Generalized Fisher index or Siegel-Shapley decomposition?
It is generally believed that index decomposition analysis (IDA) and input-output structural decomposition analysis (SDA) [Rose, A., Casler, S., Input-output structural decomposition analysis: a critical appraisal, Economic Systems Research 1996; 8; 33-62; Dietzenbacher, E., Los, B., Structural decomposition techniques: sense and sensitivity. Economic Systems Research 1998;10; 307-323] are different approaches in energy studies; see for instance Ang et al. [Ang, B.W., Liu, F.L., Chung, H.S., A generalized Fisher index approach to energy decomposition analysis. Energy Economics 2004; 26; 757-763]. In this paper it is shown that the generalized Fisher approach, introduced in IDA by Ang et al. [Ang, B.W., Liu, F.L., Chung, H.S., A generalized Fisher index approach to energy decomposition analysis. Energy Economics 2004; 26; 757-763] for the decomposition of an aggregate change in a variable in rÂ =Â 2, 3 or 4 factors is equivalent to SDA. They base their formulae on the very complicated generic formula that Shapley [Shapley, L., A value for n-person games. In: Kuhn H.W., Tucker A.W. (Eds), Contributions to the theory of games, vol. 2. Princeton University: Princeton; 1953. p. 307-317] derived for his value of n-person games, and mention that Siegel [Siegel, I.H., The generalized "ideal" index-number formula. Journal of the American Statistical Association 1945; 40; 520-523] gave their formulae using a different route. In this paper tables are given from which the formulae of the generalized Fisher approach can easily be derived for the cases of rÂ =Â 2, 3 or 4 factors. It is shown that these tables can easily be extended to cover the cases of rÂ =Â 5 and rÂ =Â 6 factors.
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- Ang, B. W. & Liu, F. L. & Chew, E. P., 2003. "Perfect decomposition techniques in energy and environmental analysis," Energy Policy, Elsevier, vol. 31(14), pages 1561-1566, November.
- Albrecht, Johan & Francois, Delphine & Schoors, Koen, 2002. "A Shapley decomposition of carbon emissions without residuals," Energy Policy, Elsevier, vol. 30(9), pages 727-736, July.
- Mark De Haan, 2001. "A Structural Decomposition Analysis of Pollution in the Netherlands," Economic Systems Research, Taylor & Francis Journals, vol. 13(2), pages 181-196.
- Erik Dietzenbacher & Bart Los, 1998. "Structural Decomposition Techniques: Sense and Sensitivity," Economic Systems Research, Taylor & Francis Journals, vol. 10(4), pages 307-324.
- Ang, B.W. & Zhang, F.Q., 2000. "A survey of index decomposition analysis in energy and environmental studies," Energy, Elsevier, vol. 25(12), pages 1149-1176.
- Gale A. Boyd and Joseph M. Roop, 2004. "A Note on the Fisher Ideal Index Decomposition for Structural Change in Energy Intensity," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 87-102.
- Chung, Hyun-Sik & Rhee, Hae-Chun, 2001. "A residual-free decomposition of the sources of carbon dioxide emissions: a case of the Korean industries," Energy, Elsevier, vol. 26(1), pages 15-30.
- Ang, B.W. & Liu, F.L. & Chung, Hyun-Sik, 2004. "A generalized Fisher index approach to energy decomposition analysis," Energy Economics, Elsevier, vol. 26(5), pages 757-763, September.
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