Notes on GEKS and RGEKS indices

von der Lippe, Peter (2012): Notes on GEKS and RGEKS indices.

Abstract

The paper criticizes the translation of the so called GEKS (Gini - Eltetö - Köves - Szulc) method to make consistent (transitive, or "drift free") international comparisons of price indices (parities), into the intertemporal framework. It shows that transitivity appears to be "over-ambitious" and too restrictive in this context, where chain indices possibly may suffice. Formulas of GEKS indices are complicated geometric averages of many (2m-3) direct Fisher indices relating to m periods in time. They are therefore much more difficult to compile in praxis than both, chained and direct Fisher indices. They are only transitive for a given m, but as we are free to choose different m's there is no unique, "drift free" index to compare any two periods, s and t. Instead there are many indices Pst depending on m. Moreover with new periods, t+1, t+2, … the method requires an updating (as m increases) and a re-computing of all previously compiled indices Pst. With chain indices the update is much easier and there is no need for a re-computing. To avoid such problems a "rolling" variant (RGEKS), a kind of moving average methodology, has been proposed. With RGEKS (of which chain indices are the limiting case of m = 2), however, desirable properties of (standard) GEKS, such as transitivity and proportionality get lost, and with a cyclical movement in the prices we can well generate a trend in the indices which is absent in the underlying price data.

• Item Type: MPRA Paper
• Language: English
• Keywords: international comparison of price indices, intertemporal comparison, transitive price indices, chain indices, chain drift
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C82 - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data ; Data Access; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E31 - Price Level ; Inflation ; Deflation; B - History of Economic Thought, Methodology, and Heterodox Approaches > B4 - Economic Methodology > B41 - Economic Methodology

References

Ivancic, L., Fox, K. J. and W. E. Diewert (2009), Scanner Data, Time Aggregation and the Construction of Price Indexes, Ottawa Group Meeting in Neuchâtel, Switzerland, 2009

Ivancic, , Diewert and J. Fox (2011), Scanner Data, Time Aggregation and the Construction of Price Indexes, Journal of Econometrics 161, 24 – 35

Ribe Martin (2012), Some properties of the RGEKS index for scanner data, Draft (corrected) 2012-06-02 in the Internet

v. d. Lippe, Peter (2007), Index Theory and Price Statistics, Frankfurt