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

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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 endpoint condition is given for the ∪shaped relationship, which corresponds to a condition for that of the generalised entropy measures. Additionally, using a mixture of lognormal 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 endpoint condition essentially determines the shape of the relationship.
Item Type:  MPRA Paper 

Original Title:  The Relationship between the Equivalence Scale and the Inequality Index and Its Impact on the Measurement of Income Inequality 
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 
Item ID:  37410 
Depositing User:  Masato Okamoto 
Date Deposited:  17. Mar 2012 12:37 
Last Modified:  12. Feb 2013 08:25 
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 nonseparable generalization of the linear expenditure system allowing nonlinear Engel curves.’ Economics Letters, vol. 9, pp. 349–354. Buhman, B., Rainwater, L., Schmaus, G. and Smeeding, T. (1988). ‘Equivalence scales, wellbeing, 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 PraisHouthakker 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. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/37410 