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Covariances and relationships between price indices: Notes on a theorem of Ladislaus von Bortkiewicz on linear index functions

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  • von der Lippe, Peter

Abstract

The note examines a generalization of a theorem of Bortkiewicz which relates the difference between a Paasche and a Laspeyres price index to a covariance between price and quantity relatives. The generalized theorem is used to demonstrate a number of interesting special applications. It turns out that some known relationships between two index functions can be expressed more elegantly. In other cases where not much is known yet about how the two functions are related to one another, we could establish an interesting equation on the basis of this theorem. This demonstrates the remarkable flexibility and usefulness of the generalized Bortkiewicz - theorem.

Suggested Citation

  • von der Lippe, Peter, 2012. "Covariances and relationships between price indices: Notes on a theorem of Ladislaus von Bortkiewicz on linear index functions," MPRA Paper 38566, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:38566
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    File URL: https://mpra.ub.uni-muenchen.de/38566/1/MPRA_paper_38566.pdf
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    References listed on IDEAS

    as
    1. Diewert W.Erwin & Lippe Peter von der, 2010. "Notes on Unit Value Index Bias," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 230(6), pages 690-708, December.
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    More about this item

    Keywords

    price indices of Laspeyres; Paasche; Drobisch; Carli; Dutot; covariance; Bortkiewicz; unit value index;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access

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