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Multiplicative Decomposition And Index Number Theory: An Empirical Application Of The Sato-Vartia Decomposition

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  • Paul De Boer

Abstract

In de Boer (2008), additive decompositions of aggregate changes in a variable into its factors were considered. We proposed using the 'ideal' Montgomery decomposition, developed in index number theory as an alternative to the commonly used methods in structural decomposition analysis, and applied it to the example analyzed by Dietzenbacher and Los (1998) (D&L). In this paper we consider multiplicative decompositions and show that the method proposed by D&L of taking the geometric mean of all elementary decompositions is 'ideal'. However, it requires the computation of an ever-increasing number of decompositions when the number of factors increases. As an alternative, we propose using the Sato-Vartia decomposition, which is also 'ideal', but requires the computation of only one decomposition. Application to the example of D&L reveals that the two methods yield results that are very close to each other.

Suggested Citation

  • Paul De Boer, 2009. "Multiplicative Decomposition And Index Number Theory: An Empirical Application Of The Sato-Vartia Decomposition," Economic Systems Research, Taylor & Francis Journals, vol. 21(2), pages 163-174.
    • Handle: RePEc:taf:ecsysr:v:21:y:2009:i:2:p:163-174
    DOI: 10.1080/09535310902937638
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    Cited by:

    1. Martin Lábaj & Karol Morvay & Martin Hudcovský, 2015. "Labour Elasticity in V4 countries: Structural decomposition analysis," Department of Economic Policy Working Paper Series 009, Department of Economic Policy, Faculty of National Economy, University of Economics in Bratislava.
    2. de Boer, P.M.C., 2008. "Energy decomposition analysis: the generalized Fisher index revisited," Econometric Institute Research Papers EI 2008-12, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Ana-Isabel Guerra & Ferran Sancho, 2013. "A Linear Price Model With Extractions," EcoMod2013 5113, EcoMod.
    4. Su, Bin & Ang, B.W., 2015. "Multiplicative decomposition of aggregate carbon intensity change using input–output analysis," Applied Energy, Elsevier, vol. 154(C), pages 13-20.
    5. Wang, H. & Ang, B.W. & Su, Bin, 2017. "Assessing drivers of economy-wide energy use and emissions: IDA versus SDA," Energy Policy, Elsevier, vol. 107(C), pages 585-599.
    6. Daniel Dujava, 2012. "Príčiny zaostávania nových členských krajín EÚ: empirická analýza na základe Montgomeryho dekompozície [Causes of Lagging Behind of New Member States of EU: Empirical Analysis by Montgomery Decomposition]," Politická ekonomie, Prague University of Economics and Business, vol. 2012(2), pages 222-244.
    7. Choi, Ki-Hong & Ang, B.W., 2012. "Attribution of changes in Divisia real energy intensity index — An extension to index decomposition analysis," Energy Economics, Elsevier, vol. 34(1), pages 171-176.
    8. Ling Yang & Michael L. Lahr, 2019. "The Drivers of China’s Regional Carbon Emission Change—A Structural Decomposition Analysis from 1997 to 2007," Sustainability, MDPI, vol. 11(12), pages 1-18, June.
    9. Cazcarro, Ignacio & Duarte, Rosa & Sánchez-Chóliz, Julio, 2013. "Economic growth and the evolution of water consumption in Spain: A structural decomposition analysis," Ecological Economics, Elsevier, vol. 96(C), pages 51-61.
    10. Wang, H. & Ang, B.W. & Su, Bin, 2017. "A Multi-region Structural Decomposition Analysis of Global CO2 Emission Intensity," Ecological Economics, Elsevier, vol. 142(C), pages 163-176.
    11. Hui Wang & Chen Pan & B.W. Ang & Peng Zhou, 2021. "Does Global Value Chain Participation Decouple Chinese Development from CO2 Emissions? A Structural Decomposition Analysis," The Energy Journal, , vol. 42(2), pages 183-204, March.
    12. Hong, Jae Pyo & Byun, Jeong Eun & Kim, Pang Ryong, 2016. "Structural changes and growth factors of the ICT industry in Korea: 1995–2009," Telecommunications Policy, Elsevier, vol. 40(5), pages 502-513.
    13. Kirill Muradov, 2021. "Structural decomposition analysis with disaggregate factors within the Leontief inverse," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 10(1), pages 1-17, December.
    14. Zhou, Xiaoyong & Zhou, Dequn & Wang, Qunwei, 2018. "How does information and communication technology affect China's energy intensity? A three-tier structural decomposition analysis," Energy, Elsevier, vol. 151(C), pages 748-759.

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