Axiomatic properties of geo-logarithmic price indices

In the axiomatic approach to composite index numbers, a list of properties is given that both price and quantity indices should satisfy in order to ensure consistent comparisons. Usually, the price index is selected first and its cofactor is consequently adopted as the (implicit) quantity index. Unfortunately, even if the price index has good axiomatic properties, its cofactor need not, so the implicit quantity comparison may be axiomatically inconsistent. In this paper, we give a comprehensive study of a family of price indices sharing good axiomatic properties (proportionality, commensurability, and homogeneity) together with their cofactors. This family, called geo-logarithmic, is relevant also because of the empirical circumstance that all known price indices sharing such properties with their cofactors belong to it or can be obtained from geo-logarithmic index numbers through simple transformations. Thus, the geo-logarithmic family seems to play a central role when the joint consistency of price and quantity comparisons is concerned.