This paper tries to investigate efficiency of electricity use of 30 administration regions and productivity change of electricity in China for the period 2003-2008. We use the Data Envelopment Analysis (DEA) method to measure the efficiency of electricity use and productivity change of electricity. From an empirical perspective, we provide a framework to investigate the situation of relative efficiency of electricity use and the growth rate of electricity’s productivity. The results indicate that the efficiency gap between regions is very large and the east areas have a higher level of electricity efficiency than the western areas. Moreover, both the technical and efficiency change in China from 2003 to 2008 is also slow. Based on these results, we propose some reasons behind and also give some suggestions about it

Chow, Sheung Chi

Wenjing, Xu

Xiaoyang, Wu

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Efficiency of electricity use and
productivity change of electricity in
China: A nonparametric approach
Sheung Chi Chow and Xu Wenjing and Wu Xiaoyang
Hong Kong Baptist University, Hong Kong Baptist University, Hong
Kong Baptist University
December 2014
Online at https://mpra.ub.uni-muenchen.de/62972/
MPRA Paper No. 62972, posted 20 March 2015 13:40 UTC
 1 
 
Efficiency of electricity use and productivity change of electricity in China: 
A nonparametric approach 
 
Sheung Chi Chow, Department of Economics, Hong Kong Baptist University 
Xu Wenjing, Department of Economics, Hong Kong Baptist University 
Wu Xiaoyang, Department of Economics, Hong Kong Baptist University 
 
 
Abstract  
 
This paper tries to investigate efficiency of electricity use of 30 administration regions and 
productivity change of electricity in China for the period 2003-2008. We use the Data 
Envelopment Analysis (DEA) method to measure the efficiency of electricity use and 
productivity change of electricity. From an empirical perspective, we provide a framework to 
investigate the situation of relative efficiency of electricity use and the growth rate of 
electricity’s productivity. The results indicate that the efficiency gap between regions is very 
large and the east areas have a higher level of electricity efficiency than the western areas. 
Moreover, both the technical and efficiency change in China from 2003 to 2008 is also slow. 
Based on these results, we propose some reasons behind and also give some suggestions about it. 
 
Keywords: Productivity analysis, efficiency of electricity use, productivity change of electricity, 
Malmquist productivity index, DEA 
 
 
Section 1 Introduction 
 
Demand for electricity in China has increased around 10% annually. The current installed 
Chinese national power-generating capacity (792.5 GW) is second only to that of the United 
States (1032 GW). Among all these power-generating capacity in China, around 80% of them are 
using coal to generate electricity (Mcelroy et al, 2009). Because of this reason, electricity 
generation and air pollution are in fact inevitably linked in China because using coal to generate 
electricity could create a lot of Carbon emission. Carbon emission has already caused much 
damage to China’s environment and China citizen’s health. For example, according to You and 
Xu (2010) the areas where pH values of rain were less than 5.6 have now spread to almost half of 
China’s total area. And after accounting this acid rain’s damage on Chinese public health and 
agriculture, according to You and Xu (2010), the total economic loss in China was around 
176.42 billion RMB in 2000. 
 
Without slowing down the economic growth, in order to stop this kind of pollution problems 
getting worse, policy marker might want to consider policy that can make the economy remain 
its current level of electricity consumption but on the other hand the economy could still use that 
electricity to produce more output. Before designing such policies, information about efficiency 
of electricity use or more generally information about the productivity of electricity is needed. 
Unfortunately on a regional or national level, to our knowledge, not much information about it is 
available. This paper tries to provide such kind of information by construct efficiency score of 
electricity use in different regions. The idea of efficiency of electricity use is similar to 
 2 
 
traditional energy efficiency index that takes energy into account as a single input to produce 
GDP output (e.g Patterson, 1996).  The efficiency scores come from the DEA method what we 
will use should provide a better indicator than a simple output-input (O/I) ratio because it allows 
more flexible assumption on the return to scale. This paper also provides the Malmquist 
productivity index which incorporates electricity as input so as to produce economic output 
(GDP) in order to provide a general picture about the productivity change of electricity in China. 
 
This paper is designed as follows. Section 2 describes the definition and estimation method of   
the efficiency score and the Malmquist productivity index. The description of the data and results 
are reported in Section 3. Section 4 will be the conclusion.  
 
Section 2 Methodology 
 
The Malmquist productivity index was introduced as a theoretical index by Caves et al. (1982) 
and has been modified by Färe et al. (1985) and Färe et al. (1994).  
 
Assuming a production technology set 𝑆 of period, the output based distance function 𝑑𝑜
𝑘(𝑦𝑗 , 𝑥𝑗)  
with output vector 𝑦 and input vector 𝑥 in period 𝑗 is defined as:  
 
𝑑𝑜
𝑘(𝑦𝑗, 𝑥𝑗) = 𝑠𝑢𝑝{𝜃: (𝜃𝑦𝑗 , 𝑥𝑗) ∈ 𝑆𝑘} 
 
The distance 𝜃 measures the inverse of the factor by which the production of all output quantities 
could be increased when the decision making unit is efficient. The 𝜃 will be the efficiency score 
of decision making unit in our study, the higher efficiency score it has the higher relative 
efficient it has. With this definition then the Malmquist productivity index is constructed as: 
 
𝑚𝑜(𝑦
𝑡+1, 𝑥𝑡+1, 𝑦𝑡, 𝑥𝑡) =
𝑑𝑜
𝑡+1(𝑦𝑡+1, 𝑥𝑡+1)
𝑑𝑜
𝑡 (𝑦𝑡, 𝑥𝑡)
[
𝑑𝑜
𝑡 (𝑦𝑡+1, 𝑥𝑡+1)
𝑑𝑜
𝑡+1(𝑦𝑡+1, 𝑥𝑡+1)
×
𝑑𝑜
𝑡 (𝑦𝑡, 𝑥𝑡)
𝑑𝑜
𝑡+1(𝑦𝑡, 𝑥𝑡)
]
1/2
 
 
Where the term  
𝑑𝑜
𝑡+1(𝑦𝑡+1,𝑥𝑡+1)
𝑑𝑜
𝑡 (𝑦𝑡,𝑥𝑡)
 could be interpreted as efficiency change ∆𝑇𝐸  and the term 
[
𝑑𝑜
𝑡 (𝑦𝑡+1,𝑥𝑡+1)
𝑑𝑜
𝑡+1(𝑦𝑡+1,𝑥𝑡+1)
×
𝑑𝑜
𝑡 (𝑦𝑡,𝑥𝑡)
𝑑𝑜
𝑡+1(𝑦𝑡,𝑥𝑡)
]
1/2
 could be interpret as technical change ∆𝑇𝐸𝐶𝐻. That means the 
TFP change could be decomposed into two components: eﬃciency change and technical change 
as follow: 
 
𝑚𝑜(𝑦
𝑡+1, 𝑥𝑡+1, 𝑦𝑡, 𝑥𝑡) = ∆𝑇𝐸(𝑦𝑡, 𝑥𝑡 , 𝑦𝑡+1, 𝑥𝑡+1) × ∆𝑇𝐸𝐶𝐻(𝑦𝑡, 𝑥𝑡 , 𝑦𝑡+1, 𝑥𝑡+1) 
 
Eﬃciency change measures the change in relative eﬃciency between year 𝑡 and 𝑡 + 1. It reﬂects 
whether production is getting closer to or farther away from the production frontier. Technical 
 3 
 
change captures the shift in technology between the two periods. It indicates whether or not 
technical progress occurred at the input–output combination for a particular region. 
 
We use a non-parametric linear-programming approach to estimate the Malmquist productivity 
index. If there are 𝑛 decision making unit, the output-oriented LP problem for estimation of 
𝑑𝑜
𝑘(𝑦𝑗 , 𝑥𝑗) under variable returns to scale for decision making unit 𝑖 is defined as follows: 
 
[𝑑𝑜
𝑘(𝑦𝑗 , 𝑥𝑗)]
−1
= max
𝜙,𝜆
𝜃, 
Subject to 
 – 𝜃𝑦𝑖𝑗 + 𝑌𝑘𝜆 ≥ 0 
𝑥𝑖𝑗 − 𝑋𝑘𝜆 ≥ 0 
𝜆 ≥ 0 
𝑁1′𝜆 = 1 
 
where 𝜃 is a scalar, 𝜆 is a 𝑛 × 1 vector of constraints and 𝑁1 is a 𝑁 × 1 vector of one.1 
 
Section 3 Data and Results 
 
The data electricity consumption (EC) and gross regional product (GRP) that used for estimation 
are collected from China Statistical Yearbook from 2004- 2009. 
2
The collected panel data set 
contains 30 regions data from 2003-2008. Descriptive statistics of the data are presented in table 
1, in addition, the output-input (O/I) ratio is also calculated in table 1.  
 
Table 1: Descriptive statistics 
  GRP   EC   O/I ratio 
        Mean SD Mean SD Mean 
2003 4635 3661 629 444 7.36 
2004 5306 4205 725 522 7.32 
2005 6151 4981 825 606 7.45 
2006 7063 5775 945 698 7.47 
2007 8059 6532 1085 800 7.43 
2008 9035 7176 1144 833 7.89 
Average 6708   892   7.52 
 
                                               
1
 For details see Coelli (1996). 
2
 The GRP we use in the analysis is deflated by CPI from China Statistical Yearbook which uses 2003 as 
base year. 
 4 
 
For a first glance, both GRP and EC have increased significantly overtime but the O/I ratio 
haven’t. This information may provide us some evidence that the productivity of electricity or 
efficiency of electricity use hasn’t changed much over time. In order to have a more accurate and 
clear picture about the productivity change and efficiency of electricity, the results from our 
model are presented in following tables and figure.
3
 In table 2 the relative efficiency score of 
different regions are presented. 
 
Table 2: Relative efficiency score of different regions 
  2003 2004 2005 2006 2007 2008 Mean 
Beijing 1.00 1.00 1.00 1.00 1.00 1.00 1.00 
Tianjin 0.78 0.77 0.80 0.79 0.74 0.82 0.78 
Hebei 0.71 0.69 0.68 0.66 0.65 0.66 0.67 
Shanxi 0.41 0.42 0.41 0.39 0.38 0.41 0.40 
Inner Mongolia 0.53 0.49 0.50 0.48 0.45 0.49 0.49 
Liaoning 0.72 0.66 0.69 0.70 0.72 0.76 0.71 
Jilin 0.73 0.71 0.80 0.82 0.83 0.87 0.79 
Heilongjiang 0.78 0.77 0.82 0.81 0.80 0.82 0.80 
Shanghai 0.94 0.95 0.92 0.93 0.95 0.91 0.93 
Jiangsu 0.98 0.94 0.92 0.91 0.91 0.91 0.93 
Zhejiang 0.90 0.90 0.83 0.83 0.84 0.80 0.85 
Anhui 0.82 0.78 0.77 0.74 0.72 0.73 0.76 
Fujian 0.84 0.79 0.77 0.76 0.76 0.75 0.78 
Jiangxi 0.86 0.87 0.86 0.83 0.78 0.79 0.83 
Shandong 1.00 1.00 1.00 1.00 1.00 1.00 1.00 
Henan 0.73 0.75 0.78 0.79 0.78 0.79 0.77 
Hubei 0.76 0.75 0.74 0.75 0.76 0.80 0.76 
Hunan 0.83 0.82 0.84 0.82 0.82 0.88 0.83 
Guangdong 1.00 1.00 1.00 1.00 1.00 1.00 1.00 
Guangxi 0.63 0.64 0.66 0.65 0.63 0.64 0.64 
Hainan 1.00 1.00 1.00 1.00 1.00 1.00 1.00 
Chongqing 0.78 0.75 0.74 0.67 0.67 0.71 0.72 
Sichuan 0.74 0.73 0.73 0.74 0.76 0.79 0.75 
Guizhou 0.33 0.31 0.34 0.30 0.29 0.32 0.32 
Yunnan 0.64 0.57 0.52 0.49 0.47 0.48 0.53 
Shaanxi 0.59 0.56 0.59 0.61 0.60 0.64 0.60 
Gansu 0.33 0.32 0.33 0.33 0.32 0.31 0.32 
Qinghai 0.23 0.21 0.22 0.21 0.21 0.21 0.22 
Ningxia 0.19 0.17 0.17 0.15 0.15 0.17 0.17 
Xinjiang 0.73 0.70 0.71 0.68 0.63 0.59 0.67 
        Mean 0.72 0.70 0.70 0.69 0.69 0.70 0.70 
 
                                               
3
 To find the results, we use the Deep program kindly provided by Coelli(1996). 
 5 
 
Among all 30 regions, Ningxia, Qinghai, Guizhou and Gansu have the lowest relative efficiency 
as well as Hainan, Guangdong, Shandong and Beijing have the highest efficiency on average. 
From table 2 we can also see that differences on efficiency between regions are very huge.  
This kind of huge inequality may due to the different technology on electricity machine and 
infrastructures between regions. According to Sul (2011), the difference of the electricity 
machines and infrastructure could lead to different machine running efficiency. Since the 
electricity machines and infrastructures of Ningxia, Qinghai, Guizhou and Gansu are insufficient 
comparing to other areas, as a result they will have a low efficiency than other regions because of 
this reason. 
 
Figure 1: Average efficiency score (2003-2008) of different regions 
 
 
We also label all 30 regions according to their relative efficiency in figure 1. In figure 1, darker 
color means that region has a higher relative efficiency; brighter color means that region has a 
lower relative efficiency. From figure 1, we find that most efficient regions are located in the east 
part of China.  The regional electricity efficiency is very imbalanced. Based on this observation, 
one may consider that industrial structure could be one reason for the big gap of electricity 
efficiency of different regions. For example, Beijing, one of the highest ranked regions, is the 
only one region whose third industry ratio is more than 50% according to Li and Hu (2012). 
Ningxia and Qinghai on the other hand have a very low third industry ratio. 
 
 6 
 
Table 3: Decomposition of Malmquist index (Annual average) 
  Technical Efficiency Productivity 
year Change Change Change 
2004 0.926 0.97 0.898 
2005 0.994 1.009 1.003 
2006 1.049 0.979 1.027 
2007 1.041 0.985 1.025 
2008 1.024 1.028 1.053 
    mean 1.006 0.994 1.000 
 
The mean value of Malmquist index is 1, which implies that the productivity of electricity 
remained almost the same from 2004 to 2008. To have a clearer picture we then decompose it 
into two parts. 
 
The mean value of technical change is only 1.006 which implies that on average technology 
didn’t change much from 2004 to 2008.The way the government subsidy the R&D projects could 
be one reason of the slow change. Although Chinese government made many policies to 
augment the R&D expenditure, there isn’t some specific measures and supervision mechanism to 
ensure the quality of the R&D projects. Besides, some direct government subsidies may lead to 
inverse effect of technology development, which is called the “inverse subsidy effect” (Li and 
Hu, 2012).  For example, a region may have more pollution problems because of its slow 
technology process. But in reality, this kind of region may receive more subsidies to develop 
new ways for pollution treatment. So the regional companies may rely on the subsidies without 
researching new technologies. In that way, government’s subsidies don’t bring about a positive 
effect on the progress of technology. 
 
On the other hand, the mean value of efficiency change is 0.994 implies that on averagely 
efficiency is decreasing. The slow development on electricity infrastructure could be one reason 
of it. The slow development on electricity infrastructure is slow in China for many years, and 
always lags behind the investment of China’s basic infrastructure and the GDP, which directly 
leads to the slow pace of the electric construction and the shortage of the electricity supply. 
What’s more, the China's industrial structure change is slow too. In the West part of China, 
primary industry and secondary industry take the higher proportion of the industrial structure at 
present. And that might be the reasons why efficiency can’t increase over time. 
 
Electricity consumers have only insufficient knowledge or information on how to use electricity 
efficiently could be another reason of lower efficiency. Like Kempton and Layne (1994) 
suggested, most electricity consumers of electricity could be weak in data electricity collection 
and analyses distort market decisions.  
 
 7 
 
Section 4 Conclusion 
 
The contributions of this study, from an empirical perspective, have provided a framework to 
investigate the situation of relative efficiency of electricity use and the growth rate of 
electricity’s productivity. This information is significant for evaluating electricity or 
environmental related economics policy. In this paper we have found out the relative efficiency 
score of different regions from 2004 to 2008. Besides the efficiency score and change rate, we 
have also found that there is serious inequality problem on efficiency between regions and the 
electricity’s productivity hasn’t changed at all between 2004 and 2008. Based on our results, we 
have suggested some potential reasons of it in the previous section. If the reasons are not wrong, 
some solutions we propose in below could be related. 
 
1. Government should promote the R&D sector and take an efficient use of expenditure in 
R&D sector. In order to avoid the “inverse subsidy effect”, Chinese government should 
make the supervision mechanism to ensure the money be used in the right position.  
 
2. Government should try to change the industrial structure from the energy intensive to 
technology intensive industries. At the same time, the government should support the 
development of high-tech industries and eliminate those high-pollution and high-energy 
consumption enterprises. 
 
3. Government could also find more ways to educate citizens on how to use electricity more 
efficiently. For example, holding some talk on teaching citizens switch off electric home 
appliances when they don’t need it. 
 
4. Electricity company in China could provide daily feedback on whole house electricity 
consumption as guidance for more efficient electricity use ( Kempton and Layne, 1994). 
 
The above reasons and solutions we have proposed is just some hypothesis. Further serious 
studies about them are needed in order to increase efficiency of electricity use and electricity 
productivity in China. And once the efficiency of electricity use and electricity productivity in 
China could be increased then we believe that many pollution and economic problem will be 
then  solved automatically. 
 
 
 
 
 
 
 
 
 
 
 
 
 8 
 
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Efficiency of electricity use and productivity change of electricity in China: A nonparametric approach

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Efficiency of electricity use and productivity change of electricity in China: A nonparametric approach

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