Discrete growth, real output, and inflation: An additive perspective on the index number problem

Abstract

This paper examines the problem of estimating real output and inflation using index numbers that are related to nominal output change through addition rather than multiplication. This approach to the development of index numbers is consistent with the manner in which nominal output actually evolves through time relative to some base year. Formulas for additive measures of real output and inflation that accurately capture the relative impacts of price and output change on nominal output are derived, and their use in separating real and nominal effects is illustrated and compared with standard indices. The additive approach is also used to understand the nature of formula bias in some traditional index numbers. Finally, through the test approach, the indices presented in this paper have a number of appealing properties.