This paper extends Diewert’s (2002) study of similarity indexes to deal with the practical problem of the values of his preferred indexes of absolute dissimilarity going to infinity as any of their (per-capita) quantity arguments goes to zero; i.e., the inability of these indexes to distinguish between two quantity vectors that, between them, contain two or more zero components. It also extends his absolute-dissimilarity-index framework to accommodate the possibly negative quantities associated with net foreign expenditures. Appropriately modified versions of Diewert’s preferred indexes are then used to generate alternative sets of weights for the purpose of implementing Hill’s (1999) minimum spanning tree (MST) approach to multilateral international comparisons on the basis of each of two cross-sectional data sets produced by the Eurostat-OECD PPP Programme. Finally, a “fixity” criterion is imposed on the generated MSTs whereby the binary links among the countries of the European Union are replaced with the official EKS PPPs.

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Keywords international comparisons, index numbers, similarity measures, axiomatic approach
Citation
Armstrong, K. (2004). Hyperextended-Real-Valued Indexes of Absolute Dissimilarity.