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Axiomatic properties of geo-logarithmic price indices

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  • Fattore, Marco

Abstract

In the axiomatic approach to composite index numbers, a list of properties is given that both price and quantity indices should satisfy in order to ensure consistent comparisons. Usually, the price index is selected first and its cofactor is consequently adopted as the (implicit) quantity index. Unfortunately, even if the price index has good axiomatic properties, its cofactor need not, so the implicit quantity comparison may be axiomatically inconsistent. In this paper, we give a comprehensive study of a family of price indices sharing good axiomatic properties (proportionality, commensurability, and homogeneity) together with their cofactors. This family, called geo-logarithmic, is relevant also because of the empirical circumstance that all known price indices sharing such properties with their cofactors belong to it or can be obtained from geo-logarithmic index numbers through simple transformations. Thus, the geo-logarithmic family seems to play a central role when the joint consistency of price and quantity comparisons is concerned.

Suggested Citation

  • Fattore, Marco, 2010. "Axiomatic properties of geo-logarithmic price indices," Journal of Econometrics, Elsevier, vol. 156(2), pages 344-353, June.
    • Handle: RePEc:eee:econom:v:156:y:2010:i:2:p:344-353
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    References listed on IDEAS

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    1. Marco Fattore, 2006. "Finite groups in Axiomatic Index Number Theory," Working Papers 20070101, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica.
    2. Hill, Robert J., 2006. "Superlative index numbers: not all of them are super," Journal of Econometrics, Elsevier, vol. 130(1), pages 25-43, January.
    3. Sato, Kazuo, 1976. "The Ideal Log-Change Index Number," The Review of Economics and Statistics, MIT Press, vol. 58(2), pages 223-228, May.
    4. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
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    1. Abe, Naohito & Rao, D.S. Prasada, 2019. "Multilateral Sato–Vartia index for international comparisons of prices and real expenditures," Economics Letters, Elsevier, vol. 183(C), pages 1-1.
    2. Białek Jacek, 2019. "Remarks on Geo-Logarithmic Price Indices," Journal of Official Statistics, Sciendo, vol. 35(2), pages 287-317, June.
    3. Zhang Li-Chun & Johansen Ingvild & Nygaard Ragnhild, 2019. "Tests for Price Indices in a Dynamic Item Universe," Journal of Official Statistics, Sciendo, vol. 35(3), pages 683-697, September.
    4. Gholamreza Hajargasht, 2022. "Reliability of Ideal Indexes," Papers 2210.13684, arXiv.org.
    5. Falbo, Paolo & Fattore, Marco & Stefani, Silvana, 2010. "A new index for electricity spot markets," Energy Policy, Elsevier, vol. 38(6), pages 2739-2750, June.
    6. Li-Chun Zhang & Ingvild Johansen & Ragnhild Nygaard, 2018. "Tests for price indices in a dynamic item universe," Papers 1808.08995, arXiv.org, revised Oct 2018.

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