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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.
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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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