# RE:st: ineqdeco by more than one subgroup, and error

 From "Stephen P. Jenkins" To Subject RE:st: ineqdeco by more than one subgroup, and error Date Wed, 31 Aug 2005 09:13:07 +0100

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Date: Tue, 30 Aug 2005 02:05:30 -0700 (PDT)
From: Brian Sartene <brisartene@yahoo.com>
Subject: st: ineqdeco  by more than one subgroup, and error

Having used ineqdeco to identify the various
components of inequality in my sample, I'd now like to
find out the joint impact of all my 'observable'
components in explaining levels of between-group
inequality (e.g., the joint impact of race, gender,
educational attainment).
I wonder if this is something ineqdeco permits?
Also is it possible to calculate the error surrounding
the between-group and within-group estimates?
With many thanks.
Brian
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Qn 1.

Regarding principles, you might like to look at:
FA Cowell and SP Jenkins "How much inequality can we explain? A
methodology and an application to the USA", Economic Journal 105(429),
March 1995, pp. 421-430.

We addressed the question that I think you wish to answer, and suggested
methods that use statistics that can be estimated by -ineqdeco-.

BTW -ineqdeco- can produce subgroup decompositions where the subgroups
are defined by more than one variable -- just put a varlist in the
bygroup() option. [This has been mentioned on Statalist before; see the
archives.] You don't get much control over the way the output appears,
however, and so you may prefer to first use
egen newvar = group(varlist)
to create subgroups in a way that suits you best, and then use newvar in
the bygroup() option.

Qn 2.

By "error", I presume that you mean "sampling error" -- you want
standard errors for the components?

The short answer is "no", though in principle one could.   Be aware that
this is a non-standard problem (made worse if there are sampling weights
and you don't want to treat them as deterministic). Note e.g. that
between-group inequality is a non-linear function of subgroup means,
each of which is estimated. Within-group inequality is a weighted sum of
subgroup inequalities where the weights and the the inequalities are
estimated.  I am aware of only one paper on this topic giving analytical
expressions for the sampling variances (and in a simplified case) -- I
think it was by Formby and collaborators in the Bulletin of Economic

Perhaps the easiest way forward for now would be to bootstrap.  To do
this you would need to write a little program wrapper, defining an
rclass program. With this program you would save the -ineqdeco- outputs
you want as r() results. (NB -ineqdeco- is a version 5 program so you
would refer to the saved results by putting a "\$" in front of the
relevant name: see help file, and Statalist archives.)  And then you
would bootstrap using the rclass program (for details, see Manuals)

Stephen (author of -ineqdeco-)
-------------------------------------------------------------
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
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/

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