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The Social Cost-of-Living: Welfare Foundations and Estimation

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  • Thomas F. Crossley
  • Krishna Pendakur

Abstract

We present a new class of social cost-of-living indices and a nonparametric framework for estimating these and other social cost-of-living indices. Common social cost-of-living indices can be understood as aggregator functions of approximations of individual cost-of-living indices. The Consumer Price Index (CPI) is the expenditure-weighted average of first-order approximations of each individual’s cost-of-living index. This is troubling for three reasons. First, it has not been shown to have a welfare economic foundation for the case where agents are heterogeneous (as they clearly are.) Second, it uses an expenditure-weighted average which downweights the experience of poor households relative to rich households. Finally, it uses only first-order approximations of each individual’s cost-of-living index, and thus ignores substitution effects. We propose a “common-scaling” social cost-of-living index, which is defined as the single scaling to everyone’s expenditure which holds social welfare constant across a price change. Our approach has an explicit social welfare foundation and allows us to choose the weights on the costs of rich and poor households. We also give a unique solution for the welfare function for the case where the weights are independent of household expenditure. A first order approximation of our social cost-of-living index nests as special cases commonly used indices such as the CPI. We also provide a nonparametric method for estimating second-order approximations (which account for substitution effects).

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Bibliographic Info

Paper provided by McMaster University in its series Social and Economic Dimensions of an Aging Population Research Papers with number 155.

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Length: 39 pages
Date of creation: Jun 2006
Date of revision:
Handle: RePEc:mcm:sedapp:155

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Keywords: Inflation; Social cost-of-living; Demand; Average derivatives;

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  1. Angus Deaton, 1998. "Getting Prices Right: What Should Be Done?," Journal of Economic Perspectives, American Economic Association, vol. 12(1), pages 37-46, Winter.
  2. Michael J. Boskin, 1998. "Consumer Prices, the Consumer Price Index, and the Cost of Living," Journal of Economic Perspectives, American Economic Association, vol. 12(1), pages 3-26, Winter.
  3. Pendakur, K., 1999. "Taking Prices Seriously in the Measurement of Inequality," Discussion Papers dp99-7, Department of Economics, Simon Fraser University.
  4. Eduardo Ley, 2001. "Whose Inflation? A Characterization of the CPI Plutocratic Gap," Public Economics 0110001, EconWPA, revised 20 Oct 2001.
  5. Pollak, Robert A., 1981. "The social cost of living index," Journal of Public Economics, Elsevier, vol. 15(3), pages 311-336, June.
  6. Vartia, Yrjo O, 1983. "Efficient Methods of Measuring Welfare Change and Compensated Income in Terms of Ordinary Demand Functions," Econometrica, Econometric Society, vol. 51(1), pages 79-98, January.
  7. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
  8. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
  9. Banks, James & Blundell, Richard & Lewbel, Arthur, 1996. "Tax Reform and Welfare Measurement: Do We Need Demand System Estimation?," Economic Journal, Royal Economic Society, vol. 106(438), pages 1227-41, September.
  10. W. Erwin Diewert, 1998. "Index Number Issues in the Consumer Price Index," Journal of Economic Perspectives, American Economic Association, vol. 12(1), pages 47-58, Winter.
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