Tag Archives: mobility

No, poverty is not a mysterious, unknowable, negative-spiral loop

I don’t have much to add on the “consensus plan” on poverty and mobility produced by the Brookings and American Enterprise institutes, referred to in their launch event as being on “different ends of the ideological spectrum” (can you imagine?). In addition to the report, you might consider the comments by Jeff Spross, Brad DeLong, or the three-part series by Matt Bruenig.

My comment is about the increasingly (to me) frustrating description of poverty as something beyond simple comprehension and unreachable by mortal policy. It’s just not. The whole child poverty problem, for example, amounts to $62 billion dollars per year. There are certainly important details to be worked out in how to eliminate it, but the basic idea is pretty clear — you give poor people money. We have plenty of it.

This was obvious yet amazingly not remarked upon in the first 40 minutes of the launch event (which is all I watched). In the opening presentation, by Ron Haskins — for whom I have a well-documented distaste — started with this simple chart of official poverty rates:


He started with the blue line, poverty for elderly people, and said:

The blue line is probably the nation’s greatest success against poverty. It’s the elderly. And it basically has declined pretty much all the time. It has no relationship to the economy, and there is good research that shows that its cause at least 90% by Social Security. So, government did it, and so Social Security is the reason we’re able to be successful to reduce poverty among the elderly.

And then everyone proceeded to ignore the obvious implication of that: when you give people money, they aren’t poor anymore. The most unintentionally hilarious illustration of this was in the keynote (why?) address from David Brooks (who has definitely been working on relaxing lately, especially when it comes to preparing keynote puff-pieces). He said this, according to my unofficial transcript:

Poverty is a cloud problem and not a clock problem. This is a Karl Popper distinction. He said some problems are clock problems – you can take them apart into individual pieces and fix them. Some problems are cloud problems. You can’t take a cloud apart. It’s a dynamic system that is always interspersed. And Popper said we have a tendency to try to take cloud problems and turn them into clock problems, because it’s just easier for us to think about. But poverty is a cloud problem. … A problem like poverty is too complicated to be contained by any one political philosophy. … So we have to be humble, because it’s so gloomy and so complicated and so cloud-like.

The good news is that for all the complexity of poverty, and all the way it’s a cloud, it offers a political opportunity, especially in a polarized era, because it’s not an either/or issue. … Poverty is an and/and issue, because it takes a zillion things to address it, and some of those things are going to come from the left, and some are going to come from the right. … And if poverty is this mysterious, unknowable, negative spiral-loop that some people find themselves in, then surely the solution is to throw everything we think works at the problem simultaneously, and try in ways we will never understand, to have a positive virtuous cycle. And so there’s not a lot of tradeoffs, there’s just a lot of throwing stuff in. And social science, which is so prevalent in this report, is so valuable in proving what works, but ultimately it has to bow down to human realities – to psychology, to emotion, to reality, and to just the way an emergent system works.

Poverty is only a “mysterious, unknowable, negative spiral-loop” if you specifically ignore the lack of money that is its proximate cause. Sure, spend your whole life wondering about the mysteries of human variation — but could we agree to do that after taking care of people’s basic needs?

I wonder if poverty among the elderly once seemed like a weird, amorphous, confusing problem. I doubt it. But it probably would if we had assumed that the only way to solve elderly poverty was to get children to give their parents more money. Then we would have to worry about the market position of their children, the timing of their births, the complexity of their motivations and relationships, the vagaries of the market, and the folly of youth. Instead, we gave old people money. And now elderly poverty “has declined pretty much all the time” and “it has no relationship to the economy.”

Imagine that.


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I overspoke myself on Twitter

Possibly not the only time.

A blog called Random Critical Analysis (RCA) has posted, “On Philip Cohen’s knee-jerk response to Chetty’s “causal mobility” data and its association with single-motherhood.” I now must admit that I overspoke myself on Twitter.

But I think the blog post I wrote holds up OK. I complained in the post that the now-famous Chetty et al. analysis of intergenerational mobility had mishandled race, leading to people like David Leonhardt (and rightward from there) to conclude that the big story of hampered social mobility is family structure. It’s part of the overall pattern of polite society embracing the issue of economic inequality but also using that as a foil to avoid the issue of race inequality.

Brad Wilcox has seized on the Chetty analysis, repeating ad nauseum the quote that single parenthood is the “single strongest correlate of upward mobility.” My beef was, and is, that the analysis that was based on — which used the rate of single parenthood at the labor market level to predict intergenerational mobility — did not control for the racial composition of the labor market. That’s an obvious problem when your map of mobility looks like this:


When your analysis is ecological, that is, based only on aggregate characteristics, you have to be very cautious about drawing conclusions. It’s especially dicey in the Chetty case because the basic data, from tax, returns, includes family structure (because of parents’ marital status) but not race (which doesn’t go on your tax form). And that’s even more dicey because we know that at the individual level single parenthood is definitely not the “single strongest correlate of upward mobility.” I’ve been writing about this for years (follow the single-mother tag), but this figure from 2012 sums it up nicely (details in the old post):

You just have to keep that in perspective when you jump to an aggregate-level analysis. The difference between averages in Atlanta versus Salt Lake City — important as it is — is never going to be as big as the difference between a rich family and a poor family. Social parents’ class matters much more for determining children’s social class than does family structure.

Anyway, RCA is reworking my very simple analysis showing the effect of single motherhood rates was reduced by two-thirds when a single control for racial composition (percent Black) was added. That’s making the obvious point that, because single parenthood and percent Black in the local area are so strongly correlated, if you don’t take percent Black into account it looks like single parenthood has a huge, independent effect — which incorporates the effects of racism or other community factors associated with historical race composition. The new RCA post goes much further in the analysis, and concludes:

It ought to be pretty clear by now single-motherhood is capturing something quite powerful and that, contrary to Cohen’s strong assertions, it is not well explained by race.  If anything, single-motherhood mediates the black association much better than the reverse.

I’m not persuaded by the conclusion; you can evaluate it yourself. But the premise of the RCA post is actually not my blog post, but my tweets. As time went by I apparently became frustrated at the continued repetitions of the single mother thing by people who were ignoring my very clever post, and with the carelessness that distance allows I overstated my own claim, so I tweeted this,

The table and the highlighting are mine. What I should have paid attention to was my own next sentence after the underlined part: “That’s not an analysis, it’s just an argument for keeping percent Black in the more complex models.” I didn’t do a serious analysis — I just did enough to prove the point that racial composition should be in the model. Without that, you shouldn’t run around saying single parenthood is the most important factor. (RCA also believes I shouldn’t have said in the post that “Percent Black statistically explains the relationship between single motherhood and intergenerational immobility.”  I think “explains” is defensible, in that the effect is no longer statistically distinguishable from zero at the conventional level, but it’s clearly not the same as proving there is no effect, so I’ll take the criticism, too.)

I actually first did the little analysis in an earlier post, debunking a univariate analysis by Scott Winship and Donald Schneider. In that case I concluded: “This [my analysis] is not a rigorous examination of the cause of intergenerational immobility. It is just debunking one bivariate story that is too easily picked up by the forces of bad.” That seems about right.

Anyway, in conclusion, it was incorrect based on what I did for me to tweet, “the single mother effect in Chetty is all in the % Black effect.” I should just say single parenthood hasn’t been proven to matter as much as its partisans say it has. Even if it’s less effective in a tweet. This is a common frustration, that it takes more work to debunk something than to bunk it in the first place. But that’s not a good excuse.

Finally, I’m grateful that what I write matters enough that someone would go to the trouble of testing my claims to hold me accountable.


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How well do teen test scores predict adult income?

Now with new figures and notes added at the end — and a new, real life headline and graph illustrating the problem in the middle!

The short answer is, pretty well. But that’s not really the point.

In a previous post I complained about various ways of collapsing data before plotting it. Although this is useful at times, and inevitable to varying degrees, the main danger is the risk of inflating how strong an effect seems. So that’s the point about teen test scores and adult income.

If someone told you that the test scores people get in their late teens were highly correlated with their incomes later in life, you probably wouldn’t be surprised. If I said the correlation was .35, on a scale of 0 to 1, that would seem like a strong relationship. And it is. That’s what I got using the National Longitudinal Survey of Youth. I compared the Armed Forces Qualifying Test scores, taken in 1999, when the respondents were ages 15-19 with their household income in 2011, when they were 27-31.*

Here is the linear fit between between these two measures, with the 95% confidence interval shaded, showing just how confident we can be in this incredibly strong relationship:


That’s definitely enough for a screaming headline, “How your kids’ test scores tell you whether they will be rich or poor.”

In fact, since I originally wrote this, the Washington Post Wonkblog published a post with the headline, “Here’s how much your high school grades predict your future salary,” with this incredibly tidy graph:


No doubt these are strong relationships. My correlation of .35 means AFQT explains 12% of the variation in household income. But take heart, ye parents in the age of uncertainty: 12% of the variation leaves a lot left over. This variable can’t account for how creative your children are, how sociable, how attractive, how driven, how entitled, how connected, or how White they may be. To get a sense of all the other things that matter, here is the same data, with the same regression line, but now with all 5,248 individual points plotted as well (which means we have to rescale the y-axis):


Each dot is a person’s life — or two aspects of it, anyway — with the virtually infinite sources of variability that make up the wonder of social existence. All of a sudden that strong relationship doesn’t feel like something you can bank on with any given individual. Yes, there are very few people from the bottom of the test-score distribution who are now in the richest households (those clipped by the survey’s topcode and pegged at 3 on my scale), and hardly anyone from the top of the test-score distribution who is now completely broke.

But I would guess that for most kids a better predictor of future income would be spending an hour interviewing their parents and high school teachers, or spending a day getting to know them as a teenager. But that’s just a guess (and that’s an inefficient way to capture large-scale patterns).

I’m not here to argue about how much various measures matter for future income, or whether there is such a thing as general intelligence, or how heritable it is (my opinion is that a test such as this, at this age, measures what people have learned much more than a disposition toward learning inherent at birth). I just want to give a visual example of how even a very strong relationship in social science usually represents a very messy reality.

Post-publication addendums

1. Prediction intervals

I probably first wrote about this difference between the slope and the variation around the slope two years ago, in a futile argument against the use of second-person headlines such as “Homophobic? Maybe You’re Gay.” Those headlines always try to turn research into personal advice, and are almost always wrong.

Carter Butts, in personal correspondence, offered an explanation that helps make this clear. The “you” type headline presents a situation in which you — the reader — are offered the chance to add yourself to the study. In that case, your outcome (the “new response” in his note) is determined by the both the line and the variation around the line. Carter writes:

the prediction interval for a new response has to take into account not only the (predicted) expectation, but also the (predicted) variation around that expectation. A typical example is attached; I generated simulated data (N=1000) via the indicated formula, and then just regressed y on x. As you’d expect, the confidence bands (red) are quite narrow, but the prediction bands (green) are large – in the true model, they would have a total width of approximately 1, and the estimated model is quite close to that. Your post nicely illustrated that the precision with which we can estimate a mean effect is not equivalent to the variation accounted for by that mean effect; a complementary observation is that the precision with which we can estimate a mean effect is not equivalent to the accuracy with which we can predict a new observation. Nothing deep about that … just the practical points that (1) when people are looking at an interval, they need to be wary of whether it is a confidence interval or a prediction interval; and (2) prediction interval can (and often should be) wide, even if the model is “good” in the sense of being well-estimated.

And here is his figure. “You” are very likely to be between the green lines, but not so likely to be between the red ones.


2. Random other variables

I didn’t get into the substantive issues, which are outside my expertise. However, one suggestion I got was interesting: What about happiness? Without endorsing the concept of “life satisfaction” as measured by a single question, I still think this is a nice addition because it underscores the point of wide variation in how this relationship between test scores and income might be experienced.

So here is the same figure, but with the individuals coded according to how they answered the following question in 2008, when they were age 24-28, “All things considered, how satisfied are you with your life as a whole these days? Please give me an answer from 1 to 10, where 1 means extremely dissatisfied and 10 means extremely satisfied.” In the figure, Blue is least satisfied (1-6; 21%), Orange is moderately satisfied (7-8; 46%), and Green is most satisfied (9-10; 32%)


Even if you squint you probably can’t discern the pattern. Life satisfaction is positively correlated with income at .16, and less so with test scores (.07). Again, significant correlation — not helpful for planning your life.

* I actually used something similar to AFQT: the variable ASVAB, which combines tests of mathematical knowledge, arithmetic reasoning, word knowledge, and paragraph comprehension, and scales them from 0 to 100. For household income, I used a measure of household income relative to the poverty line (adjusted for household size), plus one, and transformed by natural log. I used household income because some good test-takers might marry someone with a high income, or have fewer people in their households — good decisions if your goal is maximizing household income per person.


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How to illustrate a .61 relationship with a .93 figure: Chetty and Wilcox edition

Yesterday I wondered about the treatment of race in the blockbuster Chetty et al. paper on economic mobility trends and variation. Today, graphics and representation.

If you read Brad Wilcox’s triumphalist Slate post, “Family Matters” (as if he needed “an important new Harvard study” to write that), you saw this figure:


David Leonhardt tweeted that figure as “A reminder, via [Wilcox], of how important marriage is for social mobility.” But what does the figure show? Neither said anything more than what is printed on the figure. Of course, the figure is not the analysis. But it is what a lot of people remember about the analysis.

But the analysis on which it is based uses 741 commuting zones (metropolitan or rural areas defined by commuting patterns). So what are those 20 dots lying so perfectly along that line? In fact, that correlation printed on the graph, -.764, is much weaker than what you see plotted on the graph. The relationship you’re looking at is -.93! (thanks Bill Bielby for pointing that out).

In the paper, which presumably few of the people tweeting about it read, the authors explain that these figures are “binned scatter plots.” They broke the commuting zones into equally-sized groups and plotted the means of the x and y variables. They say they did percentiles, which would be 100 dots, but this one only has 20 dots, so let’s call them vigintiles.

In the process of analysis, this might be a reasonable way to eyeball a relationship and look for nonlinearities. But for presentation it’s wrong wrong wrong.* The dots compress the variation, and the line compresses it more. The dots give the misleading impression that you’re displaying the variance around the line. What, are you trying save ink?

Since the data are available, we can look at this for realz. Here is the relationship with all the points, showing a much messier relationship, the actual -.76 (the range of the Chetty et al. figure, which was compressed by the binning, is shown by the blue box):

chetty scattersThat’s 709 dots — one for each of the commuting zones for which they had sufficient data. With today’s powerful computers and high resolution screens, there is no excuse for reducing this down to 20 dots for display purposes.

But wait, there’s more. What about population differences? In the 2000 Census, these 709 commuting zones ranged in population in the 2000 Census from 5,000 (Southwest Jackson, Utah) to 16,000,000 (Los Angeles). Do you want to count Southwest Jackson as much as Los Angeles in your analysis of the relationship between these variables? Chetty et al. do in their figure. But if you weight them by population size, so each person in the population contributes equally to the relationship, that correlation that was -.76 — which they displayed as -.93 — is reduced to -.61. Yikes.

Here is what the plot looks like if you scale the commuting zones according to population size (more or less, not quite sure how Stata does this):

chetty scatters weighted

Now it’s messier, and the slope is much less steep. And you can see that gargantuan outlier — which turns out to be the New York commuting zone, which has 12 million people and with a lot more upward mobility than you would expect based on its family structure composition.

Finally, while we’re at it, we may as well attend to that nonlinearity that has been apparent since the opening figure. We can increase the variance explained from .38 to .42 by adding a quadratic term, to get this:

chetty scatters weighted quad

I hate to go beyond what the data can really tell. But — what the heck — it does appear that after 33% single-mother families, the effect hits its minimum and turns positive. These single mother figures are pretty old (when Chetty et al.’s sample were kids). Now that the country has surpassed 40% unmarried births, I think it’s safe to say we’re out of the woods. But that’s just speculation.**

*OK, OK: “wrong wrong wrong” is going too far. Absolute rules in data visualization are often wrong wrong wrong. Binning 709 groups down to 20 is extreme. Sometimes you have a zillion points. Sometimes the plot obscures the pattern. Sometimes binning is an inherent part of measurement (we usually measure age in years, for example, not seconds). None of that is an excuse in this case. However, Carter Butts sent along an example that makes the point well:


On the other hand, the Chetty et al. case is more similar to the following extreme example:

If you were interested in the relationship between age and earnings for a sample of 1,400 full-time, year-round women, you might start with this, which is a little frustrating:


The linear relationship is hard to see, but it’s about +$500 per year of age. However, the correlation is only .13, and the variance explained by linear-age alone is only 1.7%. But if you plotted the mean wage over ages, the correlation jumps to .68:


That’s a different question. It’s not, “how does age affect earnings,” it’s, “how does age affect mean earnings.” And if you binned the women into 10-year age intervals (25-34, 35-44, 45-54), and plotted the mean wage for each group, the correlation is .86.


Chetty et al. didn’t report the final correlation, but they showed it, even adding the regression line, so that Wilcox could call it the “bivariate relationship.”

**This paragraph was a joke that several people missed, so I’m clarifying. I would never draw a conclusion like that from the scraggly tale of a loose correlation like this.


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Where is race in the Chetty et al. mobility paper?

What does race have to do with mobility? The words “race,” “black,” or “African American” don’t appear in David Leonhardt’s report on the new Chetty et al. paper on intergenerational mobility that hit the news yesterday. Or in Jim Tankersley’s report in the Washington Post, which is amazing, because it included this figure: post-race-mobility That’s not exactly a map of Black America, which the Census Bureau has produced, but it’s not that far off: census-black-2010

But even if you don’t look at the map, what if you read the paper? Describing the series of maps of intergenerational mobility, the authors write:

Perhaps the most obvious pattern from the maps in Figure VI is that intergenerational mobility is lower in areas with larger African-American populations, such as the Southeast. … Figure IXa confirms that areas with larger African-American populations do in fact have substantially lower rates of upward mobility. The correlation between upward mobility and fraction black is -0.585. In areas that have small black populations, children born to parents at the 25th percentile can expect to reach the median of the national income distribution on average (y25;c = 50); in areas with
large African-American populations, y25;c is only 35.

Here is that Figure IXa, which plots Black population composition and mobility levels for groups of commuting zones: ixa Yes, race is an important part of the story. In a nice part of the paper, the authors test whether Black population size is related to upward mobility for Whites (or, people in zip codes that are probably White, since race isn’t in their tax records), and find that it is. It’s not just Blacks driving the effect. I’m thinking about the historical patterns of industrial development, land ownership, the backwardness of racist elites in the South, and so on. But they’re not. For some reason, not explained at all, Chetty et al. offer this pivot:

The main lesson of the analysis in this section is that both blacks and whites living in areas with large African-American populations have lower rates of upward income mobility. One potential mechanism for this pattern is the historical legacy of greater segregation in areas with more blacks. Such segregation could potentially affect both low-income whites and blacks, as racial segregation is often associated with income segregation. We turn to the relationship between segregation and upward mobility in the next section.

And that’s it, they don’t discuss Black population size again, instead only focusing on racial segregation. They don’t pursue this “potential mechanism” in the analysis that follows. Instead, they drop percent Black for racial segregation. I have no idea why, especially considering this Table VII, which shows unadjusted (and normalized) correlations (more or less) between each variable and absolute upward mobility (the variable mapped above): tablevii

In these normalized correlations, fraction Black has a stronger relationship to mobility than racial segregation or economic segregation! In fact, it’s just about the strongest relationship on the whole long table (except for single mothers, with which it is of course highly correlated). So why do they not use it in their main models? Maybe someone else can explain this to me. (Full disclosure, my whole dissertation was about this variable.)

This is especially unfortunate because they do an analysis of the association between commuting zone family structure (using macro-level variables) and individual-level mobility, controlling for marital status — but not race — at the individual level. From this they conclude, “Children of married parents also have higher rates of upward mobility if they live in communities with fewer single parents.” I am quite suspicious that this effect is inflated by the omission of race at either level. So they write the following, which goes way beyond what they can find in the data:

Hence, family structure correlates with upward mobility not just at the individual level but also at the community level, perhaps because the stability of the social environment affects children’s outcomes more broadly.

Or maybe, race.

I explored the percent Black versus single mother question in a post a few weeks ago using the Chetty et al. data. I did two very simple OLS regression models using only the 100 largest commuting zones, weighted for population size, the first with just single motherhood, and then a model with proportion Black added: This shows that the association between single motherhood rates and immobility is reduced by two-thirds, and is no longer significant at conventional levels, when percent Black is added to the model. That is: Percent Black statistically explains the relationship between single motherhood and intergenerational immobility across U.S. labor markets. That’s not an analysis, it’s just an argument for keeping percent Black in the more complex models. Substantively, the level of racial segregation is just one part of the complex race story — it measures one kind of inequality in a local area, but not the amount of Black, which matters a lot (I won’t go into it all, but here are three old papers: one, two, three.

The burgeoning elite conversation about economic mobility, poverty, and inequality is good news. It’s avoidance of race is not.


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Inequality, mobility, single mothers, and race: comment

I have no idea whether inequality increases intergenerational immobility. But I do know that lots of people would like to pin bad social trends on single motherhood, meaning — in their view — the bad decisions of people who already poor. And that has bad implications.

In a blog post by Scott Winship and Donald Schneider at the Manhattan Institute, they argue that the liberal argument that inequality blocks mobility is not well supported. To do that, they show simple bivariate correlations between single motherhood rates and immobility across U.S. labor markets. Their point is that, if you want to use that simple bivariate standard, you can just as well — but better — argue that immobility is caused by single motherhood rather than by income inequality, because the correlation is very strong. For their exercise they use data from the Equality of Opportunity Project, which is freely available here.

In a series of tweets, Winship clarified his point:

point wasn’t to highlight single parenthood—point was to show where low evidentiary standards on left can take you … look, single motherhood may very well be a big problem for mobility. Inequality might too…. but the left has to be held accountable when they make bad arguments skewing policy debates…  I clearly wrote that correlations shouldn’t constitute reason for getting worked up about single moms

I take him at his word on his intentions, but those with well-documented patterns of less scrupulous behavior are not so scrupulous, and so the post was bad. Despite a disclaimer about not reading causation from correlation, they also wrote:

In other words, a [labor market’s] prevalence of single motherhood predicts its relative mobility quite well all by itself. … the relationship between single motherhood and mobility holds up in all of these analyses. … On the basis of these charts, rather than a new Washington Center on Equitable Growth housed at CAP and devoted to discovering the damages that income inequality inflicts, the left should have started a Washington Center on Single Motherhood.

Again, my only dog in the fight is fighting against the easy right-wing causal association of single motherhood with bad outcomes. The Heritage Foundation, Scheider’s employer, is particularly egregious in this, as I’ve occasionally documented (here and here, e.g.)

So here’s a quick debunk on that. A simple glance at the map from the Equal Opportunity Project will tell you that race is involved here, but it didn’t come up in Winship and Schneider’s post:


So let’s just look at the relationship between immobility, single motherhood and race. (Immobility here is measured by the effect of family income on children’s incomes. Higher scores are bad.)

So first, here is the relationship between population percent Black and immobility for the 100 largest metro areas, with the larger ones shown as bigger dots:

pb-immobThat relationship is quite strong: the higher Black population proportions are strongly associated with immobility. But so is the single motherhood relationship, as Winship and Schneider reported. So, we turn to the obvious tool, a multivariate regression. Here are two models, the first with just single motherhood — in effect, the Winship and Schneider result — and then a model with proportion Black added. Both are weighted by population size.


This shows that the association between single motherhood rates and immobility is reduced by two-thirds, and is no longer significant at conventional levels, when percent Black is added to the model. That is: Percent Black statistically explains the relationship between single motherhood and intergenerational immobility across U.S. labor markets.

This is not a rigorous examination of the cause of intergenerational immobility. It is just debunking one bivariate story that is too easily picked up by the forces of bad.




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Twin peaks of intergenerational mobility

There is a lot of news about economic mobility from recent weeks. Some of it draws from Pew’s Economic Mobility Project. Not as recently, there was an excellent review and analysis by Emily Beller and Michael Hout in the Future of Children a few years ago. In between, I somehow missed a collection of economic analyses in a book titled, Unequal Chances: Family Background and Economic Success, edited by Samuel Bowles, Herbert Gintis, & Melissa Osborne Groves.

The first chapter is posted free, and it includes a good introduction to the statistical and conceptual issues that arise when trying to understand patterns of mobility across generations. It includes a discussion of heritability, genetics, IQ and the like, which is quite approachable to the reader who is ready to think about decomposing correlations.

One good example regarding genetic heritability of traits that determine income: race in South Africa, which is almost entirely inherited (since there’s very little interracial marriage) and has a huge effect on income, but the effect of which is still social/environmental, not “natural.”

Anyway, I like this “twin peaks” figure, which shows the relationship between parent and child family income decile:

Probability of offspring attaining given income decile, by parents’ income deciles, United States. Based on total family income for black and white participants in the Panel Study of Income Dynamics who were born between 1942 and 1972, and their parents. The income of the children was measured when they were aged 26 or older, and was averaged over all such years for which it was observed. The number of years of income data ranged from 1 to 29 with an average of 11.5; the median year of observation was 1991. Parents’ income was averaged over all observed years in which the child lived with the parents. The number of years of income data ranged from 1 to 27 with an average of 11.9; the median year of observation was 1974. The simple age adjusted correlation of parents’ and children’s incomes in the data set represented in the figure is 0.42.

So, 30% of children from the top decile stay there (point D), 32% of children from the bottom decile stay there (C), while the odds of making it from the top to the bottom, or vice versa, are both less than 2% (A and B).

There is a nice symmetry to the figure, but it’s important to know that what’s happening up and down the distribution is highly varied, according to the analyses in the book. For example, at the top there is a lot of transmitted wealth. At the bottom there are a lot of health crises and premature deaths, including from violence. And the bottom is much stickier for Black children than for Whites.

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