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

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.


Introduction
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.
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.
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.

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 DMU 0 is obtained by the following fractional programming: 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:

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:

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 x y x can produce y And the input distance function at time t is Following Färe et al. [21] and Boussemart et al. [22], the catch-up effect can be defined as means the efficiency of DMU ( ) The frontier-shift effect is defined as The Malmquist production index can be measured as follows: 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, , can be measured by the following two models.

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.   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.

A dynamic analysis of energy efficiencies of 30 Chinese provinces during 2000-2003
This section aims to investigate the total factor energy efficiency of main areas in china using the time-series data from 2000 to 2003. These areas shown in table 5 include 12 provinces in the east area, 10 provinces in the central area and 8 provinces in the west area. Consisting of fast-developing regions like Beijing, Shanghai, Guangdong etc., the east area owns GDP output around half of the country. The central area contains inland provinces such as Shanxi, Jilin, Henan etc. This area has a large population and tremendous potential. Compared with the other areas, the west area is the least developed region in China, containing provinces of Sichuan, Guizhou, Yunnan etc. In our study, Tibet, which is also a province in the west area, is missing due to the unavailability of data. Similar as the analysis in the above section, GDP is the only output and non-resource inputs are capital stock and labor while energy inputs are represented as crud oil, coal and electric power.  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 the west area is even worse other than Sichuan, Yunnan, Qinghai and Ningxia.

Conclusion
This chapter reviews the development process of the evaluation technique of energy efficiency and focuses on introducing the concept of energy intensity. However, missing the structure of energy consumption causes the energy efficiency estimated inaccurately. Thus, the current chapter introduces a weighed energy efficiency model based on DEA to fix it. Energy cannot produce production without non-energy inputs such as labor and capital.
That's why we extend the method to the total factor energy efficiency model. Energy efficiency of China and other 47 countries in 2003 are employed to illustrate the models. Results show that unbalance of energy efficiency exists. For china, specially, it needs to adjust energy consumption structure as its poor energy efficiency and improve GDP since its total factor energy efficiency is at a lower level than some developed countries.
As a key part, the chapter adopts Malmquist production index technique to analyze the dynamic change in energy efficiency of Chinese provinces which can further explore the reason for the variation of energy efficiency deeply. The chapter uses the proposed models to investigate the changes in energy efficiency of provinces in china during the period of 2000 to 2003. We find that the east area has better energy efficiency than the central and west area but lower improving rapid. In addition, it is interesting to find that energy efficiency of most provinces improves due to the extending frontier. Although our work mainly focuses on estimating energy efficiency at the macro-level, it can provide guidance to managers and manufacturers at the micro level.