Jointly Consistent Price and Quantity Comparisons and the Geo-Logarithmic Family of Price Indexes

Abstract

AbstractIn the axiomatic approach to composite index numbers, price and quantity indexes are dually linked since their product has to decompose the value index in a multiplicative way (Balk, 1995). In practice, the price index is often given some prominence, so that its formula is selected first and its cofactor is de facto chosen as the quantity index assuring for the value index decomposition to hold. This fact breaks the symmetry existing between price and quantity indexes and may have unexpected consequences on the consistency of the comparisons. In fact, usually no requirement is given connecting the choice of the price index to the properties satisfied by its cofactor, so that the former is very often selected irrespective of the axiomatic features of the latter. Unfortunately, few axiomatic properties of the price index are automatically inheritated by its cofactor, so that even an apparently “good”: price index may have a cofactor which is not acceptable from an axiomatic point of view.KeywordsPrice IndexQuantity ComparisonQuantity IndexAxiomatic SettingFisher IndexThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.