Properties and linkages of some index decomposition analysis methods

We study the properties and linkages of some popular index decomposition analysis (IDA) methods in energy and carbon emission analyses. Specifically, we introduce a simple relationship between the arithmetic mean Divisia index (AMDI) method and the logarithmic mean Divisia index method I (LMDI I), and show that such a relationship can be extended to cover most IDA methods linked to the Divisia index. We also formalize the relationship between the Laspeyres index method and the Shapley value in the IDA context. Similarly, such a relationship can be extended to cover other IDA methods linked to the Laspeyres index through defining the characteristic function in the Shapley value. It is found that these properties and linkages apply to decomposition of changes conducted additively. Similar properties and linkages cannot be established in the multiplicative case. The implications of the findings on IDA studies are discussed.