Stochastic Approach to Index Numbers for Multilateral Price Comparisons and Their Standard Errors

Abstract

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

The Role of Prices in Welfare Comparisons: Methodological Developments and a Selective Survey of the Empirical Literature

“…The procedures are described in detail in many subsequent papers (e.g. The CPD model has been developed further in the context of PPP estimation, and expressions for computing standard errors of the CPD estimates under alternative stochastic specifications have been derived in Hazargasht and Rao (2010) and in Rao and Hazargasht (2016). The CPD model has been developed further in the context of PPP estimation, and expressions for computing standard errors of the CPD estimates under alternative stochastic specifications have been derived in Hazargasht and Rao (2010) and in Rao and Hazargasht (2016).…”

“…Diewert, 2005;Rao, 2005). The CPD model has been developed further in the context of PPP estimation, and expressions for computing standard errors of the CPD estimates under alternative stochastic specifications have been derived in Hazargasht and Rao (2010) and in Rao and Hazargasht (2016).…”

Anatomy of regional price differentials: evidence from micro-price data

“…The gaps within these vectors, however, are larger than in the grouping approach. To deal with these gaps, we embed our PMO precept into the weighted CPD approach advocated by Rao (2001Rao ( , 2005, Rao (2010), andDiewert (2005). We develop a multi-stage variant of this approach.…”

Multilateral index number systems for international price comparisons: Properties, existence and uniqueness

“…The quest for indexes with better properties is ongoing and new indexes are being proposed e.g. see Hajargasht & Rao (2010) and Rao & Hajargasht (2016) for a new stochastic approach.…”

“…Rao (2005) has shown that the solution to this system can be obtained as weighted least squares estimates from the country-product dummy (CPD) method. Further details of the CPD method and its links with multilateral systems are discussed inHajargasht & Rao (2010) andRao & Hajargasht (2016).…”