IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_818.html
   My bibliography  Save this paper

A General Theory of Price and Quantity Aggregation and Welfare Measurement

Author

Listed:
  • Claude Hillinger

Abstract

The paper presents a general theory of the aggregation of prices and quantities that unifies the field and relates topics that in the past have been treated separately and unsatisfactorily, or not at all. The theory does without the common but unrealistic assumptions of homotheticity, or representative agents and is valid with or without an explicit utility maximization assumption. Two different derivations are given, one in continuous time, using Divisia integrals, and one employing more traditional discrete arguments. The unifying concept is the money metric, which is interpreted as a partial welfare indicator, rather than as a comprehensive welfare measure. On this basis, a consistent set of chained price and quantity indexes for a set of additive time series, such as those in the national income and product accounts, is derived. All variants of the theory lead to Törnqvist indexes defined on the appropriate data set. A numerical example confirms that in the non-homothetic case, these indexes are superior both to Fisher’s ‘ideal’ index and to the consumer surplus approximation.

Suggested Citation

  • Claude Hillinger, 2002. "A General Theory of Price and Quantity Aggregation and Welfare Measurement," CESifo Working Paper Series 818, CESifo.
  • Handle: RePEc:ces:ceswps:_818
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo_wp818.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Samuelson, Paul A & Swamy, S, 1974. "Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis," American Economic Review, American Economic Association, vol. 64(4), pages 566-593, September.
    2. Diewert, W E, 1976. "Harberger's Welfare Indicator and Revealed Preference Theory," American Economic Review, American Economic Association, vol. 66(1), pages 143-152, March.
    3. Bert M. Balk, 2005. "Divisia price and quantity indices: 80 years after," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(2), pages 119-158, May.
    4. Claude Hillinger, 2001. "Money Metric, Consumer Surplus and Welfare Measurement," German Economic Review, Verein für Socialpolitik, vol. 2(2), pages 177-193, May.
    5. Diewert, W E, 1992. "Exact and Superlative Welfare Change Indicators," Economic Inquiry, Western Economic Association International, vol. 30(4), pages 562-582, October.
    6. Apps, Patricia F & Rees, Ray, 1997. "Collective Labor Supply and Household Production," Journal of Political Economy, University of Chicago Press, vol. 105(1), pages 178-190, February.
    7. McKenzie,George W., 1983. "Measuring Economic Welfare," Cambridge Books, Cambridge University Press, number 9780521248624, November.
    8. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    9. Diewert, W Erwin, 1978. "Superlative Index Numbers and Consistency in Aggregation," Econometrica, Econometric Society, vol. 46(4), pages 883-900, July.
    10. Pollak, Robert A, 1980. "Group Cost-of-Living Indexes," American Economic Review, American Economic Association, vol. 70(2), pages 273-278, May.
    11. Chiuri, M C & Simmons, P J, 1997. "Universal Decentralisation: A Demand System for Collective and Unitary Models with Household Public Goods," Economic Journal, Royal Economic Society, vol. 107(441), pages 372-389, March.
    12. Samuelson, Paul A, 1974. "Complementarity-An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory," Journal of Economic Literature, American Economic Association, vol. 12(4), pages 1255-1289, December.
    13. Daniel T. Slesnick, 1998. "Empirical Approaches to the Measurement of Welfare," Journal of Economic Literature, American Economic Association, vol. 36(4), pages 2108-2165, December.
    14. Jorgenson, Dale W, 1990. "Aggregate Consumer Behavior and the Measurement of Social Welfare," Econometrica, Econometric Society, vol. 58(5), pages 1007-1040, September.
    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. Diane Coyle & Jen-Chung Mei, 2022. "Diagnosing the Uk Productivity Slowdown: Which Sectors Matter and Why?," Working Papers 018, The Productivity Institute.

    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. Hillinger, Claude, 2008. "Measuring Real Value and Inflation," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 2, pages 1-26.
    2. Hillinger Claude, 2003. "The Money Metric, Price and Quantity Aggregation and Welfare Measurement," The B.E. Journal of Macroeconomics, De Gruyter, vol. 3(1), pages 1-36, July.
    3. Marshall Reinsdorf & Jack E. Triplett, 2009. "A Review of Reviews: Ninety Years of Professional Thinking About the Consumer Price Index," NBER Chapters, in: Price Index Concepts and Measurement, pages 17-83, National Bureau of Economic Research, Inc.
    4. Hillinger Claude, 2001. "Money Metric, Consumer Surplus and Welfare Measurement," German Economic Review, De Gruyter, vol. 2(2), pages 177-193, May.
    5. DECANCQ, Koen & FLEURBAEY, Marc & SCHOKKAERT, Erik, 2014. "Inequality, income, and well-being," LIDAM Discussion Papers CORE 2014018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Barnett, William A. & Choi, Ki-Hong, 2008. "Operational identification of the complete class of superlative index numbers: An application of Galois theory," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 603-612, July.
    7. Gregory Kurtzon, 2022. "How much does formula versus chaining matter for a cost‐of‐living index? The CPI‐U versus the C‐CPI‐U," Economic Inquiry, Western Economic Association International, vol. 60(2), pages 645-667, April.
    8. 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.
    9. M. Fleurbaey., 2012. "Beyond GDP: The Quest for a Measure of Social Welfare," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 2.
    10. Diewert, Erwin, 2009. "Cost of Living Indexes and Exact Index Numbers," Economics working papers erwin_diewert-2009-6, Vancouver School of Economics, revised 13 Feb 2009.
    11. 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.
    12. Andrew Aitken & Martin Weale, 2020. "A Democratic Measure of Household Income Growth: Theory and Application to the United Kingdom," Economica, London School of Economics and Political Science, vol. 87(347), pages 589-610, July.
    13. M. Ali Khan & Edward E. Schlee, 2016. "On Lionel McKenzie's 1957 intrusion into 20th‐century demand theory," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 49(2), pages 589-636, May.
    14. Liao, Hua & Fan, Ying & Wei, Yi-Ming, 2007. "What induced China's energy intensity to fluctuate: 1997-2006?," Energy Policy, Elsevier, vol. 35(9), pages 4640-4649, September.
    15. Hyun H. Son & Nanak Kakwani, 2006. "Measuring the impact of prices on inequality: with applications to Thailand and Korea," Working Papers 11, International Policy Centre for Inclusive Growth.
    16. Leonard I. Nakamura, 2020. "Evidence of Accelerating Mismeasurement of Growth and Inflation in the U.S. in the 21st Century," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2020-15, Economic Statistics Centre of Excellence (ESCoE).
    17. W. Erwin Diewert, 2005. "Index Number Theory Using Differences Rather Than Ratios," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 311-360, January.
    18. Robert J. Hill & Alice O. Nakamura, 2010. "Improving Inflation And Related Performance Measures For Nations: An Introduction," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 1-10, June.
    19. Diewert, Erwin & Fox, Kevin J., 2019. "Productivity Indexes and National Statistics: Theory, Methods and Challenges," Microeconomics.ca working papers erwin_diewert-2019-8, Vancouver School of Economics, revised 25 Apr 2019.
    20. Armstrong, Keir G., 2001. "Microeconomic Foundations for the Theory of International Comparisons," Journal of Economic Theory, Elsevier, vol. 101(2), pages 585-605, December.

    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:ces:ceswps:_818. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/cesifde.html .

    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: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.