Multilateral Sato–Vartia index for international comparisons of prices and real expenditures

Abstract

The Sato–Vartia (SV) index for bilateral price comparisons has impressive analytical properties and is used intensively in recent international trade and macroeconomic analyses. We show that the SV index is only one of many logarithmic indices that satisfy the factor reversal test discussed in index number theory. In this paper we propose several transitive multilateral versions of the SV index but note that these do not satisfy factor reversal test. We derive closed form expressions for the transitive logarithmic indices and empirically implement the new indices for cross-country price comparisons using World Bank data from the 2011 International Comparison Program.