Exact relationships between fisher indexes and theoretical indexes

Emili Grifell-Tatjé, C. A Knox Lovell

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2 Citations (Scopus)

Abstract

© Springer International Publishing AG 2016. 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.
Original languageEnglish
Title of host publicationInternational Series in Operations Research and Management Science
Pages97-120
Number of pages23
Volume249
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

  • Fisher indexes
  • Implicit Malmquist and implicit Konüs indexes
  • Quantity mix and price mix functions

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    Grifell-Tatjé, E., & Lovell, C. A. K. (2016). Exact relationships between fisher indexes and theoretical indexes. In International Series in Operations Research and Management Science (Vol. 249, pp. 97-120) https://doi.org/10.1007/978-3-319-48461-7_5