by the adjusted inputs from step 2 and the outputs remain unchanged. Traditional DEA model is run again to get the efficiency without the influence of environmental factors and random factors. Three-stage virtual frontier Data Envelopment Analysis In traditional DEA model, each DMU (decision-making unit) compares its production ability with the production ability of optimal real frontier (Zhu, 2001; Xue and Harker, 2002). When its result is 1, the DMU is DEA efficient; Otherwise, the DMU is DEA inefficient. However, it cannot distinguish the difference among efficient DMUs. Aiming at above disadvantage of traditional DEA, many scholars proposed some improvements. The most representative ones are Super DEA method (Andersen and Petersen, 1993) and some models derived from Super DEA method (Zhu, 2001; Xue and Harker, 2002; Chen, 2005; Chiu et al., 2011). The principle of Super DEA model is excluding the evaluated DMU from the reference DMUs. Its model is:

hd ¼ max

s:t:

uT Y d v T Xd

uT Y i 6 1; v T Xi

u P 0;

i ¼ 1; 2; . . . ; n; i – d

v P0

In general, the results of Super DEA model do not contain same efficiency. However, it has disadvantages too. Four DMUs are taken as examples to illustrate it, as shown in Table 2. In Table 2, when Super DEA model evaluates DMU C, the inputs of reference DMUs are {3,7,4} and the outputs are {6,2,1}. But when Super DEA model evaluates DMU D, the inputs of reference DMUs are {3,7,6} and the outputs are {6,2,5}. The different reference DMUs may bring about unreasonable results. As shown in Fig. 1, when Super DEA model evaluates DMU C, the reference frontier is ADB. When Super DEA model evaluates DMU D, the reference frontier is ACB. The reference frontiers are different, so the results may be unreasonable. The principle of virtual frontier DEA is firstly introduced by the literature (Bian and Xu, 2013), but its model is very complex and the random effects have not considered. The virtual frontier DEA in this paper is the simplified one of Bian and Xu (2013) and it is the first time that virtual frontier DEA is applied in three-stage DEA model. In order to explain virtual frontier DEA better, Fig. 2 is introduced. In traditional DEA model, A, B, C, D, E are the DMUs, A, B, C, D are DEA efficient and E is DEA inefficient. The efficiencies of A, B, C, D are same as 1, so traditional DEA model cannot differentiate them. In this paper, virtual frontier DEA constructs a virtual frontier FGHI as the optimal reference frontier of A, B, C, D and E, then A, B, C, D, E are DEA inefficient. Their efficiencies can be differentiated. If f denotes the evaluated DMU set and w is the reference DMU set (the virtual frontier), the virtual frontier DEA model is

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Q. Cui, Y. Li / Transportation Research Part D 29 (2014) 1–11 Table 2 The example. DMUs

Inputs

Outputs

A B C D

3 7 6 4

6 2 5 1

A

Y

C

B D X Fig. 1. The diagram of the example.

hd ¼ max

s:t:

uT Y d v T Xd

uT Y i 6 1; v T Xi

u P 0;

i ¼ 1; 2; . . . ; n; i 2 w; d 2 f

vP0

In this model, reference DMU set and evaluated DMU set are two different sets, which offers the probability to distinguish the differences of DEA efficient DMUs in traditional DEA model. And in the evaluating process, the reference DMU set remains unchanged so that its results may be more reasonable than Super DEA model. Then this paper will introduce the selection of reference DMU set. According to the literature (Bian and Xu, 2013), the number of reference DMUs should equals to evaluated DMUs. Set x0j ¼ minfxij g and y0r ¼ maxfyir g, i = 1, 2, . . ., n stands for the DMUs, xij denotes the jth input of DMU i, yir stands for the i

i

rth output of DMU i. For reference DMU I, its inputs and outputs are randomly generated. Its inputs’ interval is set as [0.9x0j, x0j] and the outputs’ interval is set as [y0r, 1.1y0r]. Then this paper will discuss the setting of the inputs/outputs improvement targets. If the efficiency of DMU i (i = 1, 2, . . ., n), n stands for the number of DMUs) in year t is hit, its input is xit and its output is yit. In year t, the maximum

F

B

E

y

G

A

K C

J H O

D I

x Fig. 2. The principle of virtual frontier DEA.

Q. Cui, Y. Li / Transportation Research Part D 29 (2014) 1–11

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  hit  xit , that is, when yit remains unchanged, if DMU i efficiency is max ht. The input improvement target of DMU i is 1  max ht   hit improves its efficiency to the maximum efficiency, it can save 1  max  xit input. Similarly, when xit remains unchanged, if ht   hit  yit output. DMU i improves its efficiency to the maximum efficiency, it can increase 1  max ht The main steps of three-stage virtual frontier DEA are as follows: 1. Use virtual frontier DEA model to calculate the efficiency. 2. Conduct Stochastic Frontier Analysis model. The slacks of inputs are defined as the explained variables and the environmental factors are chosen as the explanatory variables, Stochastic Frontier Analysis is conducted to analyze the effects of environmental factors. 3. Run virtual frontier DEA model again. The original inputs are replaced by the adjusted inputs from step 2 and the outputs remain unchanged. Virtual frontier DEA model is run again to get the efficiencies without the impact of environmental factors.

Empirical study The data set In this paper, China’s thirty PARs (provincial administrative regions) are defined as the DMUs. Owing to lack of data, this paper does not consider Taiwan, Hong Kong, Macao and Tibet. The data set is collected and compiled for a period from 2003 to 2012. In 2003, Chinese government began to implement the policy ‘‘new style road of industrialization’’. Its main feature was ‘‘low resource consumption, high utilization efficiency, less environmental pollution’’. Then many PARs made plans to build green transportation and sustainable transportation. The core of these plans was to improve the energy efficiency in transportation sector. It is meaningful to study transportation energy efficiencies of the PARs in this period. Here, each PAR is defined as a DMU and each DMU has three inputs and two outputs. The data of labor input, capital input, passenger turnover volume and freight turnover volume is obtained from ‘‘China Statistical Yearbook’’. The data of energy input is from ‘‘China Energy Statistical Yearbook’’. The data of 2012 is taken as an example and shown in Appendix B.

The results before the inputs are adjusted In order to verify the reasonability of virtual frontier DEA model, this paper employs traditional DEA model to calculate the transportation energy efficiencies for thirty PARs firstly, as shown in Table 3. As shown in Table 3, Beijing, Shanxi, Inner Mongolia, Zhejiang, Fujian, Hainan, Sichuan and Yunnan are efficient as 1 in 2012. Traditional DEA cannot distinguish the larger one and the less one. Aiming at eliminating the effects of random inputs and random outputs, this paper runs virtual frontier DEA twenty times and sets the average value as the virtual frontier DEA efficiency of the DMU. The transportation energy efficiencies of thirty PARs are calculated through Matlab programming, as shown in Table 4. The efficiency of DEA is relative efficiency and there are relatively small differences between the two PARs rankings in Tables 3 and 4, so it is reasonable to use virtual frontier DEA to calculate transportation energy efficiency. Furthermore, in virtual frontier DEA, all the PARs are inefficient so that the efficiency difference can be shown, which improves the disadvantage of traditional DEA.

The results of Stochastic Frontier Analysis Firstly, the environmental factors should be selected. According to the existing papers in three-stage DEA (Hsu and Hsueh, 2009; Estelle et al., 2010) and the real situation of China’s transportation industry, environmental factors are the factors influencing transportation energy efficiency but outside the control of the samples. They are selected as follows: opening degree to outside, per capita Gross Domestic Product, per capita disposable income and the proportion of private capital. Opening degree to outside is the proportion of total import and export volume to Gross Domestic Product. In China, some PARs have sea ports, some have river ports and some have no ports, the endowment will affect the opening degree and the structure of transportation system. Opening degree can reflects the effects of different transportation structure on transportation energy efficiency. Per capita Gross Domestic Product is defined to reflect the effects of economic level on transportation energy efficiency. Per capita disposable income reflects the effects of market demand on transportation energy efficiency. Different income level has profound impact on people’s transportation choice, then it will influence the PAR’s transportation structure. The proportion of private capital is defined to reflect the effects of capital structure on transportation energy efficiency. It is the proportion of private capital to total capital. The data is obtained from ‘‘China Statistical Yearbook’’. The slacks of the three inputs are obtained through software DEAP 2.1. The results of SFA analysis are shown in Table 5.

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Table 3 The results of traditional DEA model. PARs

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

Average

Beijing Tianjin Hebei Shanxi Inner Mongolia Liaoning Jilin Heilongjiang Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Henan Hubei Hunan Guangdong Guangxi Hainan Chongqing Sichuan Guizhou Yunnan Shaanxi Gansu Qinghai Ningxia Xinjiang

1.000 0.652 0.484 0.393 0.391 0.416 0.522 0.521 1.000 0.487 1.000 0.384 0.558 0.453 0.539 0.418 0.597 0.511 0.611 0.577 0.990 0.684 1.000 0.633 0.835 0.499 0.663 1.000 1.000 0.727

1.000 0.658 0.259 0.493 0.474 0.657 0.486 0.576 1.000 0.590 0.700 0.325 0.541 0.592 0.241 0.344 0.657 0.483 0.779 0.625 0.992 0.666 1.000 0.709 0.933 0.527 0.855 1.000 1.000 0.939

1.000 0.722 0.179 0.497 0.567 0.656 0.509 0.519 1.000 0.675 0.615 0.322 0.564 0.795 0.214 0.356 0.778 0.527 0.887 0.657 1.000 0.808 1.000 0.715 1.000 0.539 0.679 1.000 1.000 0.939

1.000 1.000 0.319 0.544 0.856 0.541 0.449 0.481 1.000 0.920 1.000 0.523 0.796 0.919 0.600 0.588 0.961 0.620 0.860 0.663 0.945 0.817 0.895 0.747 1.000 0.606 0.613 1.000 1.000 0.798

1.000 0.718 0.415 0.761 1.000 0.731 0.629 0.581 1.000 0.971 1.000 0.580 0.940 1.000 0.729 0.750 1.000 0.777 1.000 0.844 1.000 1.000 1.000 0.873 1.000 0.718 0.697 1.000 0.714 0.852

1.000 0.758 0.572 0.586 1.000 0.879 0.595 0.513 1.000 0.645 1.000 0.511 0.645 0.743 1.000 0.598 0.828 0.627 0.876 0.619 0.698 0.736 0.785 0.626 1.000 0.510 0.493 1.000 0.891 0.794

1.000 0.840 0.562 0.601 1.000 0.808 1.000 0.556 1.000 1.000 1.000 0.754 0.705 0.754 1.000 0.751 0.771 0.665 0.791 0.648 0.717 0.975 1.000 0.676 1.000 0.665 0.476 0.789 0.911 0.826

1.000 0.928 0.731 0.535 1.000 0.779 0.677 0.488 1.000 0.613 1.000 0.675 1.000 0.517 1.000 0.478 0.799 0.578 0.786 0.607 0.739 0.817 0.909 0.721 1.000 0.616 0.481 0.959 0.902 0.784

1.000 0.845 0.659 0.837 1.000 0.743 0.634 0.657 1.000 0.705 0.981 0.645 1.000 0.453 1.000 0.498 0.750 0.696 0.866 0.745 1.000 0.974 0.952 0.959 1.000 0.715 0.473 1.000 0.807 0.791

1.000 0.855 0.737 1.000 1.000 0.684 0.649 0.802 1.000 0.689 0.817 0.596 1.000 0.468 1.000 0.424 0.716 0.878 0.844 0.704 1.000 0.924 1.000 0.911 1.000 0.757 0.485 0.818 0.703 0.760

1.000 0.798 0.492 0.625 0.829 0.689 0.615 0.569 1.000 0.730 0.911 0.532 0.775 0.669 0.732 0.521 0.786 0.636 0.830 0.669 0.908 0.840 0.954 0.757 0.977 0.615 0.592 0.957 0.893 0.821

The bold values are labled to highlight the efficient DMUs in each year.

Table 4 The results of virtual frontier DEA model. PARs

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

Beijing Tianjin Hebei Shanxi Inner Mongolia Liaoning Jilin Heilongjiang Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Henan Hubei Hunan Guangdong Guangxi Hainan Chongqing Sichuan Guizhou Yunnan Shaanxi Gansu Qinghai Ningxia Xinjiang

0.916 0.552 0.267 0.213 0.191 0.276 0.396 0.382 0.969 0.274 0.909 0.299 0.396 0.408 0.353 0.252 0.495 0.305 0.440 0.343 0.858 0.441 0.993 0.435 0.696 0.331 0.521 0.929 0.949 0.582

0.996 0.487 0.082 0.293 0.169 0.409 0.172 0.302 0.915 0.395 0.536 0.125 0.266 0.360 0.044 0.125 0.422 0.272 0.628 0.383 0.953 0.501 0.930 0.504 0.618 0.291 0.594 0.927 0.941 0.676

0.991 0.595 0.057 0.282 0.250 0.370 0.355 0.283 0.932 0.448 0.505 0.228 0.247 0.562 0.116 0.111 0.407 0.265 0.683 0.347 0.954 0.587 0.914 0.482 0.973 0.274 0.374 0.926 0.939 0.767

0.996 0.903 0.178 0.279 0.651 0.350 0.250 0.253 0.925 0.707 0.942 0.342 0.545 0.651 0.460 0.401 0.781 0.387 0.708 0.438 0.758 0.573 0.595 0.677 0.961 0.476 0.373 0.928 0.937 0.483

0.954 0.593 0.239 0.584 0.965 0.474 0.459 0.264 0.921 0.719 0.933 0.458 0.756 0.962 0.495 0.610 0.916 0.628 0.930 0.552 0.957 0.886 0.934 0.784 0.890 0.698 0.487 0.928 0.540 0.489

0.987 0.528 0.512 0.385 0.975 0.694 0.357 0.269 0.870 0.475 0.955 0.495 0.255 0.379 0.937 0.441 0.628 0.535 0.709 0.548 0.455 0.573 0.521 0.491 0.990 0.302 0.294 0.928 0.740 0.596

0.998 0.710 0.419 0.472 0.981 0.674 0.951 0.370 0.932 0.885 0.926 0.513 0.453 0.680 0.948 0.615 0.415 0.523 0.496 0.460 0.657 0.856 0.939 0.404 0.975 0.394 0.200 0.530 0.737 0.695

0.920 0.750 0.605 0.364 0.982 0.467 0.353 0.275 0.909 0.491 0.927 0.472 0.945 0.361 0.961 0.238 0.496 0.379 0.531 0.454 0.453 0.687 0.720 0.492 0.970 0.487 0.287 0.833 0.838 0.592

0.980 0.658 0.552 0.502 0.905 0.420 0.319 0.337 0.912 0.582 0.613 0.443 0.943 0.218 0.753 0.305 0.497 0.578 0.613 0.401 0.969 0.904 0.814 0.812 0.989 0.357 0.259 0.942 0.646 0.522

0.975 0.601 0.514 0.961 0.972 0.497 0.408 0.621 0.921 0.461 0.550 0.338 0.925 0.384 0.979 0.265 0.454 0.589 0.715 0.591 0.965 0.900 0.901 0.798 0.988 0.513 0.248 0.542 0.449 0.526

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According to the literatures (Kraft and Tırtırog˘lu, 1998; Cullinane et al., 2006), if one environmental factor’s coefficient is negative, its increase will lead to less input slacks. That is, its increase will result in less input waste or more outputs. If its coefficient is positive, its increase will generate more input waste or less outputs. 1. Opening degree to outside. All its coefficients on the three inputs are negative and significant on 1% level. Larger opening degree can improve transportation energy efficiency. When the outputs are fixed, larger opening degree means input decrease and less input slacks. 2. Per capita Gross Domestic Product. All its coefficients on the three inputs are positive. They are significant for labor input on 10% level and are significant for capital input and energy input on 5% level. This result is inconsistent with the expected one. Most likely, the increase of per capital GDP will increase the income expectation of transportation practitioners and bring about large scale of operation. However, blind expansion may result in extensive utilization of production factors and the increase of input slacks. 3. Per capita disposable income. All its coefficients on the three inputs are negative and can pass the significance test. Higher disposable income can improve transportation energy efficiency. When the outputs are fixed, higher disposable income means input decrease and less input slacks. 4. The proportion of private capital. All its coefficients on the three inputs are positive. It is significant for labor input and energy input but not significant for capital input. More proportion of private capital will lead to more input slacks and is unfavorable to improve transportation energy efficiency. This result has disagreement with the expected one. Probably, although private capital has higher operational efficiency, its scale is too small to gain economies of scale. The results after the inputs are adjusted According to the results of SFA analysis, environmental factors have big influence on transportation energy efficiency, so transportation energy efficiency should be calculated again after the inputs are adjusted. Virtual frontier DEA is run again and the results are shown in Table 6. As shown in Table 6, the largest average energy efficiency from 2003 to 2012 is from Jiangxi, followed by Tianjin. From the original data, it can be concluded that the high efficiency depends on high passenger turnover volume per staff and high freight turnover volume per ton standard coal. Jiangxi’s passenger turnover volume per staff is 450,322 person-kilometers and Tianjin’s corresponding data is 357,314 person-kilometers. By contrast, the least one Yunnan’s corresponding data is 37,136 person-kilometers. Jiangxi’s freight turnover volume per ton standard coal is 279,599 ton-kilometers and Tianjin’s corresponding data is 243,544 ton-kilometers. The least one Yunnan’s corresponding data is only 11,339 ton-kilometers. These results have close relationship with the transport structure. There are many mountains and tunnels in Yunnan, which leads to high road and railway construction cost. Furthermore, Yunnan is an inland provinces and it does not have sea ports. Its proportion of passengers and freights in air transport is bigger than other PARs, so the passenger turnover volume per staff and freight turnover volume per ton standard coal are very low. Consequently, its transportation energy efficiency is very low. Then it can be concluded that transport structure has important impact on transportation energy efficiency. The average transportation energy efficiency of eastern PARs (Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong and Hainan) is 0.614 and larger than the average level of thirty PARs (0.578). The

Table 5 The results of SFA analysis. Dependent variable

Labor input

Capital input

Energy input

Constant term

12.3*** (2.39) 122.3*** (2.87) 0.0353* (2.76) 0.219** (2.467) 220.4** (3.334) 140.2* (11.345) 0.0033*** (2.455)

134.7*** (5.53) 114.2*** (3.24) 0.798** (0.653) 0.207* (4.452) 2130.53 (20.398) 192.34** (3.984) 0.0266** (2.8843)

40.3*** (4.36) 10.32*** (2.42) 0.472** (0.834) 0.483*** (0.353) 41.376** (6.24) 170.35** (7.234) 0.000*** (3.523)

167.9 16.78

223.4 17.32

125.3 17.402

Opening degree to outside Per capita Gross Domestic Product Per capita disposable income The proportion of private capital

r2

c Log likelihood LR test of the one sided error Note: The number in bracket denotes t statistics. Significant on 10%. Significant on 5%. *** Significant on 1%. *

**

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Table 6 The results of three-stage virtual frontier DEA. PARs

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

Average

Beijing Tianjin Hebei Shanxi Inner Mongolia Liaoning Jilin Heilongjiang Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Henan Hubei Hunan Guangdong Guangxi Hainan Chongqing Sichuan Guizhou Yunnan Shaanxi Gansu Qinghai Ningxia Xinjiang

0.762 0.645 0.935 0.465 0.510 0.619 0.420 0.341 0.782 0.687 0.654 0.965 0.882 0.993 0.823 0.829 0.591 0.952 0.691 0.940 0.437 0.716 0.549 0.876 0.370 0.642 0.661 0.301 0.426 0.508

0.876 0.872 0.923 0.416 0.646 0.571 0.580 0.620 0.264 0.736 0.652 0.787 0.669 0.937 0.739 0.772 0.600 0.943 0.851 0.829 0.446 0.791 0.617 0.766 0.471 0.681 0.724 0.404 0.391 0.787

0.965 0.742 0.968 0.411 0.609 0.646 0.584 0.655 0.961 0.718 0.693 0.808 0.631 0.939 0.856 0.782 0.674 0.913 0.992 0.847 0.457 0.710 0.636 0.714 0.437 0.660 0.709 0.417 0.395 0.743

0.757 0.752 0.725 0.401 0.488 0.596 0.360 0.431 0.600 0.542 0.637 0.970 0.530 0.638 0.764 0.915 0.498 0.877 0.715 0.786 0.487 0.503 0.603 0.572 0.324 0.504 0.570 0.396 0.415 0.524

0.633 0.752 0.652 0.402 0.347 0.526 0.482 0.495 0.319 0.581 0.531 0.876 0.488 0.649 0.599 0.649 0.467 0.862 0.585 0.703 0.501 0.413 0.611 0.611 0.601 0.571 0.588 0.491 0.571 0.525

0.734 0.863 0.786 0.398 0.276 0.488 0.387 0.496 0.357 0.635 0.507 0.774 0.491 0.692 0.597 0.672 0.501 0.376 0.569 0.687 0.621 0.378 0.622 0.645 0.280 0.543 0.608 0.441 0.379 0.426

0.606 0.926 0.642 0.311 0.201 0.250 0.319 0.352 0.525 0.488 0.433 0.860 0.414 0.612 0.233 0.621 0.295 0.574 0.325 0.430 0.444 0.279 0.354 0.470 0.211 0.402 0.544 0.439 0.237 0.322

0.749 0.987 0.778 0.453 0.301 0.475 0.402 0.522 0.393 0.822 0.606 0.265 0.472 0.887 0.660 0.851 0.477 0.998 0.653 0.692 0.489 0.401 0.587 0.652 0.305 0.520 0.990 0.399 0.489 0.657

0.637 0.526 0.590 0.401 0.436 0.479 0.383 0.334 0.562 0.504 0.462 0.627 0.287 0.813 0.728 0.800 0.445 0.722 0.443 0.500 0.302 0.284 0.473 0.465 0.279 0.420 0.940 0.303 0.567 0.472

0.452 0.739 0.554 0.215 0.320 0.571 0.346 0.297 0.743 0.480 0.423 0.623 0.252 0.728 0.687 0.880 0.407 0.554 0.413 0.470 0.311 0.326 0.323 0.384 0.244 0.401 0.927 0.292 0.505 0.401

0.717 0.780 0.755 0.387 0.413 0.522 0.426 0.454 0.551 0.619 0.560 0.755 0.512 0.789 0.669 0.777 0.496 0.777 0.624 0.688 0.449 0.480 0.538 0.615 0.352 0.534 0.726 0.388 0.438 0.536

average one of middle PARs (Shanxi, Anhui, Jiangxi, Henan, Hubei, Hunan, Jilin and Heilongjiang) is 0.608 and larger than the average level. The average one of western PARs (Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia and Xinjiang) is 0.519 and less than the average level. Eastern PARs have good management measures to arouse people’s work efficiency. Eastern PARs’ average passenger turnover volume per staff of is 252,768 person-kilometers and its average freight turnover volume per staff is 1,834,878 ton-kilometers. By contrast, the corresponding values of middle PARs are 208,441 person-kilometers and 665,251 ton-kilometers respectively. The corresponding values of western PARs are 131,559 person-kilometers and 442,364 ton-kilometers respectively. These gaps lead to different transportation energy efficiencies. Then it can be concluded that management measures have important impact on transportation energy efficiency. The change situation of transportation energy efficiency after 2008 should cause enough attentions. In 2008, Chinese government launches 4 trillion RMB stimulus plan to cope with the financial crisis and transportation industry is an important part of the plan. A great deal of money is invested on transportation infrastructure construction and most PARs’ transportation energy efficiencies are improved by the increasing passenger turnover volume and freight turnover volume during 2009–2010. However, owing to the investment increase and the limited transportation flow volume, the transportation energy efficiencies of most PARs have been decreasing during 2010–2012. Furthermore, the increasing investment leads to high price and low consumption ability and the increase of passengers and freights falls behind the increase of transportation infrastructure inputs, so the transportation energy efficiency is decreasing. Then this paper will discuss the input/output improvement targets of all PARs. Owing to the topic transportation energy efficiency, this paper assumes other inputs remain unchanged and takes energy input saving targets as an example. The calculation methods of the saving potentials of other two inputs and the increase potentials of the two outputs are same. According to the principle of Section ‘Three-stage virtual frontier Data Envelopment Analysis’, the energy-saving potentials of all PARs are shown in Table 7.

The verification of the new model In order to verify the rationality of three-stage virtual frontier DEA model, this paper compares it with traditional DEA model, traditional three-stage DEA model and virtual frontier DEA model. The main measurement index is Spearman correlation coefficient (Bonneterre et al., 1990; Lesurtel et al., 2003). It reflects the relevance between comprehensive transportation energy efficiency and the outputs. This paper defines the average value of passenger turnover volume from 2003 to 2012 as the first output and the average value of freight turnover volume from 2003 to 2012 as the second output. Similarly,

9

Q. Cui, Y. Li / Transportation Research Part D 29 (2014) 1–11 Table 7 The energy-saving potentials of all PARs (104 tons standard coal). PARs

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

Beijing Tianjin Hebei Shanxi Inner Mongolia Liaoning Jilin Heilongjiang Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Henan Hubei Hunan Guangdong Guangxi Hainan Chongqing Sichuan Guizhou Yunnan Shaanxi Gansu Qinghai Ningxia Xinjiang

60.4 80.1 12.4 88.7 62.2 159.5 83.6 179.6 119.2 103.5 129.4 4.8 22.9 0.0 31.8 39.1 149.1 12.0 279.5 11.8 47.0 33.9 136.5 16.4 98.1 47.0 79.3 18.3 64.7 83.7

22.3 15.1 4.4 118.1 41.2 251.6 53.2 96.2 460.5 97.6 137.8 29.0 61.5 1.4 59.2 44.4 158.0 0.0 97.5 32.3 45.8 20.2 120.8 27.0 130.2 42.9 63.1 14.6 66.3 37.4

9.3 63.2 4.9 138.7 54.5 216.9 58.8 90.9 23.5 143.6 147.0 36.4 94.4 16.5 23.8 48.3 178.2 31.7 0.0 45.7 57.1 36.7 137.0 41.9 192.7 59.1 61.6 13.9 68.2 54.1

79.0 75.9 54.2 151.6 72.8 226.4 94.4 175.3 334.8 302.5 192.3 0.0 138.4 138.6 138.4 13.6 361.5 42.6 324.9 62.2 52.7 63.6 165.5 71.3 256.5 135.3 96.8 16.0 64.8 112.4

128.9 45.5 88.5 166.2 178.6 254.1 70.6 143.8 733.4 284.9 248.0 0.0 170.1 82.2 221.8 135.6 343.4 8.4 473.9 76.2 48.7 162.2 153.0 56.7 51.3 111.5 72.1 12.7 13.0 95.9

71.9 0.0 57.4 204.4 399.1 488.2 133.2 186.4 766.4 228.8 301.3 29.5 163.7 62.5 497.7 122.3 383.3 336.5 613.4 91.2 35.1 179.9 157.6 56.3 357.7 151.4 73.4 18.2 61.9 197.3

211.1 0.0 206.0 276.4 548.4 885.1 179.6 313.6 668.1 435.9 444.4 23.0 223.4 112.9 1341.4 190.8 666.1 240.9 1201.7 280.9 79.0 240.9 408.9 132.3 457.4 248.2 107.3 21.0 92.8 288.3

180.8 3.6 157.6 232.3 559.3 709.0 221.1 245.1 1060.8 178.0 362.9 291.9 247.6 38.2 668.0 100.1 556.5 0.0 706.1 176.7 84.5 255.0 328.1 113.9 443.9 243.0 2.1 42.7 67.5 157.2

268.8 162.4 267.5 443.1 498.2 659.5 276.9 290.2 727.4 534.5 509.3 139.2 421.5 46.6 469.8 106.9 639.0 137.3 1163.8 278.3 163.2 337.1 451.0 209.9 462.5 351.5 0.0 59.8 52.5 233.6

445.5 81.0 289.9 598.8 692.5 544.2 295.3 348.6 363.4 579.2 561.3 143.3 482.2 77.0 592.6 38.6 639.9 303.0 1281.7 331.7 181.2 274.4 693.3 249.2 497.5 451.7 0.0 67.2 63.8 257.0

Table 8 The comparison of the four methods. Three-stage virtual frontier DEA ***

Traditional DEA model ***

Traditional three-stage DEA model ***

Virtual frontier DEA model

The first output

0.710 (0.000)

0.479 (0.000)

0.697 (0.000)

0.589*** (0.000)

The second output

0.632*** (0.000)

0.513*** (0.000)

0.608*** (0.000)

0.524*** (0.000)

Note: The number in bracket stands for p value. Significant on 1%.

***

this paper defines the average value of transportation energy efficiencies from 2003 to 2012 as the comprehensive transportation energy efficiency. The results are shown in Table 8. The results in Table 8 show that the relevance between transportation energy efficiency and the output in three-stage virtual frontier DEA is the biggest, so the model is suitable to evaluate transportation energy efficiency. Conclusions The topic of transportation energy efficiency is studied in this paper. Transportation energy efficiency is newly defined to reflect the relationship between transportation energy inputs and its outputs. Labor input, capital input and energy input are selected as the inputs, passenger turnover volume and freight turnover volume are selected as the outputs. A new model— three-stage virtual frontier Data Envelopment Analysis is proposed and applied to evaluate transportation energy efficiencies of thirty Chinese PARs from 2003 to 2012. The results verify the rationality of the new model and show that transport structure and management measures have important impacts on transportation energy efficiency. On the whole, the contribution of this paper to the literatures is embodied in two aspects. Firstly, transportation energy efficiency is newly defined to reflect the energy utilization situation of transportation sector. Labor input, capital input and energy input are selected as its inputs, passenger turnover volume and freight turnover volume are selected as its outputs. The idea in this paper enriches the theory and method of energy research and supplies new view on evaluating the performance of transportation industry. Secondly, a new model—three-stage virtual frontier Data Envelopment Analysis is

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Q. Cui, Y. Li / Transportation Research Part D 29 (2014) 1–11

proposed. The reference DMU set and the evaluated DMU set are two different sets, which offers the probability to distinguish the DEA efficient DMUs in traditional DEA model. And in the evaluating process, the reference DMU set remains unchanged so that its results may be more reasonable than Super DEA model. The empirical study verifies the applicability of the model. Future research could focus on exploring the important influencing factors of transportation energy efficiency. Acknowledgements This research is funded by National Nature Science Foundation of China: (Nos. 71273037 and 71320107006). Appendix A There are n DMUs (decision making units) and each DMU has m inputs and s outputs. For DMU j, the ith input is marked as xij (i = 1, 2, . . ., m) and the rth output is marked as yrj (r = 1, 2, . . ., s). The efficiency of the dth DMU is

hd ¼ max

s:t:

uT Y i

u,

6 1;

v T Xi

u P 0;

uT Y d

v T Xd i ¼ 1; 2; . . . ; n

v P0

v are the output and input weight vectors, Xd = [x1d, x2d, . . ., xmd], Yd = [y1d, x2d, . . ., xsd].

Appendix B The inputs and outputs (take 2012 as an example). PARs

Energy input (104 tons standard coal)

Capital input (108 yuan)

Labor input (104 persons)

Passenger turnover (108 person kilometers)

Freight turnover (108 ton kilometers)

Beijing Tianjin Hebei Shanxi Inner Mongolia Liaoning Jilin Heilongjiang Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Henan Hubei Hunan Guangdong Guangxi Hainan Chongqing Sichuan Guizhou Yunnan

869.44 399.33 720.41 779.62 1057.54

662.50 483.74 1026.16 735.91 786.43

50.07 12.29 25.48 21.27 16.24

361.26 250.15 1043.30 352.12 359.96

731.59 9606.61 6405.15 2390.44 4116.91

1417.10 471.15 512.89 1830.89 1201.10 1032.48 436.95 662.23 358.69 2289.02 760.58 1140.68 753.00 2311.49 672.90 272.64 423.30 1064.08 425.48 675.28

757.62 423.77 651.77 882.82 1020.20 1008.70 460.06 885.41 382.04 1032.50 583.82 767.42 1027.85 1596.22 602.30 186.37 643.42 1249.97 397.15 570.87

31.78 15.32 26.15 35.63 30.70 23.94 14.74 16.19 15.62 33.25 28.78 31.83 21.76 53.54 17.52 4.24 13.46 23.75 9.14 14.25

840.69 426.56 466.28 156.99 1370.79 1103.21 1302.63 465.66 790.14 1601.25 1615.13 938.91 1233.44 1886.79 787.30 139.25 410.08 1004.67 406.61 376.13

7753.94 1167.33 1644.68 14372.56 4675.30 5659.86 6321.71 2471.34 2334.15 11022.22 6153.97 2566.36 2513.28 4769.73 2337.20 792.54 1650.49 1590.52 926.05 867.63

11

Q. Cui, Y. Li / Transportation Research Part D 29 (2014) 1–11

Appendix B (continued) PARs

Shaanxi Gansu Qinghai Ningxia Xinjiang

Energy input (104 tons standard coal) 796.04 301.86 98.17 140.06 452.85

Capital input (108 yuan) 599.48 155.00 124.15 90.05 339.90

Labor input (104 persons) 19.21 10.31 3.28 3.04 10.90

Passenger turnover (108 person kilometers) 680.59 495.90 85.49 91.75 386.68

Freight turnover (108 ton kilometers) 2218.55 1619.48 364.16 750.36 1255.91

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