In this paper we extend the methodology of index decomposition analysis (IDA) in energy studies by quantifying the contribution of individual attributes to the percent change of factors such as the real energy intensity index and structural change index. We apply the proposed method to the real energy intensity index in the multiplicative Logarithmic Mean Divisia Index (M-LMDI) approach, a major IDA technique. Since the M-LMDI is based on geometric mean type indices and chain computation, we need some appropriate method to cope with the difficulties that arise. We present a numerical illustration of the proposed method using the energy consumption and real value added data of the US manufacturing industry, and compare the results obtained by the Fisher real energy intensity index.
There is parallelism between the methodology of national accounts and that of index decomposition analysis (IDA) in the energy and environmental economics literature. Both methodologies are based on the same principle, namely the index number theory. In national accounts, the nominal GDP index is multiplicatively decomposed into the real GDP which is a quantity index and the GDP deflator which is a price index. In IDA, the aggregate energy intensity index, say expressed in terms of industrial energy consumption divided by industrial production, is multiplicatively decomposed into the real energy intensity index and the industrial structure (or product mix) index. See, for example, Choi and Ang, 2003, Boyd and Roop, 2004. In the energy economics literature, changes in the real energy intensity index are often used as a proxy for energy efficiency changes, while the industrial structure index captures changes in industrial structure.
The chain computation method was introduced together with the Divisia (log-change) decomposition method to IDA in Ang (1994). This approach was introduced to national accounts a little later. In 1996 the national statistical offices of the US and Canada changed the quantity index of the real GDP from the fixed weight Laspeyres index to the chained Fisher index. This was followed by other countries and all OECD countries now compile their real GDP using chained quantity index. This switch raised a problem for the national accounts practitioners, namely the “additive decomposition” of the real GDP using the chained Fisher quantity index.
The purpose of the additive decomposition is to allocate the percent change of the aggregate such as real GDP to various sources associated with this change. Let Q be an aggregate of interest. It is natural to define the additive decomposition for the Laspeyres index in the following arithmetic mean index form:
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