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

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  • Donaldson, David
  • Pendakur, Krishna

Abstract

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.

Suggested Citation

  • Donaldson, David & Pendakur, Krishna, 2010. "Index-Number Tests and the Common-Scaling Social Cost-of-Living Index," Economics working papers david_donaldson-2010-4, Vancouver School of Economics, revised 04 Feb 2010.
  • Handle: RePEc:ubc:bricol:david_donaldson-2010-4
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    References listed on IDEAS

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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;The Society for Social Choice and Welfare, vol. 38(3), pages 407-429, March.
    2. 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.
    3. Pendakur, Krishna, 2002. "Taking prices seriously in the measurement of inequality," Journal of Public Economics, Elsevier, vol. 86(1), pages 47-69, October.
    4. Pollak, Robert A, 1980. "Group Cost-of-Living Indexes," American Economic Review, American Economic Association, vol. 70(2), pages 273-278, May.
    5. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    6. 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.
    7. 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.
    8. 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.
    9. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    10. Pollak, Robert A., 1981. "The social cost of living index," Journal of Public Economics, Elsevier, vol. 15(3), pages 311-336, June.
    11. E. T. McPHEE., 1928. "Notes," The Economic Record, The Economic Society of Australia, vol. 4(1), pages 92-95, May.
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    Cited by:

    1. Stefan Sperlich & Raoul Theler, 2015. "Modeling heterogeneity: a praise for varying-coefficient models in causal analysis," Computational Statistics, Springer, vol. 30(3), pages 693-718, September.
    2. repec:eee:wdevel:v:97:y:2017:i:c:p:102-121 is not listed on IDEAS
    3. David Donaldson & Krishna Pendakur, 2012. "Index-number tests and the common-scaling social cost-of-living index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 407-429, March.
    4. Ingvild Almås & Anders Kjelsrud, 2016. "Pro-poor Price Trends and Inequality - The Case of India," CESifo Working Paper Series 5740, CESifo Group Munich.
    5. Rodrigo Lluberas, 2013. "Life-cycle expenditure and retirees’ cost of living," Documentos de trabajo 2013007, Banco Central del Uruguay.

    More about this item

    Keywords

    social cost of living; aggregation; welfare economics;

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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