Measures of Distributional Inequality
The Lorenz Curve shows the proportion of income earned by each income group. The Gini Coefficient measures the degree of income equality. 5 The Lorenz curve plots the actual relationship between percentages of the 12 VALUES OF THE GINI COEFFICIENT Perfect income equality = 0. The Lorenz Curve and Gini Coefficient | Intelligent Economist . is based directly on data from household surveys – one reason for the slightly.
It's similar, wealth is similar to income, but just includes also savings and things like that. It actually did visually show this way of looking at it.
So I figured I would borrow-- they said that we could share this with anybody. So here is the visual. See, we're lining everybody up, and we're putting all their money in front of them.
That basically everybody would have the same amount of money, and that's what it would look like. The difference between these two numbers then is nothing.
There is no difference. We know, though, that's certainly not the case in most countries. We know that everyone does not have the same amount of money. Here's just-- they were just saying what Americans chose as an ideal distribution, but I just wanted to show you.
It would obviously look different as there is income inequality.
See now, there is a difference between these numbers. That means that as we move up, people are making more and more money. So this is what the Gini coefficient actually measures.
- MEASURING INCOME INEQUALITIES Featuring the Lorenz Curve, the Gini Coefficient and more…
It's measuring the difference between these two figures, and it's averaging them and it uses calculus to do this. It averages these statistics over the entire population distribution to come up with a coefficient. I'm going to show you this, actually, on the Lorenz curve.
The Lorenz curve is a graphical depiction of the inequality, measured by the Gini coefficient. The first step in constructing a Lorenz curve is to make a 45 degree line.
Here we have percentage of income and percentage of families.
What that 45 degree line shows is perfect incoming equality, because it's showing you just what I did on that first visual image. That's the significance of the 45 degree line.
Then we plot the actual distribution in a country, and that is represented by this blue curve, right here.
So if all of the income in a country was actually earned by one person, so perfect income inequality, that would look like this right here. So that's important to keep in mind. Along the 45 degree line, there is no difference at all between these numbers. But as you can see, more likely there is some kind of curve here.
Gini Coefficient Tutorial | Sophia Learning
So the idea is the closer that this curve gets to that 45 degree line, the more income is equally distributed in a country. Because there aren't significant differences between the percentage of families and the percentage of income. The larger the shaded area-- so the further away this curve gets from the 45 degree line-- the more income inequality there is in a country. And that is what the Gini coefficient is measuring. It's a ratio of this shaded area right here to this triangle formed by this hypothetical, if one person in the country earned all of the income.
So as the shaded area then grows in relation to the triangle, the Gini coefficient is larger, and that shows more income disparity. Like I said, a lot of the graphics that I've been using in this tutorial come from a short video put together to show the distribution of wealth in the United States. If you're interested, you can certainly check it out.
It is pretty interesting. But that's totally up to you. I wanted to provide you with that link. Back to the Gini coefficients. This is a visual image I thought was interesting that I found on global Gini coefficients.
At the other extreme, if the highest income group earned all the income, the Lorenz curve would be flat across the vast majority of the income range,following the bottom edge of the figure, and then jump to the top of the figure at the very right-hand edge. Lorenz curves for actual income distributions fall between those two hypothetical extremes. Typically, they intersect the diagonal line only at the very first and last points. Between those points, the curves are bow-shaped below the degree line.
The Lorenz curve of market income falls to the right and below the curve for after-tax income, reflecting its greater inequality. Both curves fall to the right and below the line of equality, reflecting the inequality in both market income and after-tax income.
Lorenz curve and Gini coefficient
The intuition is straightforward although the mathematical formula will look a little messier. On a Lorenz curve, greater equality means that the line based on actual data is closer to the degree line that shows a perfectly equal distribution. Greater inequality means that the line based on actual data will be more "bowed" away from the degree line. The Gini coefficient is based on the area between the degree line and the actual data line.
As the CBO writes: Once again, the extreme cases of complete equality and complete inequality bound the measure.