 We have a clear intuition as to what mobility means, and that is it's about how the experiences of childhood and adolescence affect adult outcomes. Now that's an actually probabilistic thing to ask about after all background is in destiny. And so to measure mobility is really to try to say something about these probabilities. But even if I say that, I have to tell you what the outcomes are and what the features of childhood and adolescence are that we want to relate. And so that's just another hint as to why this is actually a pretty complicated thing to make quantitative statements about. One important distinction in thinking about what outcomes we care about is simply asking about whether we care about absolute or relative status. So one question I could ask is, what's the relationship between the level of a child's educational attainment, a child's future income in the labor market, a child's occupation in adulthood? That's absolute because it's looking at the levels of these different phenomena. In contrast, some research looks at relative mobility. If I look at where a parent is in the income distribution or the educational distribution or the occupational status distribution, however that's measured, what does that tell us about the location of the child in the distributions when the child becomes an adult? I tend personally as a researcher to be more interested in absolute mobility, but that's because I have in the back of my head concern about well-being and concern about particular mechanisms that are related to absolute mobility. On the other hand, relative mobility is clearly of great importance. Relative mobility says something about one's position in a society. Status is intimately related to one's relative position. And so I think the appropriate way to understand the many papers that study mobility is that some are going to look at different facets of the general mobility question. The second thing to understand is that the discussion, the measurement of mobility tends to be associated with what I'm going to call mobility statistics. If I said to you, I would like to, because it sounds like an ideal. I would like to tell you the conditional probabilities for all the possible incomes of a child in adulthood given their parents' income. That's a wonderful thing to know, but it's a very hard thing to talk about because probabilities are functions. The mobility literature, of course, recognizes that. And so what it does, it takes these very broad mathematically general definitions of persistence, of dependence, and reduces them down to numbers, to scalar relationships. Within economics, the most common statistic to calculate, based on that, asks a very specific question. If I were to raise the permanent income of a parent by 1%, what is the expected change in the permanent income of the child? And this has a famous name. It's called the intergenerational elasticity of income. Underlying this calculation is to say that parents and children have an earnings capability in their life courses. And permanent income is supposed to capture this learning capability. It's measured typically by taking income every year for an individual or for many years and averaging it and using that average as the estimate of permanent income. Why would this be a natural thing to look at if one is going to study the relationship between the incomes of parents and children? Well, I think that the important thing to think about is that if you ask, what is this parents are doing for children, if I'm investing in them directly or I'm purchasing a membership in a school for them, so on and so forth, what I'm doing is I'm influencing their earnings or their income capabilities. And so what permanent income is really doing is saying that a parent has an overall capability for investments in children, either direct or indirect. And we want to distinguish that from income that is just due to transitory fluctuations. And so the classic example for economists is the lottery. If I win the lottery this year, there's no necessary implication, hopefully, if it's a fair lottery that I'm going to win it next year. And so that's a very different type of income than an income that derives about my salary increases. Because presumably my salary increase is not just for this year, but it's for every year. And so it changes my lifetime capabilities for my investments in my children. So what does the literature stand? What does this intergenerational elasticity of income look like? In the late 1970s, the typical estimate was around 0.2 or 0.3. Sometimes that was called shirt sleeves to shirt sleeves in three generations. And the idea was that if you take 0.2 as a number and you were to multiply it by itself, you get 0.04, if you multiply it again, you get 0.008. That said, in three generations, the parent's income was having very little predictive power for the descendants. Interestingly, the current estimates of the stame statistic are around 0.5 or 0.6. And that's a qualitatively very different number. And so having done the arithmetic many times, if you take 0.6 and multiply it by itself twice, you get 0.216 and 0.216 versus 0.008, those are very different numbers. So in other words, if the true number is 0.6, a lot of the income is sticking around across generations. Now you might ask, why is that happening? Why would the number go up in the estimates of the last 40 to 50 years? The main reason is actually better data. Time has elapsed, social scientists have had access to better data, more years of parental incomes across which they can average to get more precise estimates of the thing that we think is the mechanism, the determinant, I should say, that's relevant, which is permanent income. And so this is a very good example of how what is often the unglamorous process of generating new data sets in social science has first-order implications for how we think about substantive phenomena. The second thing I would say is there is some limited evidence that the dependence of child income on parents has increased in the last 40 years. I think that the fair statement is that there is some evidence, but at this point it's relatively limited. What I would like to say is that in thinking about that statistic, it is also an example where a statistic can mask information. The conventional measure of mobility, the income mobility, says you take the history of a parent's incomes and you average them. You collapse them down to a single statistic. Implicit in doing that is the assumption that it doesn't matter when the parents get the income. In other words, if the only thing that matters is the average, it doesn't matter whether you have income in early childhood, middle childhood, or in adolescence. And so in recent work, where the ink is literally wet since the paper was released today with Yusung Chang, Seunghee Lee, and June Park, we actually take a standard data set, the Panelist Study of Income Dynamics, and ask the question, what if I wanted to understand how year-to-year incomes are affecting the child? And so what we do is we allow the income of a parent to have different effects when the child is at age zero versus through age 19. The blue curve in this figure tells you what the intergeneral elasticity of income is year by year. What I'd like you to see from this is something that's, I think, quite striking. And that is that the sensitivity of adult outcomes, in this case adult permanent income to parental income, is much higher in the adolescent years than it is in the early childhood years. And in fact, it's nearly monotonic, up to age 18. So why would I emphasize this? Because it tells us something about the actual mechanisms associated with mobility. The first is self-evident. Incomes in later childhood and in adolescence seem to be more important in terms of their predictive content on the margin for future adult incomes. The second thing is to say that this is a good example where, in correlation, it does not prove causation any more than any of the bivariate graphs I showed you prove causation. It is suggestive of ways to think. A question to ask is why would those incomes matter more in adolescence? That lets one think harder about what it is incomes do for children. Incomes in early childhood have to do with buying direct inputs to the children, inputs a very desiccated word for something such as food or clothing. Incomes in adolescence, of course, have to do with buying memberships in neighborhoods and memberships in schools. And so my conjecture is that what is being captured here is that the adolescent incomes are signals or they're at least proxies for the quality of the schools and neighborhoods that adolescents are experiencing. And so, again, this is open research, but I would emphasize that this tells us there's something beyond just looking at average income of parents and average income of child. Let me also add that it's interesting that the curve drops at age 18. At least speaking for my generation, there was an idea that when kids turned 18, the obligations of parents to children changed. And so that dip itself, I think, is culturally specific, American specific, maybe Southern California in the 1970s specific, but I think it speaks to something about the interactions between parents and children. With that all said, I want to emphasize a deep limitation to most of the work that is done in measuring mobility. The statistical tools that are used to generate these types of statistics are not capable of measuring the presence of poverty traps or affluent traps. When I had spoken earlier about trying to think about bottlenecks and persistence in their interactions, these are very powerful examples. We're very concerned to know whether there's configurations of family incomes as they interact with race, as they interact with education, as they interact with location, where it's extremely difficult for the children to get out of poverty. Similarly, we're also interested in the upper tail. In other words, other configurations of parental affluence as they interact with race, education, location, where the children are essentially locked into affluence. And so in reading any paper and evaluating any analysis of the measurement of intergenerational mobility, you have to ask the question, is the statistical method used capable of revealing the phenomena you're interested in? That doesn't say that the statistics I've given you are uninteresting. It says nothing more than they aren't everything. And so again, what I would say is this is a good example where mathematics matters. Part of the importance in thinking with mathematical precision about mobility is that the mathematics dictates what the data can reveal to us. And the thing I would communicate as a researcher is that the conventional ways that much of mobility is measured are using linear models. A linear model basically says that the effect of changing income 1% in a rich family is the same as the effect on exchanging it by 1% in a poor family. In contrast, affluence traps and poverty traps are essentially nonlinear phenomena. The old saying goes they don't speak for themselves. If I have a linear model that relates parents' income to offspring income, if the slope of that relationship is less than 1%, it has a very important implication. It says that no matter what the initial income of a family is, poor or rich, across time the family dynasties will converge to the same long-run income level. Any contemporary inequalities are going to eventually dissipate. Now, it may take a very long time so that the fact that they're going to eventually dissipate is not by itself a dispositive of how we should think about inequality. But the point is the logic of the model has this incapacity for the environment to have permanent inequality between families of different initial incomes. Now, it is possible that a linear model can produce an unstable divergence. The only way it can do that is if the slope of that curve is bigger than 1%. And what would happen there is if you raise my income by 1%, that changes the expectation of my child by 1.1%, for example. And so in worlds like that, you have this very extreme form of polarization in which the rich are becoming arbitrarily richer, the poor are becoming arbitrarily poor. And so you end up with this completely bifurcated income distribution. That's an interesting example to understand certain types of phenomena. But I also want to be clear that I think this tells you something about the limits of linear models. And I spent time on this because it is linear models are used to interrogate the data. And if the only type of linear model that can find long-term divergence between rich and poor is one in which the rich and poor have to become arbitrarily far apart, that's a very limited way to think about the persistence of inequality. Now, in contrast, once we live in a nonlinear world, what that means is the relationship between the income of a parent and the income of a child has different slopes to that curve, depending on what the incomes are. Then we can have phenomena such as poverty traps and affluence traps. And so this is a famous S-shaped curve in which you have two steady states, one which has the arrows going in at a low income and the other has arrows going in at a high income. And one of those we could think of as a poverty trap and one of those as an affluence trap. Now, this model actually has three steady states, but the middle one is unstable. And so if you perturb incomes around that, you don't move back to the interior one. And so what this model tells us, again, it may sound very nerdy about a piece of mathematics, it tells us something substantive, that there can be unstable configurations of incomes, but there can also be stable configurations of incomes. And in the presence of these nonlinearities, there are multiple stable configurations. That's what it means to say that the poor and their descendants are located in one configuration of incomes, which I call the poverty trap, the rich and their descendants, and the other thing I call the affluence trap. I also want to emphasize another potential source of permanent income differences, and that is group differences. So let's suppose that I have two groups of people and the world's linear for each of them. What you would have is, depending on whether an individual family is a member of group one or group two, you'd have two different steady states. So members of group two are converging to a higher income steady state than members of group one. Again, why would I emphasize that? This is the interaction of the family dynamics with group memberships. And so in thinking about black, white inequality, it's not sufficient to just ask whether or not the derivative, the rate of change of offspring income with respect to parental income, is bigger than one or less than one, you have to ask something else, which is whether the population collectively is at a high level or at another level. Or I want to say that it's the interactions of the family dynamics with features of the groups that are influencing people. As I said before, I want to be honest about lack of evidence. In my judgment, there are no systematic conclusions I can draw in reading the empirical literature with reference to affluence traps and poverty traps in American data. Of course, there's excellent papers that have demonstrated how residual inequalities between blacks and whites can't be explained, or other groups can't be explained via family income dynamics. There's evidence supportive of the theory, but there's nothing that I would say is dispositive at this point. And so this is an area that I think is ripe for new additional research. The second thing I want to say, and this is a little bit about the issue of group differences, is one thing to say that there's a statistic that measures mobility for the American population. And that's a regularity. There's a population. You can always talk about some statistical regularity. But much of the exciting work in the study of mobility is moving beyond one statistic to sets of statistics that characterize this very complicated country. One of the very important advances in this area has been looking at regional, locational heterogeneity in mobility. And so Raj Chetty, Nathan Hendren, and a team associated with the Equality of Opportunity Project at Harvard have a famous figure, which is the Geography of Upward Mobility in the United States. And what they're asking essentially is you look across the United States and ask what is the probability a child will be in the national top fifth of the income distribution given the parent is in the bottom fifth. There is massive heterogeneity in mobility with respect to regions. Much of it is concentrated in the American South, but you can also see very high levels of mobility in some of the prairie states, parts of Iowa, for example. What the figure tells you is that in thinking about mobility, it may not be sufficient to say this is the mobility measure for America. Rather, we want to say this large heterogeneous country exhibits very different levels of spatial mobility. The second thing I want to do in talking about heterogeneity is to return to the issue of race. And here I want to introduce a second way that one can measure mobility. And this is not an intrinsically linear one, because it's more has to do with looking at what are called Markov chains. You think about individuals as being in categories, and you look at the conditional probabilities. This is the approach often taken in sociology, which has been pioneering in thinking about occupational mobility. And so here's a well-defined mobility question. It's not an income question. If I think about individuals as having jobs, let's call them highly skilled white collar, less skilled white collar, more skilled blue collar, less skilled blue collar manual in agriculture, I could have a mobility table that talks about the probability that a parent is in this category versus a child. We take the occupations and put them in these categories, and we just compute numbers that tell you conditional probabilities. And so what I want to put on the table is the insalience of race in these categories. When I was in high school, I actually saw this paper, and I never forgot it. It was a study written in 1962 of occupational mobility, looking at blacks and whites, by distinguished sociologist Otis Douglas Duncan. So why am I making a big deal about this? What I want to draw your attention to is the following. And that is if you looked at African Americans in 1962 and asked the question, what is the probability of different types of jobs for a child? Given that the parent is an upper white collar worker, the number you see there is 53%. For non-blacks, it's 12%. That's an astonishing statement. It said, regardless of the success of the parent in terms of their occupation, it was extremely likely their offspring would be doing lower manual work. In contrast, if you look at the numbers for non-African Americans, you got maybe what you would have expected ex-anny, which is some correlation between the parents and the kids. I emphasize these numbers for two reasons. Number one, I found them simply shocking. Now, you could say that, of course, this was pre-civil rights, and so this is the Jim Crow era, so it may not be surprising, but nevertheless, it's horrifying to think about that. Second, it relates to what I referred to as a limit to mobility statistics if you don't respect asymmetries between upward and downward mobility. I could look at the African American numbers and say, wow, the occupation of the parent doesn't predict the kids, but it's for a bad reason. And that is families are not able to build up momentum as it were in terms of upward mobility. And so I think this is a very compelling thing to understand exactly how difficult America was for African Americans in 1962. To be clear, things are better for African Americans if you do comparisons with the rest of the country since then. You nevertheless see a fairly substantial move downward for African Americans when compared to whites. Even though you don't have this shocking result where there's no lock-in, so to speak, nevertheless, the persistence of the higher categories, which of course were associated both with income and status in America, is stronger for whites than it is for blacks. And in my judgment, that is a fundamental dimension of understanding mobility in the United States. And so that's where I want to leave you. In other words, with the idea that, if I sort of said how mobile society is, even if I can, you know, there's things I have to do to figure it out. Number one, I got to say what feature? Is it incomes and occupation? What have you? Number two, I have to ask what it is about the parent I want to condition on. And number three, I have to choose a mathematical model to let me measure it. And the choice of the mathematical model can control the answers we get. Where I think there's been a relative lack of success is we have not generalized the mathematical models in such a way to reveal poverty traps and affluence traps, which is not, even though there's evidence of those in interesting papers. Where there has been success, I think, is in demonstrating the heterogeneity in the statistics, both through respect to location and with respect to race. This is an extraordinarily active area of contemporary research, but yet one where there's lots to do.