Remarks on Geo-Logarithmic Price Indices

Open access


As is known, all geo-logarithmic indices enjoy the axiomatic properties of being proportional, commensurable and homogeneous, together with their cofactors (Martini 1992a). Geologarithmic price indices satisfying the axioms of monotonicity, basis reversibility and factor reversibility have been investigated by Marco Fattore (2010), who has shown that the superlative Fisher price index does not belong to this family of indices. In this article, we discuss geo-logarithmic price indices with reference to the Laspeyres-Paasche bounding test and we propose a modification of the considered index family that satisfies this test. We also modify the structure of geo-logarithmic indices by using an additional parameter and, following the economic approach, we list superlative price index formulas that are members of the considered price index family. We obtain a special subfamily that approximates superlative price indices and includes the Fisher, Walsh and Sato-Vartia price indices.

Allen, R.G.D. 1975. Index Numbers in Theory and Practice. London: Macmillan Press.

Balk, B.M. 1995. “Axiomatic Price Index Theory: A Survey.” International Statistical Review 63: 69–93. Doi:

Białek, J. 2012. “Proposition of the general formula for price indices.” Communications in Statistics: Theory and Methods 41(5): 943–952. Doi:

Boskin, M.J., E.R. Dulberger, R.J. Gordon, Z. Griliches, and D. Jorgenson. 1996. Toward a More Accurate Measure of the Cost of Living. Final Report to the Senate Finance Committee from the Advisory Commission to Study the Consumer Price Index.

Carlson, B.C. 1972. The logarithmic mean, Amer. Math. Monthly. 79: 615–618. Doi:

Clements, K.W. and H.Y. Izan. 1987. “The Measurement of Inflation: A Stochastic Approach.” Journal of Business and Economic Statistics 5: 339–350. Doi:

Diewert, W.E. 1976. “Exact and Superlative Index Numbers.” Journal of Econometrics 4: 114–145. Doi:

Diewert, W.E. 1993. The economic theory of index numbers: a survey, Essays in index number theory, vol. 1, Eds. W.E. Diewert and A.O. Nakamura: 177–221, Amsterdam.

Dumagan, J. 2002. “Comparing the Superlative Törnqvist and Fisher ideal indices.” Economic Letters 76: 251–258. Doi:

Eichhorn, W. and J. Voeller. 1976. Theory of the Price Index. Fisher’s Test Approach and Generalizations. New York: Springer-Verlag.

Fattore, M. 2006. On the monotonicity of the geo-logarithmic price indexes. In: Proceedings of the XLIII Scientific Meeting, Societa` Italiana di Statistica, Cleup, Padova.

Fattore, M. 2010. “Axiomatic Properties of Geo-Logarithmic Price Indices.” Journal of Econometrics 156(2): 344–353. Doi:

Hill, R.J. 2006. “Superlative Index Numbers: Not All of Them Are Super.” Journal of Econometrics 130: 25–43. Doi:

IMF. 2004. Producer Price Index Manual, International Monetary Fund.

Jorgenson, D.W. and D.T. Slesnick. 1983. Individual and social cost of living indexes, Price level measurement: proceedings of a conference sponsored by Statistics Canada, W.E. Diewert and C. Montmarquette: 241–336, Ottawa: Statistics Canada.

Krstcha, M. 1988. Axiomatic characterization of statistical price indices. Heidelberg: Physica-Verlag.

Martini, M. 1992a. I numeri indice in un approccio assiomatico. Giuffré, Milan.

Martini, M. 1992b. “General Function of Axiomatic Index Numbers.” J. Ital. Statist. Soc 3: 359–376. Doi:

Olt, B. 1996. Axiom und Struktur in der statistischen Preisindextheorie. Germany: Peter Lang.

Pollak, R.A. 1989. The theory of the cost-of-living index. Oxford: Oxford University Press.

White, A.G. 1999. “Measurement Biases in Consumer Price Indexes.” International Statistical Review 3: 301–325. Doi:

Von der Lippe, P. 2007. Index Theory and Price Statistics. Germany: Peter Lang.

Journal of Official Statistics

The Journal of Statistics Sweden

Journal Information

IMPACT FACTOR 2018: 0,837
5-year IMPACT FACTOR: 0,934

CiteScore 2018: 1.04

SCImago Journal Rank (SJR) 2018: 0.963
Source Normalized Impact per Paper (SNIP) 2018: 1.020


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 220 220 47
PDF Downloads 200 200 38