The name is absent

Thus, total inequality is perfectly decomposed into two indices that capture the
partial contribution of each multiplicative factor accounted for in global inequality
(Tf captures the contribution of energy transformation index and Tw the
contribution of final energy intensity index), and an interaction term representing
the interfactorial correlation (interf,w)⁶. A positive value of this last component
would suggest that countries that are not efficient in energy transformation
would also tend to be inefficient in energy use. So, the two inequalities would be
self-reinforcing. In turn, a negative value would mean that less efficient
countries in energy transformation tend to be more inefficient in final energy
consumption.

It should be noted that, as the factors have been formulated in equations (3)
and (4), the importance of each factor in the decomposition exercise can be
seen as the variation across countries of the factor under analysis, while the
remaining factors are set equal to mean.

On the other hand, this factorial decomposition methodology can be extended
to subgroup components of inequality. That is, the previous multiplicative
factorial decomposition can be combined with subgroup decomposition. This
would divide global inequality into an element of inter-group inequality and
another of intra-group inequality. The well known Theil index can be easiliy
decomposed into population subgroup. We adapt it here for the study of
inequalities in energy intensity across countries (Theil, 1967; Shorrocks, 1980)

/   . G    ZXG     ( e ^

T(^e,p) = ∑PgT(^e)g ⁺∑Pg *ln —

g=1              g=1         V ^eg J

⁶ Mind that if in addition σ_f,w is sufficiently small, the decomposition could be approached as:

T(e,p)≈ tVe^f,pJ + tVe^w,pJ+fw

V J V J    _ef_t

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