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Inequality of Well-Being and Isoelastic Equivalence Scales

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  • Udo Ebert
  • Patrick Moyes

Abstract

Equivalence scales are typically designed for adjusting households’ incomes for differences in size and composition. On the one hand, there is evidence that the way differences in needs across households are taken into account has a significant impact on the assessment of inequality in the society. On the other hand, equivalence scales with constant elasticity with respect to family size have been shown to provide a good approximation to a large variety of scales used in empirical work. We first show that, if one requires that the (multidimensional) inequality index is – in addition to standard properties – invariant to modifications of the relative (marginal) distributions of needs and income across households, then the equivalence scales must be isoelastic. Assuming that all individuals have the same preferences and that households maximise the sum of their members’ utilities, we also prove that the only preferences consistent with isoelastic scales are of the Cobb-Douglas type.

Suggested Citation

  • Udo Ebert & Patrick Moyes, 2011. "Inequality of Well-Being and Isoelastic Equivalence Scales," Working Papers V-333-11, University of Oldenburg, Department of Economics, revised Feb 2011.
    • Handle: RePEc:old:dpaper:333
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    References listed on IDEAS

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    1. Udo Ebert & Patrick Moyes, 2009. "Household decisions and equivalence scales," Journal of Population Economics, Springer;European Society for Population Economics, vol. 22(4), pages 1039-1062, October.
    2. Timothy Smeeding & Gunther Schmaus & Brigitte Buhmann & Lee Rainwater, 1988. "Equivalence Scales, Well-Being, Inequality and Poverty: Sensitivity Estimates Across Ten Countries Using the LIS Database," LIS Working papers 17, LIS Cross-National Data Center in Luxembourg.
    3. Cutler, David M & Katz, Lawrence F, 1992. "Rising Inequality? Changes in the Distribution of Income and Consumption in the 1980's," American Economic Review, American Economic Association, vol. 82(2), pages 546-551, May.
    4. Udo Ebert, 2010. "Dominance criteria for welfare comparisons: using equivalent income to describe differences in needs," Theory and Decision, Springer, vol. 69(1), pages 55-67, July.
    5. Udo Ebert & Patrick Moyes, 2003. "Equivalence Scales Reconsidered," Econometrica, Econometric Society, vol. 71(1), pages 319-343, January.
    6. C. Seidl & Patrick Moyes & A. F. Shorrocks, 2002. "Inequalities: Theory, experiments and applications," Post-Print hal-00157353, HAL.
    7. Udo Ebert & Patrick Moyes, 2002. "Welfare, inequality and the transformation of incomes the case of weighted income distributions," Journal of Economics, Springer, vol. 77(1), pages 9-50, December.
    8. Brigitte Buhmann & Lee Rainwater & Guenther Schmaus & Timothy M. Smeeding, 1988. "Equivalence Scales, Well‐Being, Inequality, And Poverty: Sensitivity Estimates Across Ten Countries Using The Luxembourg Income Study (Lis) Database," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 34(2), pages 115-142, June.
    9. Edwards, John H. Y., 1990. "Congestion function specification and the "publicness" of local public goods," Journal of Urban Economics, Elsevier, vol. 27(1), pages 80-96, January.
    10. Coulter, Fiona A E & Cowell, Frank A & Jenkins, Stephen P, 1992. "Equivalence Scale Relativities and the Extent of Inequality and Poverty," Economic Journal, Royal Economic Society, vol. 102(414), pages 1067-1082, September.
    11. Buhmann, Brigitte, et al, 1988. "Equivalence Scales, Well-Being, Inequality, and Poverty: Sensitivity Estimates across Ten Countries Using the Luxembourg Income Study (LIS) Database," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 34(2), pages 115-142, June.
    12. Ebert, Udo, 2000. "Sequential Generalized Lorenz Dominance and Transfer Principles," Bulletin of Economic Research, Wiley Blackwell, vol. 52(2), pages 113-122, April.
    13. Patrick Moyes & Stephen Bazen, 2003. "International Comparisons of Income Distribution," LIS Working papers 341, LIS Cross-National Data Center in Luxembourg.
    14. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
    15. Donaldson, David & Pendakur, Krishna, 2004. "Equivalent-expenditure functions and expenditure-dependent equivalence scales," Journal of Public Economics, Elsevier, vol. 88(1-2), pages 175-208, January.
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    Cited by:

    1. Stephen Bazen & Patrick Moyes, 2012. "Elitism and stochastic dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 207-251, June.

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    More about this item

    Keywords

    Inequality of Well-Being; Household Size; Equivalence Scales; Constant Elasticity; Cobb-Douglas Preferences;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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