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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.

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  • 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
    DOI: 10.1111/j.1475-4991.2010.00387.x
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    1. Robert J. Hill, 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.
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    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.
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    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. 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.
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    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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    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. Hajargasht, Gholamreza & Rao, D.S. Prasada, 2019. "Multilateral index number systems for international price comparisons: Properties, existence and uniqueness," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 36-47.
    3. José‐María Montero & Tiziana Laureti & Román Mínguez & Gema Fernández‐Avilés, 2020. "A Stochastic Model with Penalized Coefficients for Spatial Price Comparisons: An Application to Regional Price Indexes in Italy," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(3), pages 512-533, September.
    4. Laureti, Tiziana & Prasada Rao, D.S., 2018. "Measuring Spatial Price Level Differences within a Country: Current status and Future Developments /Medición de las diferencias de nivel de precios espaciales dentro de un país: Estado actual y evoluc," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 36, pages 119-148, Enero.
    5. 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.
    6. Adam Gorajek, 2018. "Econometric Perspectives on Economic Measurement," RBA Research Discussion Papers rdp2018-08, Reserve Bank of Australia.
    7. Weinand, Sebastian, 2020. "Measuring spatial price differentials: A comparison of stochastic index number methods," Discussion Papers 12/2020, Deutsche Bundesbank.
    8. 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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