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# Re: st: Ginis for negative net worth

 From Conor Hughes To statalist@hsphsun2.harvard.edu Subject Re: st: Ginis for negative net worth Date Mon, 5 Jul 2010 06:21:46 -0500

```Hi Nora,
The general formula for the Gini index 1 - 2*int_0^1 Y(x)dx, where
Y(x) is your Lorenz curve.  The only way this can be greater than 1 is
if the integral is negative.  So, in your case, the Gini isn't really
appropriate, since 1 is defined as perfect inequality.  Anything
greater than 1 will make most economists very uncomfortable.  You
should take a look at this paper by Andreas Stich in the journal
Statistical Methods and Applications (Volume 5, Number 3) called
"Inequality and negative income."  I think it will give you some
helpful ideas for dealing with this.

Cheers,
Conor

On Mon, Jul 5, 2010 at 6:01 AM, Abdel Rahmen El Lahga
<rahmen.lahga@gmail.com> wrote:
>
> Nora,
> Gini index as well as other inequality indices are defined for
> positive outcomes and can not applied for negatives observations.
> You have two alternatives:
> 1) use a trick (not so popular) proposed by Chen et al. (1982) in
> oxford economic paper (1982) page 473-478 (See also the comment by
> Berrebi and Silber in the same journal (1985 page 525-526) to deal
> with negative outcomes
> 2) You can use absolute gini index to avoid problems caused by
> negative income (but you should care about  different ethical
> judjements associated to absolute view of inequality)
> HTH
> AbdelRahmen
>
> 2010/7/5 Nora Müller <nora.mueller@uni-bamberg.de>:
> > Dear All,
> >
> > I'm trying to calculate the gini coefficient for net worth (= financial
> > assets + real assets - debts) that has some negative values.
> > I do this using the command "inequal7" written by Philippe Van Kerm.
> >
> > I'm doing an international comparison and for Poland I get a Gini that is
> > 1.15. Can anyone help me with the interpretation?
> > Why can there be a gini greater than one?
> >
> > Thanks for your consideration,
> > Nora
> >
> >
> > --
> > *********************************************
> > Nora Müller, Dipl.-Soz.
> >
> > Faculty for Social and Economic Sciences
> > Chair of Sociology I
> > Otto-Friedrich-University Bamberg
> >
> > Fakultät Sozial- und  Wirtschaftswissenschaften
> > Lehrstuhl Soziologie I
> > Otto-Friedrich-Universität Bamberg
> > Wilhelmsplatz 3
> > 96047 Bamberg
> >
> > Raum: 229
> > Tel. +49-951-863 3909
> > Fax. +49-951-863 2597
> > Email: nora.mueller@uni-bamberg.de
> > www: http://www.uni-bamberg.de/sowi/soziologie-i/
> >
> > http://gif-project.soziologie-blossfeld.de
> > *********************************************
> > *
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> >
>
>
>
> --
> AbdelRahmen El Lahga
>
> *
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--
Conor Hughes
Mathematics and Economics
University of Chicago 2011

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```