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Multilateral index number systems for international price comparisons: Properties, existence and uniqueness

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  • Hajargasht, Gholamreza
  • Rao, D.S. Prasada

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.

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  • Hajargasht, Gholamreza & Rao, D.S. Prasada, 2019. "Multilateral index number systems for international price comparisons: Properties, existence and uniqueness," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 36-47.
  • Handle: RePEc:eee:mateco:v:83:y:2019:i:c:p:36-47
    DOI: 10.1016/j.jmateco.2019.02.004
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    1. Hajargasht, Gholamreza & Prasada Rao, D.S. & Valadkhani, Abbas, 2019. "Reliability of basic heading PPPs," Economics Letters, Elsevier, vol. 180(C), pages 102-107.

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    More about this item

    Keywords

    Purchasing power parities; International prices; Nonlinear Perron–Frobenius problem; Connected graphs; DAD problem; Generalized mean;
    All these keywords.

    JEL classification:

    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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