So this last week, I wanted to talk about poverty and inequality. And I'll introduce the language we economists use and it's really ways of measuring these things. So we'll talk about how we measure inequality and I'll describe the Lorenz Curve and the Gini coefficient. then we will talk about how we define poverty and various ways of defining poverty and measuring poverty. Then I'll end with a short discussion about the need to balance our objectives of efficiency and equity. And this is describes as the efficiency and equity trade off, so let's start with how we economists measure inequality. And it's not surprising that the distribution of income is not uniform, right, it's Various people get various income. And we can see, looking at this graph, that the distribution in the United States, for example, it's not really a normal distribution. It's not a bell curve, for the simple reason that it's truncated at zero, right? There are some people who spend more money than they get in a given year, but Is mostly truncated at zero here. So we have an income distribution that looks like a bell curve that's been cut off. And I just want to point out that the reason you get this little stack here on the right is because we really try to spread out this tail as far as it goes. I actually wouldn't have room to draw it out, right? So this will go on for a long long time, probably to the other side of your room, wherever you are sitting right now, so we've sort of lumped this here on the right tail. Okay, so these are the incomes for the United States, and we could probably do the same for almost any country where you are, we would need to know a lot of information. We would need to know the income of every household in your country that we can do this and once we have this distribution we can talk about the mode income, the income that's most prevalent. We can talk about the median income. So in the United States 50% of households have an income of less than 51,000 and 50% have incomes that are greater than 51,000. And we can also go ahead, and we can calculate the average income, and the average income of a household in the United States is about $67,000. Lately, in the United States, there's been a lot of interest on this right tail of the distribution, this high end tail, so just to give you a little indication of sort of what the right tier looks like. The top 20% of the income distribution have a household income greater than 100,000. The top 5% have an income that's greater than 180,000. I like to mention this because I think most of us would think of 180,000 a year as being a really enormous amount of money. And yet, 5% of American households have an income that's greater than this. To be in the top 1% you would actually have to have an income greater than $386,000 a year. So it's really quite a hard club to join and I'm sure in the country where you're sitting right now. You could do the same type of analysis and again, you'll probably find that the right tail of distribution is very, very long. So It's pretty hard to join that club of the top 1% okay, so this is the graph of the distribution and looking at the graph is informative. It gives us a sense of what the distribution looks like and we can talk about these various cutoffs. For the sake of econometric analysis or statistics analysis of economic data It would be useful to somehow translate this whole distribution into one number. And that's what we will do in the next few steps, so we're going to do it step by step. The first step is to look at the whole pie that's generated in this economy, see you can think of all the money, all the income that's generated in the economy. And think about what section of this pi is received by which quartile of which 20% of the distribution. So again, what we're doing here is we're looking at the whole distribution from the person who gets the least to the person who gets the most. We divide this whole distribution into five segments, or five of 20% and we asked what section of the pie goes to each one of these twenty percents. So, the metaphor that I find useful here is to think maybe of a family with five brothers. And supposed you had this nice, big chocolate cake that you were thinking of dividing between your five brothers, or your five children. How would you choose to divide it? Most of us have the inclination of thinking of dividing the pie equally but of course that income distribution is not divided equally. We have one brother, here, eating half of the pie. We have another brother eating about a quarter of the pie, so that leaves three brothers eating only one quarter of the pie. Three brothers together are sharing one-fourth of the pie. And I just want to point out that one of the brothers is really getting a tiny little sliver of the pie here, just 3% of the distribution. So this is one way of thinking about how this pie is shared across the population of the economy, but remember my goal is to take this pie, and to take this idea of inequality and translate it into one number. So let's do that. The next step is to get this idea of dividing the pie across our brothers and translating it into a graph. We'll do that suing the Income Lorenz Curve. The Income Lorenz curve is a graph that shows the cumulative percentage of income earned against the cumulative percentage of households. On the horizontal axis, we'll have the cumulative percentage of households, so this is the bottom 20%. This is what happens when we add another 20%. When we add another 20%. When we add the extra 20% and here we are at 100% of the distribution of households. And as we do that we will pull out what happened to the cumulative percentage of that income, right. So, we'll have a dot somewhere here 20% and 3% and we'll add these dots together, okay. So now I have a question for you, what would this Lorenz Curve look like? Or where would this dots be if the income in our society was distributed exactly equal? Suppose this for a moment, think about this and turn it back on the game, okay. If we had complete inequality, our Lorenz Curve would be along this black line, right? This is the of perfect equality, 20% of the distribution, 20% of the pie. If we add another 20%, we have 40% of the distribution eating 40% of the pie. We add another 20%, 60% of the distribution eats 60% of the pie and so on and so forth. Okay, so now I have another question for you. What would happen if we lived in a society where no one ate anything? No one got any piece of the pie except for one person? And sometimes I call this my Bill Gates society, which is a little unfair because the Gates Foundation is really giving a lot of pie back to society. But suppose we have this society what I call my Bill Gates society when no one eats anything and Bill Gates get to eat the whole pie. What will my lime look like? Suppose me and come back when you've thought through this. Well in that case, our line would be a completely straight line along the x axes and then we would have a jump right up to this point here, right? Because Bill Gates would be eating all the pie. The real distribution in the United States is somewhere in between, right? We have 20% of the distribution eating 3% of the pie, the next 20% we add those, the next 20%. Now we have three brothers together, we know that they eat about 25% of the pie we add another one and we get close to 50% of the pie and of course we have to add the richest 20% to get all the way up here to 100. So you can see this green line it's not quite at the line of equality and it's not my Bill Gates society which would be along here. I did somewhere in between. They're not equal as the income distribution, the closer we are going to be to the line of equality. And the less equal as our distribution, the further away we will be from the line of equality. Now that we have this graph, we can compare the income distribution to for example, the wealth distribution. Let's think what the difference is. Income is the flow of money that comes in in a given period for example, in a year. Okay, the income per year is the amount of money that a household gets in that one year. The wealth is the stock of the assets that the household has. This includes, for example, the house. This includes if they have any retirement funds, if they own stocks, all of these are part of the wealth distribution. What do you think is closer to the line of equality, that income distribution, or the wealth distribution. Think about this, and then start up again. If we plot the income distribution and the wealth distribution, we will see that the income distribution is closer to the 45 degree line. In other words, inequality in wealth is greater than inequality in income. And a lot of this change comes from this left part of the distribution, the people who really don't have a lot. To start acquiring wealth you have to be able to eat less than you get, in other words you have to be able to save. In any given year, you have to have some savings at the end of the year and we can see that for the left end of the distribution, this is very hard to do and you can see that the wealth for this bond in 20% is almost zero. Okay, and that's one reason that the wealth distribution is further away from the line of equality. Okay, so remember my goal, my goal is to interpret inequality or translate inequality into one number. So I've taken this idea of a pie, and I translate it into the Lorenz curve. And now I want to do the next step, which is translating the Lorenz curve into one number and the number that I'm going to construct is called the Gini ratio. The Gini ratio is an index number and it equals the ratio of the blue area divided by the red, or the pink, area. In other words, the Gini ratio is this area here divided by this area here. So, let us think What is the range of possible Gini ratios or Gini coefficients? Let's think about two extreme society. first of all, let's think of a society of full equality. What would be the Gini ratio in this case? Well, if you thought through it, you realize that if we have a society of full equality, this green line is lying along this black line. So, the blue area is zero and zero divided by any number is zero. So the smallest value we can have of the Gini ratio is zero Let's think how big the Gini ration would be if we were in a Bill Gates society. Well, in my Bill Gates society, this green line of the Lorenz curve would be all the way down here. And in that case, this blue are would have the same size as this pink area. And in that case the Gini ratio would be 1. So we can see that the Gini ratio is a number between 0 and 1. The closer it is to 0 the more equality we have. The closer it is to 1 the less equality we have. Now that we have this Gini ratio number, we can do some fun things with it. For example, we can calculate the Gini ratio in various countries and compare them and this is what this graph is showing you. So you can choose the country of your choice. I want to note there's a lot of countries here that are white, and their white because we don't have full data. To do all this, it's not enough just to know what the average income is, what the median income is. You need to know the whole distribution of income and you don't have the data for all the countries. But these are a lot of countries that we do have data for, and we can plot the Gini ratio. And I always like to point out to my students that when we look at this graph, we can see that the United States is actually more like what? It's more like the Soviet Union than it is like Europe. We here in America always like to compare ourselves to Europeans. We think they're our closest allies, they have a democracy like we have in America. But we can see that in terms of the gini ratio, we're really not very much like them. And you can find the country where you live you can see if you live in South America, you're likely to have quite a lot of inequality. If you look here in Scandinavian countries, you are probably not surprised to learn that you have very little inequality. Their Gini ratio is very small. We can look at the data in another way. We can look at what happens to the Gini ratio over time and here's some data on a few countries around the world. And if your country isn't here, maybe you can do some research and try and graph the data for your country. And share it with us on the forum this week but here are some countries that I would like to highlight. First of all, because I'm teaching in the United States, I do like to point out that here in the United States we had a period during 70s when GINI ratio dropped, where inequality fell or equality rose. This was during the Johnson administration, where we had the war on poverty and I'll come back to this in the second segment. Since then, the GINI ratio has been more or less increasing steadily. Okay, and we have a Gini ratio that is much higher than it was in the mid 60s. We have countries where the Gini ratio has been falling, Brazil. Here we have a Gini ratio that is extremely high and in the latest expansion of the Brazilian economy, not only is the pie as a whole growing, but we also see that the equality is increasing. So the Gini ratio in Brazil is falling. Sometimes, we have economic growth and it's coupled with a decrease in the Gini ratio. On the other hand sometimes we have economic growth that's coupled with an increase in the Gini ratio. So here we have China and China had a relatively low Gini ratio. Notice please that we don't have data from before the 1990's. But here we have a very low GINI ratio, and look what has happened. The GINI ratio has really sky rocketed. So in this case we've had a lot of economic growth and economic expansion but it's been paired with an increase in inequality. As an economist I like to highlight these things because I like us to remember that despite the fact that many of us have an intrinsic interest in equality and we believe that equality is important. I just want to point out that growth is also important. If you ask, probably most people in China, would you rather have the economy that you have today with this high inequality or would you like to go back to the mid 60s? I'm sure most of them would say we would rather live today. So we are prepared to have this high inequality, despite the fact they aren't, or because we have a lot of inequality, but we also have enough pie to eat. Okay, so I'd like you to look at this data, I'd like you to find your country, and if you don't find your country here, maybe you can do some research and find this data. And I'd really like to hear your opinions here on the forum, to get a sense of what you think about this Gini ratio. How do you feel about inequality in your country? How do you think about this, trying to balance how big the pie is vs. how the pie is divided? Just to sort of finish this off, I want to mention a metaphor that I use with my students in class. I often go shopping at a grocery store called Costco, where they sell things in very, very large quantities. And you can get a chocolate pie there that is absolutely enormous. And I always try to think, if I brought this chocolate pie home, and suppose I wanted to share it among my five children, would it really be necessary to share it equally? If the chocolate pie is so enormous, maybe even having one small sliver of the pie is sufficient. So, I want you to think about that as you think about inequality and I really welcome hearing your discussion in the forums.