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Tails of Lorenz curves

Tails of Lorenz curves
Tails of Lorenz curves
The Lorenz dominance criterion is the centre piece of inequality analysis. Yet, the appeal of this criterion, which requires considering Lorenz curves in their entirety, is undermined by the practical problem that many sample Lorenz curves intersect in the tails. The commonly used inferential methods, based on central limit theorem arguments, do not apply to the tails since these contain too few observations. By contrast, we propose a test procedure for distributions whose tails lie in the domain of attraction of the Fréchet distribution, which fully takes into account the tail behaviour of Lorenz curves. Our experiments and empirical examples demonstrate the good performance of the proposed test: in many cases we are able to infer that despite sample tail crossings the population Lorenz curves do, in fact, exhibit Lorenz dominance.
Lorenz curves, statistical inference, tail behaviour, regular variation
0304-4076
151-166
Schluter, Christian
ae043254-4cc4-48aa-abad-56a36554de2b
Trede, Mark
7233d600-13a2-4c24-ae9d-16aed9bfca30
Schluter, Christian
ae043254-4cc4-48aa-abad-56a36554de2b
Trede, Mark
7233d600-13a2-4c24-ae9d-16aed9bfca30

Schluter, Christian and Trede, Mark (2002) Tails of Lorenz curves. Journal of Econometrics, 109 (1), 151-166. (doi:10.1016/S0304-4076(01)00145-2).

Record type: Article

Abstract

The Lorenz dominance criterion is the centre piece of inequality analysis. Yet, the appeal of this criterion, which requires considering Lorenz curves in their entirety, is undermined by the practical problem that many sample Lorenz curves intersect in the tails. The commonly used inferential methods, based on central limit theorem arguments, do not apply to the tails since these contain too few observations. By contrast, we propose a test procedure for distributions whose tails lie in the domain of attraction of the Fréchet distribution, which fully takes into account the tail behaviour of Lorenz curves. Our experiments and empirical examples demonstrate the good performance of the proposed test: in many cases we are able to infer that despite sample tail crossings the population Lorenz curves do, in fact, exhibit Lorenz dominance.

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More information

Published date: 2002
Keywords: Lorenz curves, statistical inference, tail behaviour, regular variation

Identifiers

Local EPrints ID: 33355
URI: http://eprints.soton.ac.uk/id/eprint/33355
ISSN: 0304-4076
PURE UUID: d212d6d2-5fa5-40e4-9a96-78496425e871

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Date deposited: 15 May 2006
Last modified: 15 Mar 2024 07:43

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Author: Mark Trede

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