IDEAS home Printed from https://ideas.repec.org/a/bes/jnlbes/v24y2006p366-377.html
   My bibliography  Save this article

Standard Errors as Weights in Multilateral Price Indexes

Author

Listed:
  • Hill, Robert J.
  • Timmer, Marcel P.

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 a
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Hill, Robert J. & Timmer, Marcel P., 2006. "Standard Errors as Weights in Multilateral Price Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 366-377, July.
    • Handle: RePEc:bes:jnlbes:v:24:y:2006:p:366-377
    as

    Download full text from publisher

    File URL: http://www.ingentaconnect.com/content/asa/jbes/2006/00000024/00000003/art00010
    File Function: full text
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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. Doris M. Iklé, 1972. "A New Approach to the Index Number Problem," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 86(2), pages 188-211.
    3. 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.
    4. 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.
    5. 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.
    6. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    7. Matthijs van Veelen, 2002. "An Impossibility Theorem Concerning Multilateral International Comparison of Volumes," Econometrica, Econometric Society, vol. 70(1), pages 369-375, January.
    8. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Robert Inklaar & Marcel P. Timmer & Bart Van Ark, 2007. "Mind the Gap! International Comparisons of Productivity in Services and Goods Production," German Economic Review, Verein für Socialpolitik, 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.
    7. repec:dgr:rugggd:gd-89 is not listed on IDEAS

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:dgr:rugggd:200473 is not listed on IDEAS
    2. W. Erwin Diewert, 2022. "Scanner Data, Elementary Price Indexes and the Chain Drift Problem," Springer Books, in: Duangkamon Chotikapanich & Alicia N. Rambaldi & Nicholas Rohde (ed.), Advances in Economic Measurement, chapter 0, pages 445-606, Springer.
    3. Diewert, Erwin & Marandola, Tina, 2018. "Scanner Data, Elementary Price Indexes and the Chain Drift Problem," Microeconomics.ca working papers tina_marandola-2018-9, Vancouver School of Economics, revised 10 Oct 2018.
    4. Barnett, William A. & Erwin Diewert, W. & Zellner, Arnold, 2011. "Introduction to measurement with theory," Journal of Econometrics, Elsevier, vol. 161(1), pages 1-5, March.
    5. Diewert, W. Erwin & Fox, Kevin J., 2017. "Substitution Bias in Multilateral Methods for CPI Construction using Scanner Data," Microeconomics.ca working papers erwin_diewert-2017-3, Vancouver School of Economics, revised 23 Mar 2017.
    6. Chihiro Shimizu & Erwin Diewert, 2023. "Scanner Data, Product Churn and Quality Adjustment," Working Papers e185, Tokyo Center for Economic Research.
    7. 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.
    8. Diewert, W. Erwin & Fox, Kevin J., 2016. "Kevin J. Fox Interview of W. Erwin Diewert," Microeconomics.ca working papers erwin_diewert-2016-6, Vancouver School of Economics, revised 02 Jun 2016.
    9. Erwin Diewert, 2010. "Understanding PPPs and PPP-Based National Accounts: Comment," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(4), pages 36-45, October.
    10. Diewert, Erwin, 2007. "Index Numbers," Economics working papers diewert-07-01-03-08-17-23, Vancouver School of Economics, revised 31 Jan 2007.
    11. Magne Mogstad, 2007. "Measuring Income Inequality under Restricted Interpersonal Comparability," Discussion Papers 498, Statistics Norway, Research Department.
    12. Nicholas Oulton, 2012. "How To Measure Living Standards And Productivity," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 58(3), pages 424-456, September.
    13. Abe, Naohito & Rao, D.S. Prasada, 2022. "Towards a simplified approach to international price comparisons: A case for the Multilateral Walsh Index," RCESR Discussion Paper Series DP22-1, Research Center for Economic and Social Risks, Institute of Economic Research, Hitotsubashi University.
    14. Angus Deaton & Alan Heston, 2010. "Understanding PPPs and PPP-Based National Accounts," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(4), pages 1-35, October.
    15. Diewert, Erwin, 2008. "New Methodology for Linking the Regions," Economics working papers erwin_diewert-2008-9, Vancouver School of Economics, revised 09 Sep 2008.
    16. Neary, Peter, 2000. "True Multilateral Indexes for International Comparisons of Real Income: Theory and Empirics," CEPR Discussion Papers 2590, C.E.P.R. Discussion Papers.
    17. Robert C. Feenstra & Robert Inklaar & Marcel P. Timmer, 2015. "The Next Generation of the Penn World Table," American Economic Review, American Economic Association, vol. 105(10), pages 3150-3182, October.
    18. Daniel Melser & Michael Webster, 2021. "Multilateral Methods, Substitution Bias, and Chain Drift: Some Empirical Comparisons," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 67(3), pages 759-785, September.
    19. 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.
    20. Fox, Kevin J. & Grafton, R. Quentin & Kirkley, James & Squires, Dale, 2003. "Property rights in a fishery: regulatory change and firm performance," Journal of Environmental Economics and Management, Elsevier, vol. 46(1), pages 156-177, July.
    21. Ivancic, Lorraine & Erwin Diewert, W. & Fox, Kevin J., 2011. "Scanner data, time aggregation and the construction of price indexes," Journal of Econometrics, Elsevier, vol. 161(1), pages 24-35, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bes:jnlbes:v:24:y:2006:p:366-377. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.