Abstract
An index of richness in a society is a measure of the extent of its affluence. This paper presents an analytical discussion on several indices of richness and their properties. It also develops criteria for ordering alternative distributions of income in terms of their richness. Given a line of richness, an income level above which a person is regarded as rich, and depending on the redistributive principle, it is shown that the ranking relation can be implemented by seeking dominance with respect to the generalized Lorenz curve of the rich or the affluence profile of the society. When the line of richness is assumed to be variable, we need to employ the stochastic dominance conditions for ordering the income distributions.
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References
Atkinson, A.B.: On the measurement of inequality. J. Econ. Theory 2, 244–263 (1970)
Atkinson, A.B.: Measuring top incomes: methodological issues. In: Atkinson, A.B., Piketty, T. (eds.) Top Incomes over the Twentieth Century, pp. 18–42. Oxford University Press, Oxford (2007)
Atkinson, A.B., Piketty, T.: Top Incomes over the Twentieth Century. Oxford University Press, Oxford (2007)
Barry, B.: Social exclusion, social isolation and the distribution of income. In: Hills, J., Grand, J.L., Piachaud, D. (eds.) Understanding Social Exclusion, pp. 13–29. Oxford University Press, Oxford (2002)
Brzezinski, M.: Income affluence in Poland. Soc. Indic. Res. 99, 285–299 (2010)
Chakravarty, S.R.: Ethical indices of affluence. Meth. Oper. Res. 63, 35–43 (1993)
Chakravarty, S.R.: Inequality, Polarization and Poverty: Advances in Distributional Analysis. Springer, New York (2009)
Clark, S., Hamming, R., Ulph, D.: On indices for the measurement of poverty. Econ. J. 91, 515–526 (1981)
Foster, J.E., Shorrocks, A.F.: Poverty orderings. Econometrica 56, 173–177 (1988)
Jenkins, S.P., Lambert, P.J.: Three I’s of poverty curves, with an analysis of UK poverty trends. Oxf. Econ. Pap. 49, 317–327 (1997)
Jenkins, S.P., Lambert, P.J.: Ranking poverty gap distributions: further TIPs for poverty analysis. Res. Econ. Inequal. 8, 31–38 (1998)
Hadar, J., Russell, W.R.: Rules for ordering uncertain prospects. Am. Econ. Rev. 59, 25–34 (1969)
Jenkins, S.P., Lambert, P.J.: Three I’s of poverty curves and poverty dominance: TIP for poverty analysis. Res. Econ. Inequal. 8, 39–56 (1998)
Leigh, A.: Top incomes. In: Salverda, W., Nolan, B., Smeeding, T. (eds.) The Oxford Handbook of Economic Inequality, pp. 150–174. Oxford University Press, Oxford (2009)
Marshall, A.W., Olkin, I.: Inequalities: Theory of Majorization and its Applications. Academic Press, New York (1979)
Medeiros, M.: The rich and the poor: the construction of an affluence line from the poverty line. Soc. Indic. Res. 78, 1–18 (2006)
Merz, J., Hirschel, D., Zwick, M.: Struktur und Verteilung Hoher Einkomen-Mikroanalysen auf der Basis der Einkommensteuerstatistik. Beitrag zum zweiten Armuts-und Reichtumsbericht 2004 der Bundesregierung (2005)
Peichl, A., Pestel, N.: Multidimensional Measurement of Richness and the Role of Income and Wealth. Institute for the Study of Labor, Bonn (2010)
Peichl, A., Pestel, N.: Multidimensional affluences: theory and applications to Germany and the US. IZA Discussion Paper No. 5926. Measurement of Richness and the Role of Income and Wealth. Institute for the Study of Labor, Bonn (2011)
Peichl, A., Schaefer, T., Scheicher, C.: Measuring richness and poverty: a micro data application to Europe and Germany. Rev. Income Wealth 56, 597–619 (2010)
Piketty, T., Saez, E.: The evolution of top incomes: a historical and international perspective. Am. Econ. Rev. 96, 200–205 (2006)
Shorrocks, A.F.: Ranking income distributions. Economica 50, 1–17 (1983)
Shorrocks, A.F.: Deprivation profiles and deprivation indices. In: Jenkins, S.P., Kapteyn, A., van Praag, B. (eds.) The Distributions of Welfare and Household Production: International Perspective, pp. 250–267. Cambridge University Press, Cambridge (1998)
Watts, H.: An economic definition of poverty. In: Moynihan, D.P. (ed.) On Understanding Poverty. Basic Books, New York (1968)
Zheng, B.: Poverty orderings. J. Econ. Surv. 14, 427–466 (2000)
Zheng, B.: Minimum distribution-sensitivity, poverty aversion and poverty orderings. J. Econ. Theory 95, 116–137 (2000)
Zheng, B.: Unit-consistent poverty indices. Econ. Theory 31, 113–142 (2007)
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Research of A. Bose was supported by J.C. Bose National Fellowship, Dept. of Science and Technology, Govt. of India.
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Bose, A., Chakravarty, S.R. & D’Ambrosio, C. Richness orderings. J Econ Inequal 12, 5–22 (2014). https://doi.org/10.1007/s10888-013-9249-4
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DOI: https://doi.org/10.1007/s10888-013-9249-4