# st: poverty/inequality analysis

 From "Stephen P. Jenkins" To Subject st: poverty/inequality analysis Date Tue, 22 Jul 2008 11:55:21 +0100

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Date: Mon, 21 Jul 2008 15:27:02 -0400
From: "Austin Nichols" <austinnichols@gmail.com>
Subject: Re: st: poverty/inequality analysis

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
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.
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>>>>>>>>>

Thanks for the plug, Austin. However, a paper that is perhaps more
closely related to Lola's needs is

"Accounting for income distribution trends: a density function
decomposition approach", Journal of Economic Inequality, 3(1), April
2005, 43-61 (Stephen P. Jenkins and Philippe Van Kerm)
"Abstract. This paper develops methods for decomposing changes in the
income distribution using
subgroup decompositions of the income density function. Overall
changes are related to changes in
subgroup shares and changes in subgroup densities, where the latter
are broken down further using
elementary transformations of individual incomes. These density
decompositions are analogous
to the widely-used decompositions of inequality indices by population
subgroup, except that they
summarize multiple features of the income distribution (using graphs),
rather than focusing on a
specific feature such as dispersion, and are not dependent on the
choice of a specific summary index.
Nonetheless, since inequality and poverty indices can be expressed as
PDF functionals, our density-based
methods can also be used to provide numerical decompositions of these.
An application of the
methods reveals the multi-faceted nature of UK income distribution
trends during the 1980s."

We decompose densities using a variation on the DiNardo-Fortin-Lemieux
idea -- using elementary transformations to explore the impacts of
changes in location, spread, and other distributional features --
what we call the three `S's of distributional change:
* sliding: a ceteris paribus shift of the PDF along the income line;
* stretching: a ceteris paribus increase in spread around a constant
mean; and
* squashing: a ceteris paribus disproportionate increase in density
mass on one side of the mode.

Stephen
-------------------------------------------------------------
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Director, Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374.  Fax: +44 1206 873151.
http://www.iser.essex.ac.uk
Survival Analysis using Stata:
http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/

Learn about the UK's new household panel survey, the United Kingdom
Household Longitudinal Study: http://www.iser.essex.ac.uk/ukhls/

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