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Efficiency, Equity, and Generalized Lorenz Dominance

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  • Christian Kleiber
  • Walter Kraemer

Abstract

We decompose the generalized Lorenz order into a size and a distribution component. The former is represented by stochastic dominance, the latter by the standard Lorenz order. We show that it is always possible, given generalized Lorenz dominance between two distributions F and G, to find distributions H1 and H2 such that F stochastically dominates H1 and H1 Lorenz-dominates G, and such that F Lorenz-dominates H2 and H2 stochastically dominates G. We also show that generalized Lorenz dominance is characterized by this property and discuss the implications of these results for choice under risk.

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File URL: http://www.cesifo-group.de/portal/page/portal/DocBase_Content/WP/WP-CESifo_Working_Papers/wp-cesifo-2000/wp-cesifo-2000-10/cesifo_wp343.pdf
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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 343.

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Date of creation: 2000
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Handle: RePEc:ces:ceswps:_343

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Related research

Keywords: Income distribution; welfare dominance; Lorenz order; stochastic dominance; decisions under risk;

References

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  1. Muller, Alfred, 1996. "Orderings of risks: A comparative study via stop-loss transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(3), pages 215-222, April.
  2. Rubin Saposnik, 1981. "Rank-dominance in income distributions," Public Choice, Springer, Springer, vol. 36(1), pages 147-151, January.
  3. Saposnik, Rubin, 1993. "A note on majorization theory and the evaluation of income distributions," Economics Letters, Elsevier, Elsevier, vol. 42(2-3), pages 179-183.
  4. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, American Economic Association, vol. 59(1), pages 25-34, March.
  5. 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.
  6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, Elsevier, vol. 2(3), pages 225-243, September.
  7. Hanoch, G & Levy, Haim, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 36(107), pages 335-46, July.
  8. 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.
  9. Salem, A B Z & Mount, T D, 1974. "A Convenient Descriptive Model of Income Distribution: The Gamma Density," Econometrica, Econometric Society, Econometric Society, vol. 42(6), pages 1115-27, November.
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Cited by:
  1. Kleiber, Christian, 2005. "The Lorenz curve in economics and econometrics," Technical Reports 2005,30, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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