A Note on Stochastic Dominance and Inequality Measures

Posted: 12 Mar 2012

See all articles by Pietro Muliere

Pietro Muliere

Bocconi University - Department of Decision Sciences

Marco Scarsini

Luiss University Dipartimento di Economia e Finanza

Date Written: March, 11 2012

Abstract

A sequence of partial orders (called inverse stochastic dominances) is introduced on the set of distribution functions (of nonnegative random variables). The partial orders previously defined are used to rank income distributions when Lorenz ordering does not hold, i.e., when Lorenz curves intersect. It is known that the Gini index is coherent with second degree stochastic dominance (and with second degree inverse stochastic dominance). It will be shown that it is coherent with third degree inverse stochastic dominance, too. It will finally be shown that a sequence of ethically flexible Gini indices due to D. Donaldson and J. A. Weymark (Ethically flexible Gini indices for income distribution in the continuum, J. Econ. Theory 29 (1983), 353–356) is coherent with the sequence of nth degree inverse stochastic dominances.

Keywords: inverse stochastic dominance, flexible Gini indices, Lorenz curve

JEL Classification: D63

Suggested Citation

Muliere, Pietro and Scarsini, Marco, A Note on Stochastic Dominance and Inequality Measures (March, 11 2012). Journal of Economic Theory, Vol. 49, No. 2, 1989, Available at SSRN: https://ssrn.com/abstract=2019815

Pietro Muliere

Bocconi University - Department of Decision Sciences ( email )

Via Roentgen 1
Milan, 20136
Italy

Marco Scarsini (Contact Author)

Luiss University Dipartimento di Economia e Finanza ( email )

Viale Romania 32
Rome, RM 00197
Italy

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