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On the Variance/Covariance Structure of the Log Fisher Index, and Implications for Aggregation Techniques

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  • James R. Cuthbert

Abstract

Several aggregation methods, including the EKS, start by calculating bilateral Fisher indices. Prices and quantities are, however, subject to measurement error. This stochastic behavior, which implies both unequal variances, and non‐zero correlations, between different Fisher indices, has to be taken into account if optimal estimates of aggregate PPPs are to be derived from the Fisher indices. This paper provides estimates of the variance/covariance structure of the Fisher indices, under two alternative models for stochastic variation at basic heading level: and it applies these formulae to the 1996 OECD data set, illustrating that the Fisher indices for this data set are indeed highly correlated. The paper also establishes a general theoretical result, proving that the EKS is optimal for a particular variance/covariance structure involving non‐zero correlations, and hence shows that the standard EKS aggregation method is likely to be near optimal for the 1996 OECD data set.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:revinw:v:49:y:2003:i:1:p:69-88
    DOI: 10.1111/1475-4991.00075
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    Cited by:

    1. Gholamreza Hajargasht, 2022. "Reliability of Ideal Indexes," Papers 2210.13684, arXiv.org.
    2. Sebastian Weinand, 2022. "Measuring spatial price differentials at the basic heading level: a comparison of stochastic index number methods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(1), pages 117-143, March.
    3. Weinand, Sebastian, 2020. "Measuring spatial price differentials: A comparison of stochastic index number methods," Discussion Papers 12/2020, Deutsche Bundesbank.
    4. Giovanni Maria Giorgi, 2011. "Corrado Gini: the man and the scientist," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 1-28.

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