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A Family of Correlation Coefficients Based on the Extended Gini Index


The extended Gini is a family of measures of variability which is mainly used in the areas of finance and income distribution. Each index in the family is defined by specifying one parameter, which reflects the social evaluation of the marginal utility of income. The higher the parameter, the more weight is attached to the lower portion of the cumulative distribution, reflecting higher concern for poverty. In this paper we list and investigate the properties of the equivalents of the correlation coefficient that are associated with the extended Gini family. In addition, we show that the extended Gini of a linear combination of random variables can be decomposed, in a way which is equivalent to the decomposition of the variance, with, in addition, terms that reflect additional properties of the random variables. The implication of these properties is that any decomposition that is performed with the coefficient of variation can be replicated by an infinite number of indices that are based on the Extended Gini coefficient.

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  1. 1.

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

    Google Scholar 

  2. 2.

    Blitz, R.C. and Brittain, J.A.: An extension of the Lorenz diagram to the correlation of two variables, Metron XXIII(1- 4) (1964), 137–143.

    Google Scholar 

  3. 3.

    Blundell, R. and Preston, I.: Consumption inequality and income uncertainty, Quart. J. Econom. 113 (1998), 603–640.

    Google Scholar 

  4. 4.

    Bukhauser, R. and Poupore, J.: A cross national comparison of permanent inequality in the United States and Germany, Rev. Econom. Statist. 79 (1997), 10–17.

    Google Scholar 

  5. 5.

    Cancian, M. and Reed, D.: Assessing the effects of wive's earnings on family inequality, Rev. Econom. Statist. 80(1) (1998) (February).

  6. 6.

    Chakravarty, S.R.: Ethical Social Index Numbers, Springer-Verlag, New York, 1990.

    Google Scholar 

  7. 7.

    De Veaux, R.: Technical Report No. 5, SIAM Institute for Mathematics and Society, Stanford University, 1976.

  8. 8.

    Donaldson, D. and Weymark, J.A.: A single-parameter generalization of the Gini-indices of inequality, J. Econom. Theory 22 (1980), 67–86.

    Google Scholar 

  9. 9.

    Donaldson, D. and Weymark, J.A.: Ethically flexible Gini indices for income distributions in the continuum, J. Econom. Theory 29 (1983), 353–358.

    Google Scholar 

  10. 10.

    Fisher, J.D. and Johnson, D.S.: Consumption mobility in the United States: Evidence from two panel data sets, Bureau of Labor Statistics, October 2002, mimeo.

  11. 11.

    Fréchet, M.: Sur les tableaux de correlation dont les marges sont données, Annals Universite de Lyon, Sect. A. Ser. 3 14 (1951), 53–77.

    Google Scholar 

  12. 12.

    Giorgi, G.M.: Bibliographic portrait of the Gini concentration ratio, Metron XLVIII(1- 4) (1990), 183–221.

    Google Scholar 

  13. 13.

    Gregory-Allen, R. and Shalit, H.: The estimation of systematic risk under differentiated risk aversion: A mean-extended Gini approach, Rev. Quantitative Finance and Accounting 12(2) (March 1999), 135–157.

    Google Scholar 

  14. 14.

    Hoeffding,W.: A nonparametric test for independence, Ann. Math. Statist. 19 (1948), 546–557.

    Google Scholar 

  15. 15.

    Kakwani, N.C.: On a class of poverty measures, Econometrica 48 (1980).

  16. 16.

    Kleiber, C. and Kotz, S.: A characterization of income distributions in terms of generalized Gini coefficients, Social Choice and Welfare 19 (2002), 789–794.

    Google Scholar 

  17. 17.

    Kruskal, W.H.: Ordinal measures of association, J. Amer. Statist. Assoc. 53 (1958), 814–861.

    Google Scholar 

  18. 18.

    Lerman, R.I.: How do income sources affect income inequality, In: J. Silber (ed.), Handbook on Income Inequality Measurement, Kluwer Academic Publishers, Dordrecht, 1999, pp. 341–357.

    Google Scholar 

  19. 19.

    Lien, D. and Tse, Y.K.: Some recent developments in futures hedging, Working paper, University of Texas at San Antonio, 2001.

  20. 20.

    Mera, K.: Experimental determination of relative marginal utilities, Quart. J. Econom. 83(3) (August 1969), 464–477.

    Google Scholar 

  21. 21.

    Schechtman, E. and Yitzhaki, S.: A measure of association based on Gini's mean difference, Comm. Statist. Theory Methods 16(1) (1987), 207–231.

    Google Scholar 

  22. 22.

    Schechtman, E. and Yitzhaki, S.: On the proper bounds of the Gini correlation, Econom. Lett. 63(2) (1999), 133–138.

    Google Scholar 

  23. 23.

    Schechtman E. and Yitzhaki, S.: Asymmetric Gini regressions, estimation and testing, Mimeo, Hebrew University of Jerusalem, Dept. of Economics, 2001.

  24. 24.

    Schweizer, B. and Wolff, E.F.:On nonparametric measures of dependence for random variables, Ann. Statist. 9 (1981), 879–885.

    Google Scholar 

  25. 25.

    Shalit, H. and Yitzhaki, S.: Estimating beta, Rev. Quantitative Finance and Accounting 18(2) (2002), 95–118.

    Google Scholar 

  26. 26.

    Shorrocks, A.F.: Ranking income distributions, Economica 50 (1983), 3–17.

    Google Scholar 

  27. 27.

    Wodon, Q. and Yitzhaki, S.: Inequality and social welfare, In: J. Klugman (ed.), PRSP Sourcebook, The World Bank, Washington DC, 2002.

    Google Scholar 

  28. 28.

    Wodon, Q. and Yitzhaki, S.: Inequality and the accounting period, Mimeo, The World Bank, March 2002.

  29. 29.

    Yaari, M.E.: The dual theory of choice under risk, Econometrica 55 (1987), 95–115.

    Google Scholar 

  30. 30.

    Yaari, M.E.: A controversial proposal concerning inequality measurement, J. Econom. Theory 44(2) (1988), 381–397.

    Google Scholar 

  31. 31.

    Yitzhaki, S.: Stochastic dominance, mean variance, and the Gini's mean difference, American Economic Review 72(1) (March 1982), 178–185.

    Google Scholar 

  32. 32.

    Yitzhaki, S.: On an extension of the Gini inequality index, Internat. Econom. Rev. 24(3) (1983), 617–628.

    Google Scholar 

  33. 33.

    Yitzhaki, S. and Wodon, Q.: Mobility, inequality, and horizontal equity, Mimeo, The World Bank, 2000.

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Correspondence to E. Schechtman.

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Schechtman, E., Yitzhaki, S. A Family of Correlation Coefficients Based on the Extended Gini Index. The Journal of Economic Inequality 1, 129–146 (2003).

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  • decomposition
  • extended Gini
  • Gini correlation