The paper presents a stochastic approach based on the country-product-dummy (CPD) method for 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.