Exact Relationships between Fisher Indexes and Theoretical Indexes

E. Grifell-TatjeÌ and C. Lovell
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E. Grifell-TatjeÌ: Universitat AutoÌ€noma de Barcelona

No WP062015, CEPA Working Papers Series from University of Queensland, School of Economics

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.

Keywords: implicit Malmquist indexes; implicit Konüs indexes; Fisher indexes; quantity mix and price mix functions (search for similar items in EconPapers)
JEL-codes: C43 D24 D61 (search for similar items in EconPapers)
Date: 2015-06
New Economics Papers: this item is included in nep-eff
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https://economics.uq.edu.au/files/5103/WP062015.pdf (application/pdf)

Related works:
Chapter: Exact Relationships Between Fisher Indexes and Theoretical Indexes (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:qld:uqcepa:104

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