Advertisement

Quality and Quantity

, Volume 28, Issue 1, pp 83–97 | Cite as

A micro-macro linkage in the measurement of inequality: Another look at the Gini coefficient

  • Kunihiro Kimura
Article

Abstract

The aim of this paper is to help readers understand the significance of the Gini coefficient. We have two major formulae for the Gini coefficient. One of the formulae bases on the idea of aggregation of the microscopic differences between individuals' incomes or wealth. The idea that underlies the other formula is macroscopic presentation of distribution or concentration of income or wealth. We will show an unabridged proof of the equivalence between these formulae to examine how the two conceptions of the measurement of inequality are linked to each other.

Key words

The Gini coefficient measurement of inequality a micro-macro linkage 

References

  1. Allison, Paul D. (1978). Measures of Inequality,American Sociological Review 43(6): 865–880.Google Scholar
  2. Aoki, Masahiko (1979).Bunpai Riron, 2nd ed. (Theories of Distribution of Income and Wealth.) (in Japanese) Tokyo: Chikuma-shobo.Google Scholar
  3. Atkinson, Anthony B. (1970). On the Measurement of Inequality,Journal of Economic Theory 2(3): 244–263.Google Scholar
  4. Blau, Peter M. (1977).Inequality and Heterogeneity: A Primitive Theory of Social Structure, New York: Free Press.Google Scholar
  5. Coulter, Philip B. (1989).Measuring Inequality: A Methodological Handbook, Boulder, Colorado: Westview Press.Google Scholar
  6. Dalton, Hugh (1920). The Measurement of the Inequality of Incomes,Economic Journal 30(3): 348–361.Google Scholar
  7. Gini, Corrado (1912).Variabilità e Mutabilità: Contributo allo studio dette distribuzioni e delle relazioni statistiche, Bologna: Tipografia di Paolo Cuppini.Google Scholar
  8. Gini, Corrado (1914). Sulla misura della concentrazione e della variabilità dei caratteri,Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, Anno accademico 1913–1914. 73 (Parte seconda): 1203–1248.Google Scholar
  9. Gini, Corrado (1936). On the Measure of Concentration with Special Reference to Income and Wealth, pp. 73–80 inAbstracts of Papers presented at the Cowles Commission Research conference on economics and statistics. Colorado Springs: Colorado College Press.Google Scholar
  10. Kendall, Maurice G. and Alan Stuart (1963).The Advanced Theory of Statistics, Vol. 1,Distribution Theory, 2nd ed. London: Charles Griffin.Google Scholar
  11. Lorenz, Max O. (1905). Methods of Measuring the Concentration of Wealth,Publications of the American Statistical Association 9: 209–219.Google Scholar
  12. Rawls, John (1971).A Theory of Justice, Cambridge, Massachusetts: Harvard University Press.Google Scholar
  13. Saeki, Yutaka (1980).‘Kime-kata’ no Ronri (The Logic of Decision Procedures) (in Japanese). Tokyo: University of Tokyo Press.Google Scholar
  14. Schwartz, Joseph and Christopher Winship (1979). The Welfare Approach to Measuring Inequality, pp. 1–36 inSociological Methodology 1980, edited by Karl F. Schuessler. San Francisco: Jossey-Bass.Google Scholar
  15. Sen, Amartya (1973).On Economic Inequality, New York: W. W. Norton.Google Scholar
  16. Sen, Amartya (1976). Poverty: An Ordinal Approach to Measurement,Econometrica 44(2): 219–231.Google Scholar
  17. Sheshinski, Eytan (1972). Relation Between a Social Welfare Function and the Gini Index of Income Inequality,Journal of Economic Theory 4(1): 98–100.Google Scholar
  18. Taagepera, Rein and James Lee Ray (1977). A Generalized Index of Concentration,Sociological Methods and Research 5(3): 367–384.Google Scholar
  19. Takayama, Noriyuki (1979). Poverty, Income Inequality, and Their Measures: Professor Sen's Axiomatic Approach Reconsidered,Econometrica 47(3): 747–759.Google Scholar
  20. Takayama, Noriyuki (1980).Fubyodo no Keizai Bunseki (An Economic Analysis of Inequality) (in Japanese). Tokyo: Toyo-Keizai-Shinpo-sha.Google Scholar
  21. Theil, Henri (1967).Economics and Information Theory, Chicago: Rand McNally.Google Scholar
  22. Umino, Michio (1986). Multi-level Analysis: A Review on the Mathematical Approaches to Micro-Macro Problems (in Japanese),Riron to Hoho (Sociological Theory and Methods) 1(1): 25–40.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Kunihiro Kimura
    • 1
  1. 1.Department of Sociology, Faculty of Humanities and Social SciencesShizuoka UniversityShizuokaJapan

Personalised recommendations