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Standard errors as weights in multilateral price indices

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  • Hill, Robert
  • Timmer, Marcel

    (Groningen University)

Abstract

A number of multilateral methods for computing price indexes use bilateral comparisons as their basic building blocks. Some of these methods, such as the weighted-EKS and minimum-spanning-tree (MST) methods, give greater weight to those bilateral comparisons that are deemed more reliable (an adjustment that is particularly important for a heterogeneous set of countries). No consensus currently exists in the literature as to the best measure of reliability. Diewert (2002), in particular, proposes a number of reliability measures in an axiomatic setting. Existing measures (including all of Diewert’s), however, fail to penalize bilateral comparisons when there is a small overlap in the products priced by each country. It is exactly in such situations that weighted methods are potentially most useful, but only if the reliability measure penalizes bilateral comparisons containing lots of gaps. Using a stochastic model, we show how the standard errors on bilateral price indexes provide a natural measure of reliability that automatically penalizes comparisons containing lots of gaps. Furthermore, we link these standard errors with the existing literature by showing that they are a generalization of one of Diewert’s reliability measures. This finding provides an interesting new link between the axiomatic and stochastic approaches to index numbers. Also, these standard errors can be modified for use in consumer data sets below the basic-heading level (where no expenditure shares are available), a scenario of direct relevance to the latest round of the International Comparison Program (ICP) currently being undertaken at the World Bank. Finally, we apply our methodology to an international data set on agricultural production that contains a lot of gaps. Our results clearly demonstrate the appeal of weighted methods and the importance of adjusting the reliability measures for gaps in the data. Failure to do so may compromise weighted methods precisely in situations where they are most needed.

Suggested Citation

  • Hill, Robert & Timmer, Marcel, 2004. "Standard errors as weights in multilateral price indices," GGDC Research Memorandum 200473, Groningen Growth and Development Centre, University of Groningen.
    • Handle: RePEc:gro:rugggd:200473
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    References listed on IDEAS

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    1. Robert J. Hill, 2004. "Constructing Price Indexes across Space and Time: The Case of the European Union," American Economic Review, American Economic Association, vol. 94(5), pages 1379-1410, December.
    2. Allen, Robert C & Diewert, W Erwin, 1981. "Direct versus Implicit Superlative Index Number Formulae," The Review of Economics and Statistics, MIT Press, vol. 63(3), pages 430-435, August.
    3. Chen, Yi Vivian & Heston, Alan & Lipsey, Robert, 2000. "International and interarea comparisons of income, output and prices," Journal of Asian Economics, Elsevier, vol. 11(3), pages 363-364, December.
    4. 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.
    5. Doris M. Iklé, 1972. "A New Approach to the Index Number Problem," The Quarterly Journal of Economics, Oxford University Press, vol. 86(2), pages 188-211.
    6. W. Erwin Diewert, 1999. "Axiomatic and Economic Approaches to International Comparisons," NBER Chapters, in: International and Interarea Comparisons of Income, Output, and Prices, pages 13-107, National Bureau of Economic Research, Inc.
    7. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    8. Matthijs van Veelen, 2002. "An Impossibility Theorem Concerning Multilateral International Comparison of Volumes," Econometrica, Econometric Society, vol. 70(1), pages 369-375, January.
    9. D. S. Prasada Rao & Marcel P. Timmer, 2003. "Purchasing Power Parities for Industry Comparisons Using Weighted Elteto–Koves–Szulc (EKS) Methods," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 49(4), pages 491-511, December.
    10. 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.
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    Cited by:

    1. 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.
    2. Chihiro Shimizu & Erwin Diewert, 2023. "Scanner Data, Product Churn and Quality Adjustment," Working Papers e185, Tokyo Center for Economic Research.
    3. Inklaar Robert & Timmer Marcel P. & Ark Bart van, 2007. "Mind the Gap! International Comparisons of Productivity in Services and Goods Production," German Economic Review, De Gruyter, vol. 8(2), pages 281-307, May.
    4. Erwin Diewert, 2010. "New Methodological Developments For The International Comparison Program," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 11-31, June.
    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. Weinand, Sebastian, 2020. "Measuring spatial price differentials: A comparison of stochastic index number methods," Discussion Papers 12/2020, Deutsche Bundesbank.
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