Energy decomposition analysis: the generalized Fisher index revisited

It is generally believed that index decomposition analysis (IDA) and input-output structural decomposition analysis (SDA) (Rose and Casler, 1996; Dietzenbacher and Los, 1998) are different approaches in energy studies; see for instance Ang, Liu and Chung (2004). In this paper it is shown that the generalized Fisher approach, introduced in IDA by Ang, c.s. (2004) for the decomposition of an aggregate change in a variable in factors is equivalent to SDA. They base their formulae on the very complicated generic formula that Shapley (1953) derived for his value of n-person games, and mention that Siegel (1945) gave their formulae using a different route. In this paper tables are given from which the formulae of the generalized Fisher approach can easily be derived for the cases of factors. It is shown that these tables can easily be extended to cover the cases of r=5 and r=6 factors.