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Sent: Friday, March 24, 2000 11:00 AM
To: Emilio Jose Chaves
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Subject: Re: On Ginis and 1947-1998 US Ginis
Just to clarify, the point I was trying to make is that I do not believe
that
the official Gini coefficient for the US is calculated from the official
quintile shares. Rather both the quintile shares and the gini coefficient
are
calculated from the individual observations in the sample surveys used to
generate the inequality measures. The procedures are likely to produce very
different results, because the Gini coefficient is a summary measure. But
the
quintile share is also a summary measure (although 5 numbers rather than 1).
But then to calculate the summary measure (the gini) from what is already a
summary measure (the quintile shares) is to introduce a very large margin of
error.
In summary, I believe that the reason you get a different result from the
official figures is that they are not using the summary data.
While the idea of the Gini coefficient is relatively straightforward, it is
actually very hard to calculate. As Koen points out, there are procedures
in
SPSS or SAS or other statistical packages that will calculate the Gini from
sample data; my memory of looking at a SPSS guide many years ago is that it
will
explain it quite well. However, when you apply the same basic methodology
to
grouped data, other issues arise - the article and book I referred to will
deal
with it.
In addition, I am fairly positive that if you contact the US Census Bureau
directly, they will tell you what their procedures were.
Nevertheless, as Koen points out official statistics will be distorted
because
of exclusions from the sampling frame, such as the homeless, people in
prison
and persons in nursing homes. In addition, the extent of earnings
inequality in
the US will be understated because of "top coding". I would point out that
it
is possible to avoid this distortion. My understanding of the Australian
data
for example is that our Statistics agency recodes everyone above a certain
income level to the mean of the recoded group. Thus, our aggregate
inequality
measure will still take account of the high incomes of the richest 1 per
cent.
Peter Whiteford
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