 Hello, today we're going to talk about how to measure inequality. That is, is there some way we can put a number on the amount of inequality there is so we can study it and understand it, in particular the genie index and what you can do with it. How much inequality is too much? We know there are poor people, rich people and people in between, but can we say anything more about how can we describe that whole situation in one concise way? To answer how much is too much, we need to be able to answer how much is there, right? So we'll look at the whole system and all the people and all the families or whatever we're studying and try to understand how much inequality is there then we can ask questions like, is it too much or what could we do about it? Let's take a very simple situation to begin with, a situation where inequality is, you could say zero, there's no inequality. Everybody has the exact one stack of cash, Betty, Jack, Jane and Bob, four people, one stack of cash each and we'll put a number on that amount of inequality and then you'll see how it works when we start looking at more realistic situations. So we'll take those four people and we'll put them in this grid, we'll put the first person could be anybody because they all have the same amount of money, Bob. Put them down there in the bottom, Bob has got, Bob is 25% of the people, he's got 25% of the money. We'll stack Jane in there next to Bob, pile Jane's money on top of Bob's, pile Jack's money on top there and then we'll complete it with Betty's money. Now they're all stacked in there, so you go from zero to 25, 50, 75, 100% of people, 20 to 0, 25, 55, 75, 100% of money. Any one person, it could be anybody but we started with Bob but they have the same amount so it doesn't matter. That first 25% of people have 25% of the income, the next 25% have another 25% and so on. So it's one to one, every 1% of people has 1% of the money. You see that diagonal line, we'll call that diagonal line equality. So inequality is zero, that's equality. Percentage of people going up matches the percentage of money going up. Now a slightly more realistic situation, Betty has four more stacks. Now Betty has five stacks of cash, Jack, Jane, and Bob still only have one. Okay, so let's go back to our grid and see what it looks like now. Now Bob, Bob, Jane, Bob, Jane, Jack, still the same. One stack, two stacks, three stacks, but that three stacks isn't 70% or 5% of the money anymore because now you put Betty in the last column and Betty's got five stacks. You can see that line of equality, that equal line, that one to one slope doesn't fit our situation anymore. In fact, if you draw that line, you're going to get something, a slope that looks more like this. So it pulls down because Bob, Jane, and Jack don't have that much and then it shoots up at the end because Betty's got all the rest of the money. So we're bending away from that line of equality. So if we take those people out, we can look at this more abstractly or more the math of it. There's that slope of equality and there is that inequality situation that's a certain distance from that slope. We're going to call that curved line the Lorenz curve after some old economist Lorenz from the early 20th century. And the further that line is, the more inequality there is. You can actually kind of see this in this very simple example because there's 16 squares overall in our grid, 8 squares in that lower right triangle, that lower right half. And that line, that curved line takes actually about three of those squares. And I drew it by hand, but it's about three of those eight squares. OK, we're going to call that area genie or the genie index is that number. And that number is the percentage of that lower right triangle that is above the Lorenz curve that's in that blue shaded area. So in this case, it's about three eighths of the three of the eight squares or about 37.5% or 0.375 is our genie index. So that's how much of the space in that lower right triangle is above the blue line. Now the genie index is that whole triangle, the percentage of that whole triangle that's above the line. So if the line is equality, the blue line and the red line totally match, it's zero, that's what we started with. And on the other hand, if Betty had all the money so that all the 99% of people before had zero and then she had all the money piled up at the end, it would be one, the entire lower right triangle would be above the blue line. OK, so our genie index goes from zero to one or from zero to 100, depending how you scale it. OK, so now let's look at the United States. The Census Bureau asks a large random sample of people, how much money does your family make? And they line up all the people, or I did in this case, but take that sample, line up all the people from lowest to highest, from poorest to richest, and we see how that curve bends when we pile it up, see how far away it is from that slope of equality. And I labeled a couple points on here so you can see, for example, the bottom 25% of families where you get up to the 25% moving across the bottom only has about 6% of the total income. Their incomes are below $42,500. About the bottom 49% of families, those are below $77,500, so the bottom half of families, they all together only have 19% of the income. So you can see we're curving away from the straight line here. Meanwhile, up at the top, 93% of families are in less than $250,000, so 7% above $250,000 a year, and they have 25% of all income. So you can see this slope actually looks, this curve looks a little bit like the Lorenz curve we had in the last one. In fact, it's not that different here in real life. The United States has a genie index of family inequality of 0.45. So 45% of the lower right triangle is above the blue line. Now, is that a lot or a little? Now that we have put a number on it, we can ask questions like, is it going up or down? Is it more or less than France? What makes it go up or down? Is it higher in New York than it is in California or things like that? So being able to take all the different numbers, everybody's income is a different number, and describe that whole distribution with one number that quantifies the amount of inequality turns out to be super useful for analyzing society. So that's our point. Now, the reason we're talking about this, in fact, is because inequality has been rising in the United States for a few decades now. So this chart shows that effort by the Census Bureau going back to 1947, you can see inequality was kind of falling until about the end of the 1960s and has been rising since, really quite a bit, from about 35 to about 45 from the early 70s to 2018. So this is why we're all concerned about inequality so much, because it really has been increasing and we can show it with just this one number. Okay, I'm not going to give a whole lecture on why this is happening, but I can say a little bit. Just give a few of the main reasons. Number one, at the very top, we're aware of the rise of the super rich. There are some of these are very visible, like Bill Gates or Jeff Bezos or certain celebrities. But even outside of famous people, we just have some top executives and bankers and lawyers and stuff of their incomes have been rising a lot. Also a decline of manufacturing industries in unions. Manufacturing industries were places where you could get a middle income job without a lot of education. So that was a big part of the middle. So when those declines are inequality increased, super rich pulling up, and then more people are relatively speaking at the bottom, some of that is because of the service economy. The service economy less than manufacturing is bifurcated. You have high income jobs and low income jobs. You have airplane, pilots and cashiers. You have doctors and janitors and less of those middle income jobs which were mitigating against overall inequality. At the bottom then for those lower income jobs, we've also had the minimum wage falling essentially because of inflation. They haven't raised it enough to keep up with inflation. And then in terms of family structure, we have more, this is family income we're looking at. Since women's employment has increased, more women making more money. We have more two earner families that are higher up and we have then low single earner families, low income single earner families more at the bottom. So that's helped contribute to inequality also. Just a few reasons, obviously we could do a whole course on why inequality has increased. So does the United States have a lot of inequality and what are we doing about it? This graph from the economist I thought nicely shows, yes, we have a lot and no, we're not doing that much about it compared to other countries. To do that, this takes that Gini coefficient, Gini index that we've been talking about and it calculates it before taxes and transfers and after. So the numbers I was showing you before were just the total income you have. How much income did you have this year? It didn't take into account how much did you end up having to pay in taxes? And what did you, what else did the government do for you? Did it give you food stamps? Did it give you rent subsidies or education subsidies or free healthcare and all that stuff. So once you take all that into account, you can see how much the amount of inequality you start with and income is changed by the government moving money around. In the simplest terms, if the government took money from rich people and gave it to poor people, you would reduce your Gini index because of taxes and transfers, taxing and transfer. So the dots across the top here show how much inequality there is before taxes and transfers by the Gini index. You can see there's the United States that red dot a way out toward the end up over 45, a very high Gini index compared to all these other countries, all have less inequality than we do. And then the diagonal slopes show, take you down to where it is after taxes and transfers. So the reason I mentioned Ireland, they have more inequality to begin with but after taxes and transfers, they have quite a bit less. They knock off 20 points from their Gini by taking money from the rich and giving it to the poor and not just cash but education and healthcare and housing and all that stuff. And you can see a lot of these other countries like France and Canada and Sweden are also doing more than the United States does to reduce the inequality they have in the pre-tax and transfer, in the post-tax and transfer. So this is a very short story about a very complicated topic but let's just say the United States has a lot of income inequality and we do less about it than a lot of other rich countries. Now let's take one other example of what you can do with this Gini index. Remember I said, we wanna measure inequality so we can ask questions like, is there a lot? Is there a little? Is it going up? Is it going down? What about inequality in the world overall? We've just been talking about inequality within countries. How much inequality is there in France versus in the United States? But what about in the world overall? That's again, a big complicated question. Here's one simple way you could do it. What if you took 116 countries and each country has an average income? The average income for the country is those rich countries and poor countries and you pretend each person in every country has the average income of their country, okay? That's what I've done here. So you can see there's India down at the bottom on our Lorenz curve, not quite at the bottom but near the bottom. India's got a lot of people over a billion people so 20% of the population but only 6% of the income. See their line only goes up a little bit after it goes all the way over 20%. Then in the middle of the world income, sort of you have China, very big, 22% of the world's population and 21% of income. So kind of near the world average of income. And then up at the top, there is the United States with, it's still pretty big but less people and a lot of the world's income. So here I've taken every country and treated them essentially like a family on our previous graph. And when we do that, we see that the genie index for the whole world is 0.46. It's actually similar to the US family income. Okay, so that's just to give you an idea of what you could do with this measure. One way you could extend it, what about a little bit of, let's kind of combine that inequality between countries with a little bit of inequality within countries and see how we could get at this global inequality question. So here instead of just 116 countries, I broke them into 812 quantiles. So this is the bottom 10% of each country, the top 10% of each country, and then the chunks in between 10 to 20, 20 to 40, 40 to 60, 60 to 80, 80 to 90. So each country's broken into seven chunks. And then we pretend that inside each one of those chunks, everybody has the same income. So just to give an example, there down the red circle the bottom there is the bottom 10% of the US. So the bottom 10% of the US is above half the world's population in terms of income. And then way up at the top, you can see the top 10% of the US income. So here instead of assuming the whole country has the average income for the, everybody in the country has the average income, which is we know not true, this kind of breaks each country into seven chunks. Well, this gets us to a genie of 0.58. You can see more inequality, but much bigger is simply the inequality between countries in the first place. So that's one lesson you could take from that. There's a lot of inequality between countries, rich countries and poor countries. And another example of what we can do with a simple measure of inequality like the genie index. Okay, to summarize, how much inequality there is matters. Inequality between incomes is a lot of different numbers. We're turning it into one number then we can analyze it going up or down, higher or lower in different places. What makes it go up and down? Putting a number on it allows us to do that. The genie index is actually just one kind of number you can use to describe an income distribution. We could get into a lot of other math and do it different ways, but this is a one simple one that kind of has an intuitive interpretation. I gave two examples, US family income inequality in comparison to some other countries and what we do about it. And then global income inequality sort of between and within countries and how big that inequality situation is in the world overall.