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Reliability of Ideal Indexes

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  • Gholamreza Hajargasht

Abstract

The Fisher and GEKS are celebrated as ideal bilateral and multilateral indexes due to their superior axiomatic and econ-theoretic properties. The Fisher index is the main index used for constructing CPI by statistical agencies and the GEKS is the index used for compiling PPPs in World Bank's International Comparison Program (ICP). Despite such a high status and the importance attached to these indexes, the stochastic approach to these indexes is not well-developed and no measures of reliability exist for these important economic statistics. The main objective of this paper is to fill this gap. We show how appropriate reliability measures for the Fisher and GEKS indexes, and other ideal price index numbers can be derived and how they should be interpreted and used in practice. In an application to 2017 ICP data on a sample of 173 countries, we estimate the Fisher and GEKS indexes along with their reliability measures, make comparisons with several other notable indexes and discuss the implications.

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  • Gholamreza Hajargasht, 2022. "Reliability of Ideal Indexes," Papers 2210.13684, arXiv.org.
    • Handle: RePEc:arx:papers:2210.13684
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    References listed on IDEAS

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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.
    2. 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.
    3. Feenstra, Robert C, 1994. "New Product Varieties and the Measurement of International Prices," American Economic Review, American Economic Association, vol. 84(1), pages 157-177, March.
    4. 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.
    5. Balk,Bert M., 2012. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9781107404960, September.
    6. Stephen J Redding & David E Weinstein, 2020. "Measuring Aggregate Price Indices with Taste Shocks: Theory and Evidence for CES Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(1), pages 503-560.
    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. James R. Cuthbert, 2003. "On the Variance/Covariance Structure of the Log Fisher Index, and Implications for Aggregation Techniques," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 49(1), pages 69-88, March.
    9. Adam Gorajek, 2018. "Econometric Perspectives on Economic Measurement," RBA Research Discussion Papers rdp2018-08, Reserve Bank of Australia.
    10. 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.
    11. Robert J. Hill, 1999. "Comparing Price Levels across Countries Using Minimum-Spanning Trees," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 135-142, February.
    12. Fattore, Marco, 2010. "Axiomatic properties of geo-logarithmic price indices," Journal of Econometrics, Elsevier, vol. 156(2), pages 344-353, June.
    13. Sato, Kazuo, 1976. "The Ideal Log-Change Index Number," The Review of Economics and Statistics, MIT Press, vol. 58(2), pages 223-228, May.
    14. E. A. Selvanathan & D. S. Prasada Rao, 1994. "Stochastic Approach to Index Numbers," Palgrave Macmillan Books, in: Index Numbers, chapter 0, pages 47-73, Palgrave Macmillan.
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