 Good afternoon, everybody. We appreciate your presence with Tony Sharak's talking next door. It's very good of you. You would have heard this morning already that the labour market is central to inequality in general, and you would have heard that education at the end of the day and people, capacitating people, is central to allowing them to participate in the labour market. So there's a very active discussion about the role of education in driving earnings inequality, and it's in turn very important in overall inequality. And this paper of ours seeks to make a small contribution in that area. Let me acknowledge my co-authors, Professor David Lamb from the University of Michigan, and Arden Finn, a Soldru researcher. Okay, I'm battling a bit here. There we go. There are two countries that are highly unequal in general, and as we heard this morning, Brazil has turned that around, and the role of education in that reduction is very interesting. And then we have South Africa that hasn't quite turned it around yet. Both countries also have very high levels of education inequality, and so it's a fascinating that they really do present very good case studies. So education is highly unequal in both. There are very strong relationships always between schooling and earnings. So in this paper, we just take a hard look at that, which is a little bit away from the big debates about trade and inequality and skill bias, technical progress and inequality, but at the end of the day, these relationships always sit at the heart of all of those theories. So this is really an important issue. So we look at what has happened to the distribution of education in both countries and what has happened to the returns and how these two factors affected earnings inequality. That's the link then, okay? We want to link the two, and then we do some theory to try and make some progress on this, to try and understand the fact that the very same expansion in education and the narrowing of inequality in Brazil in the 1990s was dis-equalising. In the 2000s, it's equalising. How do we make sense of things like that? So the theory, we try and, following Francois Boigignon's whatever encouragement to go back to theory, we try and do a bit of this. So a quick look at education in the two countries. Let's start with South Africa with a working age population. You can see that many years of schooling have gone up very strongly. A major achievement of the post-apartheid period is this increase in schooling on average from about eight years up to just over 10. At the same time, the standard deviation of schooling has declined somewhat, but the standard deviation is not such a good measure of inequality. A better measure because it normalises the standard deviation is the coefficient of variation, and so what you can see is an increase in averages of schooling and a very strong decline in education inequality. Here's Brazil. We downloaded data, it's very available. One of the great things about both South Africa and Brazil is this very good data produced and put in the public domain. So our Portuguese isn't great. We battled a little bit, but David Lamb unfortunately is way better than the rest of us. So what do we see? We see an increase in mean years of schooling, and that was, Marcello Nairi was talking about that this morning. But notice from where it starts. It's way lower than South Africa. It's quite interesting, right? It's starting at just below four, a bit further back, granted, 1976, and then going up to just over eight, eight and a half in 2012. So increasing mean years of schooling, but also very strongly declining inequality in schooling. So both countries share these features. What about earnings? We're going to look at the link between the two. Well, let's get the story straight. And if you have any questions about the South African data, I'll refer you to one of the other presenters, Martin Wittenberg, but especially for hard questions. But if you look at the, this is then the inequality of those who are earning positive earnings in the labour market using a very nice data set produced by Martin's unit called the Post-Apartite Labour Market Series, publicly available. And basically you can see that the inequality of earnings hasn't increased dramatically. There's some funny little bumps in here that I refer you to Martin about, around about the late 90s, but has gone up a little bit. That's the story, but basically is pretty flat. We give you a few measures, the Gini coefficient, we give you a tile measure as well. And then we include the unemployed just to make a point that a big part of the South African labour market are zero earners, but this is the last time we make the point. For the rest of the paper, we focus on those in employment. But it is always worth noting in South Africa we've got the massive number of people who wish they were earning something. What's happened to earnings in Brazil? Sorry, a quick... Often when you're looking at earnings inequality, you look at the variance of log earnings. And so this is just another measure. It tells you basically the same story as to what's happened in South Africa. The usefulness of the variance of log earnings is then when you put it on the left-hand side of an earnings function, you can see how much of the earnings, the inequality you're explaining. Here's Brazil. So earnings inequality, you can see the strong decline as we heard this morning in earnings inequality over time, especially kicking in from 2000 onwards. Similarly, the variance of log earnings tells the same story. The reason why we're telling you this is because we're going to use the variance of log earnings quite intensively in the paper. So it is a measure of inequality. And it's very useful, as I said, because if you've got a standard earnings function, it's what you've got on the left-hand side. Just for interest, you'll note when we talk about explained variance, I have a total variance. In an earnings function, how much of the variance, how much of the inequality are you explaining? And it's quite interesting and notable that in both South Africa and Brazil, you're explaining an increasing share of the overall inequality in an earnings function. Okay. So having said that, let's then put down an earnings function. If this is log earnings, you explain earnings by schooling. So it's a way of connecting then these two things that we've got in play here, schooling and earnings, and then inequality of schooling and inequality of earnings. So how do you connect? This is just schooling and earnings, log earnings. You can, if you take then the variance of log earnings, which is a measure of inequality of earnings using this equation, you do actually get an expression where this is the inequality of schooling, and this then is the returns to schooling squared. So this expression then maps education inequality and changes in that through to earnings inequality with what's going on in education itself and then the returns to education map in there, and then that's just the error term. And there's a section at the beginning of the paper in which we reflect on this a little bit, because even that turns out to be incredibly useful. Just talking about the returns as if there's one return or an average return across all years of schooling. You can see, for example, that if there's an increase in the return to education, it increases earnings inequality through the beta squared here. But also, and we explore this in a little bit more detail in the paper, if it's quite possible to narrow earnings inequality, sorry, to narrow schooling inequality, but for earnings inequality to go up. There's no necessary relationship between narrowing what's going on in the schools in terms of inequality and earnings inequality. Okay, so that's fine, maybe useful. If it is, you can download the paper and read it. But that interest in average returns to schooling. A lot of the arguments this morning and a lot of the arguments all the time are about changes in returns to different years of schooling across the distribution. The skills twist arguments, for example. So what can we do about that? Well, you can just expand in a sense that expression that I had to cover that. Now your log earnings are explained by years of schooling, literally. So this is a one, if you have 10 years of schooling, zero otherwise, and then there's another I here, another J will be, if you have 11 years, et cetera. And then that's the return to that specific year of schooling. You can move it to an inequality analysis in exactly the same way. And you've got the same expression here as you had before, but not for that particular year, summed, but then you've also got a covariance term. A little bit of math in the paper. If you just recognize that the schooling thing, if it's a one, zero, it's basically a proportion. So the math turns out to be quite interesting and useful. And I guess this is the key finding in the paper. If you then take the derivative of that expression with respect to the return to one year of schooling, you get the following. So two times P1, what's P1? P1 is the proportion of people in that year of schooling, with that year of schooling in the labor market. And then this is the difference between the mean earnings for those with that year of schooling and mean earnings. So this turns out to be fascinating. It turns out to be like a little anchor point that's going to help us resolve this issue of, well, how come sometimes increases of schooling lower earnings inequality? Sometimes they don't. We're saying it depends on whether the earnings for those years of schooling are below or above the average earnings. So if you're below, you're going to lower inequality. So in other words, if the earnings to those with eight years of schooling are below the average earnings in the labor market, that's going to reduce inequality. Whereas if the earnings are above, that's going to increase inequality. So this turns out to be a sort of an anchor statistic that's quite interesting. So inequality decreases if the schooling level has earnings below mean log earnings. And on the other hand, inequality increases if the schooling level has earnings above mean log earnings. And the magnitude of the change depends on two things. It depends on this distance here and then the size of the group. Great. And then we also do, I won't spend too long on this. But obviously then what about if you change the size of the group? The thing we talk about in the paper is if you shift some people, you give them one extra year of schooling, what does it do to the distribution? And it just depends on the same gaps but between the two groups that you're talking about. So those gaps remain important. And we show these results in terms of the variance of log earnings, but actually it turns out to be that's just generally true. Okay, great you say. Is there any return on this investment of ours in staring at some equations? Well, hopefully. Let's see. This is Brazil. So we're looking at mean education and the education of mean log earnings. Maybe I should just say something about to link you back to that. Obviously then this difference in earnings turns back to two key schooling differences. What's the average year of schooling associated with that mean earnings? And what's the average level of schooling associated with that group? Well, we know what that group's schooling is. So is the schooling of that group, how does it relate to the average level of schooling associated with mean log earnings? Okay, so that's why we plot on this graph mean years of education for earners. So this is just the mean years of education of those in the labour market. Right, and you can see it's Brazil. It's very low early on and it rises up there, slightly higher than the mean years of education in the population. Then this is the education level associated with mean log earnings. So this is the education level associated with Y bar in the economy. And you can see here it is and it's below the mean years of schooling of those in the labour market. Meander's along here and by the time we get to this it crosses the distribution. So this is almost a test to see if you've been following along seeing if I've been doing a good enough job, really. This is pretty low. So that could imply these mean earnings in the labour market are pretty low and so actually in this period what happened in Brazil was that there was this expansion, this increase in education. So an improvement here in these years. But this is telling you that in these periods here the improvement would have been dis-equalising, would have increased the inequality of earnings. Whereas here you're pushing in the Brazilian realms five, six, seven years those levels of education are clearly below that mean earnings level there and it becomes equalising and that's what we saw in Brazil. But that was the story we were told interestingly this morning. So mean schooling actually rose from 4.5 to 9. The crossover actually indicates that there's some change in the structure of schooling and the structure of the returns to schooling. So this is the punchline really and this is in returns to schooling in grades five to eight would have been dis-equalising up till about 2000 and then would have been equalising thereafter. So there is this conundrum that's been bothering people. Now I'm not saying this is the solution but it gives you some traction on that. What about South Africa? Well, in South Africa here's the mean years of education of the positive earners and then given the nature of the South African labour market who's been hired in etc. here's then the the education level of mean log earnings. So this is the benchmark education level. If you're below this and you push more people in there or you increase the returns associated with these levels that's equalising. If you're above it it's dis-equalising and it's quite high but nonetheless I guess we're stretching the point here a little bit for effect but so we're looking at this range which is very close to that mean. So if you're below I guess it's marginally equalising but basically we're saying in the nine to eleven range increases in returns would have been dis-equalising or not or have no impact at all. They're very close to the actual means that you're talking about but by the time you get up here in the 2000s they would be strongly equalising. Problem in South Africa is that we've had a collapse in those returns as you know, well you may know in the nine to eleven years of schooling there's been a complete collapse in those returns. So that's bad news because it would have been equalising to have increases in returns to those years of schooling now and yet what's happened is a huge collapse in those returns. So it's just equalising. So that collapse in returns to those at the bottom where all these earners are has been dis-equalising. Okay. Just to finish off then quickly. That... Was that a zero? Oh, good. Thank you. I've got a two and then I've got a zero straight away. Just checking. Okay. Now, we show that with regard to log earnings and the variance of log earnings and we also show it with regard to a tile indicator but it's not such a trivial... it's not a generalised result yet. It's not so easy. But obviously you can easily take data and do some simulations small perturbations around the returns at each level of schooling and you can see what happens. Okay. And you can even find a cut-off that divides equalising from dis-equalising returns to schooling. Okay. It may not be a single line but in South Africa it turns out it is a line. So last slide. We gave a 1% increase in the returns to schooling in South Africa and then we looked at a number of measures of inequality of earnings and that's then the line in our simulations in which it would have had no impact on earnings inequality and years of schooling down here. And you can see that in 1994, up here at the 10 years, increasing... giving a 1% increase in returns to schooling at 10 years, 11 years, 12 years was actually dis-equalising in South Africa on any measure and obviously the tertiary was also strongly dis-equalising. Come 2011, you can see that by all measures, given the collapse in the returns to schooling at below 12 in South Africa, you can see they're all strongly equalising. The negative means they would have lowered inequality in the simulation by any measure. And you can see the highly dis-equalising nature of the tertiary... complete secondary and tertiary. Okay. So what have we shown? So schooling inequalities declined substantially over time in both South Africa and Brazil, but it didn't lead to decline in earnings inequality in South Africa and did in Brazil only after some time period. But obviously we have a strong change in the returns to schooling across the distribution and in South Africa we've had collapse in everything below 12 years of schooling complete secondary. Brazil had smaller increases in returns at the top. In fact, even some slight declines in more recent periods right up at the top of the distribution and strongly increasing returns in the middle. So what we find is that increasing returns in the middle, certainly in Brazil, would have been dis-equalising in the past and in South Africa, but it's now equalising. So that's why inequality in a sense is coming down in Brazil, earnings inequality. And the problem is that we've had a collapse in those zones in South Africa and that's why earnings inequality isn't coming down. Thank you very much.