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The Relationship between the Equivalence Scale and the Inequality Index and Its Impact on the Measurement of Income Inequality

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  • Okamoto, Masato

Abstract

The paper discusses the ∪-shaped relationship between the equivalence scale n^ε and the Gini index instead of considering the equivalence scale’s relationship to the generalised entropy measures, which was studied by Coulter, et al. (1992). An end-point condition is given for the ∪-shaped relationship, which corresponds to a condition for that of the generalised entropy measures. Additionally, using a mixture of log-normal distributions approach, five factors are shown to be required for a convex relationship between size elasticity and the Gini index. Empirically, income distributions satisfy those factors. Thus, the end-point condition essentially determines the shape of the relationship.

Suggested Citation

  • Okamoto, Masato, 2012. "The Relationship between the Equivalence Scale and the Inequality Index and Its Impact on the Measurement of Income Inequality," MPRA Paper 37410, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:37410
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    References listed on IDEAS

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    1. Banks, James & Johnson, Paul, 1994. "Equivalence Scale Relativities Revisited," Economic Journal, Royal Economic Society, vol. 104(425), pages 883-890, July.
    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. repec:bla:revinw:v:37:y:1991:i:3:p:313-29 is not listed on IDEAS
    4. Masato Okamoto, 2009. "Decomposition of gini and multivariate gini indices," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(2), pages 153-177, June.
    5. Muellbauer, John, 1980. "The Estimation of the Prais-Houthakker Model of Equivalence Scales," Econometrica, Econometric Society, vol. 48(1), pages 153-176, January.
    6. 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.
    7. Jenkins, Stephen P & Cowell, Frank A, 1994. "Parametric Equivalence Scales and Scale Relativities," Economic Journal, Royal Economic Society, vol. 104(425), pages 891-900, July.
    8. 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.
    9. McClements, L. D., 1977. "Equivalence scales for children," Journal of Public Economics, Elsevier, vol. 8(2), pages 191-210, October.
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    13. Shelley Phipps & Thesia I. Garner, 1994. "Are Equivalence Scales The Same For The United States And Canada?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 40(1), pages 1-17, March.
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    Cited by:

    1. Stefan Kranzinger, 2020. "The decomposition of income inequality in the EU-28," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 47(3), pages 643-668, August.
    2. Sergey A. Surkov & Ellen G. Trofimova, 2014. "Paradoxes of Poverty in Russia in Conditions of Growth of Highly Profitable Sectors of Economy," International Journal of Economics and Empirical Research (IJEER), The Economics and Social Development Organization (TESDO), vol. 2(10), pages 420-424, October.
    3. Masato Okamoto, 2012. "Evaluation of the goodness of fit of new statistical size distributions with consideration of accurate income inequality estimation," Economics Bulletin, AccessEcon, vol. 32(4), pages 2969-2982.

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    More about this item

    Keywords

    inequality; income distribution; equivalence scale;
    All these keywords.

    JEL classification:

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

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