Skip to main content

Richness orderings

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.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Atkinson, A.B.: On the measurement of inequality. J. Econ. Theory 2, 244–263 (1970)

    Article  Google Scholar 

  2. 2.

    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)

    Google Scholar 

  3. 3.

    Atkinson, A.B., Piketty, T.: Top Incomes over the Twentieth Century. Oxford University Press, Oxford (2007)

    Google Scholar 

  4. 4.

    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)

    Google Scholar 

  5. 5.

    Brzezinski, M.: Income affluence in Poland. Soc. Indic. Res. 99, 285–299 (2010)

    Article  Google Scholar 

  6. 6.

    Chakravarty, S.R.: Ethical indices of affluence. Meth. Oper. Res. 63, 35–43 (1993)

    Google Scholar 

  7. 7.

    Chakravarty, S.R.: Inequality, Polarization and Poverty: Advances in Distributional Analysis. Springer, New York (2009)

    Book  Google Scholar 

  8. 8.

    Clark, S., Hamming, R., Ulph, D.: On indices for the measurement of poverty. Econ. J. 91, 515–526 (1981)

    Article  Google Scholar 

  9. 9.

    Foster, J.E., Shorrocks, A.F.: Poverty orderings. Econometrica 56, 173–177 (1988)

    Article  Google Scholar 

  10. 10.

    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)

    Article  Google Scholar 

  11. 11.

    Jenkins, S.P., Lambert, P.J.: Ranking poverty gap distributions: further TIPs for poverty analysis. Res. Econ. Inequal. 8, 31–38 (1998)

    Google Scholar 

  12. 12.

    Hadar, J., Russell, W.R.: Rules for ordering uncertain prospects. Am. Econ. Rev. 59, 25–34 (1969)

    Google Scholar 

  13. 13.

    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)

    Google Scholar 

  14. 14.

    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)

    Google Scholar 

  15. 15.

    Marshall, A.W., Olkin, I.: Inequalities: Theory of Majorization and its Applications. Academic Press, New York (1979)

    Google Scholar 

  16. 16.

    Medeiros, M.: The rich and the poor: the construction of an affluence line from the poverty line. Soc. Indic. Res. 78, 1–18 (2006)

    Article  Google Scholar 

  17. 17.

    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)

  18. 18.

    Peichl, A., Pestel, N.: Multidimensional Measurement of Richness and the Role of Income and Wealth. Institute for the Study of Labor, Bonn (2010)

    Google Scholar 

  19. 19.

    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)

  20. 20.

    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)

    Article  Google Scholar 

  21. 21.

    Piketty, T., Saez, E.: The evolution of top incomes: a historical and international perspective. Am. Econ. Rev. 96, 200–205 (2006)

    Article  Google Scholar 

  22. 22.

    Shorrocks, A.F.: Ranking income distributions. Economica 50, 1–17 (1983)

    Google Scholar 

  23. 23.

    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)

    Google Scholar 

  24. 24.

    Watts, H.: An economic definition of poverty. In: Moynihan, D.P. (ed.) On Understanding Poverty. Basic Books, New York (1968)

    Google Scholar 

  25. 25.

    Zheng, B.: Poverty orderings. J. Econ. Surv. 14, 427–466 (2000)

    Article  Google Scholar 

  26. 26.

    Zheng, B.: Minimum distribution-sensitivity, poverty aversion and poverty orderings. J. Econ. Theory 95, 116–137 (2000)

    Article  Google Scholar 

  27. 27.

    Zheng, B.: Unit-consistent poverty indices. Econ. Theory 31, 113–142 (2007)

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Conchita D’Ambrosio.

Additional information

Research of A. Bose was supported by J.C. Bose National Fellowship, Dept. of Science and Technology, Govt. of India.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

Keywords

  • Richness measurement
  • Poverty
  • Equity

JEL Classification

  • D63