Fisher versus Fisher: Evaluating the accuracy of additive and multiplicative price and quantity indices

Abstract

The accuracy of index numbers can be understood by evaluating the consistency of their formulas with the sources of change in total expenditure and by examining their ability to estimate actual price and output changes with precision. In terms of formulas, differences among index numbers can be seen in their treatment of the interaction term, which arises when changes in prices and quantities occur simultaneously over discrete time intervals. This paper evaluates these differences for a number of important indices, including the additive and multiplicative versions of the Fisher. Then, using the growth-rate counterparts of these measures, the accuracy of index numbers is examined in terms of their ability to estimate constant elasticity values for both demand and supply functions. For the indices considered, results show that the additive measures, especially the Additive Fisher, provide superior measurement of price and output growth effects.