Negative-value problems of the logarithmic mean Divisia index decomposition approach

doi:10.1016/j.enpol.2005.12.004

Energy Policy

Volume 35, Issue 1, January 2007, Pages 739-742

https://doi.org/10.1016/j.enpol.2005.12.004 Get rights and content

Abstract

An issue that has not been fully resolved in the Logarithmic Mean Divisia Index (LMDI) decomposition approach is how to deal with negative values in the data set. We provide an analytical solution to this problem and illustrate with an example. With the issue resolved, the LMDI approach can now be generally applied to any decomposition situation.

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 by $C = \sum_{ij} f_{i} d_{ij} u_{j} y,$ where C is the total CO₂ emissions, f_i is the CO₂ emissions per unit of production for sector i, d_ij is the amount of the ith good produced directly and indirectly to meet one unit of final demand in sector j, u_j 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

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CommunicationNegative-value problems of the logarithmic mean Divisia index decomposition approach

Abstract

Introduction

Section snippets

Strategies and guidelines for handling negative values

Case study

Conclusion

Decomposition analysis for policymaking in energy: which is the preferred method?

Energy Policy

The LMDI approach to decomposition analysis: a practical guide

Energy Policy

A decomposition technique for quantifying real process performance

Production Planning and Control

A generalized Fisher index approach to energy decomposition analysis

Energy Economics

Climate data: insights and observations

Changes in energy intensities of Thai industry between 1981 and 2000: a decomposition analysis

Energy Policy

A time-series analysis of energy-related carbon emissions in Korea

Energy Policy

Measuring thermal efficiency improvement in power generation: the Divisia decomposition approach

Energy

A residual-free decomposition of the sources of carbon dioxide emissions: a case of the Korean industries

Energy

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Decomposition of factors determining the trend of CO2 emissions from car travel in Great Britain (1970–2000)

Ecological Economics

Communication
Negative-value problems of the logarithmic mean Divisia index decomposition approach

Decomposition of factors determining the trend of CO₂ emissions from car travel in Great Britain (1970–2000)