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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

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Abstract

This paper proposes an empirically feasible method for correcting the path-dependence bias of chainindices of the cost of living. Chain indices are discrete approximations to Divisia indices and it is wellknown that the latter are path-dependent: the level of a Divisia index is affected not just by the levelof prices at the two endpoints but also by the path between the endpoints. It is also well-known that aDivisia index of the cost of living is path-independent if and only if all income elasticities are equal toone, a restriction that is decisively rejected by studies of consumer demand. In theory, the true cost ofliving index (or Konüs price index) could be derived by estimating the expenditure function. But thisseems impractical due to data limitations: the number of independent parameters rises roughly inproportion to the square of the number of commodities and consumer price indices contain hundredsof items. This paper shows how this problem can in fact be overcome empirically using a flexiblemodel of demand like the "Quadratic Almost Ideal Demand System". The proposed method requiresdata only on prices, aggregate budget shares and aggregate expenditure. The method is applied toestimate Konüs price indices for 70 products covering nearly all the UK's Retail Prices Index over1974-2004, with each year in turn as the base. The choice of base year for utility is found to have asignificant effect on the index, even in the low inflation period since 1990.

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

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Find related papers by 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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  1. Bernard, Andrew & Jensen, J Bradford & Redding, Stephen J & Schott, Peter, 2007. "Firms in International Trade," CEPR Discussion Papers 6277, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  2. Andrew B. Bernard & Stephen J. Redding & Peter K. Schott, 2006. "Multi-Product Firms and Trade Liberalization," NBER Working Papers 12782, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Anthony J. Venables, 2006. "Shifts in Economic Geography and their Causes," CEP Discussion Papers dp0767, Centre for Economic Performance, LSE. [Downloadable!]
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  4. Buiter, Willem H., 2007. "Seigniorage," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 1(10), pages 1-49. [Downloadable!]
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