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A Superlative Index Number Formula for the Hicks-Moorsteen Productivity Index

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  • Hideyuki Mizobuchi

    (Faculty of Economics, Ryukoku University)

Abstract

The Malmquist and Hicks-Moorsteen productivity indexes are the two most widely used theoretical indexes for measuring productivity growth. Since these productivity indexes are defined by unknown distance functions, it is necessary to estimate the distance functions to compute them in principle. On the other hand, the Törnqvist productivity index is an empirical index number formula that is directly computable from the prices and quantities of the inputs and outputs alone. Caves, Christensen, and Diewert (1982) (CCD) imply that the Malmquist index coincides with the Törnqvist index, under profit maximising behaviour and constant returns to scale technology. The purpose of the present paper is to point out that the Hicks-Moorsteen productivity index coincides with the Törnqvist productivity index under the same condition. We emphasize that the condition of constant returns to scale is indispensable for deriving the equivalence between two indexes. Moreover, even when this condition is relaxed to the 𠛼 returns to scale, the equivalence between the Hicks-Moorsteen and Törnqvist productivity indexes is shown to hold true.

Suggested Citation

  • Hideyuki Mizobuchi, 2016. "A Superlative Index Number Formula for the Hicks-Moorsteen Productivity Index," CEPA Working Papers Series WP032016, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:113
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    File URL: https://economics.uq.edu.au/files/5052/WP032016.pdf
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    References listed on IDEAS

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    1. Bjurek, Hans, 1996. " The Malmquist Total Factor Productivity Index," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 303-313, June.
    2. Caves, Douglas W & Christensen, Laurits R, 1980. "The Relative Efficiency of Public and Private Firms in a Competitive Environment: The Case of Canadian Railroads," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 958-976, October.
    3. Nemoto, Jiro & Goto, Mika, 2005. "Productivity, efficiency, scale economies and technical change: A new decomposition analysis of TFP applied to the Japanese prefectures," Journal of the Japanese and International Economies, Elsevier, vol. 19(4), pages 617-634, December.
    4. Hideyuki Mizobuchi, 2015. "Productivity Indexes under Hicks Neutral Technical Change," CEPA Working Papers Series WP072015, School of Economics, University of Queensland, Australia.
    5. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    6. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
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    10. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (II): Applications of the Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number fuss1978a.
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    Cited by:

    1. Hideyuki Mizobuchi, 2017. "Productivity indexes under Hicks neutral technical change," Journal of Productivity Analysis, Springer, vol. 48(1), pages 63-68, August.

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    Keywords

    Törnqvist productivity index; Hicks-Moorsteen productivity index; Malmquist productivity index; Translog functional form; Superlative index number;
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