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st: RE: Negative incomes and income components using -sgini-


From   philippe van kerm <philippe.vankerm@ceps.lu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Negative incomes and income components using -sgini-
Date   Thu, 28 Apr 2011 14:57:18 +0000

> -----Message d'origine-----
> De : owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] De la part de David Coyne
> Envoyé : Thursday, April 28, 2011 2:58 PM
> À : statalist@hsphsun2.harvard.edu
> Objet : st: Negative incomes and income components using -sgini-
> 
> Hello,
> 
> I've been attempting to decompose the Gini coefficient of a measure C,
> where C=A-B. I have two questions related to this. First, if C has some
> values that are negative, how does this affect the interpretation of
> the
> Gini coefficient? 

Negative data in relative inequality measures (such as the Gini) is a source of concern. Relative inequality measures after all summarize the distribution of shares of a total -- how should we interpret negative shares? 

Mechanically however, Gini coefficients can be computed with negative data -- at least as long as the mean is different from zero (unlike measures relying on log transformations, such as Mean Log Deviation or Theil indices). 

You may consider absolute inequality measures if negative data form a significant part of your variable of interest. However, I am not sure how to proceed with the decomposition by source in this case. It is very likely do-able but  -sgini- does not implement this (I should give this a go one day).

> Second, if B is nonnegative, (i.e. using -sgini-
> would
> have me use C=A + (-B), so if (-B) < 0 for all observations) thus
> leaving
> me with a negative contribution (s*g*r) to the Gini coefficient of C,
> does
> that mean that B has an equalizing effect on C? Not sure of the
> interpretation of this. Any insight and/or advice would be appreciated!


If all your data are negative on -B, then I think you can safely interpret a negative contribution measured by s*r*g in -sgini- output as indicative that B has equalizing impacts. 

Philippe


 
> Thanks in advance,
> 
> --
> David Coyne
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