Poverty Inequality Ethics 3 Measuring income inequality and mobility

– Okay, so we’ve already
talked about what we’re going to measure
the inequality of, and we’re going to concentrate
on measuring income inequality and how do we
measure income inequality? And that last word there is
supposed to be inequality but it got kind of smushed. So the most common way in
which people begin approaching this is they look at the overall
population and they sort of go, okay, let’s go ahead and think about the population
falling into different chunks. And we have the lowest 1/5
and sometimes this is done with tenths
instead of fifths. But 1/5 is usually the sort
of most common increment. The second lowest 1/5,
the middle 1/5, the second highest 1/5
and the top 1/5. And then sometimes we sort
of split this up into, you know, the top 5%
which would be the top 1/20 or the top 1% or so on
or so forth here. And people go okay, what is the average income
of people in the lowest 1/5 or what percent of income is earned by people
in the lowest 1/5? So we might go okay, the average income of people
in the lowest 1/5 is say here, the average income of people
in the second highest, or second lowest
1/5 is right there, and here, and here, and this one is like way
up here. Okay, so first when you start
looking at some of the data and then sometimes people go, all right, let’s look
at the ratios, say for instance of incomes
of the highest 1/5 relative to incomes in the lowest 1/5. So this is looking at the ratio
of income between these are, I believe quintiles,
so they’re fifths. So that’s one of the common
measures out there. The other is often
what percentage of income of total national
income goes to each quintile. And if the income distribution
were just completely flat, each 1/5 of the population
would earn 20% of national income if it
was completely proportional. But we might say for instance, go, okay maybe
the lowest 1/5 earn 5% and the next one earns 10%
and this is a 15% and this is a 25%
and then sort of 40 + 15 that would be 35, or 45% I think if I’ve
done my math right. So in that case the ratio of the income quintiles
would be say, for instance, the ratio
between the top and the bottom 1/5
would be nine to one. And so that’s one way people do
it or sometimes they sort of go, all right, let’s, so that sort
of emphasizes the level of inequality between the very
lowest and the very richest, sometimes people sort of go, well let’s worry
about inequality between people in the middle
and people at the top, and so on and so forth, in which case they’d
be looking at the ratio between the income
at the top percent and the income
at the middle percent, and we’d get three to one,
say for instance. So that’s one way
the people look at it, another common way sort
of a one single number summary, is what’s called
the Gini coefficient. And actually calculating the Gini coefficient is a little
bit complicated, but what we do here
is we think about lining up all the populations from lowest
income to highest income and so here’s the zero
width percentile, the person at the lowest point
in the income distribution and here’s the person
at the 100th percentile, at the highest point
of the income distribution. And we’re going
to keep track of, as we add up the incomes
of everyone up to that point, how much of total national
income have we added up to? So let’s say that by the time we
add up to the tenth percentile, everyone in the tenth percentile or less if we add up
all of their income, we get to say 4%
of overall national income. So we’re going to build here
what we call the Lorenz curve. And you can see as we start
going farther this way, we’re going to get to a higher and higher level
of national income, you know, for everyone 50th
percentile or below, maybe we have 30% of national
income is being earned by everyone in the bottom half. And once we get
to the 100th percentile, then by definition
all of national income must have been earned by someone in the 100th percentile
or below. So we’re going to have a curve
that looks something like this. So that’s the Lorenz curve. And then we figure out
what the area of this gap is, and this gap gives us
the difference between the Lorenz curve
and what the Lorenz curve would be if we had a completely
equal distribution of incomes. And you can see that like if
incomes are more unequal, then this curve is going
to be lower at the beginning
and really rise quickly at the end because we don’t
really start adding up much of national income until we get to these last
couple of people here. So the bigger this area
between this 45 degree line and the Lorenz curve the higher
the level of inequality. So what we can do here
is we can take the area there and multiply it by two, and what happens there is
we’ve gotten what’s called the Gini coefficient. And the Gini coefficient is
going to be zero if there’s complete equality, just absolute everyone has
exactly the same income. And it’s going to be one
if we have complete inequality. Everyone has zero income
except for one person. Okay, so those are some of our measures
of income inequality and how we look at that. The last thing to sort
of think about here is sometimes we think that people might
not mind inequality so much or it might not be unfair if there’s a high level
of income mobility. And there’s two different ways that people commonly
measure income mobility. So one of the ways that
people measure income mobility, and I’m going to make
a simplified example here is let’s just imagine that we’re going
to look at the top half and the bottom half
of the income distribution, and so over here
we’re going to have people who start
in the bottom half. So what half you started
in you’re thinking about there, and where you ended up up here. And if the world were
completely random, this and this would
both be 50, 50. So if you start, if you
started in the bottom half you’d have a 50% chance
of staying in the bottom half and a 50% chance
of ending in the top half. Or if you started here, in the world we’re
completely random, these two numbers
would be 50, 50. But we might say,
for instance, see, that this is 70%
and this is 30%, and this is 30%,
and this is 70%. So the closer
those numbers are to 50, 50, or a completely
equal distribution if we had more
than two categories, so the more randomness there is, mostly what people seem to care
about though is they seem to measure income mobility
as the bigger this number over here then the bigger
your chance of ending up in a higher income
distribution bracket given that you started
in a low bracket. And I’ll go ahead
and put on the class website some data on this. When we look over relatively
long periods, we actually get
some surprisingly high numbers. And I’ll let you
guys look into that. The last way, actually
one last thing, this video segment is maybe
a little bit long but easier I think to put it
in here is intergenerational income mobility. So the previous way
of looking at income mobility really keeps track typically
of people’s mobility over a 10, maybe 15, maybe
20 year time period. What sometimes happens with
that is that in the bottom half of the distribution, we might say
for instance pick up a bunch of people
who are 20 year olds. They have low income because
they’re going to college say, but maybe they
come from a family that’s actually fairly well off and so we sort
of get the question of are we really measuring
what we most want to measure if we’re sort of measuring
people’s natural transitions over the course of their life. Another way of looking
at this is how well does your parental economic status predict
your economic status? And so what we often talk
about here is what’s called the coefficient of correlation
for incomes across generation. And this gets a little
bit complicated but a common way that this might be studied would
be something like well, if your father’s income
and usually because the role of women in the labor force has changed
a lot over the generations, usually this is measured with
fathers and sons to sort of, you know, make things as
consistent as possible and not get sort of mixed up
in the changing role of women. If your father’s income is, was 20% higher than average
for his generation, what is the most
likely outcome for you? And you can see that what
we’re basically talking about here is how inheritable
are income differences. And so we might say
for instance come about here and see that we get
a fraction of, we get a correlation coefficient
of something like 0.5. And essentially
what we’d be saying here is if your father’s
income was 20% above average, then you would have,
we would expect on average, for you to have an income that’s
10% above average ’cause we expect some degree of what we
call regression to the mean, that, you know, maybe your father was unusually
lucky or something like that, and maybe the luck won’t hold, or, you know, if your father’s
income was 30% below average, then we expect some of
that is due to bad luck that he encountered
and that maybe your income then is only likely to be 15% below average if we have
this correlation coefficient. The higher
this correlation coefficient the more that income
differences are heritable. The more that people who had
parents that were low income or likely to be low income
themselves and the more that people who have parents
that are high income are likely to have high income
and essentially if we have a correlation
coefficient of zero, there’s no heritability
of income. If we have a correlation
coefficient of one, there’s no income mobility
at all, income is completely inheritable
across generations. Okay.

Author: Kennedi Daugherty

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