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Research on the energy-saving effect of energy policies in China: 1982–2006
ARTICLE IN PRESS Energy Policy 37 (2009) 2475–2480
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Research on the energy-saving effect of energy policies in China: 1982–2006 Chaoqing Yuan a,, Sifeng Liu a, Zhigeng Fang a, Junlong Wu b a b
Economics and Management College, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China College of Art, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
a r t i c l e in fo
abstract
Article history: Received 22 September 2008 Accepted 3 March 2009 Available online 19 April 2009
This paper summarizes the main energy policies of China from 1980, and divides them into three groups of policies. Two methods, with and without antitheses and linear regression, are created to evaluate the energy-saving effects of the energy policies. And the energy-saving effects of these three groups of energy policies of China are evaluated by the two methods, respectively. It is concluded that with and without antitheses is used to evaluate short-term effects and linear regression is used to evaluate longterm effects. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Energy intensity Energy policy Energy-saving effects
1. Introduction Since 1980s, economy grew rapidly in China, meanwhile energy consumption grew along with economy. Since 1982, energy intensity declined significantly. Energy intensity of China in 1982 was 2.96 tce per 104 RMB, and in 2006 was 1.16 tce per 104 RMB (energy intensity is that energy consumption divides GDP, and GDP are calculated at a constant price of 2006). But economic growth is increasingly depending on energy consumption. Elasticity ratio of energy consumption in the first years of 21st century is larger than that in the whole 1990s, as shown in Table 1. It indicates Chinese economy growth needs more energy. Because of the lack of energy, energy issues become more serious. And China has to import more energy. In 2006, China imported 19,453 104 ton oil, exported 2626.23 104 ton oil, and consumed 34,875.9 104 ton oil. Forty-eight percent of petrol consumption depended on import. The lack of energy will seriously influence the sustainable development of China. The Chinese government has created many energy policies to save energy. So it is necessary to evaluate the effects of these polices which will decrease the energy intensity.
2. The main energy policies of China Since 1980s, Chinese government has implemented many energy policies. The main energy policies are as shown in Table 2. Because of the interaction of the energy policies, it is difficult to evaluate the effects of individual energy policy. In this paper, therefore, these policies are divided into three groups Corresponding author. Tel.: +86 13851878782; fax: +86 25 52256340.
E-mail address: [email protected] (C. Yuan). 0301-4215/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.enpol.2009.03.010
according to the relationship between a principal policy and subordinate policies that the effects of each group of energy policies in a period could be evaluated. In 1991, the State Planning Commission promulgated several suggestions to further reinforcement of energy saving, which regulated the State Economic and Trade Commission should supervise the implement of energy saving of key energy-using units. In the following years, the energy-saving policies of China were constituted and enacted under this document. Law of the People’s Republic of China on Energy Conservation, amended and adopted on October 28th 2007, was promulgated in 1998, including general provisions, energy-saving management, rational and economical use of energy, technological advances in energy conservation, legal liabilities and supplementary provisions. This law had established the main energy-saving legal system and formalized the energy-saving management. Thereafter, this law was regarded as legal warrant of all following energy-saving policies. In 2004, National Development and Reform Commission compiled Medium- and Long-Term Specific Schema on Energy Saving which programmed the development aim and priorities till 2010 and announced development aim till 2020. In this schema, it emphasized energy saving should be related to adjustment of industrial structure, technological progress and sustainable development. Connection between energy saving and economy development was highly taken into account and performed as essential guidance of government. Several suggestions to further reinforcement of energy saving, Law of the People’s Republic of China on Energy Conservation, Medium- and Long-Term Specific Schema on Energy Saving are three signal energy-saving policies, and represent three different energy-saving period. So all the energy policies are divided into three energy policy groups: energy policy group 1, the energy policy group of several suggestion to further reinforcement of
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energy saving; energy policy group 2: the energy policy group of Law of the People’s Republic of China on Energy Conservation; energy policy group 3, the energy policy group of Medium- and Long-Term Specific Schema on Energy Saving.
3. Model In this paper, two models are applied to evaluate the energysaving effects of energy policies, respectively, which are with and without antitheses and linear regression.
Table 1 Elasticity ratio of energy consumption. Year
Growth rate of energy consumption over preceding year (%)
Growth rate of gross domestic product (GDP) over preceding year (%)
Elasticity ratio of energy consumption
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
1.8 5.1 5.2 6.3 5.8 6.9 5.9 0.8 4.1 1.2 3.5 3.4 6 15.3 16.1 10.6 9.61
3.8 9.2 14.2 14 13.1 10.9 10 9.3 7.8 7.6 8.4 8.3 9.1 10 10.1 10.4 11.1
0.47 0.55 0.37 0.45 0.44 0.63 0.59
0.157895 0.416667 0.409639 0.659341 1.53 1.594059 1.019231 0.865766
Resource: China Statistical Year Book (2007). http://www.stats.gov.cn/tjsj/ndsj/ 2007/html/G0708e.htm.
3.1. With and without antitheses Given that the effects of all the factors are stable except energy policies, this method works well. The first step is to collect the data of the energy intensity including historical data before implementing the energy policies and real values after implementing the energy policies. Here, real values refer to the energy intensity under the implementing of the energy policies. The second step is to predict the energy intensity according to the historical data and get the predicted values referring to the energy intensity without the effects of energy policies. The predicted values indicate the energy intensity under the hypothesis that all the influence of all the factors is stable. This study involved a long time span, lots of influencing factors, so the older data cannot reflect recent tendency, while the new data can. So the data of recent years are used to predict the energy intensity. GM(1,1) model is an important method of Grey System Theory, which can be used to predict with small sample (Liu and Lin, 1998). It means that the predicted values can be obtained by GM(1,1) with the several newer data and the predicted values can reflect the tendency of energy intensity more accurately. The calculating steps of GM(1,1) are as shown in the Appendix A. Then, the third step to calculate the differences between real values and predicted values. The real values refer to after implementing-energypolicies energy intensity. So that the differences are the energysaving effects of energy policies. The principle of with and without antitheses is shown as Fig. 1.
3.2. Linear regression Many researchers have studied the factors on Chinese energy intensity. Economy growth and energy consumption in China have strong correlations (Yuan et al., 2008). Energy intensity of China declined, and efficiency effects contributed to a majority while structure effect contributed less (Lin and Polenske, 1995; Liao et al., 1997). It is similar in Chinese industrial sectors (Sinton and
Table 2 History of comprehensive energy-saving policy. Time
Energy policy
1986 1990 1991 1991 1991 1992 1994 1996 1995 1996 1997 1998 1999 2000 2001 2004 2005 2005 2005 2005 2006 2006 2006 2006 2006 2007 2007 2007
Interim regulation of energy-saving management. Plan of energy saving in the eighth five. Regulation of energy saving for thermal power plant. Several suggestion to further reinforcement of energy saving. Regulation of grading and upgrading of energy-saving management for enterprise. Several suggestion to acceleration of house wall materials innovation and energy-saving architecture. Several suggestion to reinforcement of saving and utilization of natural resources. Regulation of technological innovation projects of energy saving and utilization. Plan of energy saving in the ninth five. Regulation of supervision of energy saving of the ministry of coal industry. Design standards of energy saving of civil construction. Law of the People’s Republic of China on Energy Conservation. Regulation of energy saving of key energy-using units. Regulation of energy-saving utilization of civil construction. Regulation of electricity saving. Medium and long term specific schema on energy saving. Notification to implementation of design standards of energy saving of new-build civil construction. Guidance of promotion of energy-and-land saving civil construction and public building. Several suggestion to further promotion of house wall materials innovation and energy-saving architecture. Regulation of energy-saving utilization of Civil construction (2005), abolishing regulation of energy-saving utilization of civil construction (2000). Implementation plan of performing energy saving of a thousand of enterprise. Notification to preventing blind re-expansion of high energy-consuming industries. Decision to reinforcing energy-saving issue. Administrative reply of plan of reduce energy intensity indexes of every region in the eleventh five. Implementation suggestion of the top ten key energy-saving projects in ‘the eleventh five’. Suggestions to energy saving and emission reduction of coal industry. Advice of comprehensive operation scheme on energy saving and reduce of pollutants emission. Emergent notification to reinforcement of industrial structure adjustment and preventing blind re-expansion of high energy-consuming industries.
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Levine, 1994; Zhong, 2003). Empirical researches reported that energy price effects accounted for the decline in energy intensity of China. (Fisher-Vanden et al., 2004a,b; Hang and Tu, 2007). And renewable energy policy in China and its regulatory law framework have potential effectiveness (Cherni and Kentish, 2007). There are critical barriers hindering the project of energy saving in China (Wang et al., 2008).The most effective means for improving the efficiency of energy consumption in China are re-adjusting the economic structure of China, improving the energy pricing system and improving the energy-generating efficiencies and end-use technologies (Wu and Wei, 1991; Fisher-Vanden et al., 2006). On the basis of these researches, the main factors effecting energy intensity of China are found including economy growth, economy structure, energy price, technical progress, energy policy, GDP which are used to indicate the influence of energy consumptions caused by economies of scale in China, secondary industry and tertiary industry proportion which are used to indicate economy structure, and total factor productivity which is used to evaluate technological progress. So, a linear regression
Historical Data Predicted Value Energy Policies
t = t0
Differences (Effect of Energy Policy) Real Value t = t1
Fig. 1. With and without antitheses.
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model is created, EI ¼ a þ b1 GDP þ b2 EP þ b3 TP þ b4 SP þ b5 TFP þ b6 P1 þ b7 P2 þ b8 P 3 EI is the energy intensity; GDP is the gross domestic production; EP is the energy price; SP is the secondary industry proportion; TP is the tertiary industry proportion; TFP is the total factor productivity; and P1, P2, P3 is the groups of energy policies.
4. Data Energy consumption, energy price indices, indices of GDP, secondary industry proportion, tertiary industry proportion and TFP of China are as shown in Table 3. For lack of energy price indices and given the high marketoriented oil price of China, ex-factory price indices of petroleum industry are used to replace energy price indices. In 2006, the GDP of China is 211,808.0 100 million RMB, and the indices of GDP is 1334.0. So real GDP is defined as the indices of GDP 211,808.0 100/1334.0. Energy intensity is defined as energy consumption/real GDP. Assume that energy price of 1981 is 1.0, energy price is defined as the product of energy price indices. Dummy variables, P1, P2, and P3 are used to indicate energy policies. P1 indicates the energy policy group 1. The values of P1 are set to be zero before 1991, one from 1991 to 1997, and zero since 1998. P1 was promulgated in 1991, so the values are set to be zero before 1991. However, after promulgating of Law of the People’s Republic of China on Energy Conservation, energy-saving management system of China changed greatly and the influence of P1 became less obvious than before. So the values of P1 are set to be zero after 1998. P2 indicates the energy policy group 2. Law
Table 3 Energy consumption, energy price indices, indices of GDP, secondary industry proportion, tertiary industry proportion and TFP of China. Year
Energy consumption
Energy price indices
Indices of GDP
Secondary industry proportion
Tertiary industry proportion
TFP
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
62646 66040 70904 76682 80850 86632 92997 96934 98703 103783 109170 115993 122737 131176 138948 137798 132214 133831 138553 143199 151797 174990 203227 224682 246270
100.5 106.3 112.0 107.2 104.6 104.0 106.8 108.4 107.1 118.8 115.3 171.3 148.7 121.2 104.6 107.4 93.0 109.6 144.3 99.1 95.2 115.6 114.2 122.4 120.3
133.1 147.6 170.0 192.9 210.0 234.3 260.7 271.3 281.7 307.6 351.4 400.4 452.8 502.3 552.6 603.9 651.2 700.9 759.9 823.0 897.8 987.8 1087.4 1200.8 1334.0
44.8 44.4 43.1 42.9 43.7 43.6 43.8 42.8 41.3 41.8 43.4 46.6 46.6 47.2 47.5 47.5 46.2 45.8 45.9 45.1 44.8 46.0 46.2 47.5 48.9
21.8 22.4 24.8 28.7 29.1 29.6 30.5 32.1 31.6 33.7 34.8 33.7 33.6 32.9 32.8 34.2 36.2 37.7 39.0 40.5 41.5 41.2 40.4 40.0 39.4
104.2 105.4 106.6 107.9 109.3 110.4 111.4 112.0 111.3 111.9 112.8 113.9 115.0 116.1 117.1 118.0 119.1 120.1 121.0 121.7 122.7 123.8 124.8 125.8 126.8
Resource: Energy consumption from China Statistical Yearbook (1996), (http://www.stats.gov.cn/ndsj/information/zh1/f021a,)China Statistical Year Book (2007) (http:// www.stats.gov.cn/tjsj/ndsj/2007/html/G0702e.htm).GDP from China Statistical Yearbook (2007) (http://www.stats.gov.cn/tjsj/ndsj/2007/indexch.htm).Secondary industry proportion, tertiary industry proportion from China Statistical Yearbook (2007).(http://www.stats.gov.cn/tjsj/ndsj/2007/indexch.htm).Energy price indices is replaced by ex-factory price indices of petroleum industry and preceding year ¼ 100., from China Statistical Yearbook (1996) (http://www.stats.gov.cn/ndsj/information/zh1/h121a), China Statistical Year Book (2007) (http://www.stats.gov.cn/tjsj/ndsj/2007/html/I0912e.htm). TFP from a research of Yang et al. (2008). The research applied latent variable approach to measure TFP. This approach treats TFP as a dependant variable, and the result excludes the influence of the other factors. So it is an appropriate method to measure technological progress.
ARTICLE IN PRESS C. Yuan et al. / Energy Policy 37 (2009) 2475–2480
2 1.5 1
real value predicted value
0.5
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
0 1986
year Fig. 2. The energy-saving effect of the energy policy group 1.
2.5 2 1.5 1
real energy intensity predicted energy intensity
0.5
02 20
01 20
00
99
20
19
98 19
97 19
96 19
19
95
0
19
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0
94
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
19
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1985
1.005 1.068315 1.196513 1.282662 1.341664 1.395331 1.490213 1.615391 1.730084 2.05534 2.369807 4.059479 6.036445 7.316171 7.652715 8.219016 7.643685 8.377479 12.0887 11.9799 11.40487 13.18403 15.05616 18.42874 22.16977
93
21,141.13815 23,435.5815 26,992.17032 30,626.98796 33,336.36667 37,197.80596 41,393.93558 43,075.8553 44,729.54813 48,835.24503 55,789.72888 63,580.38217 71,897.12967 79,751.87694 87,733.86224 95,890.50903 103,401.9452 111,281.0036 120,663.416 130,678.8627 142,547.2058 156,838.1031 172,655.2884 190,667.9944 211,808.0487
19
2.963227 2.817937 2.626836 2.50374 2.425279 2.328955 2.246633 2.250309 2.206662 2.125166 1.956812 1.824352 1.70712 1.644801 1.583744 1.437035 1.278641 1.20264 1.148257 1.09581 1.064891 1.115738 1.177066 1.178394 1.162704
1984
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
2.5
92
Policy 3
1983
Policy 2
91
Policy 1
19
Energy price
1982
Real GDP
90
EI
3
19
Year
3.5 Energy Intensity
Table 4 Energy intensity, real GDP, energy price and energy polices of China from 1982 to 2006.
Enegry of intensity
2478
Year
5. An empirical study in China Energy-saving effects of the energy policies are researched by two methods, respectively, with and without antitheses and linear regression.
Fig. 3. Energy-saving effect of energy policy group 2.
1.4 1.2 Energy Intensity
of the People’s Republic of China on Energy Conservation was promulgated in 1998 and it works well till it is amended in 2008. So the values of P2 are set to be zero before 1998, and one between 1998 and 2006. P3 indicates the energy policy group 3. In 2004, Medium- and Long-Term Specific Schema on Energy Saving was starting to be operated. So the values of P3 are set to be zero before 2004, and one between 2004 and 2006. The values of EI, real GDP, energy price, energy policies are as shown in Table 4.
1 0.8
Real energy intensity predicted energy intensity
0.6 0.4 0.2 0 2001
2002
2003
2004
2005
2006
Year
5.1. With and without antitheses Fig. 4. Energy-saving effects of energy policy group 3.
Energy-saving effects of the three energy policies are researched by with and without antitheses. (1) the energy policy group 1 The energy intensities from 1991 to 1997 are predicted with those from 1982 to 1990 by GM(1,1). The results are as shown in Fig. 2. Energy policy reduced energy intensity from 1992 to 1997. From 1991 to 1997, energy-saving effect averages 0.115214, and it grows bigger and bigger. (2) The energy policy group 2 The energy intensities from 1998 to 2002 are predicted with those from 1991 to 1997 by GM(1,1). The results are as shown in Fig. 3. From 1998 to 2002, energy-saving effect averages 0.075159, and it grows smaller and smaller. (3) The energy policy group 3 The energy intensities of 2005 and 2006 are predicted with those from 2001 to 2004 by GM(1,1). The results are as shown
in Fig. 4. Energy-saving effect 0f 2005 is 0.057674 and that of 2006 is 0.136974, and averages 0.097324. It is concluded that all the energy policies have decreased the energy intensities. It is found that the energy-saving effect of policy group 1 is the biggest. But this method has a very important assumption that the effects of all the other factors except policies are stable. However, in most of real conditions, effects of the factors are unstable, so as to generate some errors. 5.2. Linear regression Model EI ¼ a+b1GDP+b2EP+b3TP+b4SP+b5TFP+b6P1+b7P2+b8P3 is used to research the energy-saving effect. It is resolved by SPSS.
ARTICLE IN PRESS C. Yuan et al. / Energy Policy 37 (2009) 2475–2480
Table 5 R2-test and F-test. R
.997a a
R square
.993
Adjusted R square
.990
Change statistics F Change
df1
df2
Sig. F change
289.563
8
16
.000
Predictors: (constant), SP, P1, TP, P3, P2, EP, TFP, GDP.
Table 6 Coefficients and t-test. Model
Unstandardized coefficients
Standardized coefficients t
B
Beta
Std. error
Sig.
2479
The coefficient of SP is negative, which means that when other variables are controlled, energy intensity will decrease with SP increase. In spite of its higher energy consumption of secondary industry, it declines fastest comparatively. Therefore, to improve the proportion of secondary industry will reduce the energy intensity. The coefficient of P3 is positive, which means that when other variables are controlled, P3 will increase EI. The reason is the energy intensity increased after implementing P3. But as shown in Fig. 4, the growth rate of energy intensity decreased obviously after implementing P3, so P3 is effective. But the effect of P3 can not be evaluated by this method because P3 only was operated two years long.
6. Conclusion (Constant) 16.312 GDP 1.048E-5 EP .027 P1 .185 P2 .397 P3 .133 TFP .121 TP .007 SP .018
1.675 .000 .019 .061 .093 .083 .023 .017 .019
.964 .270 .139 .320 .061 1.320 .061 .058
9.739 3.842 1.416 3.014 4.272 1.606 5.269 .401 .935
.000 .001 .176 .008 .001 .128 .000 .694 .364
And the results of coefficients and related tests are as shown in Tables 5 and 6. EI ¼ 16:312 þ 0:00001048GDP 0:027EP 0:007TP 0:018SP 0:121TFP 0:185P1 0:397P 2 þ 0:133P3 That adjusted R square 0.993 and Sig. F change 0.000 show that the regression model is good and the factors explain energy intensity very well. The t-tests show that GDP, TFP, P1 and P2 have significant effect on energy intensity. The effects of EP, TP, SP and, P3 are not significant. The coefficient of GDP is positive, which means that when other variables are controlled, energy intensity will increase with economic growth. Economic development of China in the recent 20 years, to some extent, depends on large amount of small-scale factories, such as small-scale power plants, small-scale cement plants and small-scale chemical plants. In the case of the same output, these factories consume more energy than large-scale factories. Economic growth means more energy consumption and fails to gain the economies of scale. The coefficient of TFP is negative, which means that when other variables are controlled, energy intensity will decrease by technological progress. Application of new technologies, new techniques and new methods and the emergence of new products, can effectively reduce energy consumption, so technological progress is able to effectively reduce energy consumption. The coefficients of P1 and P2 are negative, which means that when other variables are controlled, energy policy group P1 and P2 reduced energy intensity, they had good effect on energy saving. The coefficient of EP is negative, which means that when other variables are controlled, energy intensity will decrease with energy price increase. The reason is that price elasticity of energy is negative, which means price of energy increases, energy consumption will decrease. The coefficient of TP is negative, which means that when other variables are controlled, energy intensity will decrease with TP increase. The reason is tertiary industry consumes less energy, compared to secondary industry. If proportion of tertiary industry is increased, energy consumption will decrease.
This paper introduces two methods to evaluate the energysaving effects of energy polices. It is found that the results calculated by different methods are different. The important assumption that energy intensity would be stably effected by other factors may cause the result calculated by with and without antitheses to contain effects induced by the other factors. The reason that energy-saving effects of P3 is not significant is that P3 has been implemented in only 2 years. It is too short to show the energy-saving effects. With and without antitheses is used to evaluate the short-term effect of the energy policy, for it is reasonable if the effects of the other factors are stable in a very short period; and linear regression model is used to evaluate the long-term effect of the energy policy, because it can discern the effects of all the factors effectively.
Acknowledgements This research is supported by Energy-saving Project from National Development and Reform Commission (ZHZB012), Jiangsu Social Science Fund (07EYA017) and Social Project from Ministry of Education (07JC630064).
Appendix A GM(1,1) (Grey Model) are applied to predict the energy intensities. The calculating step of GM(1,1) as follows: Step 1: create a non-negative sequence X(0) ¼ (x(0)(1),x(0)(2),y, (0) x (n)), where x(0)(k)X0, k ¼ 1,2,y,n; Step 2: Calculate accumulating generation operational sequence P X(1) ¼ (x(1)(1),x(1)(2),y,x(1)(n)), where x(1)(k) ¼ ik¼ 1x(0)(i), k ¼ 1,2,y,n; Step 3: calculate mean sequence of consecutive neighbours Z(1) ¼ (z(1)(2),z(1)(3),y,z(1)(n)), where z(1)(k) ¼ 1/2(x(1)(k)+x(1) (k1)), k ¼ 2,3,y,n; Step 4: solve the parameters ˆ ¼ (a,b)T is a sequence of parameters, and If a 3 3 2 ð0Þ 2 ð1Þ z ð2Þ 1 x ð2Þ 7 7 6 ð0Þ 6 ð1Þ 6 x ð3Þ 7 6 z ð3Þ 1 7 7 7 6 6 Y¼6 . 7 B¼6 7 . . .. 7 .. 6 .. 7 6 5 5 4 4 zð1Þ ðnÞ 1 xð0Þ ðnÞ Then the least square estimate sequence of GM(1,1) model x(0)(k)+az(1)(k) ¼ b satisfies a^ ¼ ðBT BÞ1 BT Y
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Step 5: solve the whitenization function ð1Þ
dx þ axð1Þ ¼ b dt and the solution which is called a time response function is b at b þ xð1Þ ðtÞ ¼ xð1Þ ð1Þ e a a Step 6: acquire time response sequence according to Step 5 b ak b ð1Þ þ ; k ¼ 1; 2; . . . ; n e x^ ðk þ 1Þ ¼ xð0Þ ð1Þ a a Step 7: calculate the restored values ð0Þ
ð1Þ ð1Þ ð1Þ x^ ðk þ 1Þ ¼ að1Þ x^ ðk þ 1Þ ¼ x^ ðk þ 1Þ x^ ðkÞ b ak ¼ ð1 ea Þ xð0Þ ð1Þ e . a
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Energy Policy journal homepage: www.elsevier.com/locate/enpol
Viewpoint
Research on the energy-saving effect of energy policies in China: 1982–2006 Chaoqing Yuan a,, Sifeng Liu a, Zhigeng Fang a, Junlong Wu b a b
Economics and Management College, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China College of Art, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
a r t i c l e in fo
abstract
Article history: Received 22 September 2008 Accepted 3 March 2009 Available online 19 April 2009
This paper summarizes the main energy policies of China from 1980, and divides them into three groups of policies. Two methods, with and without antitheses and linear regression, are created to evaluate the energy-saving effects of the energy policies. And the energy-saving effects of these three groups of energy policies of China are evaluated by the two methods, respectively. It is concluded that with and without antitheses is used to evaluate short-term effects and linear regression is used to evaluate longterm effects. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Energy intensity Energy policy Energy-saving effects
1. Introduction Since 1980s, economy grew rapidly in China, meanwhile energy consumption grew along with economy. Since 1982, energy intensity declined significantly. Energy intensity of China in 1982 was 2.96 tce per 104 RMB, and in 2006 was 1.16 tce per 104 RMB (energy intensity is that energy consumption divides GDP, and GDP are calculated at a constant price of 2006). But economic growth is increasingly depending on energy consumption. Elasticity ratio of energy consumption in the first years of 21st century is larger than that in the whole 1990s, as shown in Table 1. It indicates Chinese economy growth needs more energy. Because of the lack of energy, energy issues become more serious. And China has to import more energy. In 2006, China imported 19,453 104 ton oil, exported 2626.23 104 ton oil, and consumed 34,875.9 104 ton oil. Forty-eight percent of petrol consumption depended on import. The lack of energy will seriously influence the sustainable development of China. The Chinese government has created many energy policies to save energy. So it is necessary to evaluate the effects of these polices which will decrease the energy intensity.
2. The main energy policies of China Since 1980s, Chinese government has implemented many energy policies. The main energy policies are as shown in Table 2. Because of the interaction of the energy policies, it is difficult to evaluate the effects of individual energy policy. In this paper, therefore, these policies are divided into three groups Corresponding author. Tel.: +86 13851878782; fax: +86 25 52256340.
E-mail address: [email protected] (C. Yuan). 0301-4215/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.enpol.2009.03.010
according to the relationship between a principal policy and subordinate policies that the effects of each group of energy policies in a period could be evaluated. In 1991, the State Planning Commission promulgated several suggestions to further reinforcement of energy saving, which regulated the State Economic and Trade Commission should supervise the implement of energy saving of key energy-using units. In the following years, the energy-saving policies of China were constituted and enacted under this document. Law of the People’s Republic of China on Energy Conservation, amended and adopted on October 28th 2007, was promulgated in 1998, including general provisions, energy-saving management, rational and economical use of energy, technological advances in energy conservation, legal liabilities and supplementary provisions. This law had established the main energy-saving legal system and formalized the energy-saving management. Thereafter, this law was regarded as legal warrant of all following energy-saving policies. In 2004, National Development and Reform Commission compiled Medium- and Long-Term Specific Schema on Energy Saving which programmed the development aim and priorities till 2010 and announced development aim till 2020. In this schema, it emphasized energy saving should be related to adjustment of industrial structure, technological progress and sustainable development. Connection between energy saving and economy development was highly taken into account and performed as essential guidance of government. Several suggestions to further reinforcement of energy saving, Law of the People’s Republic of China on Energy Conservation, Medium- and Long-Term Specific Schema on Energy Saving are three signal energy-saving policies, and represent three different energy-saving period. So all the energy policies are divided into three energy policy groups: energy policy group 1, the energy policy group of several suggestion to further reinforcement of
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energy saving; energy policy group 2: the energy policy group of Law of the People’s Republic of China on Energy Conservation; energy policy group 3, the energy policy group of Medium- and Long-Term Specific Schema on Energy Saving.
3. Model In this paper, two models are applied to evaluate the energysaving effects of energy policies, respectively, which are with and without antitheses and linear regression.
Table 1 Elasticity ratio of energy consumption. Year
Growth rate of energy consumption over preceding year (%)
Growth rate of gross domestic product (GDP) over preceding year (%)
Elasticity ratio of energy consumption
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
1.8 5.1 5.2 6.3 5.8 6.9 5.9 0.8 4.1 1.2 3.5 3.4 6 15.3 16.1 10.6 9.61
3.8 9.2 14.2 14 13.1 10.9 10 9.3 7.8 7.6 8.4 8.3 9.1 10 10.1 10.4 11.1
0.47 0.55 0.37 0.45 0.44 0.63 0.59
0.157895 0.416667 0.409639 0.659341 1.53 1.594059 1.019231 0.865766
Resource: China Statistical Year Book (2007). http://www.stats.gov.cn/tjsj/ndsj/ 2007/html/G0708e.htm.
3.1. With and without antitheses Given that the effects of all the factors are stable except energy policies, this method works well. The first step is to collect the data of the energy intensity including historical data before implementing the energy policies and real values after implementing the energy policies. Here, real values refer to the energy intensity under the implementing of the energy policies. The second step is to predict the energy intensity according to the historical data and get the predicted values referring to the energy intensity without the effects of energy policies. The predicted values indicate the energy intensity under the hypothesis that all the influence of all the factors is stable. This study involved a long time span, lots of influencing factors, so the older data cannot reflect recent tendency, while the new data can. So the data of recent years are used to predict the energy intensity. GM(1,1) model is an important method of Grey System Theory, which can be used to predict with small sample (Liu and Lin, 1998). It means that the predicted values can be obtained by GM(1,1) with the several newer data and the predicted values can reflect the tendency of energy intensity more accurately. The calculating steps of GM(1,1) are as shown in the Appendix A. Then, the third step to calculate the differences between real values and predicted values. The real values refer to after implementing-energypolicies energy intensity. So that the differences are the energysaving effects of energy policies. The principle of with and without antitheses is shown as Fig. 1.
3.2. Linear regression Many researchers have studied the factors on Chinese energy intensity. Economy growth and energy consumption in China have strong correlations (Yuan et al., 2008). Energy intensity of China declined, and efficiency effects contributed to a majority while structure effect contributed less (Lin and Polenske, 1995; Liao et al., 1997). It is similar in Chinese industrial sectors (Sinton and
Table 2 History of comprehensive energy-saving policy. Time
Energy policy
1986 1990 1991 1991 1991 1992 1994 1996 1995 1996 1997 1998 1999 2000 2001 2004 2005 2005 2005 2005 2006 2006 2006 2006 2006 2007 2007 2007
Interim regulation of energy-saving management. Plan of energy saving in the eighth five. Regulation of energy saving for thermal power plant. Several suggestion to further reinforcement of energy saving. Regulation of grading and upgrading of energy-saving management for enterprise. Several suggestion to acceleration of house wall materials innovation and energy-saving architecture. Several suggestion to reinforcement of saving and utilization of natural resources. Regulation of technological innovation projects of energy saving and utilization. Plan of energy saving in the ninth five. Regulation of supervision of energy saving of the ministry of coal industry. Design standards of energy saving of civil construction. Law of the People’s Republic of China on Energy Conservation. Regulation of energy saving of key energy-using units. Regulation of energy-saving utilization of civil construction. Regulation of electricity saving. Medium and long term specific schema on energy saving. Notification to implementation of design standards of energy saving of new-build civil construction. Guidance of promotion of energy-and-land saving civil construction and public building. Several suggestion to further promotion of house wall materials innovation and energy-saving architecture. Regulation of energy-saving utilization of Civil construction (2005), abolishing regulation of energy-saving utilization of civil construction (2000). Implementation plan of performing energy saving of a thousand of enterprise. Notification to preventing blind re-expansion of high energy-consuming industries. Decision to reinforcing energy-saving issue. Administrative reply of plan of reduce energy intensity indexes of every region in the eleventh five. Implementation suggestion of the top ten key energy-saving projects in ‘the eleventh five’. Suggestions to energy saving and emission reduction of coal industry. Advice of comprehensive operation scheme on energy saving and reduce of pollutants emission. Emergent notification to reinforcement of industrial structure adjustment and preventing blind re-expansion of high energy-consuming industries.
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Levine, 1994; Zhong, 2003). Empirical researches reported that energy price effects accounted for the decline in energy intensity of China. (Fisher-Vanden et al., 2004a,b; Hang and Tu, 2007). And renewable energy policy in China and its regulatory law framework have potential effectiveness (Cherni and Kentish, 2007). There are critical barriers hindering the project of energy saving in China (Wang et al., 2008).The most effective means for improving the efficiency of energy consumption in China are re-adjusting the economic structure of China, improving the energy pricing system and improving the energy-generating efficiencies and end-use technologies (Wu and Wei, 1991; Fisher-Vanden et al., 2006). On the basis of these researches, the main factors effecting energy intensity of China are found including economy growth, economy structure, energy price, technical progress, energy policy, GDP which are used to indicate the influence of energy consumptions caused by economies of scale in China, secondary industry and tertiary industry proportion which are used to indicate economy structure, and total factor productivity which is used to evaluate technological progress. So, a linear regression
Historical Data Predicted Value Energy Policies
t = t0
Differences (Effect of Energy Policy) Real Value t = t1
Fig. 1. With and without antitheses.
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model is created, EI ¼ a þ b1 GDP þ b2 EP þ b3 TP þ b4 SP þ b5 TFP þ b6 P1 þ b7 P2 þ b8 P 3 EI is the energy intensity; GDP is the gross domestic production; EP is the energy price; SP is the secondary industry proportion; TP is the tertiary industry proportion; TFP is the total factor productivity; and P1, P2, P3 is the groups of energy policies.
4. Data Energy consumption, energy price indices, indices of GDP, secondary industry proportion, tertiary industry proportion and TFP of China are as shown in Table 3. For lack of energy price indices and given the high marketoriented oil price of China, ex-factory price indices of petroleum industry are used to replace energy price indices. In 2006, the GDP of China is 211,808.0 100 million RMB, and the indices of GDP is 1334.0. So real GDP is defined as the indices of GDP 211,808.0 100/1334.0. Energy intensity is defined as energy consumption/real GDP. Assume that energy price of 1981 is 1.0, energy price is defined as the product of energy price indices. Dummy variables, P1, P2, and P3 are used to indicate energy policies. P1 indicates the energy policy group 1. The values of P1 are set to be zero before 1991, one from 1991 to 1997, and zero since 1998. P1 was promulgated in 1991, so the values are set to be zero before 1991. However, after promulgating of Law of the People’s Republic of China on Energy Conservation, energy-saving management system of China changed greatly and the influence of P1 became less obvious than before. So the values of P1 are set to be zero after 1998. P2 indicates the energy policy group 2. Law
Table 3 Energy consumption, energy price indices, indices of GDP, secondary industry proportion, tertiary industry proportion and TFP of China. Year
Energy consumption
Energy price indices
Indices of GDP
Secondary industry proportion
Tertiary industry proportion
TFP
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
62646 66040 70904 76682 80850 86632 92997 96934 98703 103783 109170 115993 122737 131176 138948 137798 132214 133831 138553 143199 151797 174990 203227 224682 246270
100.5 106.3 112.0 107.2 104.6 104.0 106.8 108.4 107.1 118.8 115.3 171.3 148.7 121.2 104.6 107.4 93.0 109.6 144.3 99.1 95.2 115.6 114.2 122.4 120.3
133.1 147.6 170.0 192.9 210.0 234.3 260.7 271.3 281.7 307.6 351.4 400.4 452.8 502.3 552.6 603.9 651.2 700.9 759.9 823.0 897.8 987.8 1087.4 1200.8 1334.0
44.8 44.4 43.1 42.9 43.7 43.6 43.8 42.8 41.3 41.8 43.4 46.6 46.6 47.2 47.5 47.5 46.2 45.8 45.9 45.1 44.8 46.0 46.2 47.5 48.9
21.8 22.4 24.8 28.7 29.1 29.6 30.5 32.1 31.6 33.7 34.8 33.7 33.6 32.9 32.8 34.2 36.2 37.7 39.0 40.5 41.5 41.2 40.4 40.0 39.4
104.2 105.4 106.6 107.9 109.3 110.4 111.4 112.0 111.3 111.9 112.8 113.9 115.0 116.1 117.1 118.0 119.1 120.1 121.0 121.7 122.7 123.8 124.8 125.8 126.8
Resource: Energy consumption from China Statistical Yearbook (1996), (http://www.stats.gov.cn/ndsj/information/zh1/f021a,)China Statistical Year Book (2007) (http:// www.stats.gov.cn/tjsj/ndsj/2007/html/G0702e.htm).GDP from China Statistical Yearbook (2007) (http://www.stats.gov.cn/tjsj/ndsj/2007/indexch.htm).Secondary industry proportion, tertiary industry proportion from China Statistical Yearbook (2007).(http://www.stats.gov.cn/tjsj/ndsj/2007/indexch.htm).Energy price indices is replaced by ex-factory price indices of petroleum industry and preceding year ¼ 100., from China Statistical Yearbook (1996) (http://www.stats.gov.cn/ndsj/information/zh1/h121a), China Statistical Year Book (2007) (http://www.stats.gov.cn/tjsj/ndsj/2007/html/I0912e.htm). TFP from a research of Yang et al. (2008). The research applied latent variable approach to measure TFP. This approach treats TFP as a dependant variable, and the result excludes the influence of the other factors. So it is an appropriate method to measure technological progress.
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2 1.5 1
real value predicted value
0.5
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
0 1986
year Fig. 2. The energy-saving effect of the energy policy group 1.
2.5 2 1.5 1
real energy intensity predicted energy intensity
0.5
02 20
01 20
00
99
20
19
98 19
97 19
96 19
19
95
0
19
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0
94
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
19
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1985
1.005 1.068315 1.196513 1.282662 1.341664 1.395331 1.490213 1.615391 1.730084 2.05534 2.369807 4.059479 6.036445 7.316171 7.652715 8.219016 7.643685 8.377479 12.0887 11.9799 11.40487 13.18403 15.05616 18.42874 22.16977
93
21,141.13815 23,435.5815 26,992.17032 30,626.98796 33,336.36667 37,197.80596 41,393.93558 43,075.8553 44,729.54813 48,835.24503 55,789.72888 63,580.38217 71,897.12967 79,751.87694 87,733.86224 95,890.50903 103,401.9452 111,281.0036 120,663.416 130,678.8627 142,547.2058 156,838.1031 172,655.2884 190,667.9944 211,808.0487
19
2.963227 2.817937 2.626836 2.50374 2.425279 2.328955 2.246633 2.250309 2.206662 2.125166 1.956812 1.824352 1.70712 1.644801 1.583744 1.437035 1.278641 1.20264 1.148257 1.09581 1.064891 1.115738 1.177066 1.178394 1.162704
1984
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
2.5
92
Policy 3
1983
Policy 2
91
Policy 1
19
Energy price
1982
Real GDP
90
EI
3
19
Year
3.5 Energy Intensity
Table 4 Energy intensity, real GDP, energy price and energy polices of China from 1982 to 2006.
Enegry of intensity
2478
Year
5. An empirical study in China Energy-saving effects of the energy policies are researched by two methods, respectively, with and without antitheses and linear regression.
Fig. 3. Energy-saving effect of energy policy group 2.
1.4 1.2 Energy Intensity
of the People’s Republic of China on Energy Conservation was promulgated in 1998 and it works well till it is amended in 2008. So the values of P2 are set to be zero before 1998, and one between 1998 and 2006. P3 indicates the energy policy group 3. In 2004, Medium- and Long-Term Specific Schema on Energy Saving was starting to be operated. So the values of P3 are set to be zero before 2004, and one between 2004 and 2006. The values of EI, real GDP, energy price, energy policies are as shown in Table 4.
1 0.8
Real energy intensity predicted energy intensity
0.6 0.4 0.2 0 2001
2002
2003
2004
2005
2006
Year
5.1. With and without antitheses Fig. 4. Energy-saving effects of energy policy group 3.
Energy-saving effects of the three energy policies are researched by with and without antitheses. (1) the energy policy group 1 The energy intensities from 1991 to 1997 are predicted with those from 1982 to 1990 by GM(1,1). The results are as shown in Fig. 2. Energy policy reduced energy intensity from 1992 to 1997. From 1991 to 1997, energy-saving effect averages 0.115214, and it grows bigger and bigger. (2) The energy policy group 2 The energy intensities from 1998 to 2002 are predicted with those from 1991 to 1997 by GM(1,1). The results are as shown in Fig. 3. From 1998 to 2002, energy-saving effect averages 0.075159, and it grows smaller and smaller. (3) The energy policy group 3 The energy intensities of 2005 and 2006 are predicted with those from 2001 to 2004 by GM(1,1). The results are as shown
in Fig. 4. Energy-saving effect 0f 2005 is 0.057674 and that of 2006 is 0.136974, and averages 0.097324. It is concluded that all the energy policies have decreased the energy intensities. It is found that the energy-saving effect of policy group 1 is the biggest. But this method has a very important assumption that the effects of all the other factors except policies are stable. However, in most of real conditions, effects of the factors are unstable, so as to generate some errors. 5.2. Linear regression Model EI ¼ a+b1GDP+b2EP+b3TP+b4SP+b5TFP+b6P1+b7P2+b8P3 is used to research the energy-saving effect. It is resolved by SPSS.
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Table 5 R2-test and F-test. R
.997a a
R square
.993
Adjusted R square
.990
Change statistics F Change
df1
df2
Sig. F change
289.563
8
16
.000
Predictors: (constant), SP, P1, TP, P3, P2, EP, TFP, GDP.
Table 6 Coefficients and t-test. Model
Unstandardized coefficients
Standardized coefficients t
B
Beta
Std. error
Sig.
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The coefficient of SP is negative, which means that when other variables are controlled, energy intensity will decrease with SP increase. In spite of its higher energy consumption of secondary industry, it declines fastest comparatively. Therefore, to improve the proportion of secondary industry will reduce the energy intensity. The coefficient of P3 is positive, which means that when other variables are controlled, P3 will increase EI. The reason is the energy intensity increased after implementing P3. But as shown in Fig. 4, the growth rate of energy intensity decreased obviously after implementing P3, so P3 is effective. But the effect of P3 can not be evaluated by this method because P3 only was operated two years long.
6. Conclusion (Constant) 16.312 GDP 1.048E-5 EP .027 P1 .185 P2 .397 P3 .133 TFP .121 TP .007 SP .018
1.675 .000 .019 .061 .093 .083 .023 .017 .019
.964 .270 .139 .320 .061 1.320 .061 .058
9.739 3.842 1.416 3.014 4.272 1.606 5.269 .401 .935
.000 .001 .176 .008 .001 .128 .000 .694 .364
And the results of coefficients and related tests are as shown in Tables 5 and 6. EI ¼ 16:312 þ 0:00001048GDP 0:027EP 0:007TP 0:018SP 0:121TFP 0:185P1 0:397P 2 þ 0:133P3 That adjusted R square 0.993 and Sig. F change 0.000 show that the regression model is good and the factors explain energy intensity very well. The t-tests show that GDP, TFP, P1 and P2 have significant effect on energy intensity. The effects of EP, TP, SP and, P3 are not significant. The coefficient of GDP is positive, which means that when other variables are controlled, energy intensity will increase with economic growth. Economic development of China in the recent 20 years, to some extent, depends on large amount of small-scale factories, such as small-scale power plants, small-scale cement plants and small-scale chemical plants. In the case of the same output, these factories consume more energy than large-scale factories. Economic growth means more energy consumption and fails to gain the economies of scale. The coefficient of TFP is negative, which means that when other variables are controlled, energy intensity will decrease by technological progress. Application of new technologies, new techniques and new methods and the emergence of new products, can effectively reduce energy consumption, so technological progress is able to effectively reduce energy consumption. The coefficients of P1 and P2 are negative, which means that when other variables are controlled, energy policy group P1 and P2 reduced energy intensity, they had good effect on energy saving. The coefficient of EP is negative, which means that when other variables are controlled, energy intensity will decrease with energy price increase. The reason is that price elasticity of energy is negative, which means price of energy increases, energy consumption will decrease. The coefficient of TP is negative, which means that when other variables are controlled, energy intensity will decrease with TP increase. The reason is tertiary industry consumes less energy, compared to secondary industry. If proportion of tertiary industry is increased, energy consumption will decrease.
This paper introduces two methods to evaluate the energysaving effects of energy polices. It is found that the results calculated by different methods are different. The important assumption that energy intensity would be stably effected by other factors may cause the result calculated by with and without antitheses to contain effects induced by the other factors. The reason that energy-saving effects of P3 is not significant is that P3 has been implemented in only 2 years. It is too short to show the energy-saving effects. With and without antitheses is used to evaluate the short-term effect of the energy policy, for it is reasonable if the effects of the other factors are stable in a very short period; and linear regression model is used to evaluate the long-term effect of the energy policy, because it can discern the effects of all the factors effectively.
Acknowledgements This research is supported by Energy-saving Project from National Development and Reform Commission (ZHZB012), Jiangsu Social Science Fund (07EYA017) and Social Project from Ministry of Education (07JC630064).
Appendix A GM(1,1) (Grey Model) are applied to predict the energy intensities. The calculating step of GM(1,1) as follows: Step 1: create a non-negative sequence X(0) ¼ (x(0)(1),x(0)(2),y, (0) x (n)), where x(0)(k)X0, k ¼ 1,2,y,n; Step 2: Calculate accumulating generation operational sequence P X(1) ¼ (x(1)(1),x(1)(2),y,x(1)(n)), where x(1)(k) ¼ ik¼ 1x(0)(i), k ¼ 1,2,y,n; Step 3: calculate mean sequence of consecutive neighbours Z(1) ¼ (z(1)(2),z(1)(3),y,z(1)(n)), where z(1)(k) ¼ 1/2(x(1)(k)+x(1) (k1)), k ¼ 2,3,y,n; Step 4: solve the parameters ˆ ¼ (a,b)T is a sequence of parameters, and If a 3 3 2 ð0Þ 2 ð1Þ z ð2Þ 1 x ð2Þ 7 7 6 ð0Þ 6 ð1Þ 6 x ð3Þ 7 6 z ð3Þ 1 7 7 7 6 6 Y¼6 . 7 B¼6 7 . . .. 7 .. 6 .. 7 6 5 5 4 4 zð1Þ ðnÞ 1 xð0Þ ðnÞ Then the least square estimate sequence of GM(1,1) model x(0)(k)+az(1)(k) ¼ b satisfies a^ ¼ ðBT BÞ1 BT Y
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Step 5: solve the whitenization function ð1Þ
dx þ axð1Þ ¼ b dt and the solution which is called a time response function is b at b þ xð1Þ ðtÞ ¼ xð1Þ ð1Þ e a a Step 6: acquire time response sequence according to Step 5 b ak b ð1Þ þ ; k ¼ 1; 2; . . . ; n e x^ ðk þ 1Þ ¼ xð0Þ ð1Þ a a Step 7: calculate the restored values ð0Þ
ð1Þ ð1Þ ð1Þ x^ ðk þ 1Þ ¼ að1Þ x^ ðk þ 1Þ ¼ x^ ðk þ 1Þ x^ ðkÞ b ak ¼ ð1 ea Þ xð0Þ ð1Þ e . a
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