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Exact Relationships between Fisher Indexes and Theoretical Indexes

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Abstract

In this paper 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 Malmquist quantity and productivity indexes and Fisher 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 Konüs price and price recovery indexes and Fisher 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.

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  • E. Grifell-TatjeÌ & C. A. K. Lovell, 2015. "Exact Relationships between Fisher Indexes and Theoretical Indexes," CEPA Working Papers Series WP062015, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:104
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    File URL: https://economics.uq.edu.au/files/5103/WP062015.pdf
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    Keywords

    implicit Malmquist indexes; 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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