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Measuring Productivity by Quadratic-mean-of-order-of-r Indexes

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Abstract

In this paper, we propose the quadratic-mean-of-order-of-r indexes of output, input and productivity and show that all index number formulae belonging to this family are superlative indexes. In turn, this helps by deriving a generalization of the well-known Diewert’s theorem about equivalence of Fisher and Malmquist indexes. Our results also give new justifications for output and input comparison and productivity measurement via other interesting indexes such as the implicit Walsh index.

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  • Hideyuki Mizobuchi & Valentin Zelenyuk, 2018. "Measuring Productivity by Quadratic-mean-of-order-of-r Indexes," CEPA Working Papers Series WP062018, School of Economics, University of Queensland, Australia.
  • Handle: RePEc:qld:uqcepa:127
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    File URL: https://economics.uq.edu.au/files/8401/WP062018.pdf
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    1. Diewert, W. Erwin & Fox, Kevin J., 2014. "Reference technology sets, Free Disposal Hulls and productivity decompositions," Economics Letters, Elsevier, vol. 122(2), pages 238-242.
    2. Hideyuki Mizobuchi, 2017. "A superlative index number formula for the Hicks-Moorsteen productivity index," Journal of Productivity Analysis, Springer, vol. 48(2), pages 167-178, December.
    3. Balk, Bert M, 1993. "Malmquist Productivity Indexes and Fisher Ideal Indexes: Comment," Economic Journal, Royal Economic Society, vol. 103(418), pages 680-682, May.
    4. Diewert, W. Erwin & Fox, Kevin J., 2017. "Decomposing productivity indexes into explanatory factors," European Journal of Operational Research, Elsevier, vol. 256(1), pages 275-291.
    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. Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor (ed.), 2016. "Advances in Efficiency and Productivity," International Series in Operations Research and Management Science, Springer, number 978-3-319-48461-7, December.
    7. Allen, Robert C & Diewert, W Erwin, 1981. "Direct versus Implicit Superlative Index Number Formulae," The Review of Economics and Statistics, MIT Press, vol. 63(3), pages 430-435, August.
    8. Subodh Kumar & R. Robert Russell, 2002. "Technological Change, Technological Catch-up, and Capital Deepening: Relative Contributions to Growth and Convergence," American Economic Review, American Economic Association, vol. 92(3), pages 527-548, June.
    9. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    10. Daniel J. Henderson & R. Robert Russell, 2005. "Human Capital And Convergence: A Production-Frontier Approach ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(4), pages 1167-1205, November.
    11. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    12. W. Erwin Diewert, 1980. "Aggregation Problems in the Measurement of Capital," NBER Chapters, in: The Measurement of Capital, pages 433-538, National Bureau of Economic Research, Inc.
    13. Usher, Dan (ed.), 1980. "The Measurement of Capital," National Bureau of Economic Research Books, University of Chicago Press, number 9780226843001, January.
    14. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
    15. Hill, Robert J., 2006. "Superlative index numbers: not all of them are super," Journal of Econometrics, Elsevier, vol. 130(1), pages 25-43, January.
    16. Bjurek, Hans, 1996. "The Malmquist Total Factor Productivity Index," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 303-313, June.
    17. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, November.
    18. Diewert, W. E., 1973. "Functional forms for profit and transformation functions," Journal of Economic Theory, Elsevier, vol. 6(3), pages 284-316, June.
    19. Dan Usher, 1980. "The Measurement of Capital," NBER Books, National Bureau of Economic Research, Inc, number ushe80-1, January.
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    More about this item

    Keywords

    index numbers; superlative index; quadratic-mean-of-order-of-r index; Fisher index; Malmquist index; implicit Walsh index; time reversal test;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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