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A generalized flexible functional form for α-returns to scale

Author

Listed:
  • Hideyuki Mizobuchi

    (Doshisha University)

  • Valentin Zelenyuk

    (The University of Queensland)

Abstract

This study proposes a new flexible functional form for distance functions. This generalizes the existing functional form of Diewert (1992b) by allowing for α-returns to scale technology and employing the quadratic mean of order r aggregator function. Because we allow parameter α to be any strictly positive real number and r to be any non-zero real number, it includes a variety of functional forms as special cases, and all of them can now be considered as flexible functional forms.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:jproda:v:59:y:2023:i:3:d:10.1007_s11123-023-00658-3
    DOI: 10.1007/s11123-023-00658-3
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Jean-Philippe Boussemart & Walter Briec & Hervé Leleu & Paola Ravelojaona, 2019. "On estimating optimal α-returns to scale," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(1), pages 1-11, January.
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    5. Diewert, W E, 1992. "Exact and Superlative Welfare Change Indicators," Economic Inquiry, Western Economic Association International, vol. 30(4), pages 562-582, October.
    6. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-383, June.
    7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    8. 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.
    9. Hill, Robert J., 2006. "Superlative index numbers: not all of them are super," Journal of Econometrics, Elsevier, vol. 130(1), pages 25-43, January.
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    11. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275.
    12. Lau, Lawrence J., 1986. "Functional forms in econometric model building," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 26, pages 1515-1566, Elsevier.
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    More about this item

    Keywords

    Productivity and competitiveness; Flexible functional form; Distance function; α-returns to scale; Quadratic-mean-of-order-r function; CES function;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • 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

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