st: RE: Gini coefficient for spatial data

[<S.Jenkins@lse.ac.uk>]

The fundamental issues appear to be: (1) what is the unit across which
you wish to measure inequality? (2) What units are your data observed
in?  Francisco needs to clarify this.

Suppose individuals live in areas and your outcome variable is 'income'

Possibilities include:
(a) you want inequality across all individuals, but you only observe the
average income for each area
(b) you want inequality across all areas, but you only observe the
average income for each area

In (b) the unit and observation level coincide; in (a), they don't. 

If (a) is of interest, it must be the case that inequality among
individuals in the population is under-estimated.

Recall that, for generalised entropy inequality measures, one can write

Total inequality = I_B  + I_W

I_B is Within-groups inequality = weighted sum of the inequalities for
each group (region!), where the weights depend, in general, on the
group's income share and their population share

I_W is between-groups inequality = total inequality there would be were
each individual to receive the mean income of the group to which they
belong

[For more details, see the References in -ineqdeco- or -indeqec0- on
SSC]

If case (a) applies to you, and you simply apply the programs cited, you
will miss out I_W. 

If this is a serious problem, then you will have to make some
assumptions (or use external information) about the distribution of
income within regions.

Stephen

------------------------------

Date: Wed, 23 May 2012 08:49:13 +1000
From: Francisco Rowe <frowe@ucn.cl>
Subject: Re: st: RE: Gini coefficient for spatial data

Thanks Nick.

Well, I rephrase my question: Can I apply the existing Stata commands
-e.g. ineqdeco, inequal, sgini- to calculate the Gini coefficient using
spatial data? All of the commands I mentioned seem to require as input
micro data. 

What I want is to measure the degree of concentration/dispersion of
different variables at the different geographical scales.

Francisco.



Stephen
------------------
Professor Stephen P. Jenkins <s.jenkins@lse.ac.uk>
Department of Social Policy and STICERD
London School of Economics and Political Science
Houghton Street, London WC2A 2AE, UK
Tel: +44(0)20 7955 6527
Changing Fortunes: Income Mobility and Poverty Dynamics in Britain, OUP
2011, http://ukcatalogue.oup.com/product/9780199226436.do
Survival Analysis Using Stata:
http://www.iser.essex.ac.uk/survival-analysis
Downloadable papers and software: http://ideas.repec.org/e/pje7.html


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