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Chain indices of the cost of living and the path-dependence problem: an empirical solution

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  • Oulton, Nicholas

Abstract

This paper proposes an empirically feasible method for correcting the path-dependence bias of chain indices of the cost of living. Chain indices are discrete approximations to Divisia indices and it is well known that the latter are path-dependent: the level of a Divisia index is affected not just by the level of prices at the two endpoints but also by the path between the endpoints. It is also well-known that a Divisia index of the cost of living is path-independent if and only if all income elasticities are equal to one, a restriction that is decisively rejected by studies of consumer demand. In theory, the true cost of living index (or Konüs price index) could be derived by estimating the expenditure function. But this seems impractical due to data limitations: the number of independent parameters rises roughly in proportion to the square of the number of commodities and consumer price indices contain hundreds of items. This paper shows how this problem can in fact be overcome empirically using a flexible model of demand like the “Quadratic Almost Ideal Demand System”. The proposed method requires data only on prices, aggregate budget shares and aggregate expenditure. The method is applied to estimate Konüs price indices for 70 products covering nearly all the UK’s Retail Prices Index over 1974-2004, with each year in turn as the base. The choice of base year for utility is found to have a significant effect on the index, even in the low inflation period since 1990.

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  • Oulton, Nicholas, 2007. "Chain indices of the cost of living and the path-dependence problem: an empirical solution," LSE Research Online Documents on Economics 19718, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:19718
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    1. Christopher F Baum & Mark E. Schaffer & Steven Stillman, 2003. "Instrumental variables and GMM: Estimation and testing," Stata Journal, StataCorp LP, vol. 3(1), pages 1-31, March.
    2. Anthony J. Venables, 2006. "Shifts in economic geography and their causes," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 15-39.
    3. Unknown, 1967. "Index," 1967 Conference, August 21-30, 1967, Sydney, New South Wales, Australia 209796, International Association of Agricultural Economists.
    4. 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.
    5. Andrew B. Bernard & J. Bradford Jensen & Stephen J. Redding & Peter K. Schott, 2007. "Firms in International Trade," Journal of Economic Perspectives, American Economic Association, vol. 21(3), pages 105-130, Summer.
    6. Buiter, Willem H., 2007. "Seigniorage," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 1, pages 1-49.
    7. Oulton, Nicholas, 2008. "Chain indices of the cost-of-living and the path-dependence problem: An empirical solution," Journal of Econometrics, Elsevier, vol. 144(1), pages 306-324, May.
    8. 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.
    9. J. Peter Neary, 2004. "Rationalizing the Penn World Table: True Multilateral Indices for International Comparisons of Real Income," American Economic Review, American Economic Association, vol. 94(5), pages 1411-1428, December.
    10. Andrew B. Bernard & Stephen J. Redding & Peter K. Schott, 2011. "Multiproduct Firms and Trade Liberalization," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(3), pages 1271-1318.
    11. 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.
    12. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-1025, November.
    13. 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.
    14. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
    15. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers," Economic Journal, Royal Economic Society, vol. 92(365), pages 73-86, March.
    16. John Shea, 1997. "Instrument Relevance in Multivariate Linear Models: A Simple Measure," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 348-352, May.
    17. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
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    Cited by:

    1. 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.
    2. Hosseiny, Ali, 2017. "A geometrical imaging of the real gap between economies of China and the United States," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 151-161.
    3. Bettina Aten & Marshall Reinsdorf, 2010. "Comparing the Consistency of Price Parities for Regions of the U.S. in an Economic Approach Framework," BEA Papers 0098, Bureau of Economic Analysis.
    4. Ali Hosseiny, 2015. "Violation of Invariance of Measurement for GDP Growth Rate and its Consequences," Papers 1507.04848, arXiv.org, revised Aug 2016.
    5. Nicholas Oulton, 2021. "The effect of changes in the terms of trade on GDP and welfare: a Divisia approach to the SNA," Discussion Papers 2126, Centre for Macroeconomics (CFM).
    6. Matthew J Osborne & Nathan H. Miller, 2011. "Competition among Spatially Differentiated Firms: An Estimator with an Application to Cement," BEA Working Papers 0072, Bureau of Economic Analysis.
    7. Oulton, Nicholas, 2015. "Space-time (In)consistency in the national accounts: causes and cures," LSE Research Online Documents on Economics 86285, London School of Economics and Political Science, LSE Library.
    8. Oulton, Nicholas, 2015. "Understanding the space–time (in)consistency of the national accounts," Economics Letters, Elsevier, vol. 132(C), pages 21-23.
    9. Nicholas Oulton, 2019. "GDP is a measure of output, not welfare. Or, HOS meets the SNA," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2019-06, Economic Statistics Centre of Excellence (ESCoE).
    10. Hammond, Peter J. & Liberini, Federica & Proto, Eugenio, 2011. "Individual Welfare and Subjective Well-Being : Commentary Inspired by Sacks, Stevenson and Wolfers," The Warwick Economics Research Paper Series (TWERPS) 957, University of Warwick, Department of Economics.
    11. Bettina Aten & Eric Figueroa & Troy Martin, 2011. "Notes on Estimating the Multi-Year Regional Price Parities by 16 Expenditure Categories: 2005-2009," BEA Working Papers 0071, Bureau of Economic Analysis.
    12. Oulton, Nicholas, 2008. "Chain indices of the cost-of-living and the path-dependence problem: An empirical solution," Journal of Econometrics, Elsevier, vol. 144(1), pages 306-324, May.
    13. Nicholas Oulton, 2023. "The effect of changes in the terms of trade on GDP and welfare: A Divisia approach to the System of National Accounts," Manchester School, University of Manchester, vol. 91(4), pages 261-282, July.
    14. 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.
    15. Nicholas Oulton, 2022. "The Divisia approach to measuring output and productivity: with an application to the BEA-BLS integrated industry-level production account, 1987-2020," Discussion Papers 2217, Centre for Macroeconomics (CFM).

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    More about this item

    Keywords

    Index number; cost of living; Divisia; Chain; Path-dependence; Almost Ideal Demand System;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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