Hi, this is Scott Page, welcome back to Model Thinking. In this lecture, I want to talk about a specific model, and this is Thomas Piketty's model of income inequality. So in 2014, Thomas Piketty released a book called Capital in the Twenty-First Century. Now this book had been released a year earlier in France to really not much response, it wasn't a huge bestseller. But, when it got released in the United States, it had a massive impact. And this became a book, that maybe not everybody read, but most people had on their bookshelf. Now, inside this book is a very simple model, but the simple model's very powerful. So what we want to do is we want to just sort of walk through how this model works. Now to just give us a framing for the model, I want to just remind ourselves of something we talked about earlier in the course, and that is the shape of things to come. So one thing it can be, is the world can be a linear thing, as you have more of something, the more you get. Something can also have diminishing returns. So if you think about how many scoops of ice cream you want, the first scoop is great, the second scoop is great, but at some point adding more scoops doesn't make you any happier. Something also can have increasing returns and we learned this with the rule of 72. So as you continue to accumulate wealth, or money, or something like that, the interest, your total amount of wealth is going to go up and up and up. So what Piketty does, is he applies sort of an increasing returns ideas to this study of inequality. So, first, let me frame this a little bit. If you look at the income inequality in the United States, what you see is that prior to the Great Depression, the richest 10% of Americans had between 40 and 50% of the wealth. After World War II, this dropped, it fell to between 30 and 40% of the wealth. But then starting again around 1980, 1990, it started swooping back up again, and we're basically back to a place where we were during what people call the Gilded Age. I've put the graph up here of the United States, but similar graphs can be drawn for almost all of Europe, right? Where there was massive inequality leading up to World War II, in some cases, for hundreds of years. It swooped down in the post-war period and now it's starting to swoop up. And if you even look at countries like Singapore, that really didn't have massive inequality prior to the post-war period, you'll see that inequality's been creeping up there as well. And Piketty wants us to try and understand why is this happening? And if you look sort of again, here's a picture of a graph of the top 10% and the top 1% in the United States and Europe, you see similar sorts of trends. It's high, wealth inequality falls in the post-war period, and now it's starting to creep back up again. So here's PIketty's model, and it's almost ridiculously simple. The idea is this, there's a return on capital, a rate of return, a percentage rate and that's big R, and there's a growth rate of the economy. Now, one thing that economists know, is that it's typically going to be the case that the return on capital is larger than the growth rate in the economy. And if you look at charts of that, if you look again, here's a chart of the pre-war period in France and then in the post-war period. And what you see that the growth rate on capital is about 5%, and the growth rate in the economy was between 0 and 1%. And this is true, according to our best estimates, from literally the year 0 to the year 1820. But then in 1913 and 1915, you see a switch, suddenly the growth rate of the economy is higher than the return on capital. G gets bigger, then that holds true for about 50 years. Well now things have switched back to the original pattern and we're in this place where R is bigger than g. Now why does this matter? Why does it matter that R is bigger than g? Well, let's think of it again, so R is the return on capital, g is the growth rate of the economy. So now let's ask, what's the growth in wealth? So there's some wealthy people who sit on money and how much does their wealth grow? Well, their wealth is going to grow basically by the amount of wealth times the rate of return on capital. How much is the economy going to grow? Well, that's going to grow basically, the gross domestic product, GDP, times the growth rate of the economy. Well, if R is bigger than g, wealth is going to grow faster than the economy, which means the rich are going to get richer even if the economy is growing. And this is in essence, Piketty's point. R is bigger than g, the wealthy not only remain wealthy, but their relative share of the economy in some sense grows over time. So here's a picture again of France and what you see is that just in land alone, the amount of wealth was roughly, from 1700 to 1800, 400% or 4 times GDP. Now if you look at sort of how much income just came from inheritance flow, it was 20% of the economy. So 20% of all income just came from people sitting around and being rich. And if you look at this graph, that fell post 1900, but now it's starting to creep up again. Now we can do very, very simple math on this, right? Wealth is 4 x GDP. There's a 5% rate of return on wealth, we just saw that in the previous graph, right? That was true for hundreds of years. So that means capital's going to get about 20% of GDP in the form of income, and that's exactly what Piketty shows, right? Remember the previous graph, capital gets about 20% of GDP. So it's a really compelling story and it makes a lot of sense sort of in broad strokes. In fact, one of the most fascinating things about Picketty's book, and I think one reason it sold so well, is that it explains a lot of things. If you've read any Jane Austen books, she always talks about these people who have these fixed incomes. They sit around and they live and they get their 1,000 pounds a year, their 2,000 pounds a year. Well, 1,000 pounds a year was about what it took to be rich. Now you've got basically during the time that Jane Austen was alive, you've basically got fixed interest rates of about 5%, right? So the rich were guaranteed by government bonds and earn 5%. So if you had 20,000 pounds, if you had that much money, that much wealth, you could just buy government bonds, take in your 1,000 pounds a year and just hang out at parties and have people like Jane Austen write about you. It was incredibly stable and it was a society that was very unequal. Okay, so let's ask ourselves, this is very simple. R bigger than g can't explain everything in the economy. And it also can't explain the fact that why is it the case that new people have become rich and why is it the case that some people who are rich have lost their wealth? Well, we'll learn some other models about why people become rich. We'll talk about winner take all societies and stuff like that, but let's talk about how the rich lose their money. And I'm going to talk about some extensions that Brad DeLong at Berkeley has suggested that might improve Picketty's analysis. So, the first one is R bigger than g ignores taxes. If you're wealthy, you have to pay some taxes, and one thing Piketty advocates is a wealth tax to sort of reduce the amount of income and wealth that people have. Second is, there's a consumption rate. We said the wealth would grow but that assumes the rich don't spend any of that 5% and, of course, they do, so we've gotta throw in consumption. The third thing is there's a donation rate. So if you've got a lot of money, one thing people do is give it away. And a lot of people like Bill Gates, Warren Buffett give huge amounts of their wealth away because they basically say, I don't want my children to just sit around and draw interest on wealth that I've accumulated. I'd rather help poor people. I'd rather donate to places where I think I can do a lot of good. So taxes, consumption, donation all drive down to the wealth level. As does something else, which I'll call the stupidity rate. Just because your parents made a lot of money and know how to invest it, and get a good solid rate of return and earn that R, doesn't mean that you, if you inherit the money, aren't going to do silly things with that money. In fact, you may take risky investments to try and get a higher R. Well, if you make a risk investment and it doesn't pay off, it doesn't work. So perhaps the equation shouldn't be R bigger than g. It might be R- t- c- d- s. In other words, the rate of return minus taxes, consumption, donation, and just plain stupidity or bad luck has to be bigger than the growth rate for the wealthy share of the economy to be larger than what the regular share of the economy. One other caveat that Piketty talks about at length, it also depends on how fast the economy's growing in size. If the economy's becoming a lot bigger, if there's just more people, then the wealthy's share of the economy will also shrink in proportion. Okay, so the book, Capital by Thomas Piketty, fascinating book. The model, very simple, but if you don't understand the model, it's sort of hard to understand the book. And if you want to critique the book, which many people have done, it's very helpful to have sort of in your head just a basic understanding of how that model works. But what I want to say about this, my final comment on the book is this. It's a very simple model, R bigger than g. In fact, you almost couldn't have a simpler model. But that just very straightforward inequality with two variables explains a lot about the world. It's amazing how much leverage Piketty's able to accomplish, how much analytic leverage and empirical leverage he's able to accomplish, by constructing such a simple model. Thank you.
