**1. Introduction**

16 Will-be-set-by-IN-TECH

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*electrical power theft detection*, Master's thesis, University of Campinas.

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electricity-saving opportunities, *Technical report*, ACEEE.

*Electronics and Applications (ICIEA)*, pp. 2254–2259.

*and SUSTAINABLE DEVELOPMENT (EEESD'08)*.

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*Sensing Systems for Energy-Efficiency in Building (BuildSys '10)*.

United Kingdom and New York, NY, USA.

*on Circuits, System ans Signals*.

electrical appliances based on load signatures, 53(2): 653–660.

pp. 988–991.

*Processing* 5(2): 116–123.

Power signature analysis.

80(12): 1870–1891.

*Engineering (ICEE)*.

The development of world economy is closely related with energy consumption. According to the economics research by Department of Agriculture of the U.S., since 2000, the energy consumption quantity begins to rise sharply at an average annual growth rate of 2.5% which approximates with the global real GDP (gross domestic product) growth. In China, the second largest economy in the world, this index increases by 15.1% in 2004. Excessive energy consumption, together with the environmental pollution, has become a huge threat to the sustainable development of human beings. Thus, the continuous pursuing for higher energy utilization has drawn the attention of many researchers.

There are three categories of indices to evaluate energy utilization summarized by Ang[1] which are thermodynamic indicators, physical-based indicators, and monetary-based indicators. Different with the first two indicators, outputs in monetary-based indicators are measured in form of currency. This causes monetary-based indicators popularly used in measuring energy efficiency of various levels, not only the common production process at the micro-level but also the comparison between countries at the macro-level.

Ang [1] introduces some key indices belonging to the category of monetary-based indicators. Energy intensity (EI), which is defined as the quotient of total energy consumption divided by total output (GDP or GNP), is used to estimate one's energy efficiency roughly[1]. Energy coefficient is another index referring to the quotient of growth rate of total energy consumption divided by growth rate of total output, which is usually applied in comparison among various countries or regions [2]. However, the stability of energy coefficient is very poor, especially when the growth rate of one country's GDP approaches to 0. Benefit for its clear definition, simple calculation and easily improvement, EI becomes the most frequently-used index in energy efficiency evaluation from both points of practice and research.

© 2012 Liang et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Most of literatures studying energy efficiency adopt energy intensity to analyze energy utilization efficiency, for instance, Howarth et al. [3] and Greening et al. [4], both of which are quoted frequently by other researchers. However, for simplicity, total energy consumption used in EI calculation only considers the sum of all kinds of energy consumption. EI neglects the structure of energy consumption, that's why the index may estimate the energy efficiency inaccurately. Different energy storage capacities and consumption habits make energy consumption structure to be an indispensable influence factor in evaluation. In order to deal with this problem, Xu and Liang [5] introduced a weighted energy intensity model based on data envelopment analysis to evaluate the energy efficiency considering energy consumption structure.

Comparing the Dynamic Analysis of Energy Efficiency in China with Other Countries 211

countries in 2003 and section 4 presents a dynamic example of total factor energy efficiency

Suppose that there are n homogenous decision making units (DMU) to be evaluated, denoted by DMUj (j = 1, 2, …, n). Each DMU consumes m type of energy inputs xij (i = 1, 2,

Xu and Liang introduced weighted energy intensity model (WEI) based on DEA to evaluate the energy efficiency considering energy structure. Energy efficiency of DMU0 is obtained

≤ =

≥= =

*v r si m*

, 0, 1,2, , ; 1,2, , .

In the empirical example, xij stand for all kinds of energy consumption like crude oil, natural gas, coal and so on while yrj are outputs. The vector of vi stands for the weights of the energy consumption xij which represents the energy structure. In addition, the vector of μr is the weight of the output yrj. According to DEA technique, DMU0 is efficient if there is a parameter bundle (vi, μr) making the target value equal to 1. The production frontier constituted by all of

Halkos & Tzeremes have noticed that the scale of countries has influence on the energy efficiency especially when estimating the various countries and regions[17]. Some small countries could be efficient under the condition of variable return-to-scale (VRS) as there is less restrictive[18]. Banker et al.[19] improved an extension based on the variable return-to-

Here we transform Programming (1) into an integral linear programming and add the VRS

 θ

*st x x i m*

, 1,2, , .

. . , 1,2, , .

1 0

*j ij i j*

*j j rj r*

1 0

≤ =

*j n*

≥ =

*y yr s*

(1)

(2)

**2.1. Energy efficiency considering energy structure based on DEA model** 

μ

. . 1, 1,2, ,

the efficient DMUs suggests an improvement direction to the non-efficient DMUs.

*<sup>y</sup> s t j n*

1 0

1 0

*v x*

= =

*s r r r m i i i*

μ

*v x*

 

*<sup>y</sup> <sup>h</sup>*

= =

1 1

=

*s r r rj m i ij i*

*r i*

μ

0

estimation of 30 provinces in china. Section 5 concludes this chapter.

…, m) to produce s types of outputs yrj (r = 1, 2, …, s).

max

scale assumption by adding a convexity constraint.

assumption. Then we obtain the following program:

θ

min

λ

*j*

λ

=

*n*

*n*

=

=

1,

*n j j*

1

λ

λ

=

≥ =

0, 1,2, , .

by the following fractional programming:

**2. Methodology** 

Data envelopment analysis (DEA), a popular approach to evaluate the relative efficiency of homogenous decision making units (DMU) with multiple inputs and multiple outputs[6], has been widely used in the energy efficiency analysis and gained a lot of research achievement [7]. For example, in recent literatures, Mohammadi et al. [8] used DEA approach to evaluate energy efficiency of kiwifruit production in Iran. Rao et al.[9] developed an improved DEA model to analyze energy efficiency and energy savings potential in China. Bian and Yang [10] summarized several DEA models for measuring the energy efficiency and proposed an extended Shannon-DEA method to define a comprehensive concept of energy efficiency.

However, EI index based on DEA concentrates on the transforming degree of energy consumption to GDP or other economic statistical data, and ignores the function of non resource inputs such as labor and capital stock which also play an essential role during the production process. Boyd and Pang [11] introduced the concept of total factor energy efficiency (TFEE) and proposed a model to estimate the linkage between energy efficiency and productivity of the glass industry. References [12] and [13, 14] developed a series of models in estimating total factor energy efficiencies of 29 regions of China and Japan.

Except for using DEA model to analyze the energy efficiency at a given time, this chapter intends to investigate the dynamic change of energy efficiency over periods by adopting Malmquist production index (MPI) technique. First applied to study on the consumers' behavior, after improved for many years, MPI approach deserves high praise in inputoutput analysis for the reason as follows: (1) no need for the price of input or output; (2) no need for the assumption of behavior pattern; (3) to get more intensive result of dynamic change easily[15]. MPI divides the total production growth rate into two parts, catch-up effect and frontier-shift effect, from which the cause of the change in energy efficiency can be clarified[16].

The current chapter tries to compare the total factor energy efficiencies of 48 countries all over the world in 2003 and analyze the dynamic change in total factor energy efficiencies of provinces of China over the period of 2000-2003 by the proposed model. The rest of this chapter is organized as follows. In Section 2, we introduce several methods for measuring the total factor energy efficiency and the dynamic change based on DEA and MPI technique. Section 3 shows how to use the proposed approach in analyzing the energy efficiency of 48 countries in 2003 and section 4 presents a dynamic example of total factor energy efficiency estimation of 30 provinces in china. Section 5 concludes this chapter.

#### **2. Methodology**

210 Energy Efficiency – The Innovative Ways for Smart Energy, the Future Towards Modern Utilities

efficiency considering energy consumption structure.

comprehensive concept of energy efficiency.

be clarified[16].

Most of literatures studying energy efficiency adopt energy intensity to analyze energy utilization efficiency, for instance, Howarth et al. [3] and Greening et al. [4], both of which are quoted frequently by other researchers. However, for simplicity, total energy consumption used in EI calculation only considers the sum of all kinds of energy consumption. EI neglects the structure of energy consumption, that's why the index may estimate the energy efficiency inaccurately. Different energy storage capacities and consumption habits make energy consumption structure to be an indispensable influence factor in evaluation. In order to deal with this problem, Xu and Liang [5] introduced a weighted energy intensity model based on data envelopment analysis to evaluate the energy

Data envelopment analysis (DEA), a popular approach to evaluate the relative efficiency of homogenous decision making units (DMU) with multiple inputs and multiple outputs[6], has been widely used in the energy efficiency analysis and gained a lot of research achievement [7]. For example, in recent literatures, Mohammadi et al. [8] used DEA approach to evaluate energy efficiency of kiwifruit production in Iran. Rao et al.[9] developed an improved DEA model to analyze energy efficiency and energy savings potential in China. Bian and Yang [10] summarized several DEA models for measuring the energy efficiency and proposed an extended Shannon-DEA method to define a

However, EI index based on DEA concentrates on the transforming degree of energy consumption to GDP or other economic statistical data, and ignores the function of non resource inputs such as labor and capital stock which also play an essential role during the production process. Boyd and Pang [11] introduced the concept of total factor energy efficiency (TFEE) and proposed a model to estimate the linkage between energy efficiency and productivity of the glass industry. References [12] and [13, 14] developed a series of

Except for using DEA model to analyze the energy efficiency at a given time, this chapter intends to investigate the dynamic change of energy efficiency over periods by adopting Malmquist production index (MPI) technique. First applied to study on the consumers' behavior, after improved for many years, MPI approach deserves high praise in inputoutput analysis for the reason as follows: (1) no need for the price of input or output; (2) no need for the assumption of behavior pattern; (3) to get more intensive result of dynamic change easily[15]. MPI divides the total production growth rate into two parts, catch-up effect and frontier-shift effect, from which the cause of the change in energy efficiency can

The current chapter tries to compare the total factor energy efficiencies of 48 countries all over the world in 2003 and analyze the dynamic change in total factor energy efficiencies of provinces of China over the period of 2000-2003 by the proposed model. The rest of this chapter is organized as follows. In Section 2, we introduce several methods for measuring the total factor energy efficiency and the dynamic change based on DEA and MPI technique. Section 3 shows how to use the proposed approach in analyzing the energy efficiency of 48

models in estimating total factor energy efficiencies of 29 regions of China and Japan.

#### **2.1. Energy efficiency considering energy structure based on DEA model**

Suppose that there are n homogenous decision making units (DMU) to be evaluated, denoted by DMUj (j = 1, 2, …, n). Each DMU consumes m type of energy inputs xij (i = 1, 2, …, m) to produce s types of outputs yrj (r = 1, 2, …, s).

Xu and Liang introduced weighted energy intensity model (WEI) based on DEA to evaluate the energy efficiency considering energy structure. Energy efficiency of DMU0 is obtained by the following fractional programming:

$$\begin{aligned} \max \quad & h\_0 = \frac{\sum\_{r=1}^{s} \mu\_r y\_{r0}}{\sum\_{i=1}^{m} v\_i x\_{i0}} \\ \text{s.t.} \quad & \frac{\sum\_{r=1}^{s} \mu\_r y\_{rj}}{\sum\_{i=1}^{m} v\_i x\_{ij}} \le 1, \quad j = 1, 2, \dots, n \\ & \mu\_r, v\_i \ge 0, \quad r = 1, 2, \dots, s; \quad i = 1, 2, \dots, m. \end{aligned} \tag{1}$$

In the empirical example, xij stand for all kinds of energy consumption like crude oil, natural gas, coal and so on while yrj are outputs. The vector of vi stands for the weights of the energy consumption xij which represents the energy structure. In addition, the vector of μr is the weight of the output yrj. According to DEA technique, DMU0 is efficient if there is a parameter bundle (vi, μr) making the target value equal to 1. The production frontier constituted by all of the efficient DMUs suggests an improvement direction to the non-efficient DMUs.

Halkos & Tzeremes have noticed that the scale of countries has influence on the energy efficiency especially when estimating the various countries and regions[17]. Some small countries could be efficient under the condition of variable return-to-scale (VRS) as there is less restrictive[18]. Banker et al.[19] improved an extension based on the variable return-toscale assumption by adding a convexity constraint.

Here we transform Programming (1) into an integral linear programming and add the VRS assumption. Then we obtain the following program:

$$\begin{aligned} \min \quad & \theta\\ \text{s.t.} \quad & \sum\_{j=1}^{n} \lambda\_j \mathbf{x}\_{ij} \le \theta \mathbf{x}\_{i0}, \quad i = 1, 2, \dots, m. \\ & \sum\_{j=1}^{n} \lambda\_j y\_{rj} \ge y\_{r0}, \quad r = 1, 2, \dots, s. \\ & \sum\_{j=1}^{n} \lambda\_j = 1, \\ & \lambda\_j \ge 0, \quad \qquad j = 1, 2, \dots, n. \end{aligned} \tag{2}$$

#### **2.2. Total factor energy efficiency based on DEA model**

The concept of total factor energy efficiency investigates deeply into the energy consumption and production procedure and takes the non-resource inputs into account. As some representative examples, capital stock and labor are usually included. Following program is used to evaluate the total factor energy efficiency:

$$\begin{aligned} \min \quad & \theta\\ \text{s.t.} \quad & \sum\_{j=1}^{n} \mathcal{\lambda}\_{j} x\_{ij} \le \theta x\_{i0^{\prime}} \quad i = 1, 2, \dots, m. \\ & \sum\_{j=1}^{n} \mathcal{\lambda}\_{j} z\_{tj} \le \theta z\_{t0^{\prime}} \quad t = 1, 2, \dots, p. \\ & \sum\_{j=1}^{n} \mathcal{\lambda}\_{j} y\_{rj} \ge y\_{r0^{\prime}} \quad r = 1, 2, \dots, s. \\ & \mathcal{\lambda}\_{j} \ge 0, & j = 1, 2, \dots, n. \end{aligned} \tag{3}$$

Comparing the Dynamic Analysis of Energy Efficiency in China with Other Countries 213

δ δ

+ +

1 1

, *t t x y* at time t and <sup>+</sup><sup>1</sup>

(,) *t tt D xy <sup>i</sup>*

(,) *t tt D xy <sup>i</sup>*

(5)

∈

<sup>=</sup> {( , ): } *t tt t <sup>t</sup> S x y x can produce y*

δ

*ttt t tt*

 δ

− =

*t t x y* at time t.

Where + + 1 1 (,) *tt t Dx y <sup>i</sup>* means the efficiency of DMU ( ) + + 1 1

The Malmquist production index can be measured as follows:

, can be measured by the following two models.

<sup>=</sup> ∈ =

Following Färe et al. [21] and Boussemart et al. [22], the catch-up effect can be defined as

*Dxy catch up Dxy*

*<sup>i</sup> tt t Dxy x y S xy S*

<sup>1</sup> ( , ) sup{ : ( / , ) } inf{ : ( , ) }

*i*

Where +++ <sup>111</sup> (,) *ttt Dxy <sup>i</sup>* means the efficiency of DMU ( ) + + 1 1 , *t t x y* at time *<sup>t</sup>* <sup>+</sup> 1 and (,) *ttt Dxy <sup>i</sup>*

<sup>+</sup> +++ −= ×

*Dxy Dx y frontier shift D xy D x y*

*MPI catch up frontier shift* = × - -

We notice that there need four efficiencies to obtain the MPI and two of which can be

 θ

0

0

0

*j n*

≤

*t t*

 θ

≤

*z z*

*t t*

≥

*t t*

λ

0, 1,2, , .

= ≥=…

obtained by the linear program (3). The other two efficiencies, + + 1 1 (,) *tt t Dx y <sup>i</sup>* and <sup>+</sup><sup>1</sup>

+

. . ,

*j*

1

+

,

*j*

,

*j*

1

+

1

*y y*

=

1,

1

θ

min

λ

*j*

*st x x*

λ

*j*

λ

*j n j j*

λ

*j*

*t t x y* at time *t* + 1 .

*i i*

1 111 (,) ( , ) (,) ( , )

*ttt tt t i i t tt t t t*

+++

*ttt*

*ttt*

<sup>111</sup> (,) *<sup>i</sup>* (,)

And the input distance function at time t is

means the efficiency of DMU ( ) ,

The frontier-shift effect is defined as

means the efficiency of DMU ( ) ,

Here ztj (t = 1, 2, …, p) stands for the non-resource inputs of DMUj. Adding the VRS assumption turns Model (3) into the following linear programming:

$$\begin{aligned} \min \quad & \theta\\ \text{s.t.} \quad & \sum\_{j=1}^{n} \lambda\_j \mathbf{x}\_{ij} \le \theta \mathbf{x}\_{i0^{\prime}} \quad i = 1, 2, \dots, m. \\ & \sum\_{j=1}^{n} \lambda\_j \mathbf{z}\_{ij} \le \theta \mathbf{z}\_{t0^{\prime}} \quad t = 1, 2, \dots, p. \\ & \sum\_{j=1}^{n} \lambda\_j \mathbf{y}\_{rj} \ge \mathbf{y}\_{r0^{\prime}} \quad r = 1, 2, \dots, s. \\ & \sum\_{j=1}^{n} \lambda\_j = 1, \\ & \lambda\_j \ge 0, \qquad \qquad j = 1, 2, \dots, n. \end{aligned} \tag{4}$$

#### **2.3. Total factor energy efficiency based on Malmquist production index**

The above sections discuss the efficiency evaluation at a given time while this section presents the efficiency evaluating model during a period. Malmquist production index (MPI) is widely applied in measuring the dynamic variation trend of input-output efficiency by dividing the total efficiency into two parts, catch-up effect and frontier-shift effect [20]. Catch-up effect detects whether the efficiency of DMU makes progress during the period. If the numerical value of catch-up effect is more than 1, then we can make sure that the technical efficiency of DMU gets improvement and DMU is closer to the production frontier. Frontier-shift effect is used to assess the technique advancement which is measured by the transform degree of production frontier at different time-points. If the numerical value of frontier-shift effect is more than 1, it means the production technique of the latter is better than that of the former.

We assume that the production possibility set at time t, denoted by St, includes all of the feasible production bundles, input xt and output yt. For each time-point t, we have

Comparing the Dynamic Analysis of Energy Efficiency in China with Other Countries 213

$$S^t = \left[ (\mathbf{x}^t, \mathbf{y}^t) : \mathbf{x}^t \text{ can produce } \mathbf{y}^t \right]^\cdot$$

And the input distance function at time t is

212 Energy Efficiency – The Innovative Ways for Smart Energy, the Future Towards Modern Utilities

The concept of total factor energy efficiency investigates deeply into the energy consumption and production procedure and takes the non-resource inputs into account. As some representative examples, capital stock and labor are usually included. Following

> θ

*st x x i m*

. . , 1,2, , .

1 0

*j ij i j*

1 0

*j tj t j*

1 0

*j j rj r*

≤ =

(3)

(4)

 

*j n*

*j n*

≤ =

*z zt p*

*y yr s*

≥ =

 θ

 , 1,2, , . 0, 1,2, , .

Here ztj (t = 1, 2, …, p) stands for the non-resource inputs of DMUj. Adding the VRS

 θ

*st x x i m*

. . , 1,2, , .

1 0

*j ij i j*

1 0

*j tj t j*

1 0

*j j rj r*

≤ =

≤ =

*z zt p*

*y yr s*

≥ =

 θ

, 1,2, , .

, 1,2, , .

, 1,2, , .

≥ =

**2.2. Total factor energy efficiency based on DEA model** 

program is used to evaluate the total factor energy efficiency:

min

θ

λ

assumption turns Model (3) into the following linear programming:

θ

min

λ

than that of the former.

*j*

*j*

λ

=

*n*

*n*

*n*

=

=

λ

λ

λ

=

*n*

*n*

*n*

=

=

=

1,

*n j j*

1

λ

λ

λ

=

**2.3. Total factor energy efficiency based on Malmquist production index** 

≥ =

0, 1,2, , .

The above sections discuss the efficiency evaluation at a given time while this section presents the efficiency evaluating model during a period. Malmquist production index (MPI) is widely applied in measuring the dynamic variation trend of input-output efficiency by dividing the total efficiency into two parts, catch-up effect and frontier-shift effect [20]. Catch-up effect detects whether the efficiency of DMU makes progress during the period. If the numerical value of catch-up effect is more than 1, then we can make sure that the technical efficiency of DMU gets improvement and DMU is closer to the production frontier. Frontier-shift effect is used to assess the technique advancement which is measured by the transform degree of production frontier at different time-points. If the numerical value of frontier-shift effect is more than 1, it means the production technique of the latter is better

We assume that the production possibility set at time t, denoted by St, includes all of the

feasible production bundles, input xt and output yt. For each time-point t, we have

$$D\_i^t(\boldsymbol{\chi}^t, \boldsymbol{y}^t) = \sup \{ \boldsymbol{\delta} : (\boldsymbol{\chi}^t / \boldsymbol{\delta}, \boldsymbol{y}^t) \in S^t \} = \frac{1}{\inf \{ \boldsymbol{\delta} : (\boldsymbol{\delta} \boldsymbol{\chi}^t, \boldsymbol{y}^t) \in S^t \}}$$

Following Färe et al. [21] and Boussemart et al. [22], the catch-up effect can be defined as

$$catch - up = \frac{D\_i^{t+1}(\mathbf{x}^{t+1}, \mathbf{y}^{t+1})}{D\_i^t(\mathbf{x}^t, \mathbf{y}^t)}$$

Where +++ <sup>111</sup> (,) *ttt Dxy <sup>i</sup>* means the efficiency of DMU ( ) + + 1 1 , *t t x y* at time *<sup>t</sup>* <sup>+</sup> 1 and (,) *ttt Dxy <sup>i</sup>* means the efficiency of DMU ( ) , *t t x y* at time t.

The frontier-shift effect is defined as

$$f\_{froniter} - shift = \sqrt{\frac{D\_i^t(\boldsymbol{\chi}^t, \boldsymbol{y}^t)}{D\_i^{t+1}(\boldsymbol{\chi}^t, \boldsymbol{y}^t)}} \times \frac{D\_i^t(\boldsymbol{\chi}^{t+1}, \boldsymbol{y}^{t+1})}{D\_i^{t+1}(\boldsymbol{\chi}^{t+1}, \boldsymbol{y}^{t+1})}$$

Where + + 1 1 (,) *tt t Dx y <sup>i</sup>* means the efficiency of DMU ( ) + + 1 1 , *t t x y* at time t and <sup>+</sup><sup>1</sup> (,) *t tt D xy <sup>i</sup>* means the efficiency of DMU ( ) , *t t x y* at time *t* + 1 .

The Malmquist production index can be measured as follows:

$$MPI = \text{cath-up} \times \text{frontier -shift}$$

We notice that there need four efficiencies to obtain the MPI and two of which can be obtained by the linear program (3). The other two efficiencies, + + 1 1 (,) *tt t Dx y <sup>i</sup>* and <sup>+</sup><sup>1</sup> (,) *t tt D xy <sup>i</sup>* , can be measured by the following two models.

$$\begin{aligned} \min \quad & \theta\\ \text{s.t.} \quad & \lambda\_j \mathbf{x}\_j^{t+1} \le \theta \mathbf{x}\_{\mathbf{o}'}^t\\ & \lambda\_j \mathbf{z}\_{\mathbf{o}'}^{t+1} \le \theta \mathbf{z}\_{\mathbf{o}'}^t\\ & \lambda\_j \mathbf{y}\_j^{t+1} \ge \mathbf{y}\_{\mathbf{o}'}^t\\ & \sum\_{j=1}^n \lambda\_j = \mathbf{1}\_{\mathbf{y}}\\ & \lambda\_j \ge 0, \ j = 1, 2, \dots, n. \end{aligned} \tag{5}$$

$$\begin{aligned} \min \quad & \theta\\ \text{s.t.} \quad & \lambda\_j \mathbf{x}\_j^t \le \theta \mathbf{x}\_0^{t+1},\\ & \lambda\_j \mathbf{z}\_j^t \le \theta \mathbf{z}\_0^{t+1},\\ & \lambda\_j \mathbf{y}\_j^t \ge \mathbf{y}\_0^{t+1},\\ & \sum\_{j=1}^n \lambda\_j = 1,\\ & \lambda\_j \ge 0, \ j = 1, 2, \dots, n. \end{aligned} \tag{6}$$

Comparing the Dynamic Analysis of Energy Efficiency in China with Other Countries 215

interval of 0.5-1 and the typical countries are Britain, Germany, Mexico, etc; (3) the energy efficiency scores of the rest 17 countries are at very low level, less than 0.5; (4) the return-toscale situation of most developed countries is in decreasing stage while in contrast many

No. Country WEI-VRS Rank RTS 1 United States 1.0000 1 D 2 Japan 1.0000 1 D 3 Germany 0.9086 12 D 4 Britain 0.9969 11 D 5 France 1.0000 1 D 6 Italy 1.0000 1 D 7 China 0.3391 40 D 8 Canada 0.3471 38 D 9 Mexico 0.7755 18 D 10 Korea 0.3359 41 D 11 India 0.3526 36 D 12 Australia 0.8422 16 D 13 Netherlands 1.0000 1 D 14 Brazil 0.2938 42 D 15 Russian Federation 0.0707 48 D 16 Switzerland 1.0000 1 C 17 Sweden 0.8560 15 I 18 Austria 0.7669 19 D 19 Turkey 0.3469 39 D 20 Norway 0.8601 14 I 21 Poland 0.6479 22 D 22 Indonesia 0.2256 45 D 23 Greece 0.5793 26 D 24 Finland 0.7047 21 I 25 South Africa 0.4902 32 I 26 Ireland 1.0000 1 C 27 Portugal 0.5838 24 I 28 Thailand 0.1894 46 I 29 Iran 1.0000 1 C 30 Argentina 0.4893 33 I 31 Malaysia 0.2928 43 D 32 Czech Republic 0.5073 30 I 33 Hungary 0.5485 27 I 34 Egypt 0.5417 28 I 35 Pakistan 0.2818 44 I 36 Philippines 0.5805 25 I

developing countries behave increasing returns to scale.

## **3. A comparative analysis of energy efficiency of 48 countries**

In this chapter, energy efficiency analysis of 48 countries in 2003 is illustrated. The major countries and regions all over the world are included in our consideration such as the United States, China, Russia, Japan and so on. Primary energy consumption includes oil, natural gas, coal, nuclear energy and hydropower. We incorporate oil and natural gas consumption as the first part of energy input. Nuclear power and hydropower are incorporated as the second part of energy input. Coal is the third input. Labor and capital stock are adopted as the non-resource input. Gross Domestic Product (GDP) is the only output.

The data on energy input are collected from World Petroleum Yearbook (2004). GDP and labor are obtained from the World Development Indicators database (2003). Due to the unavailability on the data of capital stock of some countries, we use the index of adjust savings after consumption of fixed capital as a substitute. The data is available from the website of World Bank. All of the data collected are summarized in Table 1.


\* The units of data on energy inputs are all million tones oil equivalents. Labor is expressed in units of 10-thousand persons. Capital stock is stated in units of 100-million USD. GDP is described in units of 100-million USD.

#### **Table 1.** Summary of inputs and output

Table 2 shows the results of energy efficiency considering energy structure measured by model (2). Countries in column 2 are ranked by GDP. The third column represents energy efficiency considering energy structure. Results indicate that: (1) there are 10 efficient DMUs including US, Japan, Italy and so on; (2) 21 countries' energy efficiency scores lie on the interval of 0.5-1 and the typical countries are Britain, Germany, Mexico, etc; (3) the energy efficiency scores of the rest 17 countries are at very low level, less than 0.5; (4) the return-toscale situation of most developed countries is in decreasing stage while in contrast many developing countries behave increasing returns to scale.

214 Energy Efficiency – The Innovative Ways for Smart Energy, the Future Towards Modern Utilities

min

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λ

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**3. A comparative analysis of energy efficiency of 48 countries** 

website of World Bank. All of the data collected are summarized in Table 1.

Nuclear power &

Category Indicators Max Min Mean

Output GDP 109486 99 6828.9 \* The units of data on energy inputs are all million tones oil equivalents. Labor is expressed in units of 10-thousand persons. Capital stock is stated in units of 100-million USD. GDP is described in units of 100-million USD.

Table 2 shows the results of energy efficiency considering energy structure measured by model (2). Countries in column 2 are ranked by GDP. The third column represents energy efficiency considering energy structure. Results indicate that: (1) there are 10 efficient DMUs including US, Japan, Italy and so on; (2) 21 countries' energy efficiency scores lie on the

Oil & natural gas 1481.1 5.3 105.62

Labor 129483.9 362.1 10208.44 Capital stock 13012 8.1 933.06

hydropower 799.7 0.1 51 Coal 242.8 0.2 22.27

output.

Energy inputs

Non-energy inputs

**Table 1.** Summary of inputs and output

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In this chapter, energy efficiency analysis of 48 countries in 2003 is illustrated. The major countries and regions all over the world are included in our consideration such as the United States, China, Russia, Japan and so on. Primary energy consumption includes oil, natural gas, coal, nuclear energy and hydropower. We incorporate oil and natural gas consumption as the first part of energy input. Nuclear power and hydropower are incorporated as the second part of energy input. Coal is the third input. Labor and capital stock are adopted as the non-resource input. Gross Domestic Product (GDP) is the only

The data on energy input are collected from World Petroleum Yearbook (2004). GDP and labor are obtained from the World Development Indicators database (2003). Due to the unavailability on the data of capital stock of some countries, we use the index of adjust savings after consumption of fixed capital as a substitute. The data is available from the

=

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Comparing the Dynamic Analysis of Energy Efficiency in China with Other Countries 217

constant return-to-scale which can be viewed as pure technical efficiency. Column 5 indicates the total factor energy efficiency based on variable return-to-scale. The last column shows the status of each one's return-to-scale. It is noticed that only five countries are efficient both in CRS and VRS. Quantity of efficient country in column 5 is more than that in column 3. Notice that the return-to-scale effect of top 14 countries in the table is in

It is interesting to analyze the situation of china. It can be observed from table 4 that China is in stage of decreasing return-to-scale effect and TFEE is ranked 30, still lower than all of the developed countries and most of the developing countries. This is mainly caused by lower technical efficiency shown in column 3. Therefore, there are at least 3 ways to enhance the total factor energy efficiency of China, including (1) improving the output of GDP, (2) rearranging the allocation of energy inputs and non-resource inputs and (3) improving the

No. Country TFEE-CRS Rank TFEE-VRS Rank RTS 1 United States 0.8654 8 1.0000 1 D 2 Japan 0.9177 6 1.0000 1 D 3 Germany 0.8179 10 1.0000 1 D 4 Britain 0.8016 11 1.0000 1 D 5 France 0.6395 17 1.0000 1 D 6 Italy 0.8892 7 1.0000 1 D 7 China 0.3139 32 0.8663 30 D 8 Canada 0.5787 18 0.8417 31 D 9 Mexico 0.7008 14 1.0000 1 D 10 Korea 0.3154 31 0.7827 37 D 11 India 0.3086 33 0.8897 28 D 12 Australia 0.6449 16 0.9020 26 D 13 Netherlands 0.7462 12 1.0000 1 D 14 Brazil 0.2581 37 0.8341 33 D

Federation 0.0696 47 1.0000 1 C

16 Switzerland 1.0000 1 1.0000 1 C 17 Sweden 0.8394 9 1.0000 1 C 18 Austria 0.7431 13 0.8304 34 D 19 Turkey 0.3375 27 1.0000 1 C 20 Norway 1.0000 1 1.0000 1 C 21 Poland 0.5168 22 0.8130 35 D 22 Indonesia 0.1895 40 0.8941 27 D 23 Greece 0.5743 19 0.7196 42 D 24 Finland 0.6992 15 0.7779 38 I 25 South Africa 0.4727 25 0.7215 41 C

decreasing stage while most of the last 18 countries are in increasing stage.

technical efficiency of production.

<sup>15</sup>Russian

216 Energy Efficiency – The Innovative Ways for Smart Energy, the Future Towards Modern Utilities

\* D, I and C indicate decreasing, increasing and constant return-to-scale respectively.

**Table 2.** Energy efficiencies of 48 countries considering energy structure

It is particularly pointed out that the energy efficiency of China is only 0.3394 which is the worst among the top 10 countries ranked by GDP. The information of the input/output shown in Table 3 release that there are two reasons for that. First, the technical efficiency of energy consumption of china is lower, compared with Italy for example which has approximate output. Second, by comparison with 10 efficient countries, China has an improper construction of energy consumption that mainly relies on coal resource. Considering the heavy environmental pollution with coal's burning, adjusting the structure of energy consumption is imperative.


\* The units of data on energy inputs are all million tones oil equivalents. GDP is described in units of 100-million USD.

**Table 3.** Input/output of 10 efficient countries and China

Table 4 represents total factor energy efficiency calculated by model (3) & (4). Countries in column 2 are ranked by GDP. Column 3 and 5 show two kinds of results due to the different setting-ups of return-to-scale. Column 3 indicates the total factor energy efficiency based on constant return-to-scale which can be viewed as pure technical efficiency. Column 5 indicates the total factor energy efficiency based on variable return-to-scale. The last column shows the status of each one's return-to-scale. It is noticed that only five countries are efficient both in CRS and VRS. Quantity of efficient country in column 5 is more than that in column 3. Notice that the return-to-scale effect of top 14 countries in the table is in decreasing stage while most of the last 18 countries are in increasing stage.

216 Energy Efficiency – The Innovative Ways for Smart Energy, the Future Towards Modern Utilities

\* D, I and C indicate decreasing, increasing and constant return-to-scale respectively. **Table 2.** Energy efficiencies of 48 countries considering energy structure

of energy consumption is imperative.

**Table 3.** Input/output of 10 efficient countries and China

37 New Zealand 0.7114 20 I 38 Columbia 0.5025 31 I 39 Chile 0.4777 34 I 40 Peru 0.8972 13 D 41 Romania 0.3488 37 I 42 Bangladesh 1.0000 1 C 43 Ukraine 0.1096 47 I 44 Slovakia 0.6364 23 I 45 Kazakhstan 0.5090 29 I 46 Bulgaria 0.8084 17 I 47 Lithuania 1.0000 1 D 48 Uzbekistan 0.3637 35 I

It is particularly pointed out that the energy efficiency of China is only 0.3394 which is the worst among the top 10 countries ranked by GDP. The information of the input/output shown in Table 3 release that there are two reasons for that. First, the technical efficiency of energy consumption of china is lower, compared with Italy for example which has approximate output. Second, by comparison with 10 efficient countries, China has an improper construction of energy consumption that mainly relies on coal resource. Considering the heavy environmental pollution with coal's burning, adjusting the structure

No. Country GDP Oil & Gas Nuclear & hydropower Coal 1 Japan 43009 317.6 112.2 75 2 Ireland 1537 12.1 1.6 0.2 3 Bangladesh 519 15.2 0.4 0.2 4 Netherlands 5115 79.9 9.2 0.9 5 France 17576 133.6 12.4 114.6 6 Italy 14683 156.6 15.3 10 7 Iran 1371 126.4 0.7 2 8 Switzerland 3201 14.7 0.1 14.5 9 Lithuania 182 5.3 0.1 3.7 10 United States 109486 1481.1 573.9 242.8 11 China 14170 304.7 799.7 73.8 \* The units of data on energy inputs are all million tones oil equivalents. GDP is described in units of 100-million USD.

Table 4 represents total factor energy efficiency calculated by model (3) & (4). Countries in column 2 are ranked by GDP. Column 3 and 5 show two kinds of results due to the different setting-ups of return-to-scale. Column 3 indicates the total factor energy efficiency based on It is interesting to analyze the situation of china. It can be observed from table 4 that China is in stage of decreasing return-to-scale effect and TFEE is ranked 30, still lower than all of the developed countries and most of the developing countries. This is mainly caused by lower technical efficiency shown in column 3. Therefore, there are at least 3 ways to enhance the total factor energy efficiency of China, including (1) improving the output of GDP, (2) rearranging the allocation of energy inputs and non-resource inputs and (3) improving the technical efficiency of production.




Comparing the Dynamic Analysis of Energy Efficiency in China with Other Countries 219

Fujian, Shandong, Guangdong, Guangxi, Hainan

Henan, Hubei, Hunan, Chongqing

Xinjiang

East area Central area West area

data are collected from the Statistical Year Book of China published by National Bureau of

East area 12 Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang,

West area 8 Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia,

Curves in Figure 1 show the difference among the average TFEE scores of the provinces in the east, central and west areas using model (4). Obviously the east area is the most efficient and the west area is worst in any year. Meanwhile, it is shown that energy efficiencies for all areas are gradually improving. The detailed results are listed in Table 6. It can be easily observed from the table that most of efficient provinces are in the east area. TFEE scores of Liaoning, Shanghai, Jiangsu, Guangdong, Guangxi, Hainan, Fujian are all at a high level. Provinces in the central area are not as good as the provinces in the east area except Anhui which is adjacent to the east area. Another province in the central area, Shanxi, for specially, has very low TFEE scores during the four years and makes little progress. The situation in

Table 7 is used to clarify which part makes the energy efficiency get improvement. During 2000 to 2001, the average value of Malmquist production index (MPI) for all provinces is 1.13 which means the efficiency in 2001 is better than 2000. Catch-up effect (CE) and frontier-shift effect (FE) are two parameters to distinguish which part is functioned. The data on the last row show that the average value of CE is 1.00 and FE is 1.13. That is to say,

the west area is even worse other than Sichuan, Yunnan, Qinghai and Ningxia.

2000 2001 2002 2003

year

Central area 10 Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi,

Statistics during 2000-2003. The data on capital stock comes from Jun et al. [23].

Areas Num. Provinces

**Table 5.** Chinese provinces in different areas

**Figure 1.** TFEE of 30 provinces during 2000-2003

0.5

0.6

0.7

TFEE

0.8

0.9

1

\*D, I and C indicate decreasing, increasing and constant return-to-scale respectively.

**Table 4.** TFEE of 48 countries
