Traditional Treating of Properties of Price Indices

Abstract

The development of index theory was a dialectical process. It did not start with an ideal index, nor did it start with a perfect axiom system allowing to discriminate between real indices fulfilling it and “false” indices not fulfilling at least one of its axioms. Index theory developped by early indices and early “tests” for them. New tests improved the indices and good indices required more subtle tests etc. For instance Wolfgang Eichhorn postulated the homogeneity test (2.70). As it is failed by the Divisia index on the straight line (1.47), the axiom system presented in section 2.5.1 had to be modified. Wolfgang Eichhorn thinks that this process culminated eventually in Olt’s (1995) axiom system treated in section 2.5.2. Nevertheless, he and the author feel that this process will go further on.

The multiplicity of formulae for computing index numbers has given the impression that there must be a corresponding multiplicity in the results of these computations, with no clear choice between them. But this impression is due to a failure to discriminate between index numbers which are good, bad, and indifferent. By means of certain tests we can make this discrimination...

Fisher (1922:9)