Lola--
The problem is, there may be infinitely many "change in Gini (or other
measure)" transformations you can apply to get to a given target. You
need to impose more structure on the dispersion-changing
transformation (and I would advise that you restrict it to be
mean-preserving, or possibly median-preserving). My silly
transformation only has one parameter, so you can vary that to find
the smallest value that gets you to the requisite poverty rate or
below, but if you have a transformation with even two parameters, you
will in general have many choices--and your problem as stated seems to
allow N parameters with N people (i.e. everyone's income can change by
some unspecified amount). Once you pick a transformation, it will
have various defects that a reviewer will no doubt point out after
you've spent months writing the paper...
On Mon, Jul 21, 2008 at 4:10 PM, Lola Jackson <[email protected]> wrote:
> Dear Austin, Stas, and other Statalisters,
>
> Thank you very much for the helpful replies.
>
> Austin is correct that I am working with real income data, which is not log-normal. Actually he expressed what I want to do well when he asks 'Do
> you want to apply a mean-preserving contraction (the opposite of a
> mean-preserving spread) and a shift in the mean, to different degrees,
> to a given distribution to achieve a specified percent below a given
> threshold?' – pretty much yes. I understand that this is not really how income evolves in practices, but the objective is to illustrate what combinations of changes in distribution and growth might be required to meet a given poverty reduction goal (and to compare this with current rates).
>
> My thinking is that with a given Lorenz curve and given mean
> income, one can calculate the % of people below a numerical poverty line (or
> changes in each of these variables). So I want to work out, given a specified %
> of people below the poverty line and given a specified growth rate, what would
> be the change in Gini (or other measure) 'required'; or alternatively given a
> specified % of people below the poverty line and given a specified change in
> Gini or other distribution measure, what would be the growth rate of mean
> income 'required'.
>
> Thanks!
>
> Lola
>
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