F.Q. Zhang, B.W. Ang r Energy Economics 23 2001 179᎐190 181
decomposition, are also examined. An explanation of the difference between the decomposition results given by the two perfect decomposition methods is included
in Appendix A.
2. Decomposition methodology
A review of decomposition methodology in energy studies can be found in Ang Ž
. 1995 . Various decomposition methods have been proposed, generally given in
either the additive or multiplicative form. The analysis and discussions in our paper are based on the additive form, i.e. decomposition of the difference in total CO
2
emissions between two world regions into contributions from various pre-defined explanatory factors. We define the following variables for a region:
E s Total energy consumption of all fuel types
E s Energy consumption of fuel type i
i
C s Total CO emissions from all fuel types
2
C s CO emissions from fuel type i
i 2
Y s GDP
P s Population
The CO emissions from a region can be written as
2
Ž . Ž
. Ž . Ž
. Ž .
C s ⌺ C s ⌺ E rE C rE ErY
YrP P s ⌺ S F IGP 1
i i
i i
i i
i i
i
where S s E rE is the consumption share of fuel type i, F s C rE the CO
i i
i i
i 2
emission coefficient for fuel type i, I s ErY the aggregate energy intensity, and G s YrP
the GDP per capita or income. The decomposed components of a change in C that are associated with these factors are respectively referred to as
Ž .
Ž .
fuel share effect ⌬C
, emission coefficient effect ⌬C
, intensity effect
fsh emc
Ž .
Ž .
Ž .
⌬C , income effect ⌬C
and population effect ⌬C .
int ypc
pop
Let subscripts 1 and 2 denote variables for the two regions being compared. The difference in emission level between the regions can be expressed as
⌬C s C y C s ⌺ S F I G P y ⌺ S F I G P
1 2
i i
1 i
1 1 1
1 i
i 2
i 2 2
2 2
Ž . s ⌬
C q ⌬
C q ⌬
C q ⌬
C q ⌬
C q ⌬
C 2
fsh emc
int ypc
pop rsd
where ⌬C is a residual term which does not exist if decomposition is perfect. For
rsd
convenience, the choices of regions 1 and 2 are made in such a way that ⌬C is a Ž
. Ž .
positive number i.e. C C . Based on Eq. 2 , the decomposition formulae for
1 2
the four methods are described in the sections that follow. In each case, the derivation is not presented as this can be found in the references cited.
2.1. Laspeyres method LM The Laspeyres method has been widely adopted in decomposition analysis due to
F.Q. Zhang, B.W. Ang r Energy Economics 23 2001 179᎐190 182
ease of calculation and understanding. A discussion of this approach with the Ž
. formulae given in the additive form can be found in Park 1992 . By using the LM,
Ž .
Ž . each effect e.g. ⌬C
in Eq. 2 is isolated by letting the corresponding variable
fsh
Ž . S
change while holding the other variables at their base values. Thus in the case
i
of fuel share effect Ž .
⌬C s ⌺ ⌬
S F I GY 3
fsh i
i i i
where ⌬ S s S y S and the subscript 2 for F , I , G and Y have been omitted.
i i
1 i
2 i
i
Other effects can be derived in the same manner. The residual ⌬C is non-zero
rsd
and may be taken as the sum of all the interactions of the main effects. 2.2. Refined Laspeyres method RLM
Ž .
Sun 1998 proposed a complete decomposition model, which we shall refer to as the RLM. It is an extension of the LM with the interaction terms evenly distributed
among the main effects such that ⌬C s
0. This is done using the so-called
rsd
‘jointly created and equally distributed’ principle. Based on this formulation, it can be shown that the formula of ⌬C
in our study takes the following form:
fsh
Ž ⌬C
s ⌺ ⌬ S F I GY q
1r2 ⌺ ⌬ S ⌬ F I GY q ⌺ ⌬ S F ⌬ I GY
fsh i
i i i
i i
i i i
i i
i
. Ž
q⌺ ⌬ S F I ⌬GY q ⌺ ⌬ S F I G⌬Y q
1r3 ⌺ ⌬ S ⌬ F ⌬ I GY
i i
i i i
i i i
i i
i i
q⌺ ⌬ S ⌬ F I ⌬GY q ⌺ ⌬ S ⌬ F I G⌬Y q ⌺ ⌬ S F ⌬ I G⌬Y
i i
i i i
i i i
i i
i i
. Ž
q⌺ ⌬ S F ⌬ I ⌬GY q ⌺ ⌬ S F I ⌬G⌬Y q
1r4 ⌺ ⌬ S ⌬ F ⌬ I ⌬GY
i i
i i
i i
i i i
i i
i
. q⌺ ⌬
S ⌬ F ⌬ I G⌬Y q ⌺ ⌬ S ⌬ F I ⌬G⌬Y q ⌺ ⌬ S F ⌬ I ⌬G⌬Y
i i
i i
i i
i i i
i i
i
Ž .
Ž . q
1r5 ⌺ ⌬ S ⌬ F ⌬ I ⌬G⌬Y 4
i i
i i
For other effects, the formulae can be obtained by exchanging the place of S
i
Ž .
with the respective variables. Raggi and Barbiroli 1992 also proposed a complete model based on the LM. Through some simple manipulation, it can be shown these
two methods are very similar.
2.3. Arithmetic mean weight Di
¨
isia method ADM Ž
. This method was proposed by Boyd et al. 1988 based on the Divisia integral
index and has since been used in my decomposition studies. The formula for ⌬C
fsh
takes the following form: C q C
S
i 1
i 2
i 1
Ž . ⌬C
s ⌺ ln
5
fsh i
2 S
i 2
F.Q. Zhang, B.W. Ang r Energy Economics 23 2001 179᎐190 183
For other effects, the formulae are simply given by exchanging S with the
i j
Ž . Ž
. respective variables in Eq. 5 . Ang and Choi 1997 pointed out two problems
associated with the ADM: there is a residual after decomposition and the method Ž
. cannot accommodate zero values in the data set e.g. S s 0 . However, the
i 1
residual given by this method is generally smaller than that of the LM. 2.4. Logarithmic mean weight Di
¨
isia method LDM Ž .
Ž .
Instead of the arithmetic mean weight given in Eq. 5 , Ang et al. 1998 proposed an additive decomposition scheme using the logarithmic mean weight.
The formula for ⌬C in given by
fsh
C y C S
i 1
i 2
i 1
Ž . ⌬C
s ⌺ ln
6
fsh i
Ž .
ln C rC S
i 1
i 2
i 2
The main advantages of the LDM over the AMD are that perfect decomposition is obtained and the method can accommodate zero values in the data set. It can be
seen that the formulae of this perfect decomposition approach are much simpler Ž .
than those of the RLM. The number of terms on the right hand side of Eq. 4 Ž .
depends on the number of factors considered while Eq. 6 takes the same form irrespective of the number of factors.
3. Data and decomposition results
