Energy Indicators for Sustainable Development: Guidelines and Methodologies International Atomic Energy Agency United Nations Department of Economic and Social Affairs International Energy Agency Eurostat European Environment Agency

A
t
/A
0
 = A
t
∑
j
S
j,o 
* I
j,0
/ E
0
.
(A3.2) 
Similarly, the hypothetical change in energy use given constant aggregate activity and 
energy intensities but varying sectoral structure — the structure effect — is 
S
t
/S
0
 = A
0
∑
j
S
j,t 
* I
j,0
/ E
0
,
(A3.3) 
and the proportional change in energy use given constant activity and structure but 
varying energy intensities — the intensity effect — is 
I
t
/I
0
 = A
0
∑
j
S
j,o 
* I
j,t
/ E
0 
.
(A3.4) 
3
There are different index-number techniques that permit the analysis of this relationship over time. 
Here, the Laspeyeres indices approach is used. The Laspeyres approach yields a residual term as a 
result of interaction among the other factors in the decomposition. This means that the changes in 
the decomposition factors do not necessarily always add up exactly to the changes in energy use. In 
most cases, the residual term is relatively small compared to the effects of the other factors. 

---

159 
Thus through calculating the relative impact on energy use from changes in each of 
these components, the impacts on energy use related to improved end-use energy 
efficiency (reductions in energy intensities) can be isolated from changes derived 
from shifts in the activity and structure components. 
The resulting indices from each sector defined above can be combined further and 
weighted at base-year values of energy use to measure the impact of changes in either 
energy intensities or economy-wide activity and structure components on overall 
energy use. With E in this case representing energy use at the national level, the 
decomposition equations take the form