Measuring inequality with interval data
AbstractThis paper employs the axiomatic approach underpinning the literature on income inequality measurement to analyze measures of dispersion in interval data. We find that some widely employed measures fail to properly measure dispersion when data are not of the ratio type. We go on to prove that, under reasonable conditions, variance is the only decomposable measure that can be used to consistently measure inequality of interval data. Moreover, the only proper Lorenz dominance condition for interval data is absolute Lorenz dominance that Moyes [Moyes, P., 1987. A new concept of Lorenz domination. Economics Letters 23, 203-207] introduced.
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Bibliographic InfoArticle provided by Elsevier in its journal Mathematical Social Sciences.
Volume (Year): 58 (2009)
Issue (Month): 1 (July)
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Web page: http://www.elsevier.com/locate/inca/505565
Unit-consistency Unit-invariance Decomposable measures Variance Inequality orderings Absolute Lorenz dominance;
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- Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
- Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
- Buhong Zheng, 2007. "Inequality orderings and unit consistency," Social Choice and Welfare, Springer, vol. 29(3), pages 515-538, October.
- Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
- Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
- Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
- Buhong Zheng, 2007. "Unit-Consistent Decomposable Inequality Measures," Economica, London School of Economics and Political Science, vol. 74(293), pages 97-111, 02.
- Zheng, Buhong, 1994. "Can a Poverty Index Be Both Relative and Absolute?," Econometrica, Econometric Society, vol. 62(6), pages 1453-58, November.
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