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

Okamoto, Masato (2012): The Relationship between the Equivalence Scale and the Inequality Index and Its Impact on the Measurement of Income Inequality.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: inequality; income distribution; equivalence scale
• Subjects: D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement; D - Microeconomics > D3 - Distribution > D31 - Personal Income, Wealth, and Their Distributions

References

Banks, J. and Johnson, P. (1994). ‘Equivalence scale relativities revisited.’ Economic Journal, vol. 104, pp. 883–890. Blundell, R. and Ray, R. (1982). ‘A non-separable generalization of the linear expenditure system allowing non-linear Engel curves.’ Economics Letters, vol. 9, pp. 349–354. Buhman, B., Rainwater, L., Schmaus, G. and Smeeding, T. (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, vol. 34, pp. 115–42. Coulter, F. A. E., Cowell, F. and Jenkins, S. (1992). ‘Equivalence scale relativities and the extent of inequality and poverty.’ Economic Journal, vol. 102, pp. 1067–82. Deaton, A. S. and Muellbauer, J. (1986). ‘On measuring child costs: with applications to poor countries.’ Journal of Political Economy, vol. 94, pp. 720–744. Jenkins, S. P. and Cowell, F. A. (1994). ‘Parametric equivalence scales and scale relativities.’ Economic Journal, vol. 104, pp. 891–900. Kleiber, C. and Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences. Hoboken: John Wiley & Sons. Luxembourg Income Study (LIS) Database. (2012). http://www.lisdatacenter.org. Luxembourg: LIS. McClements, L. D. (1977). ‘Equivalence scale for children.’ Journal of Public Economics, vol. 8, pp. 191–210. Muellbauer, J. (1977). ‘Testing the Barten model of household composition effects and the cost of children.’ Economic Journal, vol. 87, pp. 460–87. Muellbauer, J. (1980). ‘The estimation of the Prais-Houthakker model of equivalence scales.’ Econometrica, vol. 48, pp. 153–176. Okamoto, M. (2009). ‘Decomposition of Gini and multivariate Gini indices.’ Journal of Economic Inequality, vol. 7, pp. 153–177. Phipps, S. and Garner, T. I. (1994). ‘Are equivalence scales the same for the United States and Canada?’ Review of Income and Wealth, vol. 40, pp. 1–17. Ray, R. (1983). ‘Measuring the costs of children.’ Journal of Public Economics, vol. 22, pp. 89–102. Yitzhaki, S. and Lerman, R. I. (1991). ‘Income stratification and income inequality.’ Review of Income and Wealth, vol. 37, pp. 313–329.