Exact Relationships Between Fisher Indexes and Theoretical Indexes

Emili Grifell-Tatje and C. Lovell

Chapter Chapter 5 in Advances in Efficiency and Productivity, 2016, pp 97-120 from Springer

Abstract: 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.

Keywords: Implicit Malmquist and implicit Konüs indexes; Fisher indexes; Quantity mix and price mix functions; C43; D24; D61 (search for similar items in EconPapers)
Date: 2016
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Working Paper: Exact Relationships between Fisher Indexes and Theoretical Indexes (2015)
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DOI: 10.1007/978-3-319-48461-7_5

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