A Factorization of Means of Order r and Its Applications to Price Indices

This article presents a factorization of means of order r , which provides a method for numerical comparison among standard index numbers. We apply it to a family of superlative indices written by the quadratic mean of order r , elementary indices (the Carli, Dutot, and Jevons indices), and the Lowe, Young, and related indices. Descriptive measures are provided to assess the differences between index numbers. Empirical data are studied and discussed to evaluate the theoretical results of the proposed factorization.