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Exact Relationships Between Fisher Indexes and Theoretical Indexes

In: Advances in Efficiency and Productivity

Author

Listed:
  • Emili Grifell-Tatjé

    (Universitat Autònoma de Barcelona)

  • C. A. Knox Lovell

    (University of Queensland)

Abstract

We develop exact relationships between empirical Fisher indexes and their theoretical Malmquist and Konüs counterparts. We begin by using implicit Malmquist price and price recovery indexes to establish exact relationships between empirical Fisher quantity and productivity indexes and theoretical Malmquist quantity and productivity indexes. We then show that Malmquist quantity and productivity indexes and Fisher price and price recovery indexes “almost” satisfy the product test with the relevant value change, and we derive a quantity mix function that ensures satisfaction of the product test. We next use implicit Konüs quantity and productivity indexes to establish exact relationships between empirical Fisher price and price recovery indexes and theoretical Konüs price and price recovery indexes. We then show that Konüs price and price recovery indexes and Fisher quantity and productivity indexes “almost” satisfy the product test with the relevant value change, we derive a price mix function that ensures satisfaction of the product test, and we show that this price mix function differs fundamentally from the quantity mix function relating Malmquist and Fisher indexes.

Suggested Citation

  • Emili Grifell-Tatjé & C. A. Knox Lovell, 2016. "Exact Relationships Between Fisher Indexes and Theoretical Indexes," International Series in Operations Research & Management Science, in: Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor (ed.), Advances in Efficiency and Productivity, chapter 0, pages 97-120, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-48461-7_5
    DOI: 10.1007/978-3-319-48461-7_5
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    Keywords

    Implicit Malmquist and implicit Konüs indexes; Fisher indexes; Quantity mix and price mix functions;
    All these keywords.

    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
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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