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Generalized Statistical Means and New Price Index Formulas, Notes on some unexplored index formulas, their interpretations and generalizations

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  • von der Lippe, Peter

Abstract

The theory of (increasingly more generalized types of) statistical means can be used to create a plethora of index formulas. Some of them are new and some were indeed discussed in the past but fallen into oblivion, because their rationale was not well understood. Surprisingly many possess interesting interpretations and attractive properties that deserve being unveiled. We begin with unweighted indices with implications to what now is called "low level aggregation" and proceed to weighted index formulas that lend themselves to productive generalizations and thereby to some new formulas. It turns out that contrary to popular belief the Laspeyres and Paasche formula are not equally well justified and that some indices from the more comprehensive system of statistical means are attractive regarding their economic interpretation and how they are related to indices of "quantity" and purchasing power of money.

Suggested Citation

  • von der Lippe, Peter, 2015. "Generalized Statistical Means and New Price Index Formulas, Notes on some unexplored index formulas, their interpretations and generalizations," MPRA Paper 64952, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:64952
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    File URL: https://mpra.ub.uni-muenchen.de/64952/1/MPRA_paper_64952.pdf
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    References listed on IDEAS

    as
    1. Lippe Peter Michael von der, 2013. "Recurrent Price Index Problems and Some Early German Papers on Index Numbers: Notes on Laspeyres, Paasche, Drobisch, and Lehr," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 233(3), pages 336-366, June.
    2. Allyn A. Young, 1921. "The Measurement of Changes of the General Price Level," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 35(4), pages 557-573.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Index Numbers; Generalized means; antiharmonic mean; index of purchasing power; unit value indices;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data; Data Access
    • E0 - Macroeconomics and Monetary Economics - - General
    • E01 - Macroeconomics and Monetary Economics - - General - - - Measurement and Data on National Income and Product Accounts and Wealth; Environmental Accounts
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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