Index Formula of Laspeyres and the Inversion Test

von der Lippe, Peter (2008): Index Formula of Laspeyres and the Inversion Test. Unpublished.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Index theory, price indices, axiomatic approach in statistics
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E31 - Price Level; Inflation; Deflation

References

Balk, Bert, Axiomatic Price index Theory: A Survey, International Statistical Review 63/1 (1995), pp. 69 - 93. von Auer, Ludwig, Spurious Inflation: The Legacy of Laspeyres and others,. in The Quarterly Review of Economic and Finance, 42 (2002), pp. 529 - 542 von der Lippe, Peter, Chain Indices, A Study in Index Theory, Wiesbaden 2001 von der Lippe, Peter, Index Theory and Price Statistics (Peter Lang Publisher), Bern etc., 2007