 Thank you everyone for coming. The work I'm gonna present is joint work with Gary Fields and George Jacobson at Cornell University. And it deals with basically two broad questions. The first question is when we want to answer who gains and who loses when there is a change in the income distribution, you could, there are several approaches you could take, but two popular approaches is take what we call the anonymous approach and what we call the panel income approach. The anonymous approach is just your standard comparison of inequality measures in period zero versus inequality in period one. I said inequality rose, it fell, or the income share of the poorest fell or rose, et cetera, et cetera. While the panel income approaches, I'm gonna get into a little bit of what we mean exactly in the context of this play. The second question we deal with is how our view of inequality is altered if instead of looking at inequality at a point in time, we look at the inequality of average incomes. So if we have the income of an individual or a household that we observe through panel data at several point in time, if we focus on the inequality of the average income that gets observed across several periods, how is our view of inequality altered? And more the question that I want to emphasize that I want to deal with is what factors, if there is an equalization or disequalization of this average income which tends to be a measure of more permanent income, right? What factors equalized or disequalized account for disequalization or disequalization of longer term incomes? So the first part of the paper, if you are familiar with economic mobility analysis, some of it will be familiar to you. We are sort of dotting the eyes on issues that have been known for practitioners of mobility analysis, but to the extent that there is a large number of people that is very familiar with the cross-sectional or anonymous analysis of inequality, but not so much with mobility analysis, there are some issues we'd like to emphasize. The second part, I'm gonna present some results that we believe are a little bit more new. So just some basic review of some key concepts. So what we mean, what we mean by the anonymous approach? Well, the anonymous approach, as I said, is just comparing inequality and two different cross-sections in different points in time. We begin, say, by looking at the Lawrence criteria, if there is Lawrence dominance, that is the least controversial way of assessing inequality. You could use a Lawrence consistent inequality index which in the case there is Lawrence crossings that would be a way of resolving whether inequality rose or fell, or you could even use Lawrence inconsistent inequality index like the variance of log incomes just because sometimes it's handy in certain statistical contexts. By the panel approach, there are several ways we could measure economic mobility and there is a long literature of what economic mobility even means. We are just gonna focus on one particular type of mobility analysis, one that is quite popular in the literature in which you relate income change that you observe over panels, in panels again, you follow people over time or you follow households over time and you relate their income change to their initial level of income. So you can see by looking at this coefficient delta, if delta is positive, it means that there is divergence, namely the initially richer got richer and the initially only poor got poorer or if delta is negative, there was convergence in a very similar way as the growth literature has analyzed. So you could plug in these regressions different measures of income. You could plug dollars, right? You would get a measure of dollar divergence or dollar convergence. You could plug income shares if what you think is the concept of interest is share mobility then you could run that regression for income shares. You could plug log dollars if you want to approximate proportional income changes which might be relevant in times of economic decline or you could even not, sometimes log dollar approximations are bad because the income changes are very large so that approximation can be actually quite poor at times so you could even run the exact proportional change on initial income. Any of these methods would give you some sort of answers, they can be sometimes, the answer is different but they are looking at all at panel income changes. And the question that we wanted to ask is how these two methods relate? So suppose you have panel data, you can look at the data anonymously or you can look at the data through panel analysis. How do these two relate? And in particular, we have a companion paper where it's a theoretical paper, there is no data in there at all where we wanted to see whether we could reconcile these four cells that you see in this table. So there are the two columns that you can have rising and falling inequality and you can have on the rows convergent and divergent panel income changes. And we were wondering to what extent it's possible in a given economy, in that case it was imaginary economies to have any of these four cells. The intuition of most practitioners that have not dealt much with mobility analysis is that these cells and these cells are quite possible. So the intuition is if there is divergent, namely if they initially reach got richer then it must be that inequality is rising and if the initially poor is getting a head faster than they initially reach, then it should be that inequality is falling. What is harder for people that have not done these very regularly is to realize that you could also have these two cells. Namely you could have convergent panel income changes and you could have divergent panel and rising inequality together with divergent panel income changes and falling inequality. And what we do in that paper is basically spell out all the conditions, dot all the I's on theoretically how this is possible, what do you need to have for these four cells to have. I'm not gonna go into detail into all these possibilities. I just want to give you gist of what is the most important ingredients in order to have these two cells that people are not that used to think they can be reconciled. So about the first cell having convergent panel income changes and rising inequality that is quite common to observe actually in the data. And just let's think for a second what it means. Having rising inequality means that you have anonymous rich and anonymous poor people getting farther apart from one period to the next. Having convergent income changes, it means that the initial poor are getting closer to the initial rich. So the only possible way that can happen is if the anonymous rich and poor are not the same people as the initial rich and poor. Okay, otherwise there would be a contradiction. So how can this be possible? Let me first give you a simple example. Let's say this is our vector of initial incomes. You have an income distribution where somebody ends 20 euros, 41, 45, 49, and then 70. And the next period, the poorest individual earns now 100 euros. The people in the middle state with the same income and the top earner went down all the way to 10. So there it's clearly convergent because the largest gains were for the poorest individual. The largest losses were for the richest individual. And there is also a rising inequality because if you just forget about the ordering, it's quite apparent that this distribution is much more spread out. So it is reconcilable, but not only is it reconcilable with simple theoretical examples, it's actually quite common to find in data that this is reconcilable. And the key ingredient, we derive this again, as I said in that other companion paper, we derive the exact conditions. But the key ingredient for this to happen is that you need to have large panel income changes that are large enough so that there are crossings between individuals, so that individuals change positions. It is a necessary condition to have these large panel income changes that generate the changes in position so that you can have the reconciliation into this cell. The second cell, it's a little bit more tricky and it's a little bit more technical and less common to find, but you could find it as well, because intuitively it's actually hard to justify. Think about it, you have that divergence is occurring at the same time that falling inequalities occur. Divergence means that the initially rich are getting ahead faster, they are becoming richer, yet inequality is falling. How can this be possible? In fact, there are in the literature some results that say that this is not possible. So for instance, if you measure inequality by looking at the log variance of income and if you analyze log divergence, it is not possible to have this situation. And we derive in that companion paper, we derive also that if you look at mobility in shares or in exact proportional changes or even mobility in dollars during recession years, you cannot have that together with a Lawrence improvement. So there are certain measures of mobility and there are certain measures of inequality for which our intuition is correct and you cannot have falling inequality together with divergent income changes. The problem or at least not the problem, but the fact of life is that for any other combination of falling inequality and divergent income changes, you could have a reconciliation. So for instance, you could have a vector of people earning five and 20 that becomes seven and 23. This is, there is a Lawrence improvement, believe me. And there, but yet there is divergence in dollar changes. So it really, the reconciliation of the other cell of falling inequality and divergent income changes, it is possible just because how we decide to measure or how you decide to measure inequality and mobility. So I guess here the message is be careful. It is very easy to find results that seem counterintuitive and the devil is hidden in the details of measurement. So if you are analyzing panel data where you have the freedom to do both inequality, anonymous analysis and mobility analysis and you find yourself in one of these cells, do not be surprised. It is possible and the reason is is because again, it really matters how you measure inequality and how you measure mobility at the same time. Okay, so now one thing that we wanted to do just to illustrate that this is not just some numbers that we are coming up with is we wanted to illustrate with some data that we have at hand from other projects. So we took a labor survey in Oregon, Mexico that measures earnings. We took labor for participants including the unemployed and this survey follows individuals not for a long time for five quarters but we can do some mobility analysis with it. So let me show you quickly what we have. Inequality as we saw, I think it was in yesterday's presentation, inequality in Mexico has a period of rising inequality in the early 90s. Then it fell and then somewhat stabilized afterwards. Yet, so this is the anonymous approach. This is the cross-sectional approach. Yet when you do a mobility analysis with the sorts of regressions that I presented before, you get that your delta is negative always. Namely, there is convergence, okay? And this is not just the Mexican weird thing or some more my type of data. This type of analysis has been done across the world and convergence is the rule rather than divergence. In fact, I can only think of the case of China in recent years, I think there has been found divergence in earnings. For the most part, convergence dominates and there is a whole sorts of reasons of why that is happening. Just to give you a feeling of what's hiding behind this, we just took some transition matrix between fixed income categories in initial learnings and in final learnings. As usual, most of the people tend to stay within their income category or in adjacent income categories. If they move, they move to close categories. They don't move much. There is some movement. There is churning in the labor market. But you have people that began in very low income groups and wound it up very high or vice versa that began very high and wound it up at very low levels. Now, some of you might say, well, yeah, of course, but you had the unemployed inside there. And yeah, part of it is the unemployed but it's not, I can assure you this is not driven by the unemployed. I could take out the unemployed of the picture and it would be the same story. So really, most labor markets, and this is, again, not exclusive in my country, most labor markets, they have a lot of churning to them. So at any point in time, there are a lot of transitory shocks and a lot of transitory fluctuations that are hidden behind it. And that's what is one of the driving forces of the convergence in the results. Not all the convergence is driven by transitory shocks but a good deal of it is. I'm gonna skip this one. So now, the question is if at a given point in time we have that any measure of inequality that we have captures permanent inequality and also an inequality associated with transitory shocks, then it would be interesting to see what would happen if you could clear out a little bit these transitory shocks. So the literature, and there is again a very important tradition in the literature on how to do this, the easiest way probably is just to look at the income distribution, at the income inequality of average earnings because if you average earnings over some periods of time, you tend to average out these transitory shocks. And what has been done in the literature, starting from Schorach's, and then Gary has some results at the effect, is to generate inequality mobility measures to see to what extent mobility, economic mobility help to equalize or desequalize longer term earnings with respect to initial earnings. Namely, you can come up with an index that compares the inequality in average earnings to the inequality in initial earnings. So that's been done in the past and we do this with our data. But the new piece that we add here is to say, okay, if we want to compare these two, we can come up with a measure of how much mobility equalize longer term earnings which is just this gap between the inequality of initial earnings minus the inequality of average earnings. If it's positive, it means that there was an equalization. If it's negative, it means that there was a desequalization. And what we do here that it's a little bit new is just to take some older compositions by fields and by UNE, an extension done by UNE in order to find out what observable characteristics can't account for desequalization or desequalization. So if I find that this gap is positive and there was equalization as it is in Mexico, I would like to find out whether it was changes in the return to education or changes across the formal and informal sector or job transitions between occupations or other characteristics that accounted for the fact that there was desequalization. So basically, the compositions here were not devised to be applied to this measure. They were devised to see whether there was what accounts for equalization or desequalization comparing two cross sections. And the only new piece we add here is say, okay, instead of applying it to two anonymous inequality measures, let's use it to analyze this gap that is a measure of equalization of longer term incomes. And this is what we find. Well, first of all, this is just to show you this is a measure of the equalizing mobility gap that I just plotted. The fact that it's positive, it tells you that if over the five quarters that I observed people, economic mobility tends to equalize earnings, longer term earnings. And if I go as to what factors account for that, I don't know if you can really see there are some shaded boxes. Can you actually see anything? I'm gonna try to point them out to you. So the biggest factor that equalizes earnings over five quarters is unemployment. So at the bottom, these are not standard errors. This is the fraction of the gap of equalization, of the equalization mobility measure that I had defined before, which I'm measuring here by the variance of log income. What fraction of that is accounted by each measure? So in this case, both in times of recession and in times of non-recession, on transitions in and out of unemployment are responsible for closing that gap for equalizing longer term incomes in about 70%. So it's a huge contribution of transitions in and out of unemployment, which I guess it shouldn't be that surprising, but still is nice to see the result. The second contributor to this decomposition is the changes in return to informality. So there are some details in the paper where we actually decompose what are the accounting due to the changes in the characteristics and what are the changes that are due to changes in the coefficients or the returns, if you want, of these characteristics. And the changes in the returns to informality, Mexico has a huge informal sector, actually desequalize longer term earnings. They contribute to make it more unequal longer term earnings. Changes in occupation and industry, they also play a role, but they tend to even each other out. So one is positive, the other is negative, and they are about the same magnitude. And interestingly enough, traditional factors like gender, age, and education that do play some role in explaining inequality levels don't play actually much of a role in explaining desequalization. So gender, age, and education do not actually account for much, except maybe here in times of recession your, the returns of education play a little bit more of a role, but it's still limited. Okay, so let me just conclude right now. Again, the message is you can get very different answers if you look at the distribution of income either from a cross-sectional approach or from a panel income approach. We think both are meaningful, but I think you really need to be careful to think which one is the one you want to use depending on the question you want to answer. And we present as a small new contribution an intuitive way to account for the observable factors that equalize average earnings relative to initial. And we think that that method has potential because okay, this is Mexican data five quarters, but if you look at longer panel data like the ones that exist in developed countries, there you could have data for five years or even longer like the PSID or the German SWEP. And then you can have a much greater degree of equalization or desequalization over longer periods. And you could even put in your list of observable characteristics you could even put policy variables and see if a given policy intervention helped equalize or desequalized permanent earnings. So we think that this is a simple technical application that can have lead to interesting answers when applied in other contexts. I stop here. Thanks very much, Robert. That's very, very interesting. I'd like to invite Daniel.