A new energy decomposition method, called the Log-Mean Divisia Index Method I (LMDI I), is presented. It has the desirable properties of perfect decomposition and consistency in aggregation. Perfect decomposition ensures that the decomposition results obtained do not contain a residual term. Consistency in aggregation allows estimates for sub-groups to be aggregated in a consistent manner. The formulation of the new method and the usefulness of aggregation consistency in energy decomposition studies are described. Two case studies on energy-related CO2 emissions are presented.
The technique of decomposing an aggregate energy indicator to give quantitative measures of the relative contributions of a set of pre-defined factors leading to the change in the aggregate indicator was first proposed in the late 1970s. A recent review of this line of research is reported in Ang and Zhang [1]. Researchers have proposed many energy decomposition methods but most of them leave an unexplained residual term in the decomposition results. Since the purpose of a decomposition study is to quantify the relative contributions of the pre-defined factors to the change in the interested aggregate, this purpose would be defeated if a large part of the change in the aggregate indicator appears as a residual and is left unexplained. This issue has been discussed by Liu et al. [2] and Ang and Choi [3]. Based on the Divisia index, Ang and Choi [3] proposed a decomposition method that gives perfect decomposition, i.e. satisfying the factor reversal test in the index number problem whereby the results obtained do not contain a residual term. We shall refer to it as the Log-Mean Divisia Index Method II (LMDI II) for easy reference and reasons to be given below.
The use of the LMDI II resolves the residual problem. However, this method is not consistent in aggregation. In energy decomposition studies, sub-groups may be formed by sector, country, fuel type, or any other attribute. Decomposition may be carried out at the sub-group level. Consistency in aggregation allows the results obtained for sub-groups to be aggregated to a higher aggregation level in a consistent manner. It is a useful property in many energy decomposition applications. In industrial energy decomposition, for instance, issues related to sub-grouping of industrial activities and linkages between estimates of effects at different levels of sector disaggregation are dealt with in Ang [4], [5].
In this paper, we propose a decomposition method that is perfect in decomposition and consistent in aggregation. We shall call this new method the Log-Mean Divisia Index Method I (LMDI I). The naming of Method I and Method II is consistent with Vartia indices I and II, two economic indices proposed by Vartia [6] which LMDI I and LMDI II are respectively related. We describe the formulation and properties of LMDI I. As the concept of consistency in aggregation is introduced for the first time in the energy decomposition context, it is discussed in detail. Two case studies on energy-related CO2 emission decomposition, one for the manufacturing industry in China and the other for energy consumption in world regions, are presented to illustrate the concept.
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