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Chain Indices of the Cost of Living and the Path-Dependence Problem: An Empirical Solution

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  • Nicholas Oulton

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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  • Nicholas Oulton, 2007. "Chain Indices of the Cost of Living and the Path-Dependence Problem: An Empirical Solution," CEP Discussion Papers dp0797, Centre for Economic Performance, LSE.
  • Handle: RePEc:cep:cepdps:dp0797
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    Cited by:

    1. 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.
    2. 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.
    3. Ali Hosseiny, 2015. "Violation of Invariance of Measurement for GDP Growth Rate and its Consequences," Papers 1507.04848, arXiv.org, revised Aug 2016.
    4. 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.
    5. 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.
    6. 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.
    7. Oulton, Nicholas, 2015. "Understanding the space–time (in)consistency of the national accounts," Economics Letters, Elsevier, vol. 132(C), pages 21-23.
    8. 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.
    9. 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.
    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.

    More about this item

    Keywords

    Index number; cost of living; Divisia; Chain; Path-dependence; Almost Ideal Demand System;

    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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