Indices of Structural Changes in the Theory of the Price Index

  • Bernhard A. Olt
Conference paper
Part of the Operations Research Proceedings book series (ORP, volume 1994)


The aim of this contribution is to present a new approach in the theory of the price index, leaving the frame of the traditional theory. One application of the price index theory is to decompose the change of a volume (i. e. expenditure or turnover) aggregate into a price and a quantity component. Unfortunately, there is no unique pair of (price and quantity) indices in the sense of Eichhorn and Voeller (1983) permitting the decomposition of the volume change, and it is rather a political decision which pair to use in a specific situation. However, there is a unique “solution” in the special case where quantities remain unchanged (or change by a common factor λ): It is generally accepted that in this case the price index number should coincide with the ratio of the two volume aggregates (q 0 · p 1/q 0 · p 0), the quantity index number yielding unity (or λ). Defining this ratio as the “pure” price (level) index, and a “pure” quantity (level) index accordingly, the difference between the volume change and the product of these indices in the general case can be attributed to a third factor. This factor should equal unity if relative prices or relative quantities do not change, i. e. if the price structure or the quantity structure remains unchanged. Thus it can be regarded a measure of structural changes.

In this paper such a measure is derived by a true statistical approach, where the level indices are uniquely determined as the indices named after Laspeyres. The structure index is a function of (1) the (generalized) coefficient of correlation between the individual price and quantity changes and the (generalized) coefficients of variation of (2) the price and of (3) the quantity changes. The latter are frequently used measures of inequality.


Price Index Structure Index Price Structure Quantity Change Volume Aggregate 
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  1. Aczél, János (1994): “Remark (at the thirty-first international symposium on functional equations)”, Aequationes Mathematical 47, 305–306Google Scholar
  2. Al, Pieter G.; Bert M. Balk; Sake de Boer; Gert P. den Bakker (1986): “The use of chain indices for deflating the national accounts”, Statistical J. of the United Nations, ECE 4, 347–368Google Scholar
  3. Balk, Bert M. (1992): “Axiomatic Price Index Theory: A Survey”, Discussion-Paper No. E7-SD-545, Netherlands Central Bureau of Statistics, to appear in Int. Statistical Review (1994)Google Scholar
  4. Bol, Georg (1993): Deskriptive Statistik, 2nd ed., München: OldenbourgGoogle Scholar
  5. von Bortkiewicz, L. (1923, 1924a, 1924b): “Zweck und Struktur einer Preisindexzahl; Erster, Zweiter und Dritter Artikel”, Nordisk Statistisk Tidskrift, 2, 369–408, 3, 208–251, 3, 494–516Google Scholar
  6. Diewert, W. Erwin (1993): “The Early History of Price Index Research”, in: Diewert, Nakamura (ed.): Essays in Index Number Theory, Volume 1, Amsterdam: North-Holland, 33–66Google Scholar
  7. Eichhorn, Wolfgang; Joachim Voeller (1983): “Axiomatic Foundation of Price Indexes and Purchasing Power Parities”, in: Diewert, Montmarquette (ed.): Price Level Measurement, Ottawa: Statistics Canada, 411–450Google Scholar
  8. Fisher, Irving (1911): The Purchasing Power of Money, London: MacmillanGoogle Scholar
  9. Fisher, Irving (1922): The Making of Index Numbers, 3rd rev. ed., 1927, Boston: Houghton MifflinGoogle Scholar
  10. Hartung, Joachim (1991): Statistik, 8th ed., München: OldenbourgGoogle Scholar
  11. Moore, John H. (1978): “A Measure of Structural Change in Output”, Review of Income and Wealth, 24, 105–118CrossRefGoogle Scholar
  12. Olt, Bernhard A. (1994): “Indices of Structural Changes”, Discussion Paper No. 443, Institut für Wirtschaftstheorie und Operations Research, Universität Karlsruhe, D-76128 KarlsruheGoogle Scholar
  13. Samuelson, Paul A.; Subramanian Swamy (1974): “Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis”, American Economic Review, 64/IV, 566–593Google Scholar
  14. Schimmler, Harry (1976): “On the Quantity Concept of Production”, Review of Income and Wealth, 22, 377–382Google Scholar
  15. Stuvel, Geer (1957): “A New Index Formula”, Econometrica, 25, 123–131CrossRefGoogle Scholar
  16. Vogt, Arthur (1978): “Divisia Indices on Different Paths”, in: Eichhorn, Henn, Opitz, Shephard (ed.): Theory and Applications of Economic Indices, Würzburg: Physica, 297–305Google Scholar
  17. Vogt, Arthur (1979): Das statistische Indexproblem im Zwei-Situationen-Fall, Zürich: JurisGoogle Scholar
  18. Vogt, Arthur (1990): “Fisher’s Test of Proportionality as to Trade and the Value-Index-Preserving Axiom”, rev. version of a talk given on Nov. 7, 1989 at the CMB Health Insurance in BernGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Bernhard A. Olt
    • 1
  1. 1.Universität KarlsruheGermany

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