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Two Types of Inequality: Inequality Between Persons and Inequality Between Subgroups

  • Jasso, Guillermina

    ()

    (New York University)

  • Kotz, Samuel

    ()

    (George Washington University)

Social scientists study two kinds of inequality: inequality between persons (as in income inequality) and inequality between subgroups (as in racial inequality). This paper analyzes the mathematical connections between the two kinds of inequality. The paper proceeds by exploring a set of two-parameter continuous probability distributions widely used in economic and sociological applications. We define a general inequality parameter, which governs all measures of personal inequality (such as the Gini coefficient), and we link this parameter to the gap (difference or ratio) between the means of subdistributions. In this way we establish that, at least in the two-parameter distributions analyzed here, and for the case of two nonoverlapping subgroups, as personal inequality increases, so does inequality between subgroups. This general inequality parameter also governs Lorenz dominance. Further, we explore the connection between subgroup inequality (in particular, the ratio of the bottom subgroup mean to the top subgroup mean) and decomposition of personal inequality into between-subgroup and within-subgroup components, focusing on an important decomposable measure, Theil’s MLD, and its operation in the Pareto case. This allows us to establish that all the quantities in the decomposition are monotonic functions of the general inequality parameter. Thus, the general inequality parameter captures the “deep structure” of inequality. We also introduce a whole-distribution graphical tool for assessing personal and subgroup inequality. Substantively, this work suggests that in at least some societies, characterized by special income distributions, whenever inequality disrupts social harmony and social cohesion, it attacks on two fronts, via subgroup inequality as well as personal inequality.

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Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 2749.

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Length: 63 pages
Date of creation: Apr 2007
Date of revision:
Publication status: published in: Sociological Methods and Research, 2008, 37 (1), 31-74
Handle: RePEc:iza:izadps:dp2749
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  1. T. Paul Schultz, 1998. "Inequality in the Distribution of Personal Income in the World: How it is Changing and Why," Working Papers 784, Economic Growth Center, Yale University.
  2. Francine D. Blau & Lawrence M. Kahn, 2000. "Gender Differences in Pay," NBER Working Papers 7732, National Bureau of Economic Research, Inc.
  3. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  4. Susan Harkness, 1996. "The gender earnings gap: evidence from the UK," Fiscal Studies, Institute for Fiscal Studies, vol. 17(2), pages 1-36, May.
  5. Berry, Albert & Bourguignon, Francois & Morrisson, Christian, 1983. "The Level of World Inequality: How Much Can One Say?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 29(3), pages 217-41, September.
  6. T. Paul Schultz, 1998. "Inequality in the distribution of personal income in the world: How it is changing and why," Journal of Population Economics, Springer, vol. 11(3), pages 307-344.
  7. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  8. Kwok Leung & Peter B Smith & Zhongming Wang & Haifa Sun, 1996. "Job Satisfaction in Joint Venture Hotels in China: An Organizational Justice Analysis," Journal of International Business Studies, Palgrave Macmillan, vol. 27(4), pages 947-962, December.
  9. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-39, November.
  10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  11. Barbara F. Reskin & Denise D. Bielby, 2005. "A Sociological Perspective on Gender and Career Outcomes," Journal of Economic Perspectives, American Economic Association, vol. 19(1), pages 71-86, Winter.
  12. William Darity, Jr. & Ashwini Deshpande, 2000. "Tracing the Divide: Intergroup Disparity across Countries," Eastern Economic Journal, Eastern Economic Association, vol. 26(1), pages 75-85, Winter.
  13. Das, T & Parikh, A, 1982. "Decomposition of Inequality Measures and a Comparative Analysis," Empirical Economics, Springer, vol. 7(1-2), pages 23-48.
  14. Kwok Leung & Peter B Smith & Zhongming Wang & Haifa Sun, 1996. "Job Satisfaction in Joint Venture Hotels in China: An Organizational Justice Analysis," Journal of International Business Studies, Palgrave Macmillan, vol. 27(5), pages 947-962, December.
  15. Claudia Goldin, 1990. "Understanding the Gender Gap: An Economic History of American Women," NBER Books, National Bureau of Economic Research, Inc, number gold90-1.
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