There are possible issues on two levels here. First,
no Stata programmer can write code for a correction
that is not specified. Perhaps it's specified in the
paper. My point in asking for the reference was just
to remind you of standard Statalist protocol on behalf
of those people working in the field who might want to
know the reference. I don't want to read it myself.
Second, on the face of it this suggestion still seems to
be intensely problematic.
Consider for example another approach to the problem.
You could always translate by
income' = income - CONSTANT
where CONSTANT is small enough (the empirical minimum,
or smaller) to ensure that you work with non-negative
numbers. But I doubt that there is a theoretical
way to choose CONSTANT, and even choosing it empirically
would probably leave you with a distribution whose Gini
is difficult to compare with any other Gini, unless
CONSTANT were the same. And if CONSTANT were the same,
that would create problems too.
Yet another take is that my impression is that inequality
statistics hinge on income being a ratio variable, i.e.
ratios of incomes make sense, so that ratios such as
Bill Gould's income
-------------------
Nick Cox's income
are the same whether measured in dollars, pounds, or
anything else. This is because zero is a natural origin.
Throw that away and you risk nonsense.
This is all presumption on my part, but I have
a strong sense here that the proposal you refer
to is just hiding the problem. Hiding the problem
is not the same as solving it.
Nick
[email protected]
G�l �NAL
> Hi Nick,
> thank you for the comments, let me make myself more clear then. First
> on the reference, here is the additional information for those of you
> who are interested:
>
> Chau-Nan Chen Tien-Wang Tsaur; Tong-Shieng Rhai. (1982) The Gini
> Coefficient and the Negative Income. Oxford Economic Papers
> (pre-1986); Nov 1982; 34, 3, pp. 473-78
>
> On the issue of "fixing the Gini": Chen et al, in their article
> suggest that when negative incomes are present regular Gini
> coefficient may overestimate the inequality.
>
> I will give the example they use in their article: Consider a
> community with ten households with the following incomes ( -500, -300,
> -300, -100, 200, 300, 300, 400, 500, 500). Normal Gini coefficient of
> such a distribution will be 1.94. When one thinks a case where one
> household has all the income and all else has nothing Gini is .99,
> then this 1.94 is an overestimation. Cheun et al.'s suggestion is to
> correct for this overestimation, which I think is sensible.
>
> Thanks for the comments, and I am looking forward to hear incase
> anyone has any experience with calculating Gini coefficients for
> datasets with negative incomes,
> On 6/6/07, Nick Cox <[email protected]> wrote:
> > I have only marginal expertise here, but two comments:
> >
> > 1. The reference here is incomplete as you give no
> > author initials or journal or book details.
> >
> > 2. Clearly negative incomes make sense in your context;
> > trying to fix the Gini as if they didn't exist seems
> > to be a denial of this and dubious practice.
> >
> > Nick
> > [email protected]
> >
> > G�l �NAL
> >
> > > I am working with a large dataset which includes agricultural
> > > households. Households have negative incomes ( since it is
> > > agricultural production, income can turn negative in some
> cases). So,
> > > my problem is that, when I use ineqdec0, to include
> negative and zero
> > > values of income, it gives me gini coefficients that is sometimes
> > > greater than 1 ( which I calculate for 500 villages) .
> This is normal,
> > > because as it is discussed in an article by Chen et al. (1982),
> > > titled: "The Gini coefficient and negative income" the
> definition of
> > > the Gini coefficient allows that to happen when there are negative
> > > incomes. Chen et al. also suggest a way to normalize it
> so that Gini
> > > coefficient would be between 0 and 1 only.
> > >
> > > Does anyone know a code or a command in Stata that would do this,
> > > i.e., normalize the Gini coefficient so that when
> negative incomes are
> > > in the data, Gini would not be larger than 1. Since I
> have been using
> > > ineqdec0 so far, I am not really familiar with the ado
> file of it, is
> > > the only way to go and change the do file based on Chen's
> suggestion
> > > to normalize it?
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