CommunicationNegative-value problems of the logarithmic mean Divisia index decomposition approach
Introduction
The Logarithmic Mean Divisia Index (LMDI) approach has been recommended for adoption in index decomposition analysis (IDA) by Ang, 2004, Ang, 2005. Lately, there have been a growing number of studies using this approach to analyse changes in an aggregate, including energy consumption or intensity, greenhouse gas emissions or intensity, electricity generation efficiency, water consumption, manufacturing process quality, and inventory turnover.1 The LMDI approach uses models that have logarithmic terms. Complications arise when the data set contains zero or negative values. The occurrence of zero or negative values is rare in energy IDA studies but it is likely in gas emissions IDA studies and in structural decomposition analysis (SDA). The zero-value problem has been resolved and the proposed procedures can be found in Ang and Liu (in press) and Wood and Lenzen (in press).
The negative-value problem of LMDI was first raised by Chung and Rhee (2001) where the CO2 emissions decomposition problem they study has negative values in the data set. Ang et al. (2004) and Lenzen (2006) point out that the LMDI approach is not negative-value robust. Ang (2004) mentions the need to opt for an alternative decomposition approach when the data set has negative values. In a recent paper, Rhee and Chung (in press) reiterate this limitation of the LMDI approach.
The first attempt to deal with the negative-value problem of LMDI is reported in Wu et al. (in press). In their study on the dynamics of energy-related CO2 emissions in China, negative values occur for variables such as exports and stock changes. They tackle the problem in two different situations which will be pointed out in the next section. In this paper, we extend and refine their ideas and integrate them with the procedure for handling zero values in Ang and Liu (in press), and then present the guidelines for dealing with negative and/or zero values in a unified framework. An illustrative example will be presented. In line with Ang and Liu (in press), we shall focus on the additive LMDI I method which has a simpler functional form in the LMDI family of decomposition methods (Ang, 2004). The analysis, however, can be similarly extended to other LMDI methods.
Section snippets
Strategies and guidelines for handling negative values
For a data set that contains negative values, we group the changes that involve these values into three types: Type I from one negative value to another negative value; Type II from/to a negative value to/from a zero, and Type III from/to a negative value to/from a positive value.
Case study
In Chung and Rhee (2001), the change in total energy-related CO2 emissions from 1990 to 1995 in Korea is decomposed. The emission identity is given bywhere C is the total CO2 emissions, fi is the CO2 emissions per unit of production for sector i, dij is the amount of the ith good produced directly and indirectly to meet one unit of final demand in sector j, uj is the share of the final demand in the jth sector, y is the GDP which is the sum of all the sectoral final demands. The
Conclusion
We describe the procedure to deal with negative values for the LMDI approach. We integrate the procedure with that for handling zero values in Ang and Liu (in press) to arrive at a set of guidelines to deal with all possible cases of changes that involve negative and/or zero values using the AL strategy. With both the negative-value problem and zero-value problem resolved, the LMDI approach can now be applied to any decomposition situation, including SDA where negative and/or zero values are
References (26)
Decomposition analysis for policymaking in energy: which is the preferred method?
Energy Policy
(2004)The LMDI approach to decomposition analysis: a practical guide
Energy Policy
(2005)- Ang, B.W., Liu, N., Handling zero values in the logarithmic mean Divisia index decomposition approach. Energy Policy,...
- et al.
A decomposition technique for quantifying real process performance
Production Planning and Control
(2000) - et al.
A generalized Fisher index approach to energy decomposition analysis
Energy Economics
(2004) - et al.
Climate data: insights and observations
(2004) - et al.
Changes in energy intensities of Thai industry between 1981 and 2000: a decomposition analysis
Energy Policy
(2005) - et al.
A time-series analysis of energy-related carbon emissions in Korea
Energy Policy
(2001) - et al.
Measuring thermal efficiency improvement in power generation: the Divisia decomposition approach
Energy
(2002) - et al.
A residual-free decomposition of the sources of carbon dioxide emissions: a case of the Korean industries
Energy
(2001)
A note on trends in European industrial pollution intensities: a Divisia index approach
The Energy Journal
Decomposing the variation of aggregate electricity intensity in Spanish industry
Energy
Decomposition of factors determining the trend of CO2 emissions from car travel in Great Britain (1970–2000)
Ecological Economics
Cited by (117)
CO<inf>2</inf> emission-mitigation pathways for China's data centers
2024, Resources, Conservation and RecyclingThe synergy between temporal and spatial effects of human activities on CO<inf>2</inf> emissions in Chinese cities
2023, Environmental Impact Assessment ReviewIntersectoral transfers and drivers of net CO<inf>2</inf> emissions in China incorporating sources and sinks
2023, Technological Forecasting and Social Change