The name is absent

energy sector in transforming energy³, while wit captures the final energy
consumption per GDP unit (final energy intensity index).

Secondly, to clarify the role of both factors in explaining energy intensity
inequalities across countries, we define two hypothetical vectors of primary
energy consumption per GDP unit and we let just one of the values of the
factors included in (2) diverge from the mean. Accordingly, we obtain the
following fictitious factors⁴:

e_it^f = f_it * w_t                        (3)

ei^wt = ft*wit                      (4)

where ft y wt are world averages of the factor being considered.

Resorting to Duro’s (2003) methodology and Duro and Padilla (2006), using the
Theil index (Theil, 1967)⁵ as the benchmark inequality index allows a synthetic
decomposition of global energy intensity inequalities into three factors:

T (e, p) = T (e^f, p) + T (e^w, p) + log 11 + ^σ ∣             (5)

ч     ^et J

T(e,p) = Tf + Tw + interf,w                         (6)

where σ is the covariance (weighted) between the two factors and e_t^f is the
world average of the first fictitious factor; e is the energy intensity and p the
weight in global GDP.

³ Nevertheless, the index will not only depend on how efficient countries are in the conversion of
one or other type of energy but also on their different energy mix. For instance, according to the
International Energy Agency, the heat generated by nuclear power plants is considered primary
energy while for hydro-electric stations, wind or photovoltaic solar power system, only the
energy value of the electricity generated is taken into account. Consequently, the efficiency in
transforming nuclear energy is less than in the case of fossil fuels, while it is always greater for
renewable energy.

⁴ This methodology as developed by Duro (2003) to analyze spatial income inequality.

⁵ The Theil index has been used in different works on environmental distribution (Alcantara and
Duro, 2004; Duro and Padilla, 2006; Padilla and Serrano, 2006; Padilla and Duro, 2009;
Cantore and Padilla, 2010a; Duro et al., 2010). Cowell (1995) highlights its analytical
advantages, which include its ability to decompose additively a series of multiplicative factors.
This is due to the fact that it is a logarithmic function.

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