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The Lorenz curve in economics and econometrics

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  • Kleiber, Christian

    (University of Basel)

Abstract

This paper surveys selected applications of the Lorenz curve and related stochastic NEWLINE orders in economics and econometrics, with a bias towards problems in statistical NEWLINE distribution theory. These include characterizations of income distributions in terms NEWLINE of families of inequality measures, Lorenz ordering of multiparameter distributions NEWLINE in terms of their parameters, probability inequalities for distributions of quadratic NEWLINE forms, and Condorcet jury theorems.

Suggested Citation

  • Kleiber, Christian, 2007. "The Lorenz curve in economics and econometrics," Working papers 2007/09, Faculty of Business and Economics - University of Basel.
    • Handle: RePEc:bsl:wpaper:2007/09
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    References listed on IDEAS

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    1. Kleiber, Christian, 2002. "Lorenz ordering of order statistics from log-logistic and related distributions," Technical Reports 2002,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Wilfling, Bernd & Kramer, Walter, 1993. "The Lorenz-ordering of Singh-Maddala income distributions," Economics Letters, Elsevier, vol. 43(1), pages 53-57.
    3. Christian Kleiber & Walter Kraemer, 2000. "Efficiency, Equity, and Generalized Lorenz Dominance," CESifo Working Paper Series 343, CESifo.
    4. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    5. Samuel Kotz & Christian Kleiber, 2002. "A characterization of income distributions in terms of generalized Gini coefficients," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 789-794.
    6. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    7. Muliere, Pietro & Scarsini, Marco, 1989. "A note on stochastic dominance and inequality measures," Journal of Economic Theory, Elsevier, vol. 49(2), pages 314-323, December.
    8. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    9. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    10. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    11. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    12. Donaldson, David & Weymark, John A., 1983. "Ethically flexible gini indices for income distributions in the continuum," Journal of Economic Theory, Elsevier, vol. 29(2), pages 353-358, April.
    13. Kleiber, Christian, 2002. "Variability ordering of heavy-tailed distributions with applications to order statistics," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 381-388, July.
    14. Kleiber, Christian, 1996. "Dagum vs. Singh-Maddala income distributions," Economics Letters, Elsevier, vol. 53(3), pages 265-268, December.
    15. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-628, October.
    16. Fellman, J, 1976. "The Effect of Transformations on Lorenz Curves," Econometrica, Econometric Society, vol. 44(4), pages 823-824, July.
    17. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 639-653.
    18. Kakwani, Nanak C, 1977. "Applications of Lorenz Curves in Economic Analysis," Econometrica, Econometric Society, vol. 45(3), pages 719-727, April.
    19. Arnold, Barry C, 1990. "The Lorenz Order and the Effects of Taxation Policies," Bulletin of Economic Research, Wiley Blackwell, vol. 42(4), pages 249-264, October.
    20. Laurent Derobert & Guillaume Thieriot, 2003. "The Lorenz curve as an archetype: A historico-epistemological study," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 10(4), pages 573-585.
    21. Jakobsson, Ulf, 1976. "On the measurement of the degree of progression," Journal of Public Economics, Elsevier, vol. 5(1-2), pages 161-168.
    22. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
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    Cited by:

    1. Christian Kleiber, 2008. "A Guide to the Dagum Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 6, pages 97-117, Springer.
    2. Michał Brzeziński, 2013. "Parametric Modelling of Income Distribution in Central and Eastern Europe," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 5(3), pages 207-230, September.
    3. Chie Aoyagi & Giovanni Ganelli & Kentaro Murayama, 2016. "How Inclusive is Abenomics?," Journal of International Commerce, Economics and Policy (JICEP), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-28, February.
    4. Philippe Van Kerm & Seunghee Yu & Chung Choe, 2016. "Decomposing quantile wage gaps: a conditional likelihood approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(4), pages 507-527, August.
    5. El-Osta, Hisham S. & Morehart, Mitchell J., 2009. "Welfare Decomposition in the Context of the Life Cycle of Farm Operators: What Does a National Survey Reveal?," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 38(2), pages 1-17, October.

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    More about this item

    Keywords

    Lorenz curve; Lorenz order; majorization; income distribution; income inequality; statistical distributions; characterizations; Condorcet jury theorem.;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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