Quadratic-mean-of-order-r Indexes of Output, Input and Productivity

Hideyuki Mizobuchi () and Valentin Zelenyuk
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Hideyuki Mizobuchi: Faculty of Economics, Ryukoku University

No WP032020, CEPA Working Papers Series from University of Queensland, School of Economics

Abstract: The use of appropriate index numbers is indispensable for measuring economic phenomena precisely. Various indexes have been proposed in the literature, spanning several centuries. In this paper, we propose the quadratic-mean-of-order-𝑟 indexes of output, input and productivity. Each index is a family of indexes that unify many of the existing indexes, including the most popular ones. We also show that all index number formulae belonging to these families are superlative indexes. This is considered as a generalization of the equivalence of Fisher and Malmquist indexes, shown by Diewert (1992). Our results also give new justifications for output and input comparison and productivity measurement via other interesting indexes such as the implicit Walsh index. We also apply the discussed indexes to the US industry production accounts.

Keywords: index numbers; superlative index; quadratic-mean-of-order-𝑟 index; Fisher index; Malmquist index; implicit Walsh index; time reversal test (search for similar items in EconPapers)
JEL-codes: C14 D24 E31 O47 (search for similar items in EconPapers)
Date: 2020-02
New Economics Papers: this item is included in nep-eff and nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Journal Article: Quadratic-mean-of-order-r indexes of output, input and productivity (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:qld:uqcepa:146

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