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The paper presents a stochastic approach based on the country-product-dummy (CPD) method to the computation of purchasing power parities (PPPs) in the International Comparison Program. The approach develops estimation strategies in conjunction with the country-product-dummy method to derive a range of multilateral index number methods for the compilation of PPPs at the basic heading level as well as at higher levels of aggregation. At the basic heading level our approach generates Jevons geometric index, arithmetic and harmonic indexes as well as the Dutot index. At higher levels of aggregation, a weighted stochastic model with alternative stochastic specifications and the method of moments (MOM) are used to derive the Geary-Khamis, Iklé, Rao and other multilateral index number methods employed in international comparisons. Expressions for computing standard errors for PPPs based on these formulae are also derived. Existence of solutions to the estimating equations derived from the weighted method of moments or the maximum weighted likelihood is also discussed. A numerical illustration based on ICP 2005 data is presented. JEL Codes: C13; C18; C43; C80

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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 weighted least squares 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 specification. 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.JEL Classification: E31 and C19

We consider mostly Bayesian estimation of stochastic frontier models where one-sided inefficiencies and/or the idiosyncratic error term are correlated with the regressors. We begin with a model where a Chamberlain-Mundlak device is used to relate a transformation of time-invariant effects to the regressors. This basic model is then extended in two directions: First an extra one-sided error term is added to allow for timevarying efficiencies. Second, a model with an equation for instrumental variables and a more general error covariance structure is introduced to accommodate correlations between both error terms and the regressors. An application of the first and second models to Philippines rice data is provided.