Lola and Stas:
Given Lola's reference to survey data, I assumed she wanted to work
with real income distributions, which are not lognormal (unfortunately
for us programmers). Here's a silly example reducing the "poverty"
rate (poverty line at 6.2 for no good reason) from 5% to 2% with
either an increase in mean or a decrease in dispersion, holding the
other constant:
webuse psidextract, clear
keep if t==7
g x=_n/100+5.6 in 1/300
kdensity lwage, at(x) g(d0) nogr
g lw1=lwage+.2
kdensity lw1, at(x) g(d1) nogr
sort lwage
g add=-((_n-1)*2/594-1)*.2
g lw2=add+lwage
kdensity lw2, at(x) g(d2) nogr
line d0 d1 d2 x, sort xli(6.2)
su lw*
Note that the mean-preserving decrease in dispersion I used does
generate some reranking. It so happens the same 12 people are poor
under either transformation, but YMMV.
No idea is that's the kind of thing Lola has in mind or not...
Lola--you may also want to read (for conceptual background)
"Trends in income inequality, pro-poor income growth, and income mobility"
by Stephen P. Jenkins and Philippe Van Kerm in
Oxford Economic Papers 2006 58(3):531-548.
On Mon, Jul 21, 2008 at 2:38 PM, Stas Kolenikov <[email protected]> wrote:
> In our paper with Tony Shorrocks
> (http://www.citeulike.org/user/ctacmo/article/86251), we assumed the
> distributions were lognormal. That way, you can find all the
> inequality measures (as functions of the variance of logs), and
> poverty measures are some normal cdfs or other relatively simple
> functions. Generally it's rather hard to come up with meaningful ways
> to play with distributions... especially if you want to control for
> both inequality and the mean.
>
> On Mon, Jul 21, 2008 at 10:38 AM, Lola Jackson <[email protected]> wrote:
>> Dear Statalisters
>>
>> I am analysing the relationship between poverty, inequality, and growth using
>> multi-year survey data. I am wondering whether there are any existing Stata
>> routines that can help me. I have looked at -gidecomposition- and it is similar
>> but not quite. I need to calculate the growth/inequality combinations that
>> would result in a given reduction in poverty (where poverty is measured as % of
>> people below a fixed numerical poverty line) over 2 periods. So in order to
>> reach an exogenously specified reduction in poverty (e.g. that no more than 5%
>> of people should be below the poverty line in period 2, down from say 7% in
>> period 1), there could either be fast growth with the existing income
>> distribution; or no growth with a shift to a more egalitarian distribution; or
>> more likely some combination of the two. In a way a similar type of thing to -gidecomposition-,
>> but sort of starting at the other end.
>>
>> I was thinking of doing this 'manually' by adjusting growth and distribution and
>> seeing what the poverty outcome is (even though the poverty outcome is actually
>> what I want to set exogenously). But this is easier on the growth part than on
>> the distribution part. I could easily impose different growth rates by
>> adjusting all incomes by different factors. I'm not sure how one could 'impose'
>> a redistribution component. Also it seems to me that there should be a more
>> efficient/accurate way of doing this! (I don't know anything about advanced programming
>> in Stata but am trying to learn!)
>>
>> Thank you for any suggestions.
>>
>> Best,
>> Lola
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