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Re: st: Inequality of education: ineqdec0?

Subject   Re: st: Inequality of education: ineqdec0?
Date   Fri, 19 Feb 2010 16:17:20 -0500

Neither of the three problems raised here are, IMHO, real problems. Let me explain.

(1) Bunch of zeros. So long as you look at the distribution of years of schooling over the population above certain age (say, 22 when almost everybody is supposed to have completed his/her education), zeros are like any number: they are real, in the sense that they show that some people have had no education. It is a real piece of information, no different from 6 years of education or 15 years of education.

Only if you look at the entire population, zeros and low numbers may be a problem because kids aged 10 obviously cannot have more than 4 years of education. Such a distribution would be truncated, along different points, at something like age - 6.

It is legitimate also to look at the distribution of years of schooling only among those who have had some schooling but such conditional distribution would be no different from looking at the distribution of income only among those who make more than (say) $10,000 per year. Both are okay, but in principle we prefer to look at everybody and to exclude some groups only if we have compelling reasons to do so.

Zeros in wealth statistics are equally legitimate. If people have (say) no financial wealth it is a _real_ piece information that we have to include, not to drop or ignore. Thus, in this case as for education, Gini or any measure of inequality should be legitimately calculated inclusive of zeros. (If the statistics automatically rejects zeros, as some do, you can solve that problem by transforming zeros into 0.00001).

(2) Discrete data. This is not a problem either because we are interested in "completed" years of education. This is normally the only thing that matters, People may leave school at mid-year but such a half school-year will not matter, that is, will not be taken into account by the employers, by schools (were a person later to try to go back to school), nor by statistical offices. So, yes, the data are discrete, but this is not a false discreteness but a substantive one. (False discreteness would be, for example, if we had income data only in intervals of $1,000. Cleanly, dollar amounts in-between matter too, but for education, as I just wrote, I think that they do not matter.)

(3) Increased inequality and higher mean years of schooling. A Kuznets curve plotted against mean years of education is very similar to a Kuznets curve plotted against mean income (gdp per capita). Both inequality and mean are important. We may even want to combine them into a Sen-type index. Still this does not invalidate (or makes less relevant) increase in inequality. When a country moves from zero years of education for all, it does _really_ and _substantively_ move from zero level of inequality to some positive level of inequality. In other words, there is a real increase in education inequality. It is not an artefact of the data.


Sunday is for me usually a very boring day, because everybody goes
somewhere and I stay here [in my house] and there is nothing to do
but go hunting or just be bored for days on end.
Josip Broz Tito, Diaries, entry for January 7, 1951, Novosti Publishing Co.,
Belgrade, 2009, p. 81 (edited by Pero Simic). First published in 2009.
[my translation]

(New quote every Saturday.)

Development Research, World Bank
Email: or branko_mi@yahoo.
tel: 202-473-6968
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Inactive hide details for Maarten buis ---02/19/2010 02:49:33 AM------ On Thu, 18/2/10, Francesco Burchi wrote: > I am using inMaarten buis ---02/19/2010 02:49:33 AM------ On Thu, 18/2/10, Francesco Burchi wrote: > I am using individual data to calculate inequality of


Maarten buis <>



02/19/2010 02:49 AM


Re: st: Inequality of education: ineqdec0?

Sent by:

--- On Thu, 18/2/10, Francesco Burchi wrote:
> I am using individual data to calculate inequality of
> educational participation across people in a country
> in 3 different year. I would like to compute the Gini
> coefficient and possibly other indices of inequality
> on the variable "years of schooling". Can I use the
> simple command:
> Ineqdec0 EDU ?
> The problems is that years of schooling is a discrete
> variable, which presents many 0-values, and I am not
> sure whether I can use the same procedure used for
> computing income inequality. Moreover, can I compare
> directly the indices for the three years?

One problem you would need to consider is that any
changes in inequality over time will be influenced by
educational expansion, i.e. more recent cohorts get more
education than older cohorts. So what usualy happens is
that initially there isn't much inequality because a
large portion of the population was bunched at the lowest
level (i.e. everybody is equally misserable). In later
cohorts people get more education, which means that there
is more possibility to differ from one another, and thus
inequality increases. So, if you see an increase in
inequality over time you need to ask yourself, do I see
an increase in inequality or an increase in the average
level of education? In my sub-discipline such an increase
in inequality would be considered a trivial consequence of
educational expansion. At least you would need to discuss
the relation between inequality and changes the average
level of education. One way to do so is to show how the
distribution of education changes over time. You could a
stacked bar chart for that.

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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