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Quadratic-mean-of-order-r Indexes of Output, Input and Productivity

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Abstract

The use of appropriate index numbers is indispensable for measuring economic phenomena precisely. Various indexes have been proposed in the literature, spanning several centuries. In this paper, we propose the quadratic-mean-of-order-𝑟 indexes of output, input and productivity. Each index is a family of indexes that unify many of the existing indexes, including the most popular ones. We also show that all index number formulae belonging to these families are superlative indexes. This is considered as a generalization of the equivalence of Fisher and Malmquist indexes, shown by Diewert (1992). Our results also give new justifications for output and input comparison and productivity measurement via other interesting indexes such as the implicit Walsh index. We also apply the discussed indexes to the US industry production accounts.

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  • Hideyuki Mizobuchi & Valentin Zelenyuk, 2020. "Quadratic-mean-of-order-r Indexes of Output, Input and Productivity," CEPA Working Papers Series WP032020, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:146
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    Cited by:

    1. Valentin Zelenyuk, 2023. "Productivity analysis: roots, foundations, trends and perspectives," Journal of Productivity Analysis, Springer, vol. 60(3), pages 229-247, December.
    2. Nicholas Oulton, 2023. "The effect of changes in the terms of trade on GDP and welfare: A Divisia approach to the System of National Accounts," Manchester School, University of Manchester, vol. 91(4), pages 261-282, July.
    3. Hideyuki Mizobuchi & Valentin Zelenyuk, 2023. "A generalized flexible functional form for α-returns to scale," Journal of Productivity Analysis, Springer, vol. 59(3), pages 217-224, June.
    4. Hideyuki Mizobuchi & Valentin Zelenyuk, 2021. "Quadratic-mean-of-order-r indexes of output, input and productivity," Journal of Productivity Analysis, Springer, vol. 56(2), pages 133-138, December.
    5. Nicholas Oulton, 2022. "The Divisia approach to measuring output and productivity: with an application to the BEA-BLS integrated industry-level production account, 1987-2020," Discussion Papers 2217, Centre for Macroeconomics (CFM).
    6. Nicholas Oulton, 2021. "The effect of changes in the terms of trade on GDP and welfare: a Divisia approach to the SNA," Discussion Papers 2126, Centre for Macroeconomics (CFM).
    7. Hideyuki Mizobuchi, 2022. "Measuring the shift in the short-run production frontier," Evolutionary and Institutional Economics Review, Springer, vol. 19(1), pages 271-300, April.
    8. Valentin Zelenyuk, 2021. "Performance Analysis: Economic Foundations & Trends," CEPA Working Papers Series WP162021, School of Economics, University of Queensland, Australia.

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    More about this item

    Keywords

    index numbers; superlative index; quadratic-mean-of-order-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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