True multilateral indexes for international comparisons of purchasing power and real income

I consider the problem of choosing index numbers of purchasing power and real income for international comparisons. I show that the desirable properties of methods based on the Fisher "Ideal" index do not extend to multilateral comparisons, except when tastes are homothetic. By contrast, the Geary method, which underlies the Penn World Tables, provides an approximation to a set of "true" exchange rate indexes which have many desirable properties. In particular, if demands exhibit generalized linearity, the true indexes measure real incomes relative to a hypothetical country whose income is an appropriate average of individual countries'' incomes.