Decomposition of aggregate CO2

Decomposition of aggregate CO 2emissions:A

production-theoretical approach

P.Zhou a,b,?,B.W.Ang b

a

College of Economics and Management,Nanjing University of Aeronautics and Astronautics,

29Yudao Street,Nanjing 210016,P .R.China

b

Department of Industrial and Systems Engineering,National University of Singapore,

10Kent Ridge Crescent,Singapore 119260

Received 24April 2007;received in revised form 18October 2007;accepted 18October 2007

Available online 25October 2007

Abstract

We present a production-theoretical approach to decomposing the change of aggregate CO 2emissions over time using the Shephard input distance functions and the environmental data envelopment analysis (DEA)technology in production theory.Application of the proposed approach requires only some aggregate data and the change of aggregate CO 2emissions can be decomposed into contributions from seven factors.These contributions are obtained through solving a series of DEA models.The key features of the proposed approach are the use of panel data to estimate the production frontier and the inclusion of several production technology related https://www.360docs.net/doc/e012132308.html,ing the proposed approach,we present two application studies on decomposing the CO 2emissions for world regions and OECD countries.A comparison between the proposed approach and other decomposition analysis methods is also presented.?2007Elsevier B.V .All rights reserved.

Keywords:Decomposition analysis;CO 2emissions;Distance function;Data envelopment analysis;Malmquist productivity index

1.Introduction

With the growing concern over the impacts of CO 2emissions on global climate change,many researchers have attempted to identify and quantify the underlying driving forces that affect changes of aggregate CO 2emissions in a country/region.Technically,this can be done by decomposing the change of aggregate emissions into some pre-defined factors using decomposition analysis.In the literature two well-known decomposition techniques,namely the structural decomposition analysis (SDA)and the index decomposition analysis (IDA),have been widely applied.

Available online at https://www.360docs.net/doc/e012132308.html,

Energy Economics 30(2008)1054–

1067

https://www.360docs.net/doc/e012132308.html,/locate/eneco

?Corresponding author.Tel.:+6565162203;fax:+6567771434.E-mail address:g0300220@https://www.360docs.net/doc/e012132308.html,.sg (P.Zhou).

0140-9883/$-see front matter ?2007Elsevier B.V .All rights reserved.doi:10.1016/j.eneco.2007.10.005

SDA is built upon the input –output model in quantitative economics.Rose and Casler (1996)provided a review on its theoretical foundation and major features.Examples of SDA studies on CO 2emission decomposition include Casler and Rose (1998),Chang and Lin (1998),and Munksgaard et al.(2000).

IDA uses index number concept in https://www.360docs.net/doc/e012132308.html,pared to SDA,it is more flexible but more aggregate in application.The studies by Ang and Zhang (2000)and Ang (2004)give details on the IDA methodology and application issues.A large number of studies on CO 2emission decomposition using IDA have been reported,such as Ang and Pandiyan (1997),Ang and Zhang (1999),Sun (1999),Wang et al.(2005),Wu et al.(2005),Diakoulaki et al.(2006),Lin et al.(2006),and Diakoulaki and Mandaraka (2007).A comparison between SDA and IDA can be found in Hoekstra and van den Bergh (2003).In addition to SDA and IDA,several researchers have recently conducted decomposition analysis within the production theory https://www.360docs.net/doc/e012132308.html,ing a joint production framework,Pasurka (2006)proposed a decomposition model to study changes in NO x and SO 2emissions from coal-fired power plants.More recently,Wang (2007)applied the Shephard output distance functions in production economics to decompose energy productivity change into five components.We follow this line of research and present an approach to decomposing the change of aggregate CO 2emissions over time using the Shephard input distance functions in a joint production (both desirable and undesirable outputs)framework.

Our proposed approach allows a change in aggregate CO 2emissions to be decomposed into the contributions from seven factors.These contributions are obtained by solving a series of data en-velopment analysis (DEA)type models.1Compared to Pasurka (2006)and Wang (2007),our proposed approach focuses on a different application area and specifies a different production technology setting.The rest of this paper is organized as follows.In the next section,we describe the proposed production-theoretical approach to decomposing the change of aggregate CO 2emissions over time.It consists of the following three sub-sections:production technology,decomposition method,and estimation https://www.360docs.net/doc/e012132308.html,ing the proposed approach,we present two application studies in Section 3.In Section 4,we compare the proposed decomposition approach with other decomposition analysis methods.Section 5concludes this study.2.The proposed approach 2.1.Production technology

Consider a production process in which aggregate energy consumption (E ),gross domestic product (Y )and energy-related CO 2emissions (C )are respectively taken as input,desirable output,and undesirable output.2The production technology can be described as

T ?E ;Y ;C eT:E can produce Y ;C eTf g

e1T

1

DEA,developed by Charnes et al.(1978),is a nonparametric frontier approach to efficiency evaluation and productivity analysis.Coelli et al.(2005)provided an introduction to some basics of DEA.The more comprehensive DEA expositions can be found in F?re et al.(1994a)and Cooper et al.(2006).Recently,Zhou et al.(in press)provided a literature survey on the application of DEA to energy and energy-related environmental studies.2

It should be pointed out that in addition to energy,capital stock and labor are also often taken as inputs in the literature of production economics.The inclusion of more inputs would result in the same decomposition formula if we simply replace D e (E ,Y ,C )in Section 2.2by a sub-vector distance function for energy input.If we consider the effects of other inputs oriented technical efficiency change in decomposition,the inclusion of more inputs will greatly complicate the decompositions but might yield more insights by giving several other production technology related components.This topic,which is not included in this study,is a potential area for further research.

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P .Zhou,B.W.Ang /Energy Economics 30(2008)1054–1067

In production theory,T is often assumed to be a closed and bounded set,which implies that finite amount of input can only produce finite amounts of outputs(F?re and Primont,1995).In addition,E and Y in T are supposed to be strongly or freely disposable,i.e.if(E,Y,C)∈T and E′≥E(or Y′≤Y) then(E′,Y,C)∈T(or(E,Y′,C)∈T).

In order to reasonably model a production process in which both desirable and undesirable outputs are jointly produced,F?re et al.(1989)introduced the following two assumptions.

(i)Outputs are weakly disposable,i.e.,if(E,Y,C)∈T and0≤θ≤1,then(E,θY,θC)∈T.3

(ii)Desirable and undesirable outputs are null-joint,i.e.,if(E,Y,C)∈T and C=0,then Y=0.

Assumption(i)implies that the reduction of CO2emissions is not free and the proportional reduction in GDP and CO2emissions is feasible.Assumption(ii)says that CO2emissions must also be produced when GDP is produced,which implies that the only way to eliminate all the CO2 emissions is to end the production process.

Up to now the reference technology for modeling the joint production of desirable(Y)and undesirable(C)outputs has been conceptually defined.In F?re et al.(2005),this technology is termed a polluting technology.Despite its completeness in concept,the polluting technology needs further characterization within a parametric or a nonparametric framework in empirical studies.In the nonparametric framework,the polluting technology can be constructed by the piecewise linear combinations of the observed data.Assume that there are k=1,2,…,K entities (e.g.countries)and for entity k the observed data are(E k,Y k,C k).Then the piecewise linear polluting technology T can be formulated as follows:

T?feE;Y;CT:

X K

k?1z k E k V E

X K k?1z k Y k z Y

X K k?1z k C k?C

z k z0;k?1;2;N;K g

e2T

In the literature,T is also referred to as the environmental DEA technology exhibiting constant returns to scale(CRS)since it is formulated in the DEA framework(Zhou et al.,2008).In energy and environmental studies,the concept of environmental DEA technology has been widely investigated.See,for example,F?re et al.(2004),Picazo-Tadeo et al.(2005),Pasurka(2006),Zaim and Taskin(2000),Zaim(2004)and Zhou et al.(2006,2007,2008,in press).

2.2.Decomposition method

We begin by defining the following two Shephard input distance functions for input(energy consumption)and undesirable output(CO2emissions):

D e E;Y;C

eT?sup k:E=k;Y;C

eTa T

f ge3T

3Like in many previous studies,we implicitly assume the weak disposability of CO

2

emissions as a kind of undesirable output although CO2emissions are still unregulated in the real world.In addition,the worldwide growing concern on climate change due to greenhouse gas emissions makes the treatment of CO2emission as weakly disposable become a logical assumption(Zaim and Taskin,2000).

1056P.Zhou,B.W.Ang/Energy Economics30(2008)1054–1067

D c

E ;Y ;C eT?sup h :E ;Y ;C =h eTa T f g e4T

where Eq.(3)attempts to shrink energy consumption as much as possible given the GDP,CO 2emissions and production technology,while Eq.(4)attempts to reduce the amount of CO 2emissions as much as possible given the energy consumption,GDP and production technology.4In addition to their functions serving as performance measures,the two Shephard input distance functions could also be used to characterize the production technology if appropriate assumptions are imposed (F?re and Primont,1995).

Now suppose that the aggregate CO 2emissions of a certain entity,i.e.entity k ,varies from C k 0in

time period 0to C k T

in time period T .Such a change can be expressed in the following multiplicative form:

D k ?C T

k C k ?C T k =E T k C k k áE T k =Y T k E k k áY T k

Y k e5TBy using the production technology in time period 0as a reference,we can decompose the change of

the aggregate CO 2emissions for entity i as follows 5:

D k ?C T k =D 0c

E T k ;Y T k ;C T k àá??á1=E T k àáC k 0c E k k k àá??k àá !?E T k =D 0e E T k ;Y T k ;C T k àá??á1=Y T

k

àáE k 0e E k k k àá??k àá? !?Y T k

Y k ?D 0c E T k ;Y T k ;C T k àáD 0c E k k k àá !?D 0e E T k ;Y T k ;C T k àáD 0e E k k k àá !

e6TOn the right hand side of Eq.(6),the first component could be interpreted as the potential carbon

factor change (PCFCH k 0)since the CO 2emission is deflated by its CO 2emissions technical efficiency.Inefficiency in CO 2emissions will result in the observed carbon factor being larger than that when there is no inefficiency.An increase in CO 2emissions technical efficiency from period 0to period T will lead to a larger carbon factor change and therefore more of the change in C being assigned to the change in C /E .The second component could be interpreted as the potential energy intensity change (PEICH k 0)since the energy consumption is deflated by its energy usage technical efficiency.6Inefficiency in energy consumption will result in the observed energy intensity to be larger compared to the case where there is no inefficiency.An increase in energy usage technical efficiency from period 0to period T will lead to a larger energy intensity change and therefore more of the change in C being assigned to the change in E /Y .The third component,i.e.GDPCH k ,accounts for the effect of GDP change.The fourth and fifth components,which are essentially two Malmquist index numbers,respectively measure the change of CO 2emissions performance (CEPCH k 0)and the change of energy usage performance (EUPCH k 0).7If there are no inefficiencies

4

Note that both D e (E ,Y ,C )and D c (E ,Y ,C )are not less than unity.Detailed discussions on the concepts and properties of the Shephard distance functions can be found in F?re and Primont (1995).5

It should be noted that the decomposition method presented in this paper does not account for fuel mix.As a result,the decomposition results it gives should be interpreted with this limitation in mind.6

The ratio of CO 2emissions to energy consumption is termed as “carbon factor ”while the ratio of energy consumption to GDP is referred to as “energy intensity ”in Ang (1999).7

The last three components might also be interpreted together in the sense that both the fourth and fifth components can be used to scale the effect of the third component.For example,in the case of the fifth component,the existence of energy usage inefficiency indicates that the level of energy consumed by the current GDP could have been used to support a higher level of GDP.The elimination of energy usage inefficiency would make it possible to increase GDP with the given level of energy consumption.An increase in energy usage technical efficiency over time will result in the decrease of the fifth component and then less of the change in C being assigned to the change in GDP.

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P .Zhou,B.W.Ang /Energy Economics 30(2008)1054–1067

pertaining to all the observations,all the distance functions used will be equal to unity and Eq.(6) will collapse to Eq.(5).

Using the notations described above,we can rewrite Eq.(6)as

D k?PCFCH0k?PEICH0k?GDPCH k?CEPCH0k?EUPCH0ke7TNote that in Eq.(7)all the components derived are based on the production technology in time period0.Alternatively,if we take the production technology in time period T as a reference,the following decomposition model could be obtained:

D k?PCFCH T k?PEICH T k?GDPCH k?CEPCH T k?EUPCH T ke8TIn Eq.(8)all the components are of the same form as those given in Eq.(6)except that the production technology in time period T is adopted.

To avoid the arbitrariness in choosing one of the two reference technologies,we can take the geometric mean of Eqs.(7)and(8):

D k?

C T k=D0c E T k;Y T k;C T k

àá

D T c

E T k;Y T k;C T k

àá

??1=2

n o

á1=E T

k

àá

C0

k

=D0c E0k;Y0k;C0k

àá

D T c E0

k

;Y0k;C0k

àá

??1=2

n o

á1=E0

k

àá

@

1

A

?

E T k=D0e E T k;Y T k;C T k

àá

D T e

E T k;Y T k;C T k

àá

??1=2

n o

á1=Y T

k

àá

E0

k

=D0e E0k;Y0k;C0k

àá

D T e E0

k

;Y0k;C0k

àá

??1=2

n o

á1=Y0

k

àá

@

1

A?Y T k

Y0

k

?

D0c E T k;Y T k;C T k

àá

D0c E0

k

;Y0k;C0k

àááD

T

c

E T k;Y T k;C T k

àá

D T c E0

k

;Y0k;C0k

àá

"#1=2

@

1

A

?

D0e E T k;Y T k;C T k

àá

D0e E0

k

;Y0k;C0k

àááD

T

e

E T k;Y T k;C T k

àá

D T e E0

k

;Y0k;C0k

àá

"#1=2

@

1

A

?PCFCH k?PEICH k?GDPCH k?CEPCH k?EUPCH ke9TIt should be pointed out that the idea of calculating geometric mean is consistent with the definition of Malmquist productivity index given by F?re et al.(1994b).This practice could be traced back to the Fisher ideal index number as explored in the IDA studies by Ang et al.(2004) and Boyd and Roop(2004).

Obviously,the last two components in Eq.(9)are essentially two Malmquist productivity indexes for entity i.The difference is that CEPCH k is an undesirable output-oriented while EUECH k is an input-oriented index.Following F?re et al.(1994b),we can further decompose the two indexes in the following way:

CEPCH k?D T c E T k;Y T k;C T k

àá

D0c E0

k

;Y0k;C0k

àá

!

?

D0c E T k;Y T k;C T k

àá

D T c

E T

k

;Y T k;C T k

àááD

c

E0

k

;Y0k;C0k

àá

D T c E0

k

;Y0k;C0k

àá

"#1=2

@

1

Ae10T

EUPCH k?D T e E T k;Y T k;C T k

àá

D0e E0

k

;Y0k;C0k

àá

!

?

D0e E T k;Y T k;C T k

àá

D T e

E T

k

;Y T k;C T k

àááD

e

E0

k

;Y0k;C0k

àá

D T e E0

k

;Y0k;C0k

àá

"#1=2

@

1

Ae11T

1058P.Zhou,B.W.Ang/Energy Economics30(2008)1054–1067

On the right hand side of Eq.(10),the first term could be interpreted as the effect of CO 2emissions technical efficiency change (CEEFCH k )and the second term measures the shift of CO 2emissions-side technology or carbon abatement technology (CATECH k ).On the right hand side of Eq.(11),the first term accounts for the effect of energy usage technical efficiency change (EUEFCH k )and the second term could be interpreted as the shift of energy usage-side technology or energy savings technology (ESTECH k ).

In summary,the change of the aggregate CO 2emissions for entity i could be decomposed into the following seven components:

D k ?C T k =C 0

k ?PCFCH k ?PEICH k ?GDPCH k ?CEEFCH k ?CATECH k

?EUEFCH k ?ESTECH k

e12T

For each component a value less than unity indicates that it contributes to a reduction,while a value greater than unity indicates that it contributes to an increase,in CO 2emissions.2.3.Estimation models

To apply the proposed decomposition approach to estimating the seven components in Eq.(12),

we need to compute eight Shephard distance functions,namely D c s (E k t ,Y k t ,C k t )and D e s (E k t ,Y k t ,C k t

)where s ,t ∈{0,T }.According to the definitions of these distance functions and the environmental DEA technology specified earlier,they can be derived by solving the following DEA type models:

D s c

E t k ;Y t k ;C t k àá??à1?min h

s :t :

X K k ?1z k E s k V E t k

X K k ?1z k Y s k z Y t

k X K k ?1

z k C s k ?h C t

k z k z 0;k ?1;N ;K

e13T

D s e

E t k ;Y t k ;C t k

àá?

?à1

?min k s :t :

X K k ?1z k E s k V k E t

k

X K k ?1

z k Y s k z Y t

k X K k ?1

z k C s k ?C t k

z k z 0;k ?1;N ;K

e14T

where s ,t ∈{0,T }.

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P .Zhou,B.W.Ang /Energy Economics 30(2008)1054–1067

1060P.Zhou,B.W.Ang/Energy Economics30(2008)1054–1067

3.Application studies

Two application studies are presented in this section to illustrate the use of our proposed approach.The first deals with the decomposition of aggregate CO2emission changes for eight world regions from2002to2004.The total primary energy supply(in million tons of oil equivalent or Mtoe),gross domestic product(in billion US$1995,PPP)and CO2emissions from fuel combustion(in million tonnes or Mt)are treated as input,desirable and undesirable outputs, respectively.The data sources are Key World Energy Statistics2004(IEA,2004a)and Key World Energy Statistics2006(IEA,2006).Table1shows the eight regions and the collected data.Based on these data,we apply the proposed approach described in Section2to derive the seven con-tributing factors on changes in CO2emissions for each region.Table2shows the decomposition results obtained and the relative changes of aggregate CO2emissions.

It can be observed from Table2that both the carbon abatement technological change(CATECH) and the energy savings technological change(ESTECH)are estimated to have led to a reduction in world CO2emissions,which may be an indication of the world-wide technological improvement in multiple aspects.Interestingly,the effects of carbon abatement technological change(CATECH)are the same for all regions(except for Latin America)although their individual distance function values used to calculate the CATECH component are different.This implies that the contributions of carbon abatement technological change to the reductions of their CO2emissions are the same. This could be attributed to the very limited observations used in the application study.However,it is also possible that the growing concern on CO2emissions and the active international technological diffusion may play a role.

From Table2,we also found that the potential energy intensity change component(PEICH)is greater than one for China,while it is less than one for other regions(except for Latin America). This indicates that from2002to2004energy usage efficiency increased more in China compared to other regions,which leads to more of the change in CO2emissions assigned to the change in the aggregate energy intensity.As a whole,among the four components which contribute to the increase in world CO2emissions,the output change component(GDPCH)is the most important in all the regions which is not surprising.

It is worth pointing out that the four components PCFCH,PEICH,CATECH and ESTECH cannot be estimated for Latin America because the linear programs for calculating D e(E,Y,C)and D c(E,Y,C)based on the reference technology in2001and the data in2002are not feasible.This is due to the fact that no benchmarking points could be found under the environmental DEA Table1

Energy consumption,GDP and CO2emissions for world regions,2002and2004

Region20022004

E(Mtoe)Y(billion US$1995,PPP)C(Mt)E(Mtoe)Y(billion US$1995,PPP)C(Mt) OECD534625,37512,554550829,49312,911 Middle East4311026109348012821183 Former USSR9311552223297919892313 Non-OECD Europe100358253104413265 China124553593307162672194769 118455082257129067772499 Asia(exclusive

of China)

Latin America45525678454853119907 Africa54016697435861997814

technology in 2001to evaluate the efficiencies of Latin America in energy consumption and CO 2emissions in 2002.As was discussed in Pasurka (2006),this phenomenon should be attributed to the assumption of weak disposability imposed on undesirable outputs,which could be considered as a limitation of our approach.Nevertheless,as was suggested by F?re et al.(2001,2007),if infeasible linear programs occur too frequently,we may use multiple year windows data to construct the reference technology in order to avoid infeasible linear programs.

In our second application study,the changes of the aggregate CO 2emissions for 30OECD countries from 2001to 2002are decomposed by the proposed approach.Similar to the first application study,the total primary energy supply (in Petajoules),gross domestic product (in billion US$1995,PPP)and CO 2emissions from fuel combustion (in million tonnes or Mt)are used as input,desirable and undesirable outputs,respectively.The data for the three variables have been collected from IEA (2004b).The countries and the data are shown in Table 3.Table 4shows the relative changes of CO 2emissions and the decomposition results obtained.

The results in Table 4show that both the carbon abatement technological change (CATECH)and the energy savings technological change (ESTECH)contribute to a reduction in CO 2emissions for the OECD countries as a whole.This may be an indication that technological progress in multiple aspects occurred in most OECD countries from 2001to 2002.Nevertheless,in this study the contributions of carbon abatement technological change (CATECH)may not be the same in all countries,while in the first application study they are the same (=0.8834)for all regions.

In addition to CATECH and ESTECH,the CO 2emissions technical efficiency change (CEEFCH)and the potential energy intensity change (PEICH)also contribute to the reduction of CO 2emissions in most countries.Interestingly,we found that the energy usage technical efficiency change (EUEFCH)has a positive rather than a negative effect on the increase of CO 2emissions in most countries.It is an indication that in these countries the energy usage efficiency declined over time.As a whole,among the components which lead to a decrease in CO 2emissions,the carbon abatement technology change (CATECH)seems to have the most important effect.On the other hand,among the components which lead to an increase in CO 2emissions,the output change (GDPCH)and the energy usage efficiency change (EUEFCH)respectively play the most and the least important roles.These findings are consistent with those in the first application study.

As shown in Table 4,the PCFCH and CATECH components for Italy and the PEICH and ESTECH components for Switzerland cannot be estimated because of the infeasibility of two linear programs involved.The underlying reasons have been elaborated in the first application study,and the infeasible linear programs could also be avoided by using the environmental DEA technology based on multiple year windows data (F?re et al.,2001,2007).However,since there

Table 2

CO 2emissions change and its seven components for world regions,2002–2004Region

C T /C 0PCFCH PEICH GDPCH CEEFCH CATECH EUEFCH ESTECH OECD

1.0284 1.12810.9462 1.1623 1.00160.8834 1.01080.9268Middle East 1.0823 1.12200.8662 1.24950.98050.8834 1.13620.9056Former USSR

1.0363 1.21870.8086 1.28160.91530.8834 1.12050.9056Non-OECD Europe 1.0474 1.10930.9139 1.1536 1.02780.8834 1.08210.9116China

1.4421 1.0314 1.0540 1.3471 1.21180.8834 1.00000.9198Asia (exclusive of China) 1.1072 1.12930.9579 1.2304 1.01870.8834 1.00240.9222Latin America 1.0734–

–

1.2150 1.0000–

1.0000–

Africa

1.0956 1.10260.9628 1.1965 1.03650.8834 1.01890.9245Geometric mean a

1.1128

1.1190

0.9271

1.2300

1.0242

0.8834

1.0516

0.9166

a

The calculation of geometric mean excludes the data for Latin America.

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P .Zhou,B.W.Ang /Energy Economics 30(2008)1054–1067

are only two infeasible linear programs,we simply leave the four components alone in order not to introduce more biases in constructing the reference technology.

The foregoing two application studies show that the proposed approach can be used to decompose a change of aggregate CO 2emissions over time into different components by using aggregate panel data.However,since no sectoral data are involved,the proposed approach could not be used to identify structure effects as could be done by IDA and SDA decomposition https://www.360docs.net/doc/e012132308.html,ing the production frontier estimated from the panel data,the proposed approach can be used to identify some production technology related components such as the effects of carbon emission technological change and energy savings technological change,which could be considered as a key feature of the proposed approach.

https://www.360docs.net/doc/e012132308.html,parisons with other decomposition analysis methods

Although their objectives are fairly similar,the decomposition techniques mentioned in Section 1have different theoretical foundations and underlying formulations.Each has its own

Table 3

Energy consumption,GDP and CO 2emissions for OECD countries,2001and 2002Country

20012002E

(petajoules)

Y

(Billion US$1995,PPP)C (Mt)E

(petajoules)Y

(Billion US$1995,PPP)C (Mt)Australia 4536.0479.2341.94719.0492.3342.9Austria 1292.0208.967.31275.0211.866.1Belgium 2470.0252.6119.62382.0254.3112.6Canada

10390.0816.5521.210468.0843.1531.9Czech Republic 1733.0136.0118.61747.0138.6115.0Denmark 838.0136.251.6827.0139.051.2Finland 1418.0123.960.51491.0126.763.5France 11152.01435.5384.311132.01452.8377.1Germany 14795.01934.7850.114501.01938.2837.5Greece 1202.0170.290.21215.0176.690.5Hungary 1071.0117.856.21066.0121.955.5Iceland 141.07.7 2.1143.07.7 2.2Ireland 634.0109.343.1641.0116.842.5Italy 7226.01333.5426.17231.01338.4433.2Japan 21646.03037.91164.621643.03042.31206.9Korea

8119.0675.2441.78520.0718.0451.6Luxembourg 161.018.88.4169.019.09.3Mexico 6366.0812.4360.06586.0819.8365.2Netherlands 3235.0406.9177.73263.0407.9177.9New Zealand 758.074.233.3754.077.434.0Norway 1107.0126.533.71110.0127.733.1Poland 3770.0367.1291.53734.0372.2282.9Portugal

1065.0162.559.11105.0163.363.0Slovak Republic 772.054.139.3776.056.537.9Spain 5352.0767.3287.35508.0783.0303.4Sweden 2143.0222.548.52137.0226.850.1Switzerland 1173.0199.543.91136.0199.942.8Turkey 2997.0379.2185.23158.0408.7193.1UK

9814.01374.1541.79483.01397.8529.3United States

94366.0

8977.8

5613.8

95895.0

9196.4

5652.3

1062P .Zhou,B.W.Ang /Energy Economics 30(2008)1054–1067

strengths and weaknesses and is suited to certain specific decomposition situations.Depending on the purpose of a study and the kind of data available,the analyst generally will opt for a specific technique that is applicable rather than having to make a choice among the various techniques as they may not be substitutable.In this light,broad comparisons of the key features of the techniques would be useful.In the discussions that follow,we shall refer to our proposed technique as the production-theoretical decomposition analysis (PDA)https://www.360docs.net/doc/e012132308.html,parison with IDA/SDA

As mentioned in Section 1,IDA and SDA are two widely used techniques in decomposition analysis.Within the scope of each technique,especially in the case of IDA,different methods or approaches have been proposed and applied to energy and environmental analysis.Following Ang and Zhang (2000)and Hoekstra and van den Bergh (2003),we may compare the PDA approach with IDA/SDA in terms of theoretical foundation,data requirements,decomposition form,and some relevant index properties.Table 5summarizes the key features of these techniques and approach.

Table 4

CO 2emissions change and its seven components for OECD countries,2001–2002Country C T /C 0PCFCH PEICH GDPCH CEEFCH CATECH EUEFCH ESTECH Australia 1.00290.98730.9775 1.02730.99430.9820 1.0201 1.0156Austria 0.9822 1.0276 1.0043 1.01390.99480.97350.97330.9957Belgium 0.9415 1.04430.9561 1.00670.95210.9819 1.00550.9964Canada 1.0205 1.02490.9890 1.0326 1.00620.98220.9747 1.0122Czech Rep.0.9696 1.01100.9515 1.01910.96870.9822 1.0187 1.0206Denmark 0.9922 1.03440.9866 1.02060.99860.9734 1.00050.9797Finland 1.04960.9725 1.0181 1.0226 1.04490.9822 1.01310.9969France 0.9813 1.0140 1.0052 1.01210.99180.9775 1.00270.9786Germany 0.9852 1.02230.9890 1.0018 1.00620.97710.99310.9960Greece 1.0033 1.02670.9728 1.03760.99090.9757 1.0000 1.0015Hungary 0.9875 1.04010.9690 1.03480.97290.98050.99610.9965Iceland 1.04760.98600.9917 1.0000 1.06660.9822 1.03920.9841Ireland 0.9861 1.39490.9618 1.06860.75370.9276 1.00000.9837Italy 1.0167–

1.0010 1.0037 1.0000–

1.00000.9961Japan 1.0363 1.0016 1.0178 1.0014 1.06020.97600.98960.9912Korea

1.0224 1.01330.9637 1.06340.97880.9822 1.0113 1.0126Luxembourg 1.10710.9624 1.0635 1.0106 1.11830.98000.98010.9965Mexico 1.01440.9752 1.0035 1.0091 1.02810.9780 1.02560.9962Netherlands 1.00110.99380.9991 1.0025 1.02110.9781 1.01110.9961New Zealand 1.0210 1.04870.9859 1.04310.99650.98220.97100.9962Norway 0.9822 1.0068 1.0046 1.00950.99280.9800 1.01070.9783Poland 0.9705 1.02370.9585 1.01390.97450.9822 1.0000 1.0192Portugal 1.06600.9683 1.0287 1.0049 1.08840.9749 1.02360.9806Slovak Rep.0.9644 1.03900.9274 1.04440.94010.9822 1.0223 1.0152Spain 1.05600.9915 1.0168 1.0205 1.06070.9757 1.00670.9853Sweden 1.0330 1.02250.7805 1.0193 1.03170.9820 1.66310.7536Switzerland 0.9749 1.1301–

1.0020 1.00000.8908 1.0000–

Turkey 1.0427 1.02310.9777 1.07780.98920.9777 1.00320.9967UK 0.9771 1.05320.9805 1.01720.98410.97560.97920.9894US

1.0069 1.00800.9839 1.0243 1.00070.98220.9968 1.0114Geometric mean a

1.0083

1.0233

0.9796

1.0234

0.9981

0.9774

1.0207

0.9871

a

The calculation of geometric mean excludes the data for Italy and Switzerland.

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As already pointed out,IDA has a close relationship with the index number theory and SDA is based on the input –output analysis in quantitative economics.In contrast,PDA is built upon the production theory in which both desirable and undesirable outputs are jointly produced.Thus the theoretical foundation varies although the decomposition formulae in SDA and PDA are based on concepts that are akin to some specific index numbers,e.g.the Laspeyres index in the case of SDA and the Malmquist index in the case of PDA.

Data requirement is another major difference between PDA and IDA/SDA.In general,IDA requires only data at the sub-sector level.The data requirements depend to a very large extent on the level of sector disaggregation which could vary significantly from one study to another.SDA is generally more data intensive as input –output tables are employed,and decomposition is often conducted for specific years only when such tables are available.In contrast,PDA uses panel aggregate data which are easy to collect.Since no sectoral data are involved,PDA does not give structural effects which are often important components in IDA and SDA studies.In addition,PDA uses the information provided by panel data to estimate the production frontiers and then give some production technology related components.As such,the results obtained are often influenced by the number of entities considered.These may be seen as limitations of the PDA approach.

Our proposed PDA approach takes the multiplicative form where changes over time are measured in terms of ratios.Both multiplicative and additive decompositions are widely adopted in IDA while additive decomposition prevails in SDA.In the additive form,changes over time are measured in terms of differences.Issues related to additive decomposition versus multiplicative decomposition,such as which is the preferred form,can be found in Ang and Zhang (2000)and Ang (2004).Ease of result presentation,interpretation and dissemination may be a consideration.Technically,it seems to be difficult to extend our approach to the additive form.In terms of implementation,IDA and SDA deal with some simple algebraic operations.The PDA approach involves the solving of a number of linear programs and computationally it may be more complex for analysts who are not familiar with linear programming.

In terms of index properties,Ang and Zhang (2000)and Liu and Ang (2003)discussed in details the properties of different IDA methods.Hoekstra and van den Bergh (2003)compared the properties of SDA and IDA methods in a unified framework.Three index properties are shown in Table 5.In decomposition analysis,satisfying this factor-reversal test ensures perfect or complete decomposition where there is no residual appearing in the decomposition results.The time-reversal test requires that if the data for periods 0and T are interchanged,the index should be equal to the reciprocal of the original index in multiplicative decomposition,and it should be the negative of the original index in additive decomposition.Some of the more desirable IDA methods consider

Table 5

Comparison between IDA/SDA and PDA Technique/approach

Theoretical foundation

Data

requirements

Decomposition form

Implementation

Index properties a Factor reversal

Time reversal Zero value robust IDA Index number Medium Additive/multiplicative Algebraic operation Yes/no Yes/no Yes/no SDA Input –output analysis

High Additive Algebraic operation Yes/no Yes/no Yes PDA

Production theory

Low

Multiplicative

Linear

programming

Yes

Yes

Yes

a

The properties in the cases of IDA and SDA depend on the specific decomposition formulae used.

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the logarithmic changes of the factors studied instead of their percentage changes.As such the existence of zero values in the data set may pose a problem,i.e.whether a method is zero value robust.In the same context as in IDA/SDA,our PDA approach passes the factor-reversal and time-reversal tests,and is zero value robust.It therefore possesses some desirable properties as a decomposition method.It should be noted that since IDA/SDA consist of a number of methods in each case,some IDA/SDA methods pass while others do not pass all the three tests as indicated in Table 5.

https://www.360docs.net/doc/e012132308.html,parison with Pasurka (2006)and Wang (2007)8

Table 6shows the similarities and differences between our PDA approach and two earlier PDA approaches proposed by Pasurka (2006)and Wang (2007).Despite their common production-theoretical framework,the application areas of the three studies are different.The approach by Pasurka deals with changes of NO x and SO 2emissions from electric power plants,while that by Wang involves energy productivity change.In contrast,our approach focuses on decomposing the change of aggregate CO 2emissions.As a result,these three studies differ in the characterization of production technology.

Wang (2007)adopts the traditional DEA technology (without considering undesirable outputs)while Pasurka (2006)and our study are based on the environmental DEA technology.The compositions of production technologies in the three studies are also different.Nevertheless,all assume that the production technology exhibits constant returns to scale.As to the decomposition method,the Shephard output distance functions are used in Pasurka (2006)and Wang (2007),while the Shephard input distance functions are used in our study.All three studies adopt nonparametric DEA models to estimate the components.

In summary,our proposed PDA approach is essentially different from the IDA/SDA techniques since they have different theoretical foundations,data requirements and implementation forms.They share some common features in decomposition form and index https://www.360docs.net/doc/e012132308.html,pared with two earlier PDA studies,our study focuses specifically on the decomposition of aggregate CO 2emissions and this differs from the two earlier studies.

Table 6

Comparison between our study and Pasurka (2006)and Wang (2007)Study Application area Production technology Decomposition foundation Estimation models Pasurka (2006)Electric power plant emissions

Environmental DEA technology,CRS Six Shephard output distance functions DEA Wang (2007)Energy productivity Tradition DEA technology,CRS Eight Shephard output distance functions DEA Our study

CO 2emissions

Environmental DEA technology,CRS

Eight Shepard input distance functions

DEA

8

Within a joint production framework,Zaim (2004)employed several subvector distance functions to calculate a composite pollution intensity index and then applied regression analysis to investigate the possible factors associated with the change in the pollution intensity index.Although regression analysis is superior to our PDA approach since it can be used to investigate any well-defined factors associate with the change in one variable,the quantification of some factors such as production technology is not an easy task.In addition,unlike the PDA approach,regression analysis is not residual free.

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5.Conclusion

Decomposition of changes in aggregate CO2emissions over time has been dealt with in a number of studies.To the best of our knowledge,all the studies use the IDA or SDA technique.In this paper, we present a production-theoretical decomposition analysis(PDA)approach based on the Shephard input distance function and the environmental DEA technology concepts.The proposed PDA approach does not require sectoral data and can decompose a change of aggregate CO2emissions over time into seven contributing factors.In practice,these factors can be obtained by solving a series of DEA type models.A key feature of the proposed PDA approach is that it uses panel data to estimate production frontiers and then provides several production technology related components.

Two application studies on decomposing the CO2emissions for world regions and OECD countries are presented.We point out some limitations of the proposed PDA approach when compared with the well-known IDA and SDA techniques.Despite its limitations,the proposed PDA approach could offer an alternative in CO2emission decomposition.We also compare our PDA approach to two earlier PDA methods.The proposed PDA approach could be easily extended to study the emissions of other energy-related pollutants.Methodologically,it is possible to extend our proposed approach to account for the fuel mix effect if the aggregate energy input is replaced by energy inputs by fuel type.Since the proposed approach focuses only on the decomposition of CO2emissions,future research could include extending it to multiple pollutants together in a joint production framework.Our study treats energy consumption as the only input.The inclusion of more inputs,such as capital stock and labor,could yield more insights by giving several other production technology related components.

Acknowledgements

The authors would like to thank the Journal editor Richard S.J.Tol and two anonymous referees for their invaluable comments and suggestions on an earlier draft of this paper.

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