Abstract
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”.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
4.8 References
Aaberge, R. (1997): “Interpretation of Changes in Rank-Dependent Measures of Inequality,” Economics Letters, 55, 215–19.
— (2000): “Characterizations of Lorenz Curves and Income Distributions,” Social Choice and Welfare, 17, 639–53.
— (2001a): “Axiomatic Characterization of the Gini Coefficient and Lorenz Curve Orderings,” Journal of Economic Theory, 101, 115–32.
Anand, S. (1983): Inequality and Poverty in Malaysia, Oxford: Oxford University Press.
Araar, A. and J.-Y. Duclos (2003): “An Atkinson-Gini Family of Social Evaluation Functions,” Economics Bulletin, 3, 1–16.
Atkinson, A. (1970): “On the Measurement of Inequality,” Journal of Economic Theory, 2, 244–63.
— (1983): The Economies of Inequality, Oxford: Clarendon Press, 2nd ed.
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.
Atkinson, A. and J. Micklewright (1992): Economic Transformation in Eastern Europe and the Distribution of Income, Cambridge: Cambridge University Press.
Barrett, C. and M. Salles (1995): “On a Generalisation of the Gini Coefficient,” Mathematical Social Sciences, 30, 235–44.
Beblo, M. and T. Knaus (2001): “Measuring Income Inequality in Euroland,” Review of Income and Wealth, 47, 301–20.
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.
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.
— (1985): “Income Inequality Indices and Deprivation: A Generalization,” Quarterly Journal of Economics, 100, 807–810.
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.
Blackburn, M. (1989): “Interpreting the Magnitude of Changes in Measures of Income Inequality,” Journal of Econometrics, 42, 21–25.
Blackorby, C., W. Bossert, and D. Donaldson (1994): “Generalized Ginis and Cooperative Bargaining Solutions,” Econometrica, 62, 1161–1178.
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.
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.
Bossert, W. (1990): “An Axiomatization of the Single-Series Ginis,” Journal of Economic Theory, 50, 82–92.
Bourguignon, F. (1979): “Decomposable Income Inequality Measures,” Econometrica, 47, 901–920.
Bourguignon, F. and C. Morrisson (2002): “Inequality among World Citizens: 1820–1992,” American Economic Review, 92, 727–44.
Chakravarty, S. (1988): “Extended Gini Indices of Inequality,” International Economic Review, 29, 147–156.
— (1990): Ethical Social Index Numbers, New York, Springer-Verlag.
— (2001): “Why Measuring Inequality by the Variance Makes Sense from a Theoretical Point of View,” Journal of Income Distribution, 10, 82–96.
Chakravarty, S. and A. Chakraborty (1984): “On Indices of Relative Deprivation,” Economics Letters, 14, 283–287.
Champernowne, D. and F. Cowell (1998): Economic inequality and income distribution, Cambridge; New York and Melbourne: Cambridge University Press.
Chantreuil., F. and A. Trannoy (1999): “Inequality Decomposition Values: The tradeoff between marginality and consistency,” Tech. Rep. 99-24, THEMA.
Chew, S. and L. Epstein (1989): “A Unifying Approach to Axiomatic Non-expected Utility Theories,” Journal of Economic Theory, 49, 207–40.
Clark, A. and A. Oswald (1996): “Satisfaction and Comparison Income,” Journal of Public Economics, 61, 359–381.
Cowell, F. (1980); “On the Structure of Additive Inequality Measures,” Review of Economic Studies, 47, 521–531.
— (1995): Measuring Inequality, Prentice Hall / Harvester Wheatsheaf
— (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.
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.
Dagum, C. (1997): “A New Approach to the Decomposition of the Gini Income Inequality Ratio,” Empirical Economics, 22, 515–31.
Dalton, H. (1920): “The Measurement of the Inequality of Incomes,” The Economic Journal, 30, 348–61.
Danziger, S. and P. Gottschalk (1995): America Unequal, Cambridge, MA.: Russell Sage Foundation and Harvard University Press.
Dasgupta, P., A. Sen, and D. Starret (1973): “Notes on the Measurement of Inequality,” Journal of Economic Theory, 6, 180–187.
Davis, J. (1959): “A Formal Interpretation of the Theory of Relative Deprivation,” Sociometry, 22, 280–296.
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.
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.
Deutsch, J. and J. Silber (1997): “Gini’s “Transvariazione” and the Measurement of Distance between Distributions,” Empirical Economics, 22, 547–54.
— (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.
— (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, 269–91
Donaldson, D. and J. Weymark (1980): “A Single Parameter Generalization of the Gini Indices of Inequality,” Journal of Economic Theory, 22, 67–86.
— (1983): “Ethically Flexible Gini Indices for Income Distributions in the Continuum,” Journal of Economic Theory, 29, 353–358.
Duclos, J.-Y. (1997a): “The Asymptotic Distribution of Linear Indices of Inequality, and Redistribution,” Economics Letters, 54, 51–57.
— (2000): “Gini indices and the Redistribution of Income,” International Tax and Public Finance, 7, 141–62.
Duclos, J.-Y. and P. Lambert (2000): “A Normative Approach to Measuring Classical Horizontal inequity,” Canadian Journal of Economics, 33, 87–113.
Duro, J. and J. Esteban (1998): “Factor Decomposition of Cross-Country Income Inequality, 1960–1990” Economics Letters, 60, 269–75.
Ebert, U. (1999): “Using Equivalent Income of Equivalent Adults to Rank Income Distributions,” Social Choice and Welfare, 16, 233–58.
Ebert, U. and P. Moyes (2000): “An Axiomatic Characterization of Yitzhaki’s Index of Individual Deprivation,” Economics Letters, 68, 263–70.
Essama Nssah, B. (2000): Inégalité, pauvreté et bien-être social — Fondements analytiques et normatifs, Bruxelles: De Boeck & Larcier.
Festinger, L. (1954); “A Theory of Social Comparison Processes,” Human Relations, 7, 117–140.
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.
Foster, J. and E. Ok (1999): “Lorenz Dominance and the Variance of Logarithms,” Econometrica, 67, 901–07.
Foster, J. and A. Sen (1997): On Economic Inequality after a Quarter Century, Oxford, Clarendon Press.
Foster, J. and A. Shneyerov (1999): “A General Class of Additively Decomposable insequality Measures,” Economic Theory, 14, 89–111.
— (2000): “Path Independent Inequality Measures,” Journal of Economic Theory, 91, 199–222.
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.
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.
— (2005): “On the measurement of concentration and variability of characters,” Metron: International Journal of Statistics, 63, 3–38.
Goerlich Gisbert, F. (2001): “On Factor Decomposition of Cross-Country Income Inequality: Some Extensions and Qualifications,” Economics Letters, 70, 303–09.
Gottschalk, P. and T. Smeeding (1997): “Cross-National Comparisons of Earnings and income Inequality,” Journal of Economic Literature, 35, 633–87.
— (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.
Mainsworth, G. (1964): “The Lorenz Curve as a General Tool of Economic Analysis,” Economic Record, 40, 426–41.
Hey, J. and P. Lambert (1980): “Relative Deprivation and the Gini Coefficient: Comment,” Quarterly Journal of Economics, 95, 567–573.
Hyslop, D. (2001): “Rising U.S. Earnings Inequality and Family Labor Supply: The Covariance Structure of Intrafamily Earnings,” American Economic Review, 91, 755–77.
Jantti, M. (1997): “Inequality in Five Countries in the 1980s: The Role of Demographic Shifts, Markets and Government Policies,” Economica, 64, 415–40.
Jenkins, S. (1995): “Accounting for Inequality Trends: Decomposition Analyses for the UK, 1971–86,” Economica, 62. 29–63.
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.
Kakwani, N. (1977a): “Applications of Lorenz Curves in Economic Analysis,” Econometrica, 45, 719–28.
— (1980): “On a Class of Poverty Measures,” Econometrica, 48, 437–446.
Kolm, S.-C. (1969): “The Optimal Production of Justice,” in Public Economics, ed. by J. Mar-golis and S. Guitton, London: MacMillan.
Lambert, P. (2001): The distribution and redistribution of income, Third edition. Manchester and New York: Manchester University Press; distributed by Palgrave, New York.
Lorenz, M. (1905): “Method of measuring the concentration of wealth,” Publications of the American Statistical Association, 70.
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.
Milanovic, B. (1994b): “The Gini-Type Functions: An Alternative Derivation,” Bulletin of Economic Research, 46, 81–90.
— (1997): “A Simple Way to Calculate the Gini Coefficient, and Some Implications,” Economics Letters, 56, 45–49.
— (2002): “True World Income Distribution, 1988 and 1993: First Calculation Based on Household Surveys Alone,” Economic Journal, 112, 51–92.
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.
Mookherjee, D. and A. Shorrocks (1982): “A Decomposition Analysis of the Trend in U.K. Income Inequality,” Economic Journal, 92, 886–902.
Nolan, B. and C. Whelan (1996): “The Relationship between Income and Deprivation: A Dynamic Perspective,” Revue Economique, 47, 709–17.
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.
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.
Paul, S. (1991): “An Index of Relative Deprivation,” Economics Letters, 36, 337–41.
Podder, N. (1996): “Relative Deprivation, Envy and Economic Inequality,” Kyklos, 49, 353–76.
Rothschild, M. and J. Stiglitz (1973): “Some Further Results on the Measurement of Inequality,” Journal of Economic Theory, 6, 188–204.
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.
Sastry, D. and U. Kelkar (1994): “Note on the Decomposition of Gini Inequality,” Review of Economics and Statistics, 76, 584–86.
Saunders, P. (1994): Welfare and Inequality: National and International Perspectives on the Australian Welfare State, Cambridge University Press.
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.
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.
Sen, A. (1973): On Economic Inequality, Oxford Clarendon Press.
— (1992): Inequality Reexamined, New York, Cambridge: Harvard University Press.
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.
Shorrocks, A. (1980): “The Class of Additively Decomposable Inequality Measures,” Econo-metrica, 48, 613–625.
— (1984): “IDecomposition by Population Subgroups,” Econometrica, 52, 1369–1385.
— (1999): “Decomposition procedures for distributional analysis: A unified framework based on the Shapley value,” Tech. rep., University of Essex
Silver, H. (1994): “Social Exclusion and Social Solidarity: Three Paradigms,” International Labour Review, 133, 531–576.
Subramanian, S. (2002): “An Elementary Interpretation of the Gini Inequality Index,” Theory and Decision, 52, 375–79.
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.
Wang, Y. Q. and K. Y. Tsui (2000): “A New Class of Deprivation-Based Generalized Gini Indices,” Economic Theory, 16, 363–77.
Weymark, J. (1981): “Generalized Gini Inequality Indices,” Mathematical Social Sciences, 1, 409–30.
Yaari, M. (1988): “A Controversial Proposal Concerning Inequality Measurement,” Journal of Economic Theory, 44, 381–97.
Yitzhaki, S. (1979): “Relative Deprivation and the Gini Coefficient,” Quarterly Journal of Economics, 93, 321–324.
— (1982a): “Relative Deprivation and Economic Welfare,” European Economic Review, 17, 99–113.
— (1983): “On an Extension of the Gini Index,” International Economic Review, 24, 617–628.
— (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.
Yitzhaki, S. and R. Lerman (1991): “Income Stratification and Income Inequality,” Review of Income and Wealth, 37, 313–29.
Zandvakili, S. (1999): “Income Inequality among Female Heads of Households: Racial Inequality Reconsidered,” Economica, 66, 119–33.
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
(2006). Measuring Inequality and Social Welfare. In: Poverty and Equity. Economic Studies in Inequality, Social Exclusion and Well-Being, vol 2. Springer, Boston, MA. https://doi.org/10.1007/0-387-33318-5_4
Download citation
DOI: https://doi.org/10.1007/0-387-33318-5_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-25893-5
Online ISBN: 978-0-387-33318-2
eBook Packages: Business and EconomicsEconomics and Finance (R0)