F.Q. Zhang, B.W. Ang r Energy Economics 23 2001 179᎐190 185
Table 3 Ž
. Decomposition results of the difference in CO emissions BTCO
between world regions in 1993:
2 2
OECD-ROW GDP
Method ⌬C
⌬C ⌬C
⌬C ⌬C
⌬C
tot fsh
int ypc
pop rsd
Purchasing LM
4.11 y
1.08 1.86
44.92 y
5.90 y
35.69 power GDP
y 26
45 1093
y 143
y 869
RLM 4.11
y 2.48
3.49 27.98
y 24.88
y 60
85 681
y 605
ADM 4.11
y 1.38
2.12 18.52
y 14.97
y 0.18
y 34
52 451
y 364
y 4
LDM 4.11
y 1.43
2.07 18.08
y 14.61
y 35
50 440
y 356
Exchange rate LM
4.11 y
1.08 y
4.13 140.12
y 5.90
y 124.90
converted y
26 y
101 3410
y 143
y 3039
GDP RLM
4.11 y
3.79 y
19.17 62.88
y 35.81
y 92
y 466
1530 y
871 ADM
4.11 y
1.38 y
7.71 28.34
y 14.97
y 0.18
y 34
y 188
690 y
3641 y
4 LDM
4.11 y
1.43 y
7.52 27.67
y 14.61
y 35
y 183
673 y
356
energy intensity of ROW is higher than that of OECD based on exchange-rate- converted GDP but the converse is true when it is based on purchasing power
GDP. The decomposition results given by the four decomposition methods are shown
in Tables 2᎐4. The estimated effects are also expressed as percentages of the actual total difference in emissions between regions for ease of comparison. With
the same set of emission coefficients used for all regions, ⌬C is always zero and
emc
is therefore not shown. Residuals for the RLM and LDM are also zero because Ž
these are perfect decomposition methods. In absolute terms, income effect GDP .
per capita and population effect are generally the dominant forces leading to different emission levels among the three world regions, while fuel share effect is
the smallest.
4. Impacts of variations in explanatory factors
We now use the results in Tables 2᎐4 to highlight the main differences between the conventional methods and the perfect methods. The perfect methods give
complete decomposition results regardless of the data pattern, as opposed to the conventional methods. The results given by the LM contain residuals that are so
large that this effectively makes the method unsuitable for cross-countryrregion decomposition analysis. In comparison, the ADM gives smaller residuals, which
range from 4 to 14 of the actual difference in emissions between regions.
F.Q. Zhang, B.W. Ang r Energy Economics 23 2001 179᎐190 186
Table 4 Ž
. Decomposition results of the difference in CO emissions BTCO
between world regions in 1993:
2 2
ROW-FSUrCEE GDP
Method ⌬C
⌬C ⌬C
⌬C ⌬C
⌬C
tot fsh
int ypc
pop rsd
Purchasing LM
3.56 0.45
y 2.49
y 2.03
35.41 y
27.78 power GDP
13 y
70 y
57 994
y 780
RLM 3.56
1.04 y
9.85 y
7.13 19.51
29 y
277 y
200 548
ADM 3.56
0.78 y
5.81 y
4.21 13.09
y 0.29
22 y
163 y
118 368
y 8
LDM 3.56
0.67 y
5.47 y
3.96 12.32
19 y
154 y
111 346
Exchange rate LM
3.56 0.45
y 2.62
y 1.83
35.41 y
27.84 converted
13 y
74 y
51 994
y 782
GDP RLM
3.56 1.04
y 10.91
y 6.19
19.61 29
y 306
y 174
551 ADM
3.56 0.78
y 6.39
y 3.63
13.09 y
0.29 22
y 180
y 102
368 y
8 LDM
3.56 0.67
y 6.02
y 3.41
12.32 19
y 169
y 96
346
As shown in Table 1, the exchange-rate-converted GDP exhibits larger variations as compared to the purchasing power GDP. Residuals given by the LM in the case
of exchange-rate-converted GDP are also much larger than those given by purchas- ing power GDP, as shown in Tables 2 and 3. The case of ROW-FSUrCEE
decomposition is an exception, as the relative size of their GDP is about the same irrespective of the GDP measure used. Hence for the LM, the magnitude of
residual increases with the variations in explanatory factors. Interestingly the residual for the ADM is not affected by how GDP is measured. It can be shown
Ž . Ž .
from Eqs. 5 and 6 that for Divisia-based methods, different GDP measures only Ž
. affect those effects directly related to GDP, i.e. intensity ⌬C
and income
int
Ž .
⌬C effects.
ypc
Fig. 1 shows the results given by the RLM and the LDM for OECD-ROW decomposition. It can be seen that the disparities in the results given by the two
methods increase when the GDP measure is switched from purchasing power GDP to exchange-rate-converted GDP. Such a switch introduces greater variability in
the explanatory factors which in turn leads to greater disparity between the results given by the two methods. It may be suggested that, generally, there are greater
deviations between the decomposition results given by these two perfect decompo- sition methods in cross-countryrregion studies as compared with time-series de-
composition studies. This arises from the fact that, in general, variations in explanatory factors are smaller in the latter case. The implication is that decompo-
sition results are more method-specific in the case of cross-countryrregion studies.
It can be seen from Tables 2᎐4 that in absolute terms all the estimated effects
F.Q. Zhang, B.W. Ang r Energy Economics 23 2001 179᎐190 187
Ž .
Fig. 1. Decomposition results OECD-ROW given by the RLM and the LDM. Plot 1 refers to RLM with purchasing power GDP, plot 2 refers to LDM with purchasing power GDP, plot 3 referes to RLM
with exchange-rate-converted GDP, and plot 4 refers to LDM with exchange-rate-converted GDP.
given by the RLM are larger than the corresponding estimates given by the LDM, irrespective of how GDP is measured. It seems that the LDM, which contains
logarithmic terms in its formulae, gives more stable decomposition results. In contrast, the RLM tends to introduce greater ‘overlaps’ among effects such that
the estimated effects are larger in absolute terms and the degree of cancellation among effects is greater when they are added up to give the actual total change.
This is illustrated in a numerical example in the Appendix A, which shows that, when the amplitude of variations in explanatory variables increases, the RLM
yields less stable decomposition results as compared to the LDM. It may, therefore, be suggested that the results given by the LDM are more robust than those given
by the RDM.
5. Impacts of the choice of GDP measure
