Measuring energy rebound effect in the Chinese economy: An economic accounting approach

Energy Economics 50 (2015) 96–104

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Energy Economics journal homepage: www.elsevier.com/locate/eneco

Measuring energy rebound effect in the Chinese economy: An economic accounting approach Boqiang Lin a,b,⁎, Kerui Du c a b c

The School of Economics, China Center for Energy Economics Research, Xiamen University, Xiamen, Fujian, 361005, PR China Newhuadu Business School, Minjiang University, Fuzhou, Fujian, 350108, PR China School of Energy Research, B201 College of Economics, Xiamen University, Xiamen 361005, China

a r t i c l e

i n f o

Article history: Received 11 August 2014 Received in revised form 17 April 2015 Accepted 22 April 2015 Available online 4 May 2015 JEL classification: Q41 Q43 Q48 Q47 O13 O33

a b s t r a c t Estimating the magnitude of China's economy-wide rebound effect has attracted much attention in recent years. Most existing studies measure the rebound effect through the additional energy consumption from technological progress. However, in general technological progress is not equivalent to energy efficiency improvement. Consequently, their estimation may be misleading. To overcome the limitation, this paper develops an alternative approach for estimating energy rebound effect. Based on the proposed approach, China's economy-wide energy rebound effect is revisited. The empirical result shows that during the period 1981–2011 the rebound effects in China are between 30% and 40%, with an average value of 34.3%. © 2015 Elsevier B.V. All rights reserved.

Keywords: Energy rebound effect Energy efficiency Index decomposition analysis Ridge regression

1. Introduction In past decades, China's energy consumption had been rising dramatically. According to NBSC-a (2012), in 2011 China's energy consumption reached 3480 million tons of coal equivalent (Mtec) which increased from 602.75 Mtec in 1980, indicating an annual growth rate of 5.8%. Moreover, as shown in Fig. 1, the consumption grew even more dramatically after 2002. At present, China has been the largest energy consumer as well as the largest emitter of greenhouse gas (GHS) in the world. It was also projected that China's energy consumption will grow steadily in the next decade due to the fact that China is still in the process of industrialization and urbanization. Consequently, China is facing increasing pressure on energy security and environmental pollutions. Energy efficiency has been widely regarded as the most costeffective way for dealing with energy challenges and environmental

⁎ Corresponding author at: Newhuadu Business School, Minjiang University, Fuzhou, Fujian, 350108, PR China. Tel.: t865922186076; fax: t865922186075. E-mail addresses: [email protected], [email protected] (B. Lin).

http://dx.doi.org/10.1016/j.eneco.2015.04.014 0140-9883/© 2015 Elsevier B.V. All rights reserved.

deterioration (Ang et al., 2010). In practice, the Chinese government has taken measures to improve energy efficiency for controlling or slowing down the growth of energy consumption. For instance, in the “11th Five-Year (2006–2010) Plan” the Chinese government set a target of reducing its energy intensity by 20% compared to that in 2005 and also initiated detailed policies to realize the target. However, taking into account the energy rebound effect, the impact of improving energy efficiency on energy use may be discounted. Energy rebound effect means that an increase in energy efficiency may not lead to an expected decrease in energy use owing to the behavior change of economic agents (Wang et al., 2012). The idea can date back to Jeavons (1865). Over the past decades, energy rebound effect has been a hot topic in energy economics. There is already a large body of studies in this field. Representative literatures include Van Es et al. (1998), Schipper and Grubb (2000), Grepperud and Rasmussen (2004), Barker et al. (2007), Brännlund et al. (2007), Guerra and Sancho (2010), Wei (2010), Wang et al. (2012), and Ghosh and Blackhurst (2014). Some excellent reviews can also be found in the existing literatures, e.g., Greening et al. (2000), Dimitropoulos (2007), Sorrell and Dimitropoulos (2008), Sorrell et al. (2009), and Madlener and Alcott (2009).

B. Lin, K. Du / Energy Economics 50 (2015) 96–104

Fig. 1. Energy consumption in China, 1980–2011.

Estimating the magnitude of China's economy-wide rebound effect1 has attracted much attention in recent years. There are mainly two methods used in the existing studies, i.e., the computable general equilibrium (CGE) model and the economic accounting approach. For example, Zha and Zhou (2010) constructed a CGE model and use China's 2002 input–output table to estimate China's energy rebound effect. They found that a 4% improvement of energy efficiency would generate a 33% energy rebound. Li and Lu (2011) also used a CGE model to measure the energy rebound effect in China. But the data they used is China's 2007 input–output table. They found that a 5% increase in energy efficiency would lead to a 178.61% rebound in the long run. The CGE model is a system modeling method which describes explicitly the response of economic agents to energy efficiency change. One distinct merit of the CGE model is that it has microeconomic foundations so that the mechanisms of the rebound effect can be explained in depth. However, a series of strict assumptions are needed for CGE modeling, e.g., utility function, production function, and technological change, etc. Saunders (2008) shows that the choice of function can inadvertently pre-determine results. Another shortcoming of CGE models is that simulation analysis based on the subjective setting of energy efficiency improvement is conducted to estimated energy rebound effect (Shao et al., 2014). Consequently, the result may be far away from the actual rebound. Compared to the CGE model, economic accounting approach is designed to estimate the rebound effect directly. Due to the ease of use, this approach has widely been employed in recent years. The accounting framework was first proposed by Zhou and Lin (2007). Their estimation is built on the logical relationships among technological progress, economic growth, energy intensity, and energy consumption. Specifically, Zhou and Lin (2007) based on the change of energy intensity to estimate the efficiency derived savings and used Solow remainder method to measure the increment of energy consumption due to economic growth which is derived by technological progress. Taking into account the fact that industrial structure change also contributes to energy intensity change, Wang and Zhou (2008) proposed an improved model based on the LMDI method which can exclude the influence of industrial structure change. In view of the limitations of Solow remainder method, Lin and Liu (2012) proposed using DEA method to estimate the technological change. A recent study, Shao et al. (2014), further revised Zhou and Lin (2007) model and provided the theoretical basis for the accounting framework. Additionally, Shao et al. (2014) used the latent variable approach to estimate the contribution of technological progress to economic growth which can overcome the shortcomings of the Solow remainder method and the DEA method. 1 According to Greening et al. (2000), there are mainly three types of energy rebound effect, i.e., direct, indirect and economy-wide rebound effect. This paper focuses on economy-wide energy rebound effect.

97

Thanks to the contribution of pioneer studies, the accounting framework of economy-wide energy rebound effect has been well developed. However, one particular issue is needed to be noted. In previous studies technological progress is regarded equivalently to energy efficiency improvement. It is true when technological progress is Hicks neutral. But this is very strict and strong assumption which may be far away from the reality. Despite energy efficiency gains, capital-saving or laborsaving technology can also improve the productivity. Therefore, in general the energy rebound arising from energy efficiency improvement may be not equal to that derived from technological progress. As a result, the estimate of energy rebound effect would be biased. The purpose of our paper is to further refine the economic accounting approach and revisit China's economy-wide energy rebound effect. To estimate the energy rebound arising from energy efficiency gains consistently, we distinguish energy efficiency improvement from technological progress through constructing an energy efficiency index. This strategy enables us to measure the contribution of energy efficiency improvement to economic growth directly and then calculate the actual energy rebound effect. The rest of our paper is organized as follows. In Section 2 we describe the methodology in detail. Section 3 presents the results and discussion of our empirical studies. Section 4 concludes the paper. 2. Methodology 2.1. Theoretical background According to Brookes (1984) and Sorrell et al. (2009), the economywide energy rebound effect can be tracked down as the additional energy consumption derived by output growth which stems from the energy efficiency gains. Specifically, energy consumption is induced by the demand of goods (services). The improved energy efficiency reduces the effective price of energy service, thereby cutting down the cost of the supply of goods (services). Furthermore, the decreased cost will bring down the price of goods (services) which stimulates the demand and then promotes output growth. Consequently, energy consumption is driven to go up so that the original energy savings are partly offset. In empirical studies, energy rebound effect at economy-wide level is often calculated as the ratio of the additional energy consumption from the growth effect to the original energy savings. See, for example, Zhou and Lin (2007), Lin and Liu (2012), and Shao et al. (2014). In this paper, we distinguish the growth effect derived from energy efficiency improvement from that derived from technological progress which is often represented by total factor productivity. The definition of economy-wide rebound effect can be formulated as Eq. (1). RE ¼

AE  100% OE

ð1Þ

where RE denotes the energy rebound effect; AE represents the additional energy consumption caused by economic growth derived from energy efficiency improvement; and OE represents the original energy saving. In this sense, the key to measure energy rebound effect lies in the estimate of the additional energy consumption and the original energy savings. The original energy savings directly result from energy efficiency gains2 while the calculation of the additional energy consumption is not very straightforward. We first need to quantify the impact of output growth on energy consumption. Then we need to account the contribution of energy efficiency improvement to output growth so that the additional energy consumption from energy efficiency gains can be singled out. To serve our purpose, Index decomposition analysis (IDA) and growth accounting approach are used in this paper. The procedure of our approach is described detailedly in the following sections. 2 That is to say, an increase in efficiency is equivalent to a decrease in energy consumption.

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B. Lin, K. Du / Energy Economics 50 (2015) 96–104

2.2. Accounting the role of output growth and energy efficiency improvement in energy demand Index decomposition analysis (IDA) is a useful framework for investigating the mechanisms of energy consumption change and has been widely used not only in academic studies but also in national statistical agencies and International organizations (Liu and Ang, 2007). In this paper, IDA is used to quantify the impact of output growth and the direct effect of energy efficiency improvement on energy consumption. Specifically, we adopt the multilevel–hierarchical (M–H) IDA model which was proposed by Xu and Ang (2014) recently. As pointed in Xu and Ang (2014), single-level IDA model may provide results that are somewhat specific due to different choice of sector disaggregation level. Moreover, using single-level IDA models at different levels may cause issues of consistency in result aggregation and interpretation. To address these shortcomings, Xu and Ang (2014) proposed two multilevel decomposition procedures: the multilevel–parallel (M–P) model and the multilevel–hierarchical (M–H) model.3 Considering that M–H model accommodate data with an asymmetric hierarchy which enables us make good use of available information, we employ the M–H model in this paper. The idea of M–H index decomposition analysis can be depicted in Fig. 2. For simplicity, consider a two-level case where the whole economy can be decomposed into n sectors at level 1 and sector j can be further disaggregated into mj sub-sectors at level 2. For convenience, we define the following variables. E0 E1j E2ji Y0 Y1j Y2ji

E1j ¼

j¼1

I1j ¼

E1j Y 1j

¼

n E1 Y 1 X j j 1 j¼1 Y j

mj X E2ji Y 2ji 2 i¼1 Y ji

Y 1j

Y

¼

0

Y0 ¼

n X

I 1j S1j Y 0

ð2Þ

j¼1 mj X

I2ji S2ji :

ð3Þ

i¼1

Using the multiplicative forms of LMDI, we can decompose the total energy consumption change between time periods t and τ as follows: D0tot jt;τ

  0 n L E1 ; E1 X j;τ j;t Eτ   ¼ ¼ exp@ 0 0 Et j¼1 L Eτ ; E t   0 n L E1 ; E1 X j;τ j;t   ln  exp@ 0 0 j¼1 L E τ ; Et   0 n L E1 ; E1 X j;τ j;t @   ln  exp 0 0 j¼1 L E τ ; Et ¼

D1int jt;τ



D1str jt;τ



ln

I 1j;τ

!1 A

I1j;t !1 S1j;τ A S1j;t !1 Y 0τ A

ð4Þ

Y 0t

D0Y jt;τ

where L(⋅,⋅) is a weighting scheme called logarithmic mean weight which is described as follows:  Lðx; yÞ ¼

3

ðx−yÞ=ð ln x− ln yÞ; x≠y : x; x¼y

See Xu and Ang (2014) for more details.

I 1j;t

  0 !1 m j L I 2 S2 ; I 2 S2 X I2ji;τ ji;τ ji;τ ji;t ji;t   ln 2 A ¼ exp@ I ji;t L I1j;τ ; I 1j;t i¼1   0 !1 2 2 2 2 mj L I X S2ji;τ ji;τ S ji;τ ; I ji;t S ji;t   ln 2 A  exp@ S ji;t L I1j;τ ; I1j;t i¼1

ð6Þ

¼ D2j; int jt;τ  D2j;str jt;τ : Substituting Eq. (6) into D1int|t,τ gives the following equation:   0 0 !11 m j L I 2 S2 ; I 2 S2 n X X I2ji;τ ji;τ ji;t ji;τ ji;t AA   ln 2 D1int jt;τ ¼ exp@ @ I ji;τ L I 1j;τ ; I1j;t j¼1 i¼1   0 0 !11 m j L I 2 S2 ; I 2 S2 n X X S2ji;τ ji;τ ji;τ ji;t ji;t AA   ln 2  exp@ @ S ji;τ L I1j;τ ; I1j;t j¼1 i¼1

ð7Þ

It is easy to generalize the above derivation to a data hierarchy with k levels of sector disaggregation:

Based on the above definitions, we have the following equations: n X

I1j;τ

¼ D2int jt;τ  D2str jt;τ :

Aggregate energy consumption at level 0. Energy consumption of sector j at level 1. Energy consumption of sub-sector i of sector j at level 2. Aggregate output of the economy at level 0. Output of sector j at level 1. Output of sub-sector i of sector j at level 2.

E0 ¼

Eq. (4) shows that the change of aggregate energy consumption can be attributed to three components. The first component (D1int|t,τ) represents the intensity effect which describes the impact from energy intensity changes of sectors at level 1. The second component (D1str|t,τ) is economic structure effect which describes output structure shifts across sectors at level 1. The third component (D0Y|t,τ) is economic growth effect which reflects the impact from output growth on energy consumption change. Similarly, energy intensity change in sector j between time periods t and τ can be decomposed as:

ð5Þ

9 D0tot jt;τ ¼ D1int jt;τ  D1str jt;τ  D0Y jt;τ > > = D1int jt;τ ¼ D2int jt;τ  D2str jt;τ > ⋮ > ; k k Dk−1 int jt;τ ¼ Dint jt;τ  Dstr jt;τ 0 k 1 2 ⇒Dtot jt;τ ¼ Dint jt;τ  Dstr jt;τ  Dstr jt;τ  …  Dkstr jt;τ  D0Y jt;τ :

ð8Þ

Eq. (8) shows that aggregate energy consumption change can be attributed to energy intensity effect (D kint | t,τ ) at level k, output structure effect at each level (D 1str | t,τ , …, D kstr | t,τ ) and economic growth effect (D 0Y | t,τ ). Since energy intensity given at a more disaggregate level is a better proxy of energy efficiency (Xu and Ang, 2014), D kint| t,τ is preferred to D1int|t,τ for quantifying the direct effect of energy efficiency on consumption change. Thus, using Eq. (8) we can account the contributions of energy efficiency change and economic growth to aggregate energy consumption change. In the multiplicative form of decomposition, if the value of any component is greater (less) than 1, then it will increase (reduce) the energy consumption. Thus, Dkint|t,τ b 1 indicates the improvement of energy efficiency while Dkint|t,τ N 1 means that energy efficiency is decreasing. The meanings of Dkint|t,τ can be interpreted as follows. Take Dkint|t,τ = 0.8 as an example. It means that without other impacts, energy consumption at time period τ would be 80% of that at time period t, suggesting energy efficiency improvement would gain 20% of energy savings. As such, the original energy saving (OE, the denumerator of Eq. (1)) can be calculated as (1 − Dint|t − 1,t)Et − 1. In a similar logic, the increment of energy consumption originated from output growth as (DY|t − 1,t − 1)Et − 1. We can also interpret the above case from another angle. When energy efficiency increases, energy becomes more productive. The utility of one unit of energy consumption at time period τ is

B. Lin, K. Du / Energy Economics 50 (2015) 96–104

99

Fig. 2. Hierarchical decomposition structure 10. Source: Xu and Ang (2014).

equivalent to 1.25 (1/0.8) times of that at time period t. In this sense, we can construct the energy efficiency index (EEI) as follows.

symbol “U”) as: U t ¼ θt Et

EEI 0 ¼ 1   EEIt ¼ EEIt−1  1=Dkint jt−1;t :

ð9Þ

2.3. Accounting the contribution of energy efficiency enhancement to economic growth Energy has been widely regarded as a fundamental factor of production as labor and capital. Many studies have investigated the role of energy in production. For example, Tintner et al. (1977) extended the CES function to include energy input, and then applied it to Austrian economy for the period 1955–1972. Kümmel et al. (1985) proposed another energy dependent production function to fit the output growth of industries in West Germany and the US. From the angle of physics, energy is converted into physical work4 to serve the production activity. Thus, the improvement of thermodynamic efficiency5 would also contribute to output growth. Using energy directly as input of production will neglect the role of thermodynamic efficiency. Therefore, Ayres and Warr (2005) substituted physical work for “raw” energy as a factor of production. They found that replacing raw energy input by physical work as a factor of production could explain the historical growth path of the US from 1900 to the mid-1970s without introducing the slow residual. In their paper, physical work is defined as the product of energy input and thermodynamic efficiency. However, in practice not each unit of physical work generated by energy is efficiently used for production activity. For instance, a machine may be turned on without producing anything due to management inefficiency. As pointed out by Ayres and Warr (2005), thermodynamic efficiency is not related to economic efficiency. Thus, we further generalize their idea to replace physical work by useful energy service as a factor of production which takes into account managerial (economic) efficiency as well as physical conversion efficiency. We use a broader concept of energy efficiency which indicates the efficiency of energy converted into useful service for production activity. In this sense, both managerial efficiency and physical conversion efficiency are considered. This idea helps us to quantify the impact of energy efficiency enhancement on output growth. We formulate the useful energy service (denoted by the

where θt denote energy efficiency. Generally speaking, energy efficiency is unobserved at the macroeconomic level. Ang et al. (2010) advocates tracking economy-wide efficiency change through IDA method. As we discussed in Section 2.2, the EEIt reflects energy efficiency change over time. As a result, it can be approximated to the ratio of θt to θ0. In view of this, the EEIt can be a proxy of θt. In general, a three-factor production function can be described as: Y t ¼ f ðK t ; Lt ; U t Þ þ εt

Physical work is a concept from thermodynamics and physics. Thermodynamic efficiency is a straightforward ratio between output (physical work) and resource input (Ayres and Warr, 2005).

ð11Þ

where εt is a residual term which denotes the part of output that cannot be explained by capital, labor and useful energy service. Taking the derivative of both sides of Eq. (11) gives: 

Yt ¼

∂Y t ∂Y t ∂Y t ∂Y t Kt þ Lt þ Ut þ εt ∂K t ∂Lt ∂U t ∂εt 







ð12Þ

where Ẋt is the shorthand for dXt/dt. Dividing both sides of Eq. (12) by Yt, we get the following equation: 









Y t K t ∂Y t K t Lt ∂Y t Lt U t ∂Y t U t ∂Y t εt ¼ þ þ þ Y t Y t ∂K t K t Y t ∂Lt Lt Y t ∂U t U t ∂ε t Y t Kt Lt Ut ¼ ηK ðt Þ þ ηL ðt Þ þ ηU ðt Þ þ ξt Kt Lt Ut ! Kt Lt θt E t ¼ ηK ðt Þ þ ξt þ ηL ðt Þ þ ηU ðt Þ þ Kt Lt θt E t 











ð13Þ



where ηK(t), ηL(t), and ηU(t) represent the output elasticities of capital, labor and useful energy service, respectively. Based on Eq. (13), we can quantify the contributions of capital, labor, raw energy and energy efficiency to economic growth through the following equations. 

α K ðt Þ ¼

ηK ðt ÞK t =K t 

Y t =Y t

ð14Þ



α L ðt Þ ¼

ηL ðt ÞLt =Lt 

Y t =Y t

ð15Þ



4 5

ð10Þ

α E ðt Þ ¼

ηU ðt ÞEt =Et 

Y t =Y t

ð16Þ

100

B. Lin, K. Du / Energy Economics 50 (2015) 96–104 

α θ ðt Þ ¼

ηU ðt Þθt =θt 

Y t =Y t

ð17Þ

Once the contribution of energy efficiency to economic growth is identified, we can further calculate the increment of energy consumption from energy efficiency gains (AE, the numerator of Eq. (1)) as αθ(t)(DY|t,t − 1 − 1)Et − 1. Based on the definition we described in Section 2.1, energy rebound effect at economy-wide effect can be further expressed as:   α θ ðt Þ D0Y jt−1;t −1   100%: REt ¼  1−Dkint jt−1;t

ð18Þ

It is very intuitive that the numerator of Eq. (18) denotes the indirect effect of energy efficiency improvement, i.e., the increment of energy consumption induced by output growth which is derived by energy efficiency improvement while the denumerator is the original energy savings, i.e., the decrease of energy consumption induced by energy efficiency improvement given other conditions unchanged. 3. Empirical studies 3.1. Data We collected original data from China Energy Statistical Yearbook (CESY), China Statistical Yearbook (CSY) and China Premium Database.6 The sample period ranges from 1980 to 2011. For M–H index decomposition analysis, the whole economy is first decomposed into three major industries, namely the primary, secondary and tertiary industries. The secondary industry comprises two subsectors: “Industry (S1)” and “construction (S2)”. The “Industry” sector is further decomposed into “Mining (S11)”, “Manufacturing (S12)”, and “Electric Power, Gas and Water (13)”.7 The tertiary industry is also composed of three subsectors: “Transport, Storage and Post (T1)”, “Wholesale, Retail, Hotels and Catering Services (T2)”, and “Financial Intermediation, Real Estate and other Tertiary Industries (T3)”. The structure of sector decomposition is shown in Fig. 3. Following Ma and Stern's (2008) suggestion, energy intensity is measured by energy consumption per unit of value-added in order to make aggregation consistent. Data on capital stock of China from 1980 to 2006 is obtained from Shan (2008). We extend the series to 2011 using the PIM method described in Shan (2008). Data on valueadded and capital stock are converted into constant prices in 1990. 3.2. Results and discussion The detailed results of decomposing China's energy consumption change using M–H index composition analysis are presented in Table 1. We can observe that the average growth rate of China's energy consumption during 1980–2011 reached 5.8%, increasing its consumption by 5.7 times compared to that in 1980. As shown in Table 1, economic growth was the major driving force to China's increasing energy consumption. Without changes in other factors, economy growth would have increased China's energy consumption by 20 times from 1980 to 2011, which indicates an average growth rate of 10.2%. By contract, in most of years energy efficiency improvement contributed negatively to China's rapid consumption growth. On average, the improvement of energy efficiency reduces China's energy consumption by 4.6%. The cumulative effect of energy efficiency enhancement on energy consumption can be calculated as −77.2%. Compared to the effects of economic growth and energy efficiency enhancement, we find that impacts from output structure change were trivial. In past years, 6

Available at: http://www.ceicdata.com. “Manufacturing” is composed of 38 finer subsectors. However due to data limitation, the finer decomposition is not conducted in this paper. 7

the Chinese government had taken varied measures to optimize its economic structure for slowing down energy consumption growth. However, our results reveal that the effect of such measures had not been significantly effective. Based on the results of Table 1, we construct the energy efficiency index as we described in Section 2.2. The result is presented in Fig. 4. It can be observed that energy efficiency index had been increasing steadily in the 1980s. Since then, the increasing trend sped up until 2002. During 2003–2005, the energy efficiency was declining which is in accordance with the finding of Ma and Stern (2008). After 2005, energy efficiency started increasing again. For quantifying the contribution of energy efficiency enhancement to economic growth, we have to assume an explicit form of production function. In this paper, we choose the translog form function which can be regarded as a second order approximation to the unknown production function so that we can reduce the risk of model misspecification. The econometric equation is presented in Eq. (19). lnY t ¼ α 0 þ α K ln K t þ α L ln Lt þ α L lnU t þ α KL ½ ln K t  lnLt  2 þ α KU ½ lnK t  ln U t  þ α LU ½ lnLt  ln U t  þ α KK ½ ln K t  2 2 þ α LL ½ lnLt  þ α UU ½ ln U t  þ εt :

ð19Þ

Since cross and square terms of input variables are included in the translog function, regressors in Eq. (19) may be significantly correlated. Consequently, ordinary estimation of Eq. (19) would suffer the problem of multi-collinearity. A simple method for detecting multi-collinearity is to calculate the correlation coefficients between any two of the regressors. If these coefficients are greater than 0.8, then it is an indication of multi-collinearity. The Pearson's correlation coefficients of the regressors in Eq. (19) is calculated and reported in Table A1. It is seen that most of coefficients are greater than 0.9 which provides evidence of strong multi-collinearity among the regressors. Furthermore, Farrar– Glauber statistics is used for the formal test. The value of Chi-square statistics is calculated as 2430.57, significant at 1% level. The result indicates that significant multi-collinearity does exist among our variables. To deal with the multi-collinearity data, we adopt ridge regression proposed by Hoerl and Kennard (1970a,b). The essential idea of ridge regression is to trade a small amount of bias in the coefficient estimates for a substantial reduction in coefficient sampling variance. The ridge  −1 0 ^ ðkÞ ¼ X 0 X þ kI X Y where I is an identity estimator is formulated as β ^ ð0Þ is the OLS estimator). It matrix and k ≥ 0 is called ridge constant (β can be proved that the larger ridge constant is the larger is the bias of ^ ðkÞ, but the smaller the variance (Judge et al., 1985). To select the opβ timal k, we adopt ridge trace plot which is the most popular diagnostic tool and widely used in empirical studies (e.g., Lin and Wesseh, 2013; Smyth et al., 2011). The ridge trace plot for our data is presented in Fig. 5. It is seen that the estimated coefficients become quite steadily when the ridge constant arrives at 0.3. Therefore, we take k = 0.3 for the ridge regression. The estimated results are reported in Table A2. Based on the results of ridge regression, we can calculate the output elasticities of input factors. The computing results are presented in Table A3. All of the output elasticities are positive which is consistent with production theory. They are found to be relatively stable over the sample period. Moreover, the summation of output elasticities are above 1.3, significantly greater than unit which indicates the increasing returns to scale in China's economy. Based on Table A3, we further calculate the contributions of capital, labor, energy and energy efficiency to economic growth using Eqs. (14)–(17). Table 2 presents the computing results. It can be observed that capital is the dominant contributor of China's output growth with an average contribution of 39.7%. The result is consistent with the fact that China's economic growth is investmentdriven. After the international financial crisis in 2007, the Chinese government issued a four trillion economic stimulus which significantly increased the contribution of capital to economic growth. On the contrary, with the deceleration of employment growth, the contribution

B. Lin, K. Du / Energy Economics 50 (2015) 96–104

101

Fig. 3. The structure of sector decomposition.

D3str

D3int

0.9863 1.0441 1.064 1.0737 1.0815 1.0544 1.0715 1.0735 1.0423 1.0183 1.0514 1.0519 1.0625 1.0582 1.0688 1.0306 1.0053 1.002 1.0322 1.0353 1.0335 1.06 1.1528 1.1614 1.1056 1.0961 1.0844 1.039 1.0522 1.0596 1.071 5.7735 1.0582

1.0472 1.0856 1.1069 1.1499 1.1389 1.0891 1.1174 1.116 1.0399 1.0381 1.0899 1.2378 1.1354 1.127 1.107 1.0983 1.0908 1.0768 1.0745 1.0823 1.0826 1.0893 1.0952 1.0988 1.1115 1.1248 1.1391 1.0956 1.0904 1.1005 1.0901 20.0608 1.1016

0.9864 0.9837 1.004 1.0022 1.0394 1.0141 1.0175 1.0231 1 0.9931 1.024 1.053 1.025 1.022 1.0129 1.0093 1.0065 1.0052 1.0036 1.0052 1.0028 1.004 1.0082 1.0036 1.0039 1.0041 1.0049 1.0017 1.0029 1.0053 1.0031 1.3108 1.0088

0.9893 1.0112 0.9942 0.9995 0.9891 0.9996 0.9989 1.0047 1.0196 1.0049 1.0048 1.0050 1.0025 1.0041 1.0014 1.0026 1.0052 1.0006 1.0027 1.0016 1.0012 1.0003 0.9995 1.0038 0.9969 0.9952 0.9972 0.9982 0.9907 0.9979 0.9999 1.0217 1.0007

0.9999 0.9999 0.9999 1.0003 0.9991 0.9993 0.9994 0.9995 1.0018 1.001 0.9974 1.0023 0.9855 0.9952 1.014 0.9913 0.9963 1.0044 0.9974 0.9894 0.9951 0.993 0.9867 1.001 0.9953 0.9956 1.0008 0.9971 1.0034 0.9991 1 0.9416 0.9981

0.9652 0.967 0.9631 0.9319 0.9245 0.9558 0.9439 0.9363 0.9814 0.982 0.9401 0.8012 0.924 0.9193 0.9387 0.9354 0.9143 0.921 0.9572 0.9602 0.9556 0.9757 1.0587 1.0482 0.9986 0.9796 0.9492 0.9513 0.9679 0.9606 0.9796 0.2282 0.9535

5

D2str

4

D1str

3

DY

Energy efficiency index

1980–1981 1981–1982 1982–1983 1983–1984 1984–1985 1985–1986 1986–1987 1987–1988 1988–1989 1989–1990 1990–1991 1991–1992 1992–1993 1993–1994 1994–1995 1995–1996 1996–1997 1997–1998 1998–1999 1999–2000 2000–2001 2001–2002 2002–2003 2003–2004 2004–2005 2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 1980–2011 Geometric mean

Dtot

2

Table 1 Results of decomposition of energy consumption change in China.

arising from energy efficiency policies 2000–2010 and find a total rebound effect of around 26%. Van Es et al. (1998) applied a CGE model to examine the impact of energy efficiency improvement in Holland and find a rebound effect of 15%. Small and Van Dender (2007) found that the energy rebound effect in the US Department of Transportation was 22.2%. The rebound effect in China showed a growing tendency during the “Sixth Five-Year” (1981–1985) and became slight fluctuation around 33% during the “Seventh Five-Year” (1986–1990). During the period of 1991–2000, the rebound effect first climbed to the peak (40.7%) and then returned to a stable level around 35%. After that the rebound effect began to decrease during the “Tenth Five-Year” (2001–2005). This phenomenon may arise from the deterioration of energy efficiency, which weakened the rebound effect. It is interesting to find that the energy rebound effect stayed around 35% steadily during the “Eleventh Five-Year” (2006–2010). It means that the great impetus for energy saving through promoting energy efficiency in “Eleventh Five-Year Plan” had been discounted because of the existence of energy rebound effect. It implies that stimulating improvement in energy efficiency alone cannot address the dilemma between maintaining economic growth and accomplishing energy conservation and emission reduction targets. Compared to the previous studies on China's country-wide energy rebound effect, our estimated results are more reasonable. It can be seen in Fig. 6 that the estimated results of other studies not only dramatically fluctuate over years but also reveal some abnormal cases. For instance, in Zhou and Lin (2007) and Wang and Zhou (2008), the rebound effect for 2002 was estimated to be less than −300%. In Shao et al. (2014), the value for 1989 was calculated as 717.58%. It is very difficult to interpret such results. One possible reason for the abnormal results is that additional energy consumption arising from technological

1

of labor was gradually declining. The growth of useful energy service is the second driving force to China's economic expansion. On average, it contributed 34.1% of China's economic growth. As shown in Eq. (13), the contribution of useful energy service can be attributed to physical energy growth and energy efficiency enhancement. The last column of Table 2 shows that energy efficiency improvement also played an important role in China's economic growth. The annual average contribution is calculated as 15.3%. Based on the previous results, we can further calculate China's energy rebound effect using Eq. (18). The computing results are reported in Table 3. Our results show that energy rebound effect in China is between 30% and 40% during the sample period. The average value of energy rebound effect is calculated as 34.3% which means that 34.3% of energy savings originated from efficiency improvement are offset by the increment of energy demand induced by economic growth. The result in this paper is higher than those of most studies on developed countries. For example, Barker et al. (2007) use the macroeconomic model, MDM-E3 to examine the macroeconomic rebound effect for the UK economy

1980

1985

1990

1995

2000

2005

Year

Fig. 4. Energy efficiency index in China, 1980–2011.

2010

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B. Lin, K. Du / Energy Economics 50 (2015) 96–104 0.16 0.14 lnK lnL lnU lnK*lnL lnK*lnU lnU*lnL

0.12 0.1 0.08

(lnK)2 (lnL)2

0.06

(lnU)2 0.04 0.02

0

0.1

0.2

0.3

0.4

0.5 0.6 Ridge constant k

0.7

0.8

0.9

1

Fig. 5. Ridge trace plot of the coefficient estimates in translog production function.

progress is mistaken as the rebound from energy efficiency gains. Energy efficiency is just one component of technological progress. In the real world, many factors (e.g., climate change, institutional change and war) would influence technological progress. As a result, it is generally driven to be fluctuating. Moreover, some special events would cause the extreme change of technology which may lead to the abnormal results in the studies we mentioned above. As shown in Fig. 4 the energy efficiency change is estimated to be quite steadily. As such, dramatical change of energy rebound effect might not be reasonable. It seems that our approach can rule out the abnormal value of energy rebound effect because of the distinguishment of energy efficiency improvement from technological progress.

Table 2 Contributions of production factors to output growth (%). Year

Capital

Labor

Useful energy service Total

Physical energy

Energy efficiency

1981 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 2007 2008 2009 2010 2011 Average

43.9789 25.9935 23.1114 20.7304 25.0312 38.5950 31.4935 30.4718 50.0872 49.0527 26.4613 13.9034 31.2731 36.1070 42.8835 44.5257 42.8865 49.3062 47.3501 42.2904 42.8547 43.2899 46.8116 46.3757 43.5510 39.4731 31.0515 49.8801 62.7779 54.4089 56.2073 39.7489

54.0198 33.3138 18.7791 20.2349 20.1054 25.5406 20.1436 20.5378 37.3166 36.5834 10.4483 3.4925 6.0430 6.3089 7.0157 11.0087 11.5982 12.7374 12.0572 9.8709 10.0615 6.2643 5.5214 6.1354 3.9262 3.0232 2.8045 2.8847 3.3114 3.1214 3.9560 13.8118

14.2721 27.7108 29.1817 30.0514 36.3009 35.0779 34.8189 38.3270 48.4550 30.4281 40.7831 40.5122 34.5046 37.3252 40.9346 33.2539 35.9708 37.7887 34.2984 31.0470 32.3961 31.9058 34.4733 39.5602 32.6374 32.0253 34.0543 32.5526 32.6933 34.8334 35.5854 34.3148

−8.7925 15.6208 18.2641 15.0799 18.1321 18.9466 19.0233 19.8989 33.4659 15.1921 18.2082 7.0133 14.8983 14.8793 20.9940 10.2060 1.9341 0.8559 14.3762 14.2860 13.5822 22.5525 54.1003 55.3116 32.2140 26.3173 20.8328 14.0687 19.9800 20.6423 27.5243 19.0196

23.0646 12.0900 10.9177 14.9715 18.1688 16.1313 15.7956 18.4280 14.9891 15.2360 22.5749 33.4989 19.6063 22.4459 19.9407 23.0479 34.0367 36.9328 19.9222 16.7610 18.8140 9.3533 −19.6270 −15.7514 0.4233 5.7080 13.2215 18.4840 12.7133 14.1910 8.0611 15.2952

4. Conclusion Economy-wide energy rebound effect means that part of the energy conservation due to energy efficiency improvement vanishes because of the growth effect. Improving energy efficiency has been regarded as a critical policy approach for saving energy (Shao et al., 2014). It is of great interest and very important to estimate how much of initial energy savings are lost through energy rebound effect. Many researchers have devoted to estimating the magnitude of economy-wide energy rebound effect in China. However, there is still empirical controversy over this issue. The magnitude of China's energy rebound effect varies greatly with different studies. More importantly, previous studies mistake the additional energy use derived from technological progress as the energy rebound which is not consistent with the definition of the rebound effect, thereby generally giving rise to biased estimated results. Our paper contributes to the existing literature on estimating economywide energy rebound effect through revising the economic accounting approach. Based on the improved approach, this study re-estimates China's economy-wide energy rebound effect from 1981 to 2011. Our results reveal that during the sample period energy rebound effect in China is between 30% and 40%, with an average value of 34.3%. It means that on average 34.3% of initial energy savings in China are offset by energy rebound effect. This figure is much less than the estimates of Zhou and Lin (2007), Wang and Zhou (2008), and Lin and Liu (2012), and slightly less than the finding of Shao et al. (2014). From the perspective of international comparison, China's energy rebound effect is higher than developed countries such as US, UK, and Holland.

Table 3 Estimation results of China's energy rebound effect: 1981–2011. Year

Rebound effect (%)

Year

Rebound effect (%)

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

31.316 31.387 31.659 32.930 33.418 32.486 33.087 33.558 32.112 32.270 33.858 40.078 34.952 35.335 34.795 35.081

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Average

36.049 35.928 34.690 34.707 34.992 34.409 31.841 32.303 34.061 34.890 36.189 36.254 35.781 36.212 35.653 34.267

B. Lin, K. Du / Energy Economics 50 (2015) 96–104

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Fig. 6. Comparing our results with other studies. Note: the right figure is just the left one whose vertical ordinate is restricted to between −150 and 150.

Our empirical results also provide important policy implications for China's energy conservation effort. In the past 20 years, the Chinese government has tried very hard to promote energy conservation and emission reduction. Our results indicated that the energy-saving effect of efficiency gains in China was discounted considerably due to the rebound effect. For the purpose of supporting economic growth and social stability, the Chinese government has been administratively maintaining energy price at a low level, and has created price distortions that led to the rebound effect, as economic agents would be motivated to use more energy when energy efficiency increases. The existence of the energy rebound effect highlights the importance of energy pricing reforms to energy conservation and emission reduction. Therefore, to accomplish energy conservation and emission reduction targets, measures to promote energy efficiency should include energy pricing reforms. The recent slowdown in energy demand and lower energy prices (particularly coal prices), have provided a good opportunity for China's energy pricing reforms. The Chinese government should use the opportunity to speed up the energy pricing reforms. If energy subsidies are unavoidable, better energy subsidy designs should be provided to avoid price distortions. Finally, there are some limitations in this paper which should be duly noted. First, the (M–H) IDA is applied to account the impacts of energy efficiency improvement and output growth on energy consumption change. As pointed out by Ma (2014), the IDA model is a descriptive approach so that the interactions between energy efficiency improvement and output growth cannot be disentangled. The generalized Divisia decomposition method proposed by Vaninsky (2014) might be a solution. For this method, some explicit conditions are needed to be incorporated in the decomposition process. Once these conditions are satisfied, we can directly quantify energy rebound effect in a single decomposition model.8 It would be a perfect framework. However, we have not found any feasible condition to isolate the interaction of energy efficiency improvement and output growth. Second, this paper just focus on accounting China's economy-wide energy rebound effect. The potential determinants of energy rebound effect have not been investigated. Further studies should be carried out to examine this issue, which can yield more interesting insights for policy makers.

Acknowledgments The paper is supported by Newhuadu Business School Research Fund, the China Sustainable Energy Program (G-1311-19436, and G8 Our proposed approach actually contains two stages. The first stage applies an IDA method. The second stage is economic growth accounting.

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