– 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.