On purchasing power parities calculation at the basic heading level

Abstract

This paper analyses two procedures for calculating Purchasing Power Parities (ppps) at the basic heading level: the first one suggested by UNSO and the second one used by EUROSTAT For the synthesis of the prices of items, UNSO resorts to the "characteristicity" or "asterisk" approach and proposes the unweighted geometric mean of the ratios with at least one asterisk, whereas EUROSTAT transforms the above approach into that of "equi-characteristicity" and introduces pseudo Laspeyres and Paasche indexes and finally Fisher forms which in some sense are weighted geometric means. For the purpose of producing a complete and transitive matrix of ppps, both resort to the EKS procedure, or GEKS, as this paper proposes to rename it. As far as the EUROSTAT procedure is concerned, the formulas for pseudo L and P are analyzed (leaving aside the simple geometric mean suggested by UNSO which gives biased results because of the Gerschenkron effect) and it is shown that the ratios of sums are proper L and P indexes which advantage is that of having a simple and reasonable economic meaning. As for the GEKS iterative procedure, the paper proves that the minimization over the L and P matrices of parities instead of over the matrix of the Fs leads the process to converge in many more cases - therefore giving complete and transitive matrices - than one would obtain through minimization of the matrix of the Fs, which results in a minor loss of information.