Tag Archives: single mothers

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.

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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:

immobilitymap

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.

pb-immob-reg

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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To Prevent Poverty, Reduce the Penalty for Single-Motherhood

I wrote an essay for Spotlight on Poverty and Opportunity. It originally appeared on their site, here, and I reproduce it below with their permission. 

The increase in unmarried parenthood in the U.S. remains a genuine concern for children’s well-being and for intergenerational mobility. Unmarried parents in the U.S. are much more likely to be poor than their married counterparts. Single parents juggling many competing priorities work more, earn less, and have less time or fewer resources to devote to advancing their own education. But does this ongoing increase in unmarried parenthood consign the country to continuously increasing inequality? Not necessarily.

The problem of poor children in single-parent families is a problem of poverty much more than it is one of family structure. A generation of research shows that the primary source of trouble in these families is low income. Too often these families lack the material resources necessary to provide a secure and stable environment for their children. Additional challenges, such as low parental involvement or supervision, largely result from time poverty—another consequence of low income for the parents in poor families.

Still, there is no denying that single-parent families have high poverty rates. Wouldn’t policies aimed at altering the long-term trend in family structure be a sure-fire way to reduce poverty?

Under this assumption, the federal government – working with some zealous states – has spent hundreds of millions of dollars over nearly a decade attempting to promote marriage among the poor. So sure were the proponents of this policy that it would solve the problem that they paid for it with money from the federal welfare program. The result was no measureable increase in marriage rates – or in, more importantly, well-being – among the targeted groups. Further, the 1996 welfare reform, which shortened welfare eligibility periods and increased other program requirements, was specifically intended to discourage single parenthood and encourage marriage. Although it increased employment among single mothers with limited education, it did nothing to change the direction of the family structure trend.

This experience in failed policies and decades of cultural exhortation and shaming intended to prevent single parenting, combined with evidence that poverty itself is harmful to the future well-being of children, should be enough to show that reducing poverty, rather than changing family structure, is the more rational approach to improving children’s lives.

The persistent poverty gap between single-parent and married-parent families illustrates just how pervasive the problem of poverty is. Of all the challenges single-parent families face, poverty need not be one of them. A recent paper in the journal Demography, by David Brady and Rebekah Burroway, analyzed the relative poverty of single mothers versus the total population, after accounting for taxes and government transfers, in 18 countries. Not only does the U.S. have the highest poverty rate for single mothers among these countries – 41 percent – but we also have a very large difference in poverty rates between single-mother families and the population overall (see figure below). In countries such as Sweden, Norway, Denmark, and even Italy, single mothers are hardly more likely to be poor than everyone else. In the U.S. the gap is 24 percentage points, a huge penalty for single motherhood.

Based on their analysis, Brady and Burroway argue that universal anti-poverty programs, rather than those targeted directly at single mothers, appear to hold the most promise. In the context of the American political climate, that provides an important insight. As economic inequality has risen on our political and policy radar, the social stigma for single mothers remains strong. Policy directed toward supporting (seen by opponents as “rewarding”) single-mother families seems unlikely to gain favor among today’s political leaders. On the other hand, universalist policies such as living-wage laws, publicly supported universal preschool education, and universal health care, may fare better.

Regardless, an approach that favors reducing poverty broadly – with the side-effect of trimming the single-mother penalty – likely would be far more effective in improving child well-being than efforts to counsel or coerce low-income people into marriage.

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Diverging responses to family inequality

I have written up my comment from Penn State Symposium on Family Issues. It was prepared in response to a presentation by Sarah McLanahan and Wade Jacobsen titled, “Diverging Destinies Revisited.” Their paper is a followup to McLanahan’s 2003 Population Association of American presidential address. (I wrote a comment on the symposium itself here.) When they finish the volume it will go behind an expensive paywall, so I put the draft paper here in PDF.

Here is the abstract:

Single parenthood, resulting from nonmarital births and divorce, is increasingly becoming associated with lower levels of education for women. Cross-sectional comparisons show that children of married parents are less likely to suffer material deprivation. To reduce hardships for children, therefore, some analysts advocate policies that would increase marriage. I argue that alternative approaches offer more chance of success: increasing education levels and reducing the penalty for single parenthood. There is ample evidence to support both approaches. Education levels are increasing, and are associated with lower levels of child hardship net of family structure. And comparative research shows the negative economic consequences of single parenthood are ameliorable through state policy. In contrast, the hundreds of millions of dollars spent promoting marriage, and the reform of national welfare policy intended to compel poor mothers to marry, have produced no discernible effects on marriage rates or child wellbeing.

Or, even shorter than the abstract, this figure, which shows the logical alternatives for addressing the issue of family structure and poverty for children.

psufig

 

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Is the rising tide of falling crime driven by fatherlessness?

Kay Hymowitz, who sometimes works out of a PO Box rented by Brad Wilcox, writes in the LA Times (excerpting heavily):

As far back as the 1970s, family researchers began noticing that, although both girls and boys showed distress when their parents split up, they had different ways of showing it. …  Boys … “externalized” or “acted out”: They became more impulsive, aggressive and “antisocial.”… Boys from broken homes were more likely than their peers to get suspended and arrested. … And justice experts have long known that juvenile facilities and adult jails overflow with sons from broken families. Liberals often assume that these kinds of social problems result from our stingy support system for single mothers and their children. But the link between criminality and fatherlessness holds even in countries with lavish social welfare systems. … If the trends of the last 40 years continue — and there’s little reason to think that they won’t — the percentage of boys growing up with single mothers will keep growing. No one knows how to stem that tide.

Ah, the link between criminality and fatherlessness again. So ingrained is the assumption that crime rates always go up that conservatives making this argument do not even see the need to account for the incredible, world-historical drop in violence that has accompanied the collapse of the nuclear family. I know Kay Hymowitz knows this, because we’ve argued about it before. But if her editors and readers don’t, why should she make a big deal out of it?

In this graph I show the scales down to zero so you can see the proportional change in each trend: father-not-present boys ages 10-14 and male juvenile violent-crime arrest rates.

fatherless-juvenile-arrests

I’m not arguing about whether boys living without fathers are more likely to commit crimes. I’m just saying that this is very unlikely to be the major cause of male juvenile violent crime if the trends can move so drastically in opposite directions at the same time. These aren’t little fluctuations. Even if you leave out the late-80s-early-90s spike in crime, arrests fell about 40% from 1980 to 2010 while father-absent boys increased almost 50%.

If you are going to argue for a strong association — which Hymowitz does — and use words like “tide,” you should at least acknowledge that the problem you are trumpeting is getting better while the cause you are bemoaning is getting worse.

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Two notes on the poverty report

Two quick notes on the new Census poverty report, which mostly showed poverty and income levels flat from the previous year.

Note 1. The share of poor people who live in single-mother families has declined. It’s now 34%, down from a peak of 39% in 1996. That is, 34% of poor people live in single-mother families. It’s been between 34% and 39% for 27 years. I point that out because it’s important to realize the rise of single mothers (see Note #2 below) is not driving poverty rates. I don’t know if it’s significant, but the poverty rate for single-mother families fell from 34.2% to 33.9%, while the overall rate was steady at 15.0%. Here’s the first chart:

povertybyhouseholdtypeNote 2: There was an unusual blip down in the percentage of all (civilian non-institutionalized) people living in single-mother families. And a continued increase in people living in no family (which includes unmarried cohabitors if they have no kids). In the absence of a rise in marriage, I’m guessing this decline in the single-mother family population (a drop of half a million) is related to the recession-driven decline in fertility.

singlemomunrelated

Both charts are from Current Population Survey data, as reported in the hispov2 table (link to spreadsheet file).

 

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More married mothers earn more than their husbands

For this Washington Post article by Brigid Schulte, I did some calculations that allowed her to add, “In a trend accelerated by the recent recession” to the first sentence. When you line up the numbers this way — percentage of married mothers with children present who have higher incomes their husbands — there was a steep acceleration:

pew-post-trendSource: My calculation from Census and American Community Survey data from IPUMS.

My explanation for this was:

“The decade of the 2000s witnessed the most rapid change in the percentage of married mothers earning more than their husbands of any decade since 1960,” said Philip Cohen, a University of Maryland sociologist who studies gender and family trends. “This reflects the larger job losses experienced by men at the beginning of the Great Recession. Also, some women decided to work more hours or seek better jobs in response to their husbands’ job loss, potential loss or declining wages.”

The trend was reported by Pew Research in this report, titled “Breadwinner Moms,” which wrote:

A record 40% of all households with children under the age of 18 include mothers who are either the sole or primary source of income for the family, according to a new Pew Research Center analysis of data from the U.S. Census Bureau. The share was just 11% in 1960.

I just did the married mothers earning more, and added the data from the years between 2000 and 2011, to show the recession-period acceleration of the higher-earning mothers. Pew added polling numbers about attitudes toward women’s income, and Schulte added exemplary interviews.

Breadwinning

A wife who earns $1 more than her husband for one year is not the “breadwinner” of the family. That’s not what made “traditional” men the breadwinners of their families — that image is of a long-term pattern in which the husband/father earns all or almost all of the money, which implies a more entrenched economic domination.

However, she can be the “primary breadwinner,” a post-1970s concept acknowledging the rise of secondary breadwinners (usually women) in families. Here is the Google ngrams trend showing appearances of “primary breadwinner” as a fraction of all uses of “breadwinner” since 1920 (click to enlarge):

breadwinner-ngrams

I have previously complained about lumping single mothers together with higher-earning wives to construct an image of “female breadwinners.” That’s partly because the $1-more-for-one-year problem, and partly that I object to using the single-mother trend to inflate descriptions of women’s advancement.

Anyway, it’s hard to capture the trends without overdoing it, but Brigid Schulte and the Pew authors (Wendy Wang, Kim Parker and Paul Taylor) did a nice job.

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The Connection Between Unemployment and Unmarried Parents

Originally posted at TheAtlantic.com.

The states with more single men without jobs have higher rates of nonmarital births.

cohen_baby_post.jpg

“Le berceau” by Berthe Morisot

The Census Bureau has a new report on nonmarital births. Based on the American Community Survey—the largest survey of its kind, and the only one big enough to track all states—the report shows that 35.7 percent of births in 2011 were to unmarried mothers.

Beneath the headline number, two patterns in the data will receive a lot of attention: education and race/ethnicity. I have a brief comment on both patterns.

Education
The education patterns show a very steep dropoff in nonmarital births as women’s education increases. From 57 percent unmarried among those who didn’t finish high school to just nine percent among those who have graduated college.

cohen_unmarrieded.png

Given the hardships faced by single mothers (especially in the United States), it looks like women with more education are making the more rational decision to avoid childbearing when they’re not married. And I don’t doubt that’s partly the explanation. But we need to think about marriage, education and childbearing as linked events that unfold over time. The average high-school dropout mother was 26, while the average college-graduate mother was 33. Delaying childbearing and continuing education are decisions that are made together, based on the opportunities people have. And completing more education increases both thelikelihood of marriage and the earning potential of one’s spouse.

So I think you could tell the story like this: Women with better educational opportunities delay childbearing, which increases their marriage prospects, and makes it more likely they will be married and financially better off when they have children in their 30s.

Race/ethnicity
The differences in nonmarital birth rates between race/ethnic groups in the U.S. are shocking, from about two-thirds for black and American Indian women to 29 percent for whites and 11 percent for Asians.

cohen_unmarriedrace.png

This pattern is related to the education trend, naturally, but that’s not the whole story. One aspect of the story is race/ethnic geography of opportunity in this country. I’ve written before about the shortage of employed men available for women to marry, a particular expression of racial disparity first popularized by sociologist William Julius Wilson a quarter century ago.

Using the new numbers on nonmarital birth rates for each state from the Census report, I compared them to the male non-employment rate—specifically, the percentage of unmarried men ages 22-50 that are not currently employed. Here’s the relationship:

cohen_unmarriedunemployed.png

The states with more single men out of work have higher rates of nonmarital births. Single mother, meet jobless man.

My conclusion from these patterns is that unmarried parenthood is primarily a symptom of lack of opportunity, especially for education and employment. Surely that’s not the whole story. Maybe we should be persuading people to marry younger or shaming them into avoiding parenthood. But I think those approaches increase stigma more than they change behavior or improve wellbeing—Pew surveys show that 77 percent of people already say raising a family is easier if you’re married and only 12 percent of single people say they don’t want to marry. So who needs convincing? Meanwhile, if we addressed the problems of education and employment, is there any doubt family security and stability would improve, and with it the wellbeing of children and their parents?

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How many prisoners grew up with both parents?

A couple clarifications.

In her commentary on my commentary, Kay Hymowitz offered some evidence that single parenthood causes crime (or at least incarceration). She wrote:

Regardless, there is no disagreement that the majority, and perhaps the large majority, of inmates grew up in fatherless homes. It’s difficult to get up-to-date data since the Bureau of Justice doesn’t reliably track the family background of inmates. (They also put intact and step families in the same “two parent” category, though at least one study has found the later to be predictive of juvenile incarceration.) The 1987 “Survey of Youth in Custody” found that 70% did not grow up with both parents. Another 1994 study of Wisconsin juveniles was even more stark: only 13% grew up with their married parents. Here’s the conclusion of Cynthia Harper and Sara McLanahan, the doyenne of researchers about single parenthood: “[C]ontrolling for income and all other factors, youths in father-absent families (mother only, mother-stepfather, and relatives/other) still had significantly higher odds of incarceration than those from mother-father families.”

You can follow the links to see her sources, except the Harper and McLanahan link, which is dead. Shockingly, Brad Wilcox also provided a dead link to the same quote. I was curious to see it because I would be surprised if any social scientist used the words “controlling for … all other factors.”

Anyway, for some reason Hymowitz missed the large, national study the Bureau of Justice Statistics does on inmates, which includes family background information, repeated since 1991. If you look at their report on the 2004 survey (which focused on drug issues), and make a few simple calculations, you can figure out that 55% of state and federal prisoners did not “live most of the time while growing up” with both parents. They don’t count “fatherless homes” separately, but even assuming most of the those 55% were living with their mothers, “large majority” is a stretch.

But what does that tell us anyway? The survey also shows these folks have experienced high rates of poverty, homelessness, substance abuse, physical abuse, and family members’ incarceration. If only 55% of this population is from non-married-parents homes, that’s not a very strong case for an independent effect of family structure.

As importantly, the 2004 survey shows that 74% of state and federal inmates had previously been sentenced to prison or probation. By Hymowitz’s logic, maybe the biggest cause of crime is incarceration. This is not crazy at all, of course, it’s just not the point she wants to make.

People who think incarceration reduces crime often don’t appreciate how many people get out of prison — like Elizabeth Marquardt, who described the policy as, “lock up a lot more of those fatherless boys and throw away the key.” But BJS statistics show that 44% of inmates were released in 2010 (roughly 700,000 out, 700,000 in).

In case you have lost the thread, I think Hymowitz and the others that are so exercised by my little post are trying to protect this narrative: Marriage decline substantially caused the increase in crime in the 1980s and 1990s, and then continued to apply this upward pressure while incarceration was so effective that crime rates fell anyway. I don’t buy it on either end.

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Conservatives doubling down on single mothers and crime

The reaction from the right-wing family folks to my post about single mothers and crime.

In a post that appeared here and on TheAtlantic.com — but got extra attention when the figure appeared on Jezebel, Mother Jones, Slate, Andrew Sullivan’s Dish, Family Scholars, and Alas! — my point was that conservatives had been quick to attribute the rise in crime in the 1980s to the “breakdown of the family” and single parents. But then they didn’t revise their stories when crime dropped drastically without a reversal of the family structure trends. I thought single mothers deserved an apology.

They’ll have to keep waiting, I guess.

Within a few hours on Tuesday, we heard from some of the leading lights on the issue. Their conclusion was that if I don’t want more marriage then I must want more incarceration.

Maggie (let’s “drive a wedge between blacks and gays!”) Gallagher, on Family Scholars:

The ending of the violent crime wave was a great policy achievement. It seems however to involve massively incarcerating millions of young men we have not succeeded in civilizing. There is never only one way to skin a cat. But I’m not sure our souls should rest too comfortably on the solution we found.

Ross (Charles Murray is “brilliant!”) Douthat tweeted:

Fortunately, family breakdown doesn’t create any problems that mass incarceration of young men can’t solve.

(One good turn deserves another, I guess: Murray himself tweeted back: “Lovely. Menckenesque. Maybe even Wildeian (if Oscar had been a social scientist).”

Soon Elizabeth Marquardt, who is always committed to “excellent arguments and accurate data,” chimed in:

Well for pete’s sake, one thing we now do is lock up a lot more of those fatherless boys and throw away the key. Which means less crime.

Then Brad (recession is good news for marriage!) Wilcox produced a 10-year old graph of incarceration rates under the title, “Who Needs An Intact Family? Jail Will Do Just Fine,” suggesting that we might be “forced to choose between a stronger marriage culture and mass incarceration.”

What followed on all these blogs was a debate about all the interesting possible explanations for the decline of crime in America. Lost in all of it was that none of the old “family values” folks backed off the original story that crime rose in the first place because of family “breakdown.” Just to clarify: It is one thing to say that children who grow up with one parent present are more likely to commit violent crime. As a statistical association that is true, though the causal story is muddied by important confounds. But it is another — unjustified — thing to say that the crime wave of the 1980s and 1990s was substantially driven by the rise of single parents, which was a common claim, as I illustrated in the post.

Ballpark-acts of violence

(Here is the part where I spend more time thinking about the actual evidence than the pundits I’m complaining about. What follows isn’t scientific analysis: this is data ballparking and rumination.)

As Stephen Demuth and Susan Brown wrote in a 2004 article, identifying the causal effect of family structure itself on whether kids become violent is very difficult. You need to consider parental monitoring and supervision, the quality of the relationship between parents and children, the level of conflict in the home, as well as poverty, education, family transitions, housing, neighborhood factors, and so on.

In that article, however, they offered some numbers we can look at to ballpark the relationship between single-parents and violent crime.

Using the National Adolescent Survey of Adolescent Health, they added up the self-reported violent acts of students in grades 7 to 12 in 1995. The kids were asked how many times in the last year they (1) “hurt someone badly enough to need bandages or care from a doctor or nurse,” (2) “use or threaten to use a weapon to get something from someone,” and (3) “take part in a fight where a group of your friends is against another group.” They didn’t ask the specific number of times, but rather asked kids to report “0 (never), 1 (once or twice), 2 (three or four times), or 3 (five or more times).”

That’s enough to get a sense of what was going on in 1995, when the survey was done. If you take the scores on the three items added together, and take the mean of that sum for kids in different family structures, you can ballpark how many of these acts of violence kids in each family type committed. The idea is just to get a sense of the magnitude of the family structure difference and the relative contribution of kids in each group.

I’ve turned the scale into the average number of acts to make the figure below. For example, the mean for children living with single mothers was 1.2 on the scale. I gave them 1.5 (for “once or twice”), and then, for the additional 0.2, added 0.2*2 (with 2 representing the difference between 1.5 and 3.5 for “three or four times”). That’s a total of 1.9 “ballpark-acts”:

To show the relative contribution of the different groups of kids, I set the width of the bars to their share of the sample, in which 26% were living with either a single mother or single father, which is about right for that period. You can see from the estimate, for example, that kids living with single mothers admitted to 0.7 more ballpark-acts of violence per year, and those with single fathers admitted to 1.1 more.

With the amount of violence committed by each kid, and the relative size of the groups, it’s easy to calculate that those 26% of kids living with single parents committed 35% of the violent acts — more than their share, but not most of the total.

Remember, there are no controls in that analysis – it’s just compositional. There are a host of real reasons children with single parents commit more violence. This is just to see how big is the difference we are trying to understand.

Still, I have no trouble believing the decline of married-couple living arrangements contributed to the rise in violent crime rates since the 1960s, especially if you set aside the huge spike in violence from the mid-1980s to the mid-1990s. Single-parent families have lots of challenges and shortages — mostly of money and time — that make it harder on average to keep their kids in line. (And, of course, one of the causes of single-parenthood is the rise of incarceration.) In the absence of sufficient big-government nanny-state infrastructure to help them get by, it’s not surprising that the problems they experience include a higher risk of violence.

But I see nothing to justify the apocalyptic end-of-civilization associations that were commonly served up then — and which apparently are still palatable to many of today’s family conservatives.

Aside: scale

In that Demuth and Brown article, they have multivariate models that allow us to compare effect sizes on violence. They show, for example, that having a parent who graduated college is associated with odds of committing violent acts 3.5-times as much as living with a single mother, once other factors are controlled (-.42 versus .12). It’s always easier to say there is an association than to ascertain how important it is relative to other things — and especially for how it contributes to a trend over time.

Consider some other findings in this literature that allow us to compare the scale of effects:

  • A study of religion and family structure effects on delinquency (an amalgamated concept) reported that living with a single parent increased the odds of delinquency about as much as 6 years of education reduced the odds.
  • A study from one school district found that, for boys (but not girls), having a single mother increased the odds of being referred for delinquency by 13%, compared with 9% for being poor.
  • Many studies — like this, this, and this, find no effect of family structure on delinquency once aspects of the parent-child relationship are controlled.

A common finding is that the level of attachment children feel with their mothers swamps the family structure effect, as was found in this study, in which there was no effect of family structure on serious or non-serious delinquency. Some, like this one, find that living with a single mother has a significant effect on delinquency, but it is smaller than the effect of maternal closeness.

Given the importance of factors such as poverty level, parents’ education, and peer and network effects – as well as family relationships – the more important and useful questions have to do with how we can improve the environment and outcomes for children with single parents (and for their parents). The causal impact of family structure itself is less pressing.

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