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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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Bibliographic Info

Paper provided by Centre for Economic Performance, LSE in its series CEP Discussion Papers with number dp0797.

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Date of creation: May 2007
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Handle: RePEc:cep:cepdps:dp0797

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Web page: http://cep.lse.ac.uk/_new/publications/series.asp?prog=CEP

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

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References

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  1. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-25, November.
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  8. 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.
  9. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June.
  10. 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.
  11. 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.
  12. 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.
  13. Andrew Bernard & Stephen Redding & Peter Schott, 2009. "Multi-Product Firms and Trade Liberalization," Working Papers 09-21, Center for Economic Studies, U.S. Census Bureau.
  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. 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 566-93, September.
  16. 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.
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Cited by:
  1. Nicholas Oulton, 2009. "How to measure living standards and productivity," LSE Research Online Documents on Economics 28678, London School of Economics and Political Science, LSE Library.
  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. 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.
  4. 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.
  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. 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.

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