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Decomposing Bjurek Productivity Indexes into Explanatory Factors

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  • Diewert, Erwin
  • Fox, Kevin J.

Abstract

Caves, Christensen, Diewert introduced Malmquist output, input and productivity indexes into production theory in a systematic way. This paper revisits the debate on how to decompose Bjurek’s concept of a Malmquist productivity index into explanatory factors, with a focus on extracting technical progress, technical efficiency change, and returns to scale components. In order to define these components, a reference technology is required. The paper does not make any convexity assumptions on the reference technology but instead follows the example of Tulkens and his coauthors in assuming that the reference technology satisfies free disposability assumptions. The existence and properties of the underlying distance functions of the productivity decomposition are proven under relatively unrestrictive assumptions. The paper provides for the first time a theoretical justification for the geometric average form of the Bjurek productivity index.

Suggested Citation

  • Diewert, Erwin & Fox, Kevin J., 2014. "Decomposing Bjurek Productivity Indexes into Explanatory Factors," Economics working papers erwin_diewert-2014-32, Vancouver School of Economics, revised 30 Jun 2014.
  • Handle: RePEc:ubc:bricol:erwin_diewert-2014-32
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    References listed on IDEAS

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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. R. Russell & William Schworm, 2009. "Axiomatic foundations of efficiency measurement on data-generated technologies," Journal of Productivity Analysis, Springer, vol. 31(2), pages 77-86, April.
    3. Ray, Subhash C & Desli, Evangelia, 1997. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries: Comment," American Economic Review, American Economic Association, vol. 87(5), pages 1033-1039, December.
    4. Afriat, Sidney N, 1972. "Efficiency Estimation of Production Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(3), pages 568-598, October.
    5. Grosskopf, S, 1986. "The Role of the Reference Technology in Measuring Productive Efficiency," Economic Journal, Royal Economic Society, vol. 96(382), pages 499-513, June.
    6. Shawna Grosskopf, 2003. "Some Remarks on Productivity and its Decompositions," Journal of Productivity Analysis, Springer, vol. 20(3), pages 459-474, November.
    7. C. Lovell, 2003. "The Decomposition of Malmquist Productivity Indexes," Journal of Productivity Analysis, Springer, vol. 20(3), pages 437-458, November.
    8. Henry Tulkens, 1993. "On FDH efficiency analysis: Some methodological issues and applications to retail banking, courts, and urban transit," Journal of Productivity Analysis, Springer, vol. 4(1), pages 183-210, June.
    9. Bjurek, Hans, 1996. " The Malmquist Total Factor Productivity Index," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 303-313, June.
    10. Diewert, Erwin & Fox, Kevin J., 2010. "Malmquist and Törnqvist Productivity Indexes: Returns to Scale and Technical Progress with Imperfect Competition," Economics working papers erwin_diewert-2010-5, Vancouver School of Economics, revised 13 Jul 2010.
    11. Valentin Zelenyuk, 2014. "Scale efficiency and homotheticity: equivalence of primal and dual measures," Journal of Productivity Analysis, Springer, vol. 42(1), pages 15-24, August.
    12. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
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    15. 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.
    16. Kerstens, Kristiaan & Van de Woestyne, Ignace, 2014. "Comparing Malmquist and Hicks–Moorsteen productivity indices: Exploring the impact of unbalanced vs. balanced panel data," European Journal of Operational Research, Elsevier, vol. 233(3), pages 749-758.
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    20. W. Diewert & Kevin Fox, 2010. "Malmquist and Törnqvist productivity indexes: returns to scale and technical progress with imperfect competition," Journal of Economics, Springer, vol. 101(1), pages 73-95, September.
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    Cited by:

    1. Hideyuki Mizobuchi, 2015. "Multiple Directions for Measuring Biased Technical Change," CEPA Working Papers Series WP092015, School of Economics, University of Queensland, Australia.

    More about this item

    Keywords

    Productivity indexes; Malmquist Moorsteen Bjurek indexes; technical efficiency; technical progress; returns to scale; Data Envelopment Analysis; Free;

    JEL classification:

    • 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
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production

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