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Stochastic Approach To Index Numbers For Multilateral Price Comparisons And Their Standard Errors

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  • Gholamreza Hajargasht
  • D. S. Prasada Rao

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 Iklé, 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. Copyright 2010 The Authors. Journal compilation International Association for Research in Income and Wealth 2010.

Suggested Citation

  • Gholamreza Hajargasht & D. S. Prasada Rao, 2010. "Stochastic Approach To Index Numbers For Multilateral Price Comparisons And Their Standard Errors," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 32-58, June.
  • Handle: RePEc:bla:revinw:v:56:y:2010:i:s1:p:s32-s58
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    References listed on IDEAS

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    1. Hill, Robert J, 1997. "A Taxonomy of Multilateral Methods for Making International Comparisons of Prices and Quantities," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 43(1), pages 49-69, March.
    2. Selvanathan, E A, 1989. "A Note on the Stochastic Approach to Index Numbers," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 471-474, October.
    3. D.S. Prasada Rao, 2004. "The Country-Product-Dummy Method: A Stochastic Approach to the Computation of Purchasing Power Parities in the ICP," CEPA Working Papers Series WP032004, School of Economics, University of Queensland, Australia.
    4. D. S. Prasada Rao, 2005. "On The Equivalence Of Weighted Country-Product-Dummy (Cpd) Method And The Rao-System For Multilateral Price Comparisons," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 51(4), pages 571-580, December.
    5. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers," Economic Journal, Royal Economic Society, vol. 92(365), pages 73-86, March.
    6. Selvanathan, E. A. & Prasada Rao, D. S., 1992. "An econometric approach to the construction of generalized Theil-Tornqvist indices for multilateral comparisons," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 335-346.
    7. Erwin Diewert, 2005. "Weighted Country Product Dummy Variable Regressions And Index Number Formulae," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 51(4), pages 561-570, December.
    8. Cameron,A. Colin & Trivedi,Pravin K., 2008. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9787111235767, May.
    9. Clements, Kenneth W & Izan, H Y, 1981. "A Note on Estimating Divisia Index Numbers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 745-747, October.
    10. Rao, D S Prasada & Selvanathan, E A, 1992. "Computation of Standard Errors for Geary-Khamis Parities and International Prices: A Stochastic Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(1), pages 109-115, January.
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    Cited by:

    1. Rao, D.S. Prasada & Hajargasht, Gholamreza, 2016. "Stochastic approach to computation of purchasing power parities in the International Comparison Program (ICP)," Journal of Econometrics, Elsevier, vol. 191(2), pages 414-425.
    2. repec:lrk:eeaart:36_1_9 is not listed on IDEAS
    3. Ludwig Auer, 2012. "Räumliche Preisvergleiche: Aggregationskonzepte und Forschungsperspektiven," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 6(1), pages 27-56, December.
    4. Robert J. Hill & Alice O. Nakamura, 2010. "Improving Inflation And Related Performance Measures For Nations: An Introduction," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 1-10, June.

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