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Multilateral Index Number Systems for International Price Comparisons: Properties, Existence and Uniqueness

Gholamreza Hajargasht () and D.S. Prasada Rao

No WP032019, CEPA Working Papers Series from University of Queensland, School of Economics

Abstract: Over the past five decades a number of multilateral index number systems have been proposed for spatial and cross-country price comparisons. These multilateral indexes are usually expressed as solutions to systems of linear or nonlinear equations. In this paper, we provide general theorems that can be used to establish necessary and sufficient conditions for the existence and uniqueness of the Geary-Khamis, IDB, Neary and Rao indexes as well as potential new systems including two generalized systems of index numbers. One of our main results is that the necessary and sufficient conditions for existence and uniqueness of solutions can often be stated in terms of graph-theoretic concepts and a verifiable condition based on observed quantities of commodities.

Keywords: purchasing power parities; international prices; nonlinear Perron-Frobenius problem; connected graphs; DAD problem; generalized mean (search for similar items in EconPapers)
JEL-codes: E31 C19 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-int
Date: 2019-02
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https://economics.uq.edu.au/files/12951/WP032019.pdf (application/pdf)

Related works:
Journal Article: Multilateral index number systems for international price comparisons: Properties, existence and uniqueness (2019) Downloads
Working Paper: Multilateral Index Number Systems for International Price Comparisons: Properties, Existence and Uniqueness (2018) Downloads
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Persistent link: https://EconPapers.repec.org/RePEc:qld:uqcepa:133

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