@inbook{373a37e6e71d4ab5866278bb934c3921,
title = "Exact relationships between fisher indexes and theoretical indexes",
abstract = "We develop exact relationships between empirical Fisher indexes and their theoretical Malmquist and Kon{\"u}s 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 Kon{\"u}s quantity and productivity indexes to establish exact relationships between empirical Fisher price and price recovery indexes and theoretical Kon{\"u}s price and price recovery indexes. We then show that Kon{\"u}s 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 = "Fisher indexes, Implicit Malmquist and implicit Kon{\"u}s indexes, Quantity mix and price mix functions",
author = "Emili Grifell-Tatj{\'e} and Lovell, {C. A.Knox}",
note = "{\textcopyright} Springer International Publishing AG 2016.",
year = "2016",
month = dec,
day = "24",
doi = "10.1007/978-3-319-48461-7_5",
language = "English",
isbn = "978-3-319-48459-4",
volume = "249",
series = "Operations Research & Management Science,",
publisher = "Springer",
pages = "97--120",
booktitle = "Advances in Efficiency and Productivity",
}