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Index Formula of Laspeyres and the Inversion Test


  • von der Lippe, Peter


The fact that the famous price index of Laspeyres is unable to pass the so called inversion test (IT) gave rise to the idea that this formula tends to measure "spurious inflation" which renders it useless and fallacious. In the IT prices and quantities of n goods, relating to two periods, the base period 0 and the current period t are interchanged in way that the sums of prices, quantities as well as values (products of prices and quantities) remain constant. It therefore appears nonsensical that Laspeyres' price index nonetheless indicates "inflation" under such conditions. Yet this result can be explained and justified. The paper shows that violation of the IT does not prove uselessness of an index function. On the contrary a number of good reasons can be given why compliance with the IT does not at all make a formula preferable to other formulas and that the message of the IT and its relation to other tests is rather dubious.

Suggested Citation

  • von der Lippe, Peter, 2008. "Index Formula of Laspeyres and the Inversion Test," MPRA Paper 7045, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:7045

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    Index theory; price indices; axiomatic approach in statistics;

    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

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