Handling zero values in the logarithmic mean Divisia index decomposition approach

The Logarithmic Mean Divisia Index (LMDI) decomposition approach has many desirable properties. It has been recommended by Ang [2004a. Decomposition analysis for policymaking in energy: which is the preferred methods? Energy Policy 32, 1131–1139] for adoption in energy and energy-related environmental index decomposition analysis (IDA). A complication associated with this approach is the treatment of zero values in the data set. Several studies show that replacing the zero values with a small number gives converging results. In a recent paper, Wood and Lenzen [Zero-value problems of the logarithmic mean Divisia index decomposition method. Energy Policy, in press] argue that this strategy is not necessarily robust and recommend using the analytical limits proposed in Ang et al. [1998. Factorizing changes in energy and environmental indicators through decomposition. Energy 23, 489–495]. We compare these two strategies and extend earlier works by generalizing the analytical limits of LMDI.