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Axiomatic and Economic Approaches to International Comparisons

In: International and Interarea Comparisons of Income, Output, and Prices


  • W. Erwin Diewert


The paper considers the problem of choosing a multilateral system of index numbers in order to make aggregate price and quantity comparisons between many countries and regions. The problems involved in choosing functional forms in order to make these comparisons are both theoretically and empirically more difficult than the problems involved in choosing a bilateral index number formula. The great variation in relative prices and quantities in the international context means that the choice of a multilateral method is empirically important: different methods will give very different answers. The paper reviews ten classes of multilateral methods both from the viewpoint of the axiomatic approach as well as the economic approach. A new system of 11 desirable axioms or properties for multilateral systems is suggested. With respect to the economic approach, the concept of a superlative bilateral index number formula (which can adequately model substitution effects) is adapted to the multilateral context. Each of the 10 classes of multilateral methods is evaluated from the axiomatic and economic perspectives. Four classes of methods are identified as being `best' They are all superlative and satisfy slightly different sets of axioms.
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Suggested Citation

  • 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.
  • Handle: RePEc:nbr:nberch:8385

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    References listed on IDEAS

    1. Hill, T P, 1984. "Introduction: The Special Conference on Purchasing Power Parities," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 30(2), pages 125-133, June.
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    4. Diewert, W E, 1974. "Functional Forms for Revenue and Factor Requirements Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 119-130, February.
    5. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
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    7. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
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    9. Gerardi, Dino, 1982. "Selected Problems of the Inter-Country Comparisons on the Basis of the Experience of the EEC," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 28(4), pages 381-405, December.
    10. Sato, Kazuo, 1976. "The Ideal Log-Change Index Number," The Review of Economics and Statistics, MIT Press, vol. 58(2), pages 223-228, May.
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    Cited by:

    1. 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.
    2. Etienne Gagnon & David López-Salido & Jason Sockin, 2017. "The Cyclicality of Sales, Regular, and Effective Prices: Business Cycle and Policy Implications: Comment," American Economic Review, American Economic Association, vol. 107(10), pages 3229-3242, October.
    3. Mick Silver, 2009. "The Hedonic Country Product Dummy Method and Quality Adjustments for Purchasing Power Parity Calculations," IMF Working Papers 09/271, International Monetary Fund.
    4. Takanobu Nakajima & Alice Nakamura & Emi Nakamura & Masao Nakamura, 2007. "Technical change in a bubble economy: Japanese manufacturing firms in the 1990s," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 34(3), pages 247-271, July.
    5. Richard Grieve & Richard Nixon & Simon G. Thompson & Charles Normand, 2005. "Using multilevel models for assessing the variability of multinational resource use and cost data," Health Economics, John Wiley & Sons, Ltd., vol. 14(2), pages 185-196.
    6. Robert C. Feenstra & Alan Heston & Marcel P. Timmer & Haiyan Deng, 2009. "Estimating Real Production and Expenditures across Nations: A Proposal for Improving the Penn World Tables," The Review of Economics and Statistics, MIT Press, vol. 91(1), pages 201-212, February.
    7. David H. Good & M. Ishaq Nadiri & Robin C. Sickles, 1996. "Index Number and Factor Demand Approaches to the Estimation of Productivity," NBER Working Papers 5790, National Bureau of Economic Research, Inc.
    8. Diewert, W. Erwin & Fox, Kevin J., 2016. "Kevin J. Fox Interview of W. Erwin Diewert," working papers erwin_diewert-2016-6, Vancouver School of Economics, revised 02 Jun 2016.
    9. Travis D. Nesmith, 2006. "Rational seasonality," Finance and Economics Discussion Series 2007-04, Board of Governors of the Federal Reserve System (U.S.).
    10. Diewert, W. Erwin & Fox, Kevin J., 2017. "Substitution Bias in Multilateral Methods for CPI Construction using Scanner Data," working papers erwin_diewert-2017-3, Vancouver School of Economics, revised 23 Mar 2017.
    11. Almås, Ingvild & Sørensen, Erik Ø., 2012. "Global Income Inequality and Cost-of-Living Adjustment: The Geary–Allen World Accounts," Discussion Paper Series in Economics 20/2012, Norwegian School of Economics, Department of Economics.
    12. Tomasz Kuszewski & Agata Sielska, 2010. "The Useful art of the social-economic Rankings," Contemporary Economics, University of Finance and Management in Warsaw, vol. 4(1), March.
    13. Aten, Bettina & Heston, Alan, 2003. "Regional Output Differences in International Perspective," WIDER Working Paper Series 055, World Institute for Development Economic Research (UNU-WIDER).
    14. 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.
    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. 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.
    17. Magne Mogstad, 2007. "Measuring Income Inequality under Restricted Interpersonal Comparability," Discussion Papers 498, Statistics Norway, Research Department.
    18. Neary, J Peter, 2000. "True Multilateral Indexes for International Comparisons of Real Income: Theory and Empirics," CEPR Discussion Papers 2590, C.E.P.R. Discussion Papers.

    More about this item

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • F31 - International Economics - - International Finance - - - Foreign Exchange


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