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Index-Number Tests and the Common-Scaling Social Cost-of-Living Index

  • Donaldson, David
  • Pendakur, Krishna

For a change in prices, the common-scaling social cost-of-living index is the equal scaling of every individual's expenditure level needed to restore the level of social welfare to its pre-change value. This index does not, in general, satisfy two standard index-number tests. The reversal test requires the index value for the reverse change to be the reciprocal of the original index. And the circular test requires the product of index values for successive price changes to be equal to the index value for the whole change. We show that both tests are satisfied if and only if the Bergson-Samuelson indirect social-welfare function is homothetic in prices, a condition which does not require individual preferences to be homothetic. If individual preferences are homothetic, however, stronger conditions on the Bergson-Samuelson indirect must be satisfied. Given these results, we ask whether the restrictions are empirically reasonable and find, in the case that individual preferences are not homothetic, that the restrictions make little difference to estimates of the index.

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Paper provided by Vancouver School of Economics in its series Economics working papers with number david_donaldson-2010-4.

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Length: 24 pages
Date of creation: 04 Feb 2010
Date of revision: 04 Feb 2010
Handle: RePEc:ubc:bricol:david_donaldson-2010-4
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  1. David Donaldson & Krishna Pendakur, 2012. "Index-number tests and the common-scaling social cost-of-living index," Social Choice and Welfare, Springer, vol. 38(3), pages 407-429, March.
  2. Pendakur, K., 1999. "Taking Prices Seriously in the Measurement of Inequality," Discussion Papers dp99-7, Department of Economics, Simon Fraser University.
  3. Crossley, Thomas F. & Pendakur, Krishna, 2010. "The Common-Scaling Social Cost-of-Living Index," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 523-538.
  4. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
  5. E. T. McPHEE., 1928. "Notes," The Economic Record, The Economic Society of Australia, vol. 4(1), pages 92-95, 05.
  6. Pollak, Robert A., 1981. "The social cost of living index," Journal of Public Economics, Elsevier, vol. 15(3), pages 311-336, June.
  7. Pollak, Robert A, 1980. "Group Cost-of-Living Indexes," American Economic Review, American Economic Association, vol. 70(2), pages 273-78, May.
  8. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  9. Blackorby,Charles & Bossert,Walter & Donaldson,David J., 2005. "Population Issues in Social Choice Theory, Welfare Economics, and Ethics," Cambridge Books, Cambridge University Press, number 9780521532587, October.
  10. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
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