Stochastic approach to index numbers for multilateral price comparisons and their standard errors

The main objective of the paper is to demonstrate that a number of widely used multilateral index numbers for international comparisons of purchasing power parities (PPPs) and real incomes can be derived using the stochastic approach. The paper shows that price index numbers from commonly used methods like the Ikle, the Rao-weighted, and an additive multilateral system are all estimators of the parameters of the country-product-dummy (CPD) model. The advantage of the stochastic approach is that we can derive standard errors for the estimates of the purchasing power parities (PPPs). The PPPs and the parameters of the stochastic model are estimated using a weighted maximum likelihood procedure under different stochastic specifications for the disturbance term. Estimates of PPPs and their standard errors for OECD countries using the proposed methods are presented. The paper also outlines a method of moments approach to the estimation of PPPs under the stochastic approach. The paper shows how the Geary-Khamis system of multilateral index numbers is a method of moments estimator of the parameters of the CPD model. The paper therefore provides a coherent stochastic framework for the Geary-Khamis system and derives standard errors of the Geary-Khamis PPPs