# Re: st: poverty/inequality analysis

 From "Stas Kolenikov" To statalist@hsphsun2.harvard.edu Subject Re: st: poverty/inequality analysis Date Mon, 21 Jul 2008 16:52:24 -0500

```Lola,

it looks to me like you might want to read about generalized Lorenz
curve (that reach the upper point equal to the mean income rather than
the value of 1). In general, a great book on the topic is Lambert's
Distribution and Redistribution of Income
(http://www.amazon.com/Distribution-Redistribution-Income-Third/dp/0719057329/).
If you are not familiar with it, you might want to stop for a couple
of days and go through at least first three chapters. The economically
natural mean preserving transformations are taxes and transfers, so an
experiment you might think of is levying a flat rate tax and
redistributing it in lump sum transfers, to reduce inequality. It will
preserve rankings, too, as both operations are monotone. And take a
look at that paper I mentioned, anyway -- it provides some
decompositions that will be relevant for you.

On Mon, Jul 21, 2008 at 3:10 PM, Lola Jackson <lola_jackson@ymail.com> 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

--
Stas Kolenikov, also found at http://stas.kolenikov.name