Tag Archives: single mothers

A few ways Isabel Sawhill is wrong on single mothers

Photo from Flickr Creative Commons by Mikey G. Ottawa

Photo from Flickr Creative Commons by Mikey G. Ottawa

Writing for the 50th anniversary of the Moynihan Report – which I will comment more on soon – Isabel Sawhill offers a summary of Moynihan’s prescience. Here’s an excerpt:

…the trends [Moynihan] identified have not gone away. Indeed, they have “trickled up” to encompass not just a much larger fraction of the African American community but a large swath of the white community as well. Still, the racial gaps remain large. The proportion of black children born outside marriage was 72 percent in 2012, while the white proportion was 36 percent.

The effects on children of the increase in single parents is no longer much debated. They do less well in school, are less likely to graduate, and are more likely to be involved in crime, teen pregnancy, and other behaviors that make it harder to succeed in life. Not every child raised by a single parent will suffer from the experience, but, on average, a lone parent has fewer resources—both time and money—with which to raise a child. Poverty rates for single-parent families are five times those for married-parent families. The growth of such families since 1970 has increased the overall child poverty rate by about 5 percentage points (from 20 to 25 percent).

Rates of social mobility are also lower for these families. Harvard researcher Raj Chetty and his colleagues find that the incidence of single parenthood in a community is one of the most powerful predictors of geographic differences in social mobility in the United States. And our research at the Brookings Institution also shows that social mobility is much higher for the children of continuously married parents than for those who grow up with discontinuously married or never-married.

At least three things wrong here:

1. This is a very common logical sequence followed by those who say that the decline of marriage (or rise of single parenthood) is the major social welfare problem we face today. They point to the rise of single parenthood. Then they say that children of single parents are doing worse on a variety of indicators. What they don’t say is that while single parenthood has, in fact, skyrocketed, most of the problems they’re concerned with have gotten better, not worse. While single motherhood has been rising, education is up, poverty is down, life expectancy is up, and (since the 1990s) crime is way, way down – for Blacks as well as Whites. The proportion of Black children living with single mothers has almost doubled since the 1960s, but the Black poverty rate is less than it was in 1974.

2. It is one thing to observe that children of single parents do worse in some ways than children of married parents. But Sawhill knows, and should tell you, that studies seeking to identify the direction of causality in that relationship are plagued by unresolved problems of selection bias. We know for sure the effects of single parenthood on children are dwarfed by other social trends.

3. That use of Chetty is completely wrong, a meme started by Brad Wilcox and fueled by credulous reporters. Notice the pivot in Sawhill’s text. First it’s, “Rates of social mobility are also lower for these families.” Then, “Harvard researcher Raj Chetty and his colleagues find that the incidence of single parenthood in a community…” As if the second (the one that mentions Harvard) is related to the first. It’s not. The Chetty paper did not study single-parent families. What they did was look at rates of single parenthood in communities, and use them to predict social mobility. But – and Sawhill would know this matters if she had read the beginning of her own piece, which mentioned the big racial disparity in single parenthood – the paper did not control for race! Please, before spreading this claim, or retweeting (without necessarily endorsing) the supposed experts who do, read this. Because you know what really affects social mobility in the U.S.? Race.

2 Comments

Filed under In the news

Policy, politics, and promoting education versus marriage

Here are three ideas I disagree with:

1. Most people aren’t smart enough to make going to college worth it.

Maybe the best-known purveyor of this idea is Charles Murray, who argued in his 2008 book Real Education (offshore bootlegged copy here) that the “consensus intellectual benchmark” for understanding real college-level material is an IQ of 115, which by definition is only 16% of the population — but probably only 10% are really, truly smart enough (and efforts to improve education at lower levels to prepare more people for college are futile, so don’t even think about spending more on education, because so many people are “born lazy“).

2. We’ve done so much for poor people, it’s time for them to do something for themselves.

This is clearly related to idea #1, insofar as the government spends billions of dollars educating people for college — and subsidizing the colleges they attend — who could instead just work hard and enjoy life in a job requiring less education. But it extends to all kinds of social welfare and anti-poverty programs, as illustrated by the exasperated people in the policy establishment from Brookings to Heritage.

3. Poor women should get married before they have children.

This idea is pervasive, as I’ve discussed many times under the single mothers tag, in response to people blaming single mothers for rising inequality, poverty, low upward mobility, and crime.

One response

Here I offer one response to these three ideas combined. It is possible to increase access to college education, which would increase stability and opportunity for poor people and their children.

In demography, there is a long-running debate over whether there is a biological limit to human longevity, and whether and how fast we may be approaching it. Regardless of the ultimate answer, so far it’s clear that projections based on an inevitable tapering off of increases in life expectancy have repeatedly proved wrong (here’s a review and a recent paper). The same might be said of college education. Here is the trend in 25-34 year-old U.S. civilians with at least a BA degree, from Census numbers:

college completion trends.xlsx

There was more talk about hitting the limits of college access 10 years ago, but even then it was increasing rapidly among women. Yes, we can and should improve college education. But I see nothing here to suggest a ceiling approaching. Still, people keep assuming that expanding education isn’t feasible.

For example, while Murray holds forth on the intelligence limitations among the poor, his colleague Brad Wilcox argues for a cultural press on those with less than a college degree:

They can go down the road of not having marriage as the keystone to their family formation, family life, or we can hold the line, if you will, and try to figure out creative strategies for strengthening marriage in this particular middle demographic in the United States.

In addition to upscaling their deficient values, however, couldn’t we also move them out of the less-than-college category altogether? Not so fast, says Wilcox in a recent interview:

On the education front, the U.S. spends a ton of money and devotes unparalleled attention to college. But the reality is that only one-third of adults, even today, will get a college degree, a B.A. or B.S. We can do a lot better in both funding and focusing on vocational education and apprenticeship training.

Really, America, be reasonable: Our “ton of money” is “unparalleled.” Don’t set your sights too high. Who do you think you are, anyway, Poland (college graduation rate: 53%), Ireland (46%), or Portugal (41%)? From OECD numbers:

college graduation rates OECD.xls

I know expanding college access (the real kind, not the for-profit kind) suggests expanding a broken financial aid system, and the economic returns aren’t guaranteed, but for my purposes it’s not just about getting a better job. People who go to college — and those who know they are going to go to college before they do — usually delay having children, not because some moralizing think tank tells them it’s wrong, but because they’re trying to rationally sequence their lives. Of course, married couples have relatively low poverty rates, but even for parents who aren’t married, higher education sure helps. From the American Community Survey via IPUMS.org:

H8.xlsx

Trying to get more poor people to get married is both offensive and useless. But increasing access to higher education is both uplifting and useful. The choice between early birth with low education and later birth with higher education is not hard to make, but unless it’s feasible — with a readily apparent, practical, path toward completion — there is no choice to make.

The increase in college education has already helped keep child poverty levels from rising as marriage rates have fallen. Among women old enough to have finished college (ages 22-44) the percentage of babies born to mothers with college degrees (married or not) has increased from 23% in 1990 to 35% in 2010. From the Current Population Survey via IPUMS.org:

H8.xlsx

Promoting marriage among the poor is a moralizing salve for the self-esteem — and anti-tax self-interest — of pious elites, with zero proven success in helping anybody poor. Promoting access to higher education is good policy and good politics.

19 Comments

Filed under In the news

Turns out marriage and income inequality go pretty well together

Diatribe first, then critique.

Brad Wilcox and Bob Lerman have a new report arguing, among other things:

Had marriage rates not declined substantially among parents, many more families would have attained middle-class incomes, and the inequality across families would have increased at a slower rate.

It’s well established that falling marriage rates are contributing to family income inequality. However, increasing inequality is not an inevitable result of low marriage rates. In general, among rich countries, higher marriage rates are associated with higher levels of income inequality. The USA is a clear outlier here:

marriage-inequality2

It’s possible marriage increases income inequality in general. It’s also possible that people don’t get married as much when they’re not worried about inequality. Regardless, this shows high marriage rates are quite compatible with high inequality.

Falling marriage does contribute to rising inequality in the USA, because of how it’s manifesting: increasing selectivity in marriage, so that richer people are getting and staying married more; and increasing social class endogamy, so that there are more two-high-income families lording over more one-low-income families. And all of that is exacerbated by widening underlying inequality, with high-end incomes pulling away from low-end incomes, relatively unchecked by income redistribution.

One obvious solution is to take money away from married high-income people and give it to single low-income people. With all the benefits that married people get — many of them through no special effort of their own, but rather as a result of their social status at birth, race, health, good looks, legal perks, or lucky breaks — it seems reasonable to tax marriage, like a windfall profits tax, or an inheritance tax, or a progressive income tax. But, if you’re squeamish about taxing something “good” like marriage, then just taxing wealth a little more would accomplish much the same thing. This elegant solution would decrease inequality, increase well-being for poor people, and equalize life chances for children (who are the future, I believe). In other words, it’s out of the question.

A second, less-obvious (but more-often mentioned) solution is more marriage. Low-income single people could become high-income married people. Or, failing that (which they would) they could settle for becoming low-income married people. Besides the fact that efforts to promote marriage have been a complete failure, would this even make poor single people and their children better off?

The family science right-wing establishment says Yes. To the poor singles, they say: “See how well married people are doing? Get married and you’ll be like them (also: you won’t get raped so much, you sluts.)” To their rich donors and political allies, they say, “Make them earn their benefits by demonstrating their moral fiber and manning up.” The welfare reform attempted this, and successfully forced many single mothers into the labor force in the cause of character development  — but it failed in its goal of marrying them off.

So more marriage is the new agenda — and the family right has a plan that leads inexorably to success (for them): either by successfully raising marriage rates among the poor (extremely unlikely), or by justifying the continued denial of basic welfare to the poor and shoring up the political case against economic redistribution (extremely likely).

A few notes on the first part of their report

Question: Why should we think the unmarried people would get the same benefits from marriage that currently married people do? If marriage is becoming increasingly selective, then you can’t assume the benefits observed among actually married people would be reaped by those who have been left out (or opted out) of the increasingly stringent marriage selection process. They may not have the assets that lead to marriage benefits — skills of many kinds, wealth, social networks, and so on.

Wilcox and Lerman say family income would have risen more — and there would be less inequality — if more people were married, because married couple incomes rose faster than average. They show this:

willerfaminc

Setting aside the completely misleading use of an area chart, and the gruesome y-axis truncation, this shows that married-parent families have had faster than average income growth. One obvious reason for this is women’s rising labor force participation, at least into the 1990s. That has a big effect on income at the median, which is the line this is showing for each group (though the area form makes it look like it’s some kind of distribution). Rising income at the median would reduce income inequality. The fact that single-parent families are dragging down the average contributes to growing inequality and a stagnant overall median.

But the top is where most inequality is being generated. Looking at the top will help us see not just growing inequality, but also why getting poor people to get married won’t help them as much as Wilcox and Lerman think it would. Let’s add the 90th and 10th percentiles to the married parent income trends. My figure shows that the married parent family’s 90th percentile’s income has risen 39% since 1979, while the median has risen 14%. But the 10th percentile’s income has fallen 12%.

married couple ineq.xlsx

So, if poor single people finally get with it and start getting married, which married parents are they going to look like?

The chart shows dramatically increasing inequality among married-couple families. Pouring more married couples into the bottom of the distribution doesn’t seem likely to fix that. And, as Jordan Weissman pointed out, the family structure story has nothing to do with the huge rise in incomes in the top 1% and .1%, which are central to the inequality story.

Till now I’ve skirted some thorny technical issues to make a comparison comparable to Wilcox/Lerman’s data. But assessments of family income inequality are tricky. Marrying two low earners creates one family household with twice the income. That shows up as a rise in incomes per family, but what is the real gain? They get economies of scale, but most descriptions (like Wilcox/Lerman’s) don’t take that into account. And the children might increase their consumption from greater access to the second income, but that’s hidden within the family black box.

To see how changes in family income distributions affect children, it’s useful to use a family size adjustment. I like one in here that counts kids as seven-tenths of an adult, and scales the family income by .65. (So you just divide family income by this: [(adults+(.70*kids)).^65].) Now you can track children’s cash on hand much better. I also prefer to use household rather than family income and composition, because the Census definition of families is narrow. In the charts so far, for example, parents’ cohabiting partners’ income is not included.

So here is the inequality trend for children — using the Gini index for needs-adjusted household income (code here) — by parents’ marital status:

kid-gini-1980-2012.xlsx

This shows that the increase in family inequality has been much more dramatic for married-couple families than single-parent families. That’s those high-income couples pulling away from the middle and the bottom. On the other hand, inequality has been and remains higher for single-parent families. Note that the inequality for all children is not just the average of the two other lines, because it also includes the inequality between married-couple and single-parent families.

So moving people from single to married would have reduce inequality more in 1980 than now, but just on composition it might still help if it boosted cash per kid through access and efficiency. Whether that benefit would outweigh the costs is not clear. If people not married yet aren’t just like the people who are — they may have lower skills and resources of various kinds, for example — marriage might not facilitate those transfers. Plus, it’s only good if the people want to be married.

Anyway, point is, married-couple families are doing pretty well at increased income inequality all by themselves.

20 Comments

Filed under Research reports

To know poverty proportions, know your terms (Fox News edition)

In a recent interview on Fox & Friends, despite preparing, I found myself not prepared for Tucker Carlson to ask me this:

It’s pretty conclusive that kids who grow up with married parents — biological parents — do way better than kids who don’t. So the fact that the percentage of kids growing up in that environment has been dropping, why shouldn’t we call that a tragedy?

After a little back-and-forth, I came out with this pretty inarticulate statement:

I think we want to think about pros and cons and and challenges that people face in all different arrangements. And part of the point of this report is that we can’t put people in one category and try to come up with a solution. Our poverty problem for example: Only a third of people in poverty now are living in single-mother families. So we have a large problem of poverty in married couple families as well.

My inarticulateness would probably have been even worse if I had noticed that the Fox audience at that moment was being treated to a completely wrong statistic in the caption below our talking heads:

foxbadcaption

The report I provided to the Fox staff had actually shown that one-third — not two-thirds — of children under 15 live with unmarried parents.

Anyway, my statement, “Only a third of people in poverty now are living in single-mother families,” is pretty much true. On the other hand, the oft-cited Heritage Foundation statement, “Nearly three out of four poor families with children in America are headed by single parents,” is pretty much true, too. How can that be?

To put it as confusingly as possible, the basic issue is that poverty numbers can be reported for different data universes: individuals, families, family households, individuals in families, and families with children. Some families are sub-families — that is, they are in someone else’s household — and some children (if they live in group quarters, or are ages 16-18 and live on their own as neither married nor parents) don’t live in families.

Here are some poverty numbers for 2013 (from various tables here). The rates are just for your information; it’s the numbers in poverty that I refer to below — you can use them to mix and match your own proportions:

poverty2013

Notice that there are 14 million poor people who don’t live in families at all. Some of them have housemates or cohabiting partners that they are sharing income with, but because they’re not technically families that shared income doesn’t count as shared income.

Because, from the 1st and 3rd rows of the table, 15,606/45,318 = .34, my statement that only a third of poor people live in single-mother families was pretty much true. I say “pretty much” because a few of those female-householder-no-husband families aren’t single mothers of children, but rather single women hosting some other family member in their households (such as an older relative).

And because, from rows 12-14, (3,937+607)/6,482 = .70, the Heritage Foundation’s statement that, “Nearly three out of four poor families with children in America are headed by single parents” is pretty much true, too.

So, who’s right?

Well, if you want to talk about the whole poverty problem, it’s fair to say that only a third of it involves people in single-mother families. Maybe by excluding the single fathers from that I’m guilty of shading the number downward to minimize the problem (and I definitely shouldn’t have implied that the rest of the poor people live in married-couple families). I actually did that because the table I get those numbers from (hstpov2) doesn’t report single-man families.

If you want to talk about the problem of children in poverty, then you should use the second panel, which tells you that 57% of children in poverty live with single mothers (8,339/14,659), or if you include single fathers, 65%. That’s what Heritage should do.

The “nearly three out of four” number is true — if you’re OK with 70% as nearly three out of four — but there’s no reason families is the more logical unit of analysis instead of children.

Marriage tracks poverty

Anyway, I was reminded of all this because Brad Wilcox tweeted a link to this editorial from the Tyler Morning Telegraph. The editorial includes the Heritage statistic, and explains why poverty rates haven’t fallen much in the last few years, while unemployment rates have. Quoting Joe Carter of the Acton Institute:

“The findings align with what many family scholars and economists have been predicting: the decline of marriage leads to an increase in poverty. From 2007 to 2011, the American population increased by 10,360,000 while the number of marriages decreased during that same period by 79,000. Over the last few years we’ve seen the same trend: more people, fewer marriages. … The effect of the decline in marriage, coupled with an increase in single parenthood, is that many more children live in poverty than they would if marriage was more common.”

That’s why the headline for the editorial is, “Marriage statistics track with poverty.” To illustrate marriage tracking poverty, I’ve put the two historical trends on the same graph, using this for marriage and this for poverty:

poverty and marriage 1960-2013

As the chart clearly shows (since 1977 at least), when marriage falls, poverty goes up. Also, when marriage falls, poverty goes down. In math-grammar terms, those two equations reduce to: marriage falls; poverty goes up and down.

2 Comments

Filed under Uncategorized

Doing math one-handed? Inequality and the marriage problem (#asa14)

I’m at the American Sociological Association meetings in San Francisco, on my way over to present the following slides at a session on “Closing the Economic Marriage Gap: The Policy Debate.” Looks like a great session, organized by Melanie Heath, Orit Avishai, and Jennifer Randles, and including Andrew Cherlin, Sarah Halpern-Meekin, Mignon Moore, and Ronald Mincy – with a discussion by Barbara Risman.

I’ve uploaded the slides for my talk, here.

The background is in this post, which I wrote in 2011, called, “Is it a ‘marriage problem’?” Here it is again:

Is it a “marriage problem”?

A self-described liberal (Andrew Cherlin) and conservative (W. Bradford Wilcox) pair of academics have produced a “policy brief”* for the Brookings Institution entitled, The Marginalization of Marriage in Middle America.

There’s no new information or analysis in the report, so I won’t dwell on it. But I’d like to use it to point out a logical problem with pro-marriage social science in general. Here’s an excerpt from the introduction, with my comment following:

This policy brief reviews the deepening marginalization of marriage and the growing instability of family life among moderately-educated Americans: those who hold high school degrees but not four-year college degrees and who constitute 51 percent of the young adult population (aged twenty-five to thirty-four). … [b]oth of us agree that children are more likely to thrive when they reside in stable, two-parent homes. … Thus, we conclude by offering six policy ideas, some economic, some cultural, and some legal, designed to strengthen marriage and family life among moderately-educated Americans. … To be sure, not every married family is a healthy one that benefits children. Yet, on average, the institution of marriage conveys important benefits to adults and children. … The fact is that children born and raised in intact, married homes typically enjoy higher quality relationships with their parents, are more likely to steer clear of trouble with the law, to graduate from high school and college, to be gainfully employed as adults, and to enjoy stable marriages of their own in adulthood. Women and men who get and stay married are more likely to accrue substantial financial assets and to enjoy good physical and mental health. In fact, married men enjoy a wage premium compared to their single peers that may exceed 10 percent. At the collective level, the retreat from marriage has played a noteworthy role in fueling the growth in family income inequality and child poverty that has beset the nation since the 1970s. For all these reasons, then, the institution of marriage has been an important pillar of the American Dream, and the erosion of marriage in Middle America is one reason the dream is increasingly out of reach for men, women, and children from moderately-educated homes.

It’s obvious empirically that adults and children in married-couple families, on average, are doing better on many measures than those not in such families. The logical problem is when people conclude from this pattern that the obvious response is to “strengthen marriage and family life.” But, why not try to reduce that disparity instead?

This is the logical equivalent of the Republican mantra that “We don’t have a revenue problem in Washington; we have a spending problem.” That’s only true if you’re doing one-handed math. And the same holds for marriage.

Yes, there is less marriage, and many people are less well off without it. Does that mean we have a “marriage” problem, or a family inequality problem? Is there any other way to help people develop high quality relationships with their parents, complete more education, get better jobs, accrue financial assets and maintain good physical and mental health?

In the categorical math of inequality, you can try (with little chance of success in this case) to reduce the number of people in the disadvantaged category (non-married families), or you can try to reduce the size of the disparity between the two categories.

*I’m not sure, but I think a “policy brief” is a blog post about policy matters, produced on the PDF letterhead of a foundation. Not that there’s anything wrong with that. As far as I can tell, this one is a non-peer-reviewed essay which handles sourcing like this: “the findings detailed in this policy brief come from a new report by Wilcox, When Marriage Disappears: The New Middle America.” As I’ve pointed out (here andhere), Wilcox’s reports at the National Marriage Project are also non-peer-reviewed essays with a lot of substantially misleading and erroneous content.

11 Comments

Filed under Me @ work

Poverty is not just for single mothers

CORRECTION: The original version of this post had a major error – the second trend was coded wrong, showing percent married instead of percent single! I’ve correct it, and apologize for the error.

Earlier this month there was a funny segment on Fox and Friends where they took seriously a fake social media campaign, supposedly led by feminists, to end Father’s Day. “More of this nasty feminist rhetoric,” and The Princeton Mom (Susan Patton). “They’re not just interested in ending Father’s Day, they’re interested in ending men.”

Then Tucker Carlson jumped in to ask, “Why is it good for women? I mean, there’s a reason there are more women living in poverty now than at any time in my lifetime, it’s because there are fewer married women. I mean, when you crush men, you hurt women.”

His comment is doubly twisted. First, it supposes that the historical rise of single mothers is the result of feminists crushing men (thanks, Hanna Rosin). The decline in marriage is related to the falling economic fortunes of men, especially relative to women, but I don’t think you can lay much of that at the feet of feminists.

Second, are there really more women in poverty now because of single motherhood? Yes and no. Here are three trends (all based on civilian non-institutionalized women ages 18+, from the Current Population Survey):

1. Poverty is rising among all women (but still hasn’t reached 1990s levels)

Although the proportion of children born to women who aren’t married has increased – doubling in the past three decades – that doesn’t tell the whole poverty story. Because women’s employment opportunities increased during that time (and fertility rates fell), women’s poverty rates are lower now than they were in the 1980s and 1990s peaks.

Zooming in on the period from the low poverty point in 2001, you can see that the recent increase in poverty has affected single and married women, and the proportional increase is actually twice as great for married women (more than a one-third increase).

womenspoverty.xlsx

2. The percentage of poor women who are not married has risen (corrected trend)

Nevertheless, the percentage of poor women who are not married has risen. During the 2000s recession, the percentage of poor women who are married hit an all-time low of 30%. Over the last four decades, as marriage rates have fallen, women’s poverty has become more concentrated among unmarried women. Single women have much higher poverty rates than married women, and the vast majority of poor women are not married. However, in the last 15 years, as single motherhood has become more common, the percentage of poor women who are not married has been basically flat.

fatra-pov2

3. The percentage of poor people who are women is falling

Diane Pearce wrote, “The Feminization of Poverty: Women, Work, and Welfare” in 1978, as single motherhood was increasing and women’s wages relative to men’s appeared flat. As the proportion of poor adults that were women approached two-thirds, this shocking term caught on. However, since then — as women’s earnings increased and wages fell for many men — that proportion has fallen to 58%.

womenspoverty.xlsx

These facts are not the whole story of poverty in the U.S. But they should be enough to stop the politically convenient simplification repeated by the Tucker Carlsons of our time. The problem of poverty is not a problem of women’s failure to marry.

Cross-posted on Families As They Really Are

4 Comments

Filed under Uncategorized

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:

chetty-in-wilcox

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:

841101_10201299565666336_1527199648_o

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:

age-wage1

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:

age-wage2

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.

age-wage3

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.

13 Comments

Filed under Research reports