Measuring Inequality and Social Welfare

Part of the Economic Studies in Inequality, Social Exclusion and Well-Being book series (EIAP, volume 2)


The Lorenz curve has been for several decades the most popular graphical tool for visualizing and comparing income inequality. As we will see, it provides complete information on the whole distribution of incomes relative to the mean. It therefore gives a more comprehensive description of relative incomes than any one of the traditional summary statistics of dispersion can give, and it is also a better stalling point when looking at income inequality than the computation of the many inequality indices that have been proposed. As we will see, its popularity also comes from its usefulness in establishing orderings of distributions in terms of inequality, orderings that can then be said to be “ethically robust”.


Social Welfare Total Income Gini Index Lorenz Curve Social Welfare Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

4.8 References

  1. Aaberge, R. (1997): “Interpretation of Changes in Rank-Dependent Measures of Inequality,” Economics Letters, 55, 215–19.zbMATHCrossRefGoogle Scholar
  2. — (2000): “Characterizations of Lorenz Curves and Income Distributions,” Social Choice and Welfare, 17, 639–53.Google Scholar
  3. — (2001a): “Axiomatic Characterization of the Gini Coefficient and Lorenz Curve Orderings,” Journal of Economic Theory, 101, 115–32.Google Scholar
  4. Anand, S. (1983): Inequality and Poverty in Malaysia, Oxford: Oxford University Press.Google Scholar
  5. Araar, A. and J.-Y. Duclos (2003): “An Atkinson-Gini Family of Social Evaluation Functions,” Economics Bulletin, 3, 1–16.Google Scholar
  6. Atkinson, A. (1970): “On the Measurement of Inequality,” Journal of Economic Theory, 2, 244–63.CrossRefMathSciNetGoogle Scholar
  7. — (1983): The Economies of Inequality, Oxford: Clarendon Press, 2nd ed.Google Scholar
  8. Atkinson, A. and F. Bourguignon (2000): Handbook of income distribution. Volume 1. Handbooks in Economics, vol. 16. Amsterdam; New York and Oxford: Elsevier Science, North-Holland.Google Scholar
  9. Atkinson, A. and J. Micklewright (1992): Economic Transformation in Eastern Europe and the Distribution of Income, Cambridge: Cambridge University Press.Google Scholar
  10. Barrett, C. and M. Salles (1995): “On a Generalisation of the Gini Coefficient,” Mathematical Social Sciences, 30, 235–44.zbMATHCrossRefMathSciNetGoogle Scholar
  11. Beblo, M. and T. Knaus (2001): “Measuring Income Inequality in Euroland,” Review of Income and Wealth, 47, 301–20.CrossRefGoogle Scholar
  12. Ben Porath, E. and I. Gilboa (1994): “Linear Measures, the Gini index, and the Income-Equality Trade-off,” Journal of Economic Theory, 64, 443–67.zbMATHCrossRefMathSciNetGoogle Scholar
  13. Berrebi, Z. and J. Silber (1981): “Weighting Income Ranks and Levels: A Multiple-Parameter Generalization For Absolute and Relative Inequality Indices,” Economics Letters, 7, 391–397.CrossRefGoogle Scholar
  14. — (1985): “Income Inequality Indices and Deprivation: A Generalization,” Quarterly Journal of Economics, 100, 807–810.Google Scholar
  15. Bishop, J., J. Formby, and J. Smith (1993): “International Comparisons of Welfare and Poverty: Dominance Orderings for Ten Countries,” Canadian Journal of Economics, 26, 707–26.CrossRefGoogle Scholar
  16. Blackburn, M. (1989): “Interpreting the Magnitude of Changes in Measures of Income Inequality,” Journal of Econometrics, 42, 21–25.CrossRefGoogle Scholar
  17. Blackorby, C., W. Bossert, and D. Donaldson (1994): “Generalized Ginis and Cooperative Bargaining Solutions,” Econometrica, 62, 1161–1178.zbMATHCrossRefMathSciNetGoogle Scholar
  18. Blackorby, C. and D. Donaldson (1978): “Measures of Relative Equality and Their Meaning in Terms of Social Welfare,” Journal of Economic Theory, 18, 59–80.zbMATHCrossRefMathSciNetGoogle Scholar
  19. Blackorby, C., D. Donaldson, and M. Auersperg (1981): “A New Procedure for the Measurement of Inequality Within and Among Population Subgroups,” Canadian Journal of Economics, 14, 665–686.CrossRefGoogle Scholar
  20. Bossert, W. (1990): “An Axiomatization of the Single-Series Ginis,” Journal of Economic Theory, 50, 82–92.zbMATHCrossRefMathSciNetGoogle Scholar
  21. Bourguignon, F. (1979): “Decomposable Income Inequality Measures,” Econometrica, 47, 901–920.zbMATHCrossRefMathSciNetGoogle Scholar
  22. Bourguignon, F. and C. Morrisson (2002): “Inequality among World Citizens: 1820–1992,” American Economic Review, 92, 727–44.CrossRefGoogle Scholar
  23. Chakravarty, S. (1988): “Extended Gini Indices of Inequality,” International Economic Review, 29, 147–156.zbMATHCrossRefMathSciNetGoogle Scholar
  24. — (1990): Ethical Social Index Numbers, New York, Springer-Verlag.Google Scholar
  25. — (2001): “Why Measuring Inequality by the Variance Makes Sense from a Theoretical Point of View,” Journal of Income Distribution, 10, 82–96.Google Scholar
  26. Chakravarty, S. and A. Chakraborty (1984): “On Indices of Relative Deprivation,” Economics Letters, 14, 283–287.CrossRefGoogle Scholar
  27. Champernowne, D. and F. Cowell (1998): Economic inequality and income distribution, Cambridge; New York and Melbourne: Cambridge University Press.Google Scholar
  28. Chantreuil., F. and A. Trannoy (1999): “Inequality Decomposition Values: The tradeoff between marginality and consistency,” Tech. Rep. 99-24, THEMA.Google Scholar
  29. Chew, S. and L. Epstein (1989): “A Unifying Approach to Axiomatic Non-expected Utility Theories,” Journal of Economic Theory, 49, 207–40.zbMATHCrossRefMathSciNetGoogle Scholar
  30. Clark, A. and A. Oswald (1996): “Satisfaction and Comparison Income,” Journal of Public Economics, 61, 359–381.CrossRefGoogle Scholar
  31. Cowell, F. (1980); “On the Structure of Additive Inequality Measures,” Review of Economic Studies, 47, 521–531.zbMATHCrossRefGoogle Scholar
  32. — (1995): Measuring Inequality, Prentice Hall / Harvester WheatsheafGoogle Scholar
  33. — (2000); “Measurement of Inequality,” in Handbook of income distribution. Volume 1. Handbooks in Economics, vol. 16, ed. by A. B. Atkinson and F. Bourguignon, Amsterdam; New York and Oxford: Elsevier Science, North-Holland, 87–166.Google Scholar
  34. Cowell, F. and S. Jenkins (1995): “How Much Inequality Can We Explain? A Methodology and an Application to the United States,” Economic Journal, 105, 421–30.CrossRefGoogle Scholar
  35. Dagum, C. (1997): “A New Approach to the Decomposition of the Gini Income Inequality Ratio,” Empirical Economics, 22, 515–31.CrossRefGoogle Scholar
  36. Dalton, H. (1920): “The Measurement of the Inequality of Incomes,” The Economic Journal, 30, 348–61.CrossRefGoogle Scholar
  37. Danziger, S. and P. Gottschalk (1995): America Unequal, Cambridge, MA.: Russell Sage Foundation and Harvard University Press.Google Scholar
  38. Dasgupta, P., A. Sen, and D. Starret (1973): “Notes on the Measurement of Inequality,” Journal of Economic Theory, 6, 180–187.CrossRefMathSciNetGoogle Scholar
  39. Davis, J. (1959): “A Formal Interpretation of the Theory of Relative Deprivation,” Sociometry, 22, 280–296.CrossRefGoogle Scholar
  40. Del Rio, C. and J. Ruiz Castillo (2001): “Intermediate Inequality and Welfare: The Case of Spain, 1980–81 to 1990–91,” Review of Income and Wealth, 47, 221–37.CrossRefGoogle Scholar
  41. Del Rio, C. and J. Ruiz Castillo (2001): “TIPs for Poverty Analysis: The Case of Spain, 1980–81 to 1990–91,” Investigations Economicas, 25, 63–91.Google Scholar
  42. Deutsch, J. and J. Silber (1997): “Gini’s “Transvariazione” and the Measurement of Distance between Distributions,” Empirical Economics, 22, 547–54.CrossRefGoogle Scholar
  43. — (1999a): “Inequality Decomposition by Population Subgroups and the Analysis of Inter-distributional Inequality,” in Handbook of income inequality measurement. With a foreword by Amartya Sen, ed. by J. Silber, Boston; Dordrecht and London: Kluwer Academic, Recent Economic Thought, 363–97.Google Scholar
  44. — (1999b): “On Some Implications of Dagum’s Interpretation of the Decomposition of the Gini Index by Population Subgroups,” in Advances in econometrics, income distribution and scientific methodology: Essays in honor of Camilo Dagum, ed. by D. J. Slottje, Heidelberg: Physica, 269–91Google Scholar
  45. Donaldson, D. and J. Weymark (1980): “A Single Parameter Generalization of the Gini Indices of Inequality,” Journal of Economic Theory, 22, 67–86.zbMATHCrossRefMathSciNetGoogle Scholar
  46. — (1983): “Ethically Flexible Gini Indices for Income Distributions in the Continuum,” Journal of Economic Theory, 29, 353–358.Google Scholar
  47. Duclos, J.-Y. (1997a): “The Asymptotic Distribution of Linear Indices of Inequality, and Redistribution,” Economics Letters, 54, 51–57.zbMATHCrossRefGoogle Scholar
  48. — (2000): “Gini indices and the Redistribution of Income,” International Tax and Public Finance, 7, 141–62.CrossRefGoogle Scholar
  49. Duclos, J.-Y. and P. Lambert (2000): “A Normative Approach to Measuring Classical Horizontal inequity,” Canadian Journal of Economics, 33, 87–113.CrossRefGoogle Scholar
  50. Duro, J. and J. Esteban (1998): “Factor Decomposition of Cross-Country Income Inequality, 1960–1990” Economics Letters, 60, 269–75.zbMATHCrossRefGoogle Scholar
  51. Ebert, U. (1999): “Using Equivalent Income of Equivalent Adults to Rank Income Distributions,” Social Choice and Welfare, 16, 233–58.zbMATHCrossRefGoogle Scholar
  52. Ebert, U. and P. Moyes (2000): “An Axiomatic Characterization of Yitzhaki’s Index of Individual Deprivation,” Economics Letters, 68, 263–70.zbMATHCrossRefGoogle Scholar
  53. Essama Nssah, B. (2000): Inégalité, pauvreté et bien-être social — Fondements analytiques et normatifs, Bruxelles: De Boeck & Larcier.Google Scholar
  54. Festinger, L. (1954); “A Theory of Social Comparison Processes,” Human Relations, 7, 117–140.CrossRefGoogle Scholar
  55. Fields, G. and G. Yoo (2000): “Falling Labor Income Inequality in Korea’s Economic Growth: Patterns and Underlying Causes,” Review of Income and Wealth, 46, 139–59.CrossRefGoogle Scholar
  56. Foster, J. and E. Ok (1999): “Lorenz Dominance and the Variance of Logarithms,” Econometrica, 67, 901–07.CrossRefGoogle Scholar
  57. Foster, J. and A. Sen (1997): On Economic Inequality after a Quarter Century, Oxford, Clarendon Press.Google Scholar
  58. Foster, J. and A. Shneyerov (1999): “A General Class of Additively Decomposable insequality Measures,” Economic Theory, 14, 89–111.zbMATHCrossRefMathSciNetGoogle Scholar
  59. — (2000): “Path Independent Inequality Measures,” Journal of Economic Theory, 91, 199–222.Google Scholar
  60. Fournier, M. (2001): “inequality Decomposition by Factor Component: A “Rank-Correlation” Approach Illustrated on the Taiwanese Case,” Recherches Economiques de Umvain/Louvain Economic Review, 67, 381–403.Google Scholar
  61. Gini, C. (1914): “Sulla misura della concentrazione e della variabilita dei caratteri,” Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, 73, 1203–1248.Google Scholar
  62. — (2005): “On the measurement of concentration and variability of characters,” Metron: International Journal of Statistics, 63, 3–38.Google Scholar
  63. Goerlich Gisbert, F. (2001): “On Factor Decomposition of Cross-Country Income Inequality: Some Extensions and Qualifications,” Economics Letters, 70, 303–09.zbMATHCrossRefGoogle Scholar
  64. Gottschalk, P. and T. Smeeding (1997): “Cross-National Comparisons of Earnings and income Inequality,” Journal of Economic Literature, 35, 633–87.Google Scholar
  65. — (2000): “Empirical Evidence on Income Inequality in Industrial Countries,” in Handbook of income distribution. Volume 1. Handbooks in Economics, vol. 16, ed. by A. B. Atkinson and F. Bourguignon, Amsterdam; New York and Oxford: Elsevier Science, North-Holland, 261–307.Google Scholar
  66. Mainsworth, G. (1964): “The Lorenz Curve as a General Tool of Economic Analysis,” Economic Record, 40, 426–41.Google Scholar
  67. Hey, J. and P. Lambert (1980): “Relative Deprivation and the Gini Coefficient: Comment,” Quarterly Journal of Economics, 95, 567–573.CrossRefGoogle Scholar
  68. Hyslop, D. (2001): “Rising U.S. Earnings Inequality and Family Labor Supply: The Covariance Structure of Intrafamily Earnings,” American Economic Review, 91, 755–77.CrossRefGoogle Scholar
  69. Jantti, M. (1997): “Inequality in Five Countries in the 1980s: The Role of Demographic Shifts, Markets and Government Policies,” Economica, 64, 415–40.CrossRefGoogle Scholar
  70. Jenkins, S. (1995): “Accounting for Inequality Trends: Decomposition Analyses for the UK, 1971–86,” Economica, 62. 29–63.CrossRefGoogle Scholar
  71. Johnson, D. and S. Shipp (1997): “Trends in Inequality Using Consumption-Expenditures: The U.S. from 1960 to 1993,” Review of Income and Wealth, 43, 133–52.CrossRefGoogle Scholar
  72. Kakwani, N. (1977a): “Applications of Lorenz Curves in Economic Analysis,” Econometrica, 45, 719–28.zbMATHCrossRefMathSciNetGoogle Scholar
  73. — (1980): “On a Class of Poverty Measures,” Econometrica, 48, 437–446.zbMATHCrossRefMathSciNetGoogle Scholar
  74. Kolm, S.-C. (1969): “The Optimal Production of Justice,” in Public Economics, ed. by J. Mar-golis and S. Guitton, London: MacMillan.Google Scholar
  75. Lambert, P. (2001): The distribution and redistribution of income, Third edition. Manchester and New York: Manchester University Press; distributed by Palgrave, New York.Google Scholar
  76. Lorenz, M. (1905): “Method of measuring the concentration of wealth,” Publications of the American Statistical Association, 70.Google Scholar
  77. Merton, R. K. and A. S. Rossi (1957): “Contributions to the Theory of Reference Group Behaviour,” in Social Theory and Social Structure, ed. by R. Merton, Glencoe.Google Scholar
  78. Milanovic, B. (1994b): “The Gini-Type Functions: An Alternative Derivation,” Bulletin of Economic Research, 46, 81–90.CrossRefGoogle Scholar
  79. — (1997): “A Simple Way to Calculate the Gini Coefficient, and Some Implications,” Economics Letters, 56, 45–49.zbMATHCrossRefGoogle Scholar
  80. — (2002): “True World Income Distribution, 1988 and 1993: First Calculation Based on Household Surveys Alone,” Economic Journal, 112, 51–92.CrossRefGoogle Scholar
  81. Milanovic, B. and S. Yitzhaki (2002): “Decomposing World Income Distribution: Does She World Have a Middle Class?” Review of Income and Wealth, 48, 155–78.CrossRefGoogle Scholar
  82. Mookherjee, D. and A. Shorrocks (1982): “A Decomposition Analysis of the Trend in U.K. Income Inequality,” Economic Journal, 92, 886–902.CrossRefGoogle Scholar
  83. Nolan, B. and C. Whelan (1996): “The Relationship between Income and Deprivation: A Dynamic Perspective,” Revue Economique, 47, 709–17.CrossRefGoogle Scholar
  84. Owen, G. (1977): “Values of games with a priori unions,” in Essays in Mathematical Economics and Game Theory, ed. by R. Heim and O. Moeschlin, New York: Springer Verlag.Google Scholar
  85. Parker, S. (1999): “The Inequality of Employment and Self-Employment Incomes: A Decomposition Analysis for the U.K,” Review of Income and Wealth, 45, 263–74.CrossRefGoogle Scholar
  86. Paul, S. (1991): “An Index of Relative Deprivation,” Economics Letters, 36, 337–41.zbMATHCrossRefGoogle Scholar
  87. Podder, N. (1996): “Relative Deprivation, Envy and Economic Inequality,” Kyklos, 49, 353–76.CrossRefGoogle Scholar
  88. Rothschild, M. and J. Stiglitz (1973): “Some Further Results on the Measurement of Inequality,” Journal of Economic Theory, 6, 188–204.CrossRefMathSciNetGoogle Scholar
  89. Runciman, W. (1966): Relative Deprivation and Social Justice: A Study of Attitudes to Social Inequality in Twentieth-Century England, Berkeley and Los Angeles: University of California Press.Google Scholar
  90. Sastry, D. and U. Kelkar (1994): “Note on the Decomposition of Gini Inequality,” Review of Economics and Statistics, 76, 584–86.CrossRefGoogle Scholar
  91. Saunders, P. (1994): Welfare and Inequality: National and International Perspectives on the Australian Welfare State, Cambridge University Press.Google Scholar
  92. Schultz, P. (1998): “Inequality in the Distribution of Personal Income in the World: How It Is Changing and Why,” Journal of Population Economics, 11, 307–44.CrossRefGoogle Scholar
  93. Schwarze, J. (1996): “How Income Inequality Changed in Germany following Reunification: An Empirical Analysis Using Decomposable Inequality Measures,” Review of Income and Wealth, 42, 1–11.CrossRefGoogle Scholar
  94. Sen, A. (1973): On Economic Inequality, Oxford Clarendon Press.Google Scholar
  95. — (1992): Inequality Reexamined, New York, Cambridge: Harvard University Press.Google Scholar
  96. Shapley, L. (1953): “A value for n-persou games,” in Contributions to the Theory of Games, ed. by H. W. Kuhn and A. W. Tucker, Princeton: Princeton University Press, vol. 2 of Annals of Mathematics Studies, 303–317.Google Scholar
  97. Shorrocks, A. (1980): “The Class of Additively Decomposable Inequality Measures,” Econo-metrica, 48, 613–625.zbMATHMathSciNetGoogle Scholar
  98. — (1984): “IDecomposition by Population Subgroups,” Econometrica, 52, 1369–1385.Google Scholar
  99. — (1999): “Decomposition procedures for distributional analysis: A unified framework based on the Shapley value,” Tech. rep., University of EssexGoogle Scholar
  100. Silver, H. (1994): “Social Exclusion and Social Solidarity: Three Paradigms,” International Labour Review, 133, 531–576.Google Scholar
  101. Subramanian, S. (2002): “An Elementary Interpretation of the Gini Inequality Index,” Theory and Decision, 52, 375–79.zbMATHCrossRefGoogle Scholar
  102. Tsui, K. Y. (1998): “Trends and Inequalities of Rural Welfare in China: Evidence from Rural Households in Guangdong and Sichuan,” Journal of Comparative Economics, 26, 783–804.CrossRefGoogle Scholar
  103. Wang, Y. Q. and K. Y. Tsui (2000): “A New Class of Deprivation-Based Generalized Gini Indices,” Economic Theory, 16, 363–77.zbMATHCrossRefMathSciNetGoogle Scholar
  104. Weymark, J. (1981): “Generalized Gini Inequality Indices,” Mathematical Social Sciences, 1, 409–30.zbMATHCrossRefMathSciNetGoogle Scholar
  105. Yaari, M. (1988): “A Controversial Proposal Concerning Inequality Measurement,” Journal of Economic Theory, 44, 381–97.zbMATHCrossRefMathSciNetGoogle Scholar
  106. Yitzhaki, S. (1979): “Relative Deprivation and the Gini Coefficient,” Quarterly Journal of Economics, 93, 321–324.CrossRefGoogle Scholar
  107. — (1982a): “Relative Deprivation and Economic Welfare,” European Economic Review, 17, 99–113.Google Scholar
  108. — (1983): “On an Extension of the Gini Index,” International Economic Review, 24, 617–628.Google Scholar
  109. — (1998): “More Than a Dozen Alternative Ways of Spelling Gini,” in Research on economic inequality. Volume 8. Stamford, Conn, ed. by D. J. Slottje, and London: JAI Press, 13–30.Google Scholar
  110. Yitzhaki, S. and R. Lerman (1991): “Income Stratification and Income Inequality,” Review of Income and Wealth, 37, 313–29.CrossRefGoogle Scholar
  111. Zandvakili, S. (1999): “Income Inequality among Female Heads of Households: Racial Inequality Reconsidered,” Economica, 66, 119–33.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Personalised recommendations