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The Lorenz curve in economics and econometrics

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  • Kleiber, Christian

Abstract

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

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Paper provided by Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen in its series Technical Reports with number 2005,30.

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Date of creation: 2005
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Handle: RePEc:zbw:sfb475:200530

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Keywords: Lorenz curve; Lorenz order; majorization; income distribution; income inequality; statistical distributions; characterizations;

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  1. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, Econometric Society, vol. 44(5), pages 963-70, September.
  2. Kakwani, Nanak C, 1977. "Applications of Lorenz Curves in Economic Analysis," Econometrica, Econometric Society, Econometric Society, vol. 45(3), pages 719-27, April.
  3. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, Elsevier, vol. 2(3), pages 244-263, September.
  4. 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.
  5. Jakobsson, Ulf, 1976. "On the measurement of the degree of progression," Journal of Public Economics, Elsevier, Elsevier, vol. 5(1-2), pages 161-168.
  6. Fellman, J, 1976. "The Effect of Transformations on Lorenz Curves," Econometrica, Econometric Society, Econometric Society, vol. 44(4), pages 823-24, July.
  7. Kleiber, Christian, 2002. "Variability ordering of heavy-tailed distributions with applications to order statistics," Statistics & Probability Letters, Elsevier, Elsevier, vol. 58(4), pages 381-388, July.
  8. Christian Kleiber & Walter Kraemer, 2000. "Efficiency, Equity, and Generalized Lorenz Dominance," CESifo Working Paper Series 343, CESifo Group Munich.
  9. Kleiber, Christian, 1996. "Dagum vs. Singh-Maddala income distributions," Economics Letters, Elsevier, Elsevier, vol. 53(3), pages 265-268, December.
  10. DONALDSON, David & WEYMARK, John A., . "Ethically flexible Gini indices for income distributions in the continuum," CORE Discussion Papers RP -520, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Wilfling, Bernd & Kramer, Walter, 1993. "The Lorenz-ordering of Singh-Maddala income distributions," Economics Letters, Elsevier, Elsevier, vol. 43(1), pages 53-57.
  12. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer, Springer, vol. 17(4), pages 639-653.
  13. Arnold, Barry C, 1990. "The Lorenz Order and the Effects of Taxation Policies," Bulletin of Economic Research, Wiley Blackwell, vol. 42(4), pages 249-64, October.
  14. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, Econometric Society, vol. 39(6), pages 1037-39, November.
  15. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, Econometric Society, vol. 52(3), pages 647-63, May.
  16. Ramos, Hector M. & Ollero, Jorge & Sordo, Miguel A., 2000. "A Sufficient Condition for Generalized Lorenz Order," Journal of Economic Theory, Elsevier, Elsevier, vol. 90(2), pages 286-292, February.
  17. Muliere, Pietro & Scarsini, Marco, 1989. "A note on stochastic dominance and inequality measures," Journal of Economic Theory, Elsevier, Elsevier, vol. 49(2), pages 314-323, December.
  18. Samuel Kotz & Christian Kleiber, 2002. "A characterization of income distributions in terms of generalized Gini coefficients," Social Choice and Welfare, Springer, Springer, vol. 19(4), pages 789-794.
  19. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-28, October.
  20. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
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Cited by:
  1. Michał Brzeziński, 2013. "Parametric Modelling of Income Distribution in Central and Eastern Europe," Central European Journal of Economic Modelling and Econometrics, CEJEME, CEJEME, vol. 5(3), pages 207-230, September.

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