Category Archives: Research reports

Does happy marriage cause happy marriage?

I don’t know how I missed this one, from two Valentine’s Days ago…

For an introductory methods course discussion on: when does something cause something else. Question: Are happier couples happier? Some writers think so:

I can see the study design now: a randomized group of couples were given coupons for date nights, and some time later were compared with a control group without the coupons. Or not. Cosmo summarized:

For their study, researchers from the University of Virginia’s National Marriage Project surveyed 1,600 couples and asked them about everything from relationship satisfaction to sex. They discovered that couples who spend at least one night a week alone together say they’re more committed to their relationship than those who don’t hang out together as much.

(The report, by Brad Wilcox and Jeffery Dew and posted online at the National Marriage Project, is here.)

BREAKING: Researchers discover murder less common among happy couples.

BREAKING: Researchers discover murder less common among happy couples.

Is that it? A simple association between being together and being happy? Almost. First, they say (there are no tables) that they “control for factors such as income, age, education, race, and ethnicity.” Such as? Anyway.

Second, they also claim to have analyzed historical data from the National Survey of Families and Households (1987-1994). They write:

Because we had data from spouses at two time points in the NSFH, we were also able to examine the direction of effects—to determine whether or not couple time reported during the first wave of the survey was associated with marital quality at the second wave. Here, the more couple time individuals reported at the time of the first survey, the more likely they were to be very happy in their marriage at the second survey, five years later. Although the NSFH evidence does not provide us with definitive proof that couple time causes increases in marital quality, the longitudinal character of the data suggests that the relationship may indeed be causal.

So, Wilcox and Dew point #1: If something happened before something else, “the relationship may indeed be causal.” They go on:

It is certainly intuitively true that greater satisfaction with one’s partner should also lead to more time spent in positive, shared activities. Nevertheless, it would be absurd to assume that two partners who intentionally set out to increase positive couple time spent together would typically not benefit from such time with increases in connection and happiness.

So, point #2 is, We already knew the answer before we did the research, because it’s flipping obvious, so who cares about this analysis — it’s almost Valentine’s Day!

There are ways to actually get at “the direction of effects,” like the randomized trial I suggested, or even using longitudinal data and assessing changes in happiness, or controlling for happiness at time 1. Not this.

Anyway, can we think of examples of things that occur before other things without causing them? Here are a few off the top of my head:

  • One sibling dies of a genetic disease now, and then the other one dies from the same disease later: Shocking new evidence that genetics works sideways!
  • Someone has tennis elbow now, and is playing sports later: The surprising way that getting hurt makes you athletic!
  • People who spend more money now have more money later: The more you spend, the more you save!
  • And of course, people who have a lot of sex now are good looking later: Sex up your looks!

I’m open to suggestions for better examples.

Note: I guess in some social science neighborhoods it’s common to analyze the effects of extremely similar things on each other, like pleasure being associated with happiness, or strong left arms being associated with strong right legs. Dew and Wilcox actually published a peer-reviewed article, using this survey, on the association between small acts of kindness in marriage and marital satisfaction. And the result? Couples who are nice to each other are happier.

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Divorce drop and rebound: paper in the news

My paper on divorce and the recession has been accepted by the journal Population Research and Policy Review, and Emily Alpert Reyes wrote it up for the L.A. Times today. The paper is online in the Maryland Population Research Center working paper collection.

latimes-divorce

Married couples promise to stick together for better or worse. But as the economy started to rebound, so did the divorce rate.

Divorces plunged when the recession struck and slowly started to rise as the recovery began, according to a study to be published in Population Research and Policy Review.

From 2009 to 2011, about 150,000 fewer divorces occurred than would otherwise have been expected, University of Maryland sociologist Philip N. Cohen estimated. Across the country, the divorce rate among married women dropped from 2.09% to 1.95% from 2008 to 2009, then crept back up to 1.98% in both 2010 and 2011.

To reach the figure of 150,000 fewer divorces, I estimated a model of divorce odds based on 2008 data (the first year the American Community Survey asked about divorce events). Based on age, education, marital duration, number of times married, race/ethnicity and nativity, I predicted how many divorces there would have been in the subsequent years if only the population composition changed. Then I compared that predicted trend with what the survey actually observed. This comparison showed about 150,000 fewer than expected over the years 2009-2011:

divorce-fig2

Notice that the divorce rate was expected to decline based only on changes in the population, such as increasing education and age. That means you can’t simply attribute any drop in divorce to the recession — the question is whether the pace of decline changed.

Further, the interpretation that this pattern was driven by the recession is tempered by my analysis of state variations, which showed that states’ unemployment rates were not statistically associated with the odds of divorce when individual factors were controlled. Foreclosure rates were associated with higher divorce rates, but this didn’t hold up with state fixed effects.

So I’m cautious about the attributing the trend to the recession. Unfortunately, this all happened after only one year of ACS divorce data collection, which introduced a totally different method of measuring divorce rates, which is basically not comparable to the divorce statistics compiled by the National Center for Health Statistics from state-reported divorce decrees.

Finally, in a supplemental analysis, I tested whether unemployment and foreclosures were associated with divorce odds differently according to education level. This showed unemployment increasing the education gap in divorce, and foreclosures decreasing it:

Microsoft Word - Divorce PRPR-revision-revision.docx

Because I didn’t have data on the individuals’ unemployment or foreclosure experience, I didn’t read too much into it, but left it in the paper to spur further research.

Aside: This took me a few years.

It started when I felt compelled to debunk Brad Wilcox’s fatuous and deliberately misleading interpretation of divorce trends — silver lining! — at the start of the recession, which he followed up with an even worse piece of conservative-foundation bait. Unburdened by the desire to know the facts, and the burdens of peer review, he wrote in 2009:

judging by divorce trends, many couples appear to be developing a new appreciation for the economic and social support that marriage can provide in tough times. Thus, one piece of good news emerging from the last two years is that marital stability is up.

That was my introduction to his unique brand of incompetence (he was wrong) and dishonesty (note use of “Thus,” to imply a causal connection where none has been demonstrated), which revealed itself most egregiously during the Regenerus affair (the full catalog is under this tag). Still, people publish his un-reviewed nonsense, and the American Enterprise Institute has named him a visiting scholar. If they know this record, they are unscrupulous; if they don’t, they are oblivious. I keep mentioning it to help differentiate those two mechanisms.

Check the divorce tag and the recession tag for the work developing all this.

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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:

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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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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Marriage promotion: That’s some fine print

In a (paywalled) article in the journal Family Relations, Alan Hawkins, Paul Amato, and Andrea Kinghorn, attempt to show that $600 million in marriage promotion money (taken from the welfare program!) has had beneficial effects at the population level. A couple quick comments on the article (see also previous posts on marriage promotion).

After a literature review that is a model of selective and skewed reading of previous research (worth reading just for that), they use state marriage promotion funding levels* in a year- and state-fixed effects model to predict the percentage of the population that is married, divorced, children living with two parents, one parent, nonmarital births, poverty and near-poverty, each in separate models with no control variables, for the years 2000-2010 using the American Community Survey.

To find beneficial effects — no easy task, apparently — they first arbitrarily divided the years into two periods. Here is the rationale for that:

We hypothesized that any HMI [Healthy Marriage Initiative] effects were weaker (or nonexistent) early in the decade (when funding levels were uniformly low) and stronger in the second half of the decade (when funding levels were at their peak).

This doesn’t make sense to me. If funding levels were low and there was no effect in the early period, and then funding levels rose and effects emerged in the later period, then the model for all years should show that funding had an effect. Correct me if I’m wrong, but I don’t think this passes the smell test.

Then they report their beneficial effects, which are significant if you allow them p<.10 as a cutoff, which is kosher under house rules because they had directional hypotheses.

However, then they admit their effects are only significant because they included Washington, DC. That city had per capita funding levels about 9-times the mean (“about $22″ versus “about $2.50″), and had an improving family well-being profile during the period (how much of an outlier DC is on the dependent variables they didn’t discuss, and I don’t have time to show it now, but I reckon it’s pretty extreme, too). To deal with this extreme outlier, they first cut the independent variable in half for DC, bringing it down to about 4.4-times the mean and a third higher then the next most-extreme state, Oklahoma (itself pretty extreme). That change alone cut the number of significant effects down from six to three.

coupdegrace

Then, in the tragic coup de grâce of their own paper, they remove DC from the analysis, and nothing is left. They don’t quite see it that way, however:

But with the District of Columbia excluded from the data (right panel of Table 3), all of the results were reduced to nonsignificance. Once again, most of the regression coefficients in this final analysis were comparable to those in Table 2 (right panel) in direction and magnitude, but they were rendered nonsignificant by a further increase in the size of the standard errors.

Really. What is “comparable in direction and magnitude” mean, exactly? I give you (for free!) the two tables. First, the full model:

tab2

Then, the models with DC rescaled or removed (they’re talking about the comparison between the right-hand panel in both tables):

tab3

Some of the coefficients actually grew in the direction they want with DC gone. But two moved drastically away from the direction of their preferred outcome: the two-parent coefficient is 44% smaller, the poor/near-poor coefficient fell 78%.

Some outlier! As they helpfully explain, “The lack of significance can be explained by the larger standard errors.” In the first adjustment, rescaling DC, all the standard errors at least doubled. And all of the standard errors are at least three-times larger with DC gone. I’m not a medical doctor, but I think it’s fair to say that when removing one case triples your standard errors, your regression model is not feeling well.

One other comment on DC. Any outlier that extreme is a serious problem for regression analysis, obviously. But there is a substantive issue here as well. They feebly attempt to turn the DC results in their favor, by talking about is unique conditions. But what they don’t do is consider the implications of DC’s unique change over this time for their analysis. And that’s what matters in a year- and state-fixed effects model. How did DC change independently of marriage promotion funds? Most importantly, 8% of the population during 2006-2010 was new to town each year. That’s four-times the national average of in-migration in that period. This churning is of course a problem for their analysis, which is trying to measure cumulative effects of program spending in that place — hard to do when so many people moved there after the spending occurred. But it’s also not random churning: the DC population went from 57% Black to 52% Black in just five years. DC is changing, and it’s not because of marriage promotion programs.

Finally, their own attempt at a self-serving conclusion is the most damning:

Despite the limitations, the current study is the most extensive and rigorous investigation to date of the implications of government-supported HMIs for family change at the population level.

Ouch. Oh well. Anyway, please keep giving the programs money, and us money for studying them**:

In sum, the evidence from a variety of studies with different approaches targeting different populations suggests a potential for positive demographic change resulting from funding of [Marriage and Relationship Education] programs, but considerable uncertainty still remains. Given this uncertainty, more research is needed to determine whether these programs are accomplishing their goals and worthy of continued support.

*The link to their data source is broken. They say they got other data by calling around.

**The lead author, Alan Hawkins, has received about $120,000 in funding from various marriage promotion sources.

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Brad Wilcox tries to save saving marriage for the marriage movement

Bradford Wilcox and the right-wing family policy community have found a way to make millions of dollars, taking from the welfare budget, to do battle on behalf of the institution of marriage. The premise of their boondoggle is twofold: that increasing the number of marriages will reduce poverty, and that the federal government can accomplish that if it just spends enough of poor single parents’ former money. They’ve gotten the project written into the welfare law. And they have the over-assetted conservative foundations convinced that this is a useful waste of their millions. So they are understandably defensive when social scientists point out that it’s a scam.

 In this guest post, Ohio State University sociologist Kristi Williams responds to Wilcox’s latest commentary.

hands-huckster-cross

By Kristi Williams

In a recent article for the American Enterprise Institute and an op-ed in the Deseret News, W. Bradford Wilcox, director of the National Marriage Project critiques my recent briefing report for the Council on Contemporary Families. My report, “Promoting Marriage among Single Mothers: An Ineffective Weapon in the War on Poverty” discusses the most rigorous experimental evidence available about the effectiveness of federally-funded relationship skills training programs to promote marriage among unmarried parents. The conclusion: They have failed spectacularly.

Wilcox points to one of the programs in Oklahoma as a success. He writes, “Indeed, the Oklahoma Marriage Initiative has succeeded in helping poor, unmarried couples with children enjoy more stable relationships.” Really? After 36 months, participation in the Oklahoma program failed to improve: (a) couples’ relationship quality or the probability of being married (b) the quality of the co-parenting relationship, (c) father involvement and parenting behavior or, most importantly, (c) child poverty and socioemotional development. From the “Building Strong Families” program report:

mathematica null effects

More concerning is the fact that across the 8 program sites included in the study, participation was associated with modest negative effects on father involvement, father financial support of children, and the likelihood that couple would be living together or romantically involved (although they were no more likely to be married). Although children whose parents were in the control group had slightly higher average scores (1.41) on an index of behavior problems and socioemotional development than children of participating parents (1.38), these benefits were only seen in the 4 sites that included home visits and parenting training. Therefore, the report concludes that the modest effect on behavior problems “is more likely due to the home visiting services offered in these 4 BSF sites than it is to the relationship skills education services that were offered in all BSF sites.”

mathematica negative effects

Why does Wilcox call the Oklahoma program a success? There is only one thing he can possibly be talking about: At the 3-year follow up, slightly more children whose parents participated had lived with both parents since birth (49% compared to 41% in the control group).  But what did this get the children? Not lower poverty, not fewer behavior problems and not more father involvement.  This underscores the point of my briefing report: Focusing on keeping low income single parents together at all costs is unlikely to solve the biggest problems facing single mothers and their children.

The only explanation for Wilcox pointing to Oklahoma as a success is that what he really cares about is keeping couples together and promoting marriage at all costs—regardless of whether doing so reduces poverty and helps children and single mothers live better lives.  It’s one thing if you want to preach publicly about the value of marriage from an ideological or religious perspective. But when you claim that you are doing so out of a desire to reduce poverty and you distort the research evidence in order to support your argument, it’s time to omit the Ph.D. from your byline.

The other central argument in Wilcox’s piece is that pointing to the failure of marriage promotion policies is a straw man because no one believes that marriage is a panacea for the problems facing single mothers and their children. But the public dialogue, much of it framed by Wilcox himself, suggests otherwise. One needs only about 5 seconds and a search engine to find Wilcox telling unmarried parents to “put a ring on it” in the New York Times and in public lectures. More troubling, Florida Republican Senator Marco Rubio recently said, “The truth is that the greatest tool to lift people, to lift children and families from poverty, is one that decreases the probability of child poverty by 82 percent. But it isn’t a government program. It’s called marriage.” We could quibble about the meaning of the word, “panacea,” but Wilcox is just wrong when he implies that no one thinks marriage is a central answer to poverty among single mothers. Incidentally, Rubio’s conclusion relies on a fundamental misunderstanding of causality, as described here. Maybe we should forgive Senator Rubio for misunderstanding the data because he is not a trained social scientist. But what is Brad Wilcox’s excuse?

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State of Utah falsely claims same-sex marriage ban makes married, man-woman parenting more likely

This hasn’t been peer-reviewed, but it’s pretty simple, and I will give the results, data, and code to anyone who wants it. Also, ask me about my low-low expert witness rates ($0 per hour + expenses for federal same-sex marriage cases). If you know the Utah lawyers and they’re looking for this kind of thing, pass it on!

The State of Utah’s “Application to Stay Judgment Pending Appeal,” to stop same-sex marriage from continuing while they appeal their most recent loss, has nothing new to offer, legally. And the social science claims they make are by now a familiar patter of discredited blather, featuring the writing of Regnerus, Wilcox, Blankenhorn, and Allen (follow the links for debunking).

But I either never noticed or never thought about one of their stranger claims, which I felt compelled to debunk. They wrote (excerpting):

A final reason to believe there is a strong likelihood this Court will ultimately invalidate the district court’s injunction is the large and growing body of social science research contradicting the central premise of the district court’s due process and equal protection holdings: i.e., its conclusion (Decision at 2) that there is “no rational reason”—much less any compelling reason—for restricting marriage to opposite-sex couples. That research … confirms … (b) that limiting the definition of marriage to man-woman unions, though it cannot guarantee that outcome, substantially increases the likelihood that children will be raised in such an arrangement. (p. 14)

And then again:

[B]y holding up and encouraging man-woman unions as the preferred arrangement in which to raise children, the State can increase the likelihood that any given child will in fact be raised in such an arrangement. … [T]he district court ignored this fundamental reality. … [p. 18] … By contrast, a State that allows same-gender marriage necessarily loses much of its ability to encourage gender complementarity as the preferred parenting arrangement. And it thereby substantially increases the likelihood that any given child will be raised without the everyday influence of his or her biological mother and father—indeed, without the everyday influence of a father or a mother at all. (p. 17)

Wait a minute. Are they claiming that banning same-sex marriage actually results in more children being raised by married, man-woman couples? Unless you make heterogamous marriage and childbearing compulsory, this doesn’t seem like a sure bet. In fact, now that we have so many people living under the same-sex marriage regime, we can start to investigate this.

Does banning gay marriage work to put kids under heterogamously-married roofs?

Seven states plus the District of Columbia permitted legal same-sex marriage by 2012: Washington, New York, New Hampshire, D.C., Iowa, Vermont, Connecticut, and Massachusetts, which led the way in 2004. And as of very recently we have the 2012 American Community Survey, with ample sample size to assess family structure for every state in every year since 2004.

This analysis is very simple and not a causal analysis of family structure. I am simply testing the assertion by the State of Utah that banning gay marriage “can increase the likelihood that any given child will in fact be raised in such an arrangement.” I do this in a very simple way, and then a pretty simple way.

First, just the raw trends. This shows very simply that children are more likely to live with married parents in states that permit same-sex marriage (red lines) than in states that don’t (blue lines):

ssm-married-kidsI did this both for age 0, to capture marital status at birth, and for all children ages 0-14, to get closer to the concept of “raised.” Here is a table showing the numbers, with the differences calculated, showing exactly how much more likely children are to live with married parents if their states permit same-sex marriage:

ssm-married-kids-table

Whatever the reason, then, children in states that permit same-sex marriage have been 2% – 10% more likely to live with married parents over the last decade. (The same-sex couples themselves do not contribute to this pattern, because the public-use ACS files do not yet count them as married.)

Two potential problems with that as the analysis. First, maybe those states were just more pro-marriage places in the first place (the obvious inference to draw from the fact that they permit same-sex marriage). And second, the declining tendency of children to live with married parents nation-wide might be driving this, as more states join the same-sex marriage pool over time.

To fix these problems, I conducted a simple fixed-effects logistic regression, entering dummy variables for every state and every year into a model predicting whether children live with married parents or not. The only other variable indicates whether the child lives in a state that permits same-sex marriage. By holding constant each state’s average rate, and the national trend over time, the model isolates the statistical association with same-sex marriage legal status. This asks, in essence, whether states that change from not-legal same-sex marriage to legal same-sex marriage have lower or higher odds of their children living with married parents after the change.

Here are the results:

ssm-married-kids-logit

The odds ratios for the same-sex marriage variable are above 1.0, indicating the children in same-sex marriage states are more likely to live with married parents. The effect is not statistically significant from zero at conventional levels for infants, but it is for all children ages 0-14. Again, for whatever reason — it’s not important for this — children are more likely to live with married parents if they live in states where same-sex marriage is legal. All that matters is that the State of Utah’s claim is refuted.

Summarizing all the experience we have data for so far — 34 state-years of data — there is no evidence that allowing same-sex marriage reduces the likelihood that children will be born to or live with married, man-woman parents. If that’s your goal, this policy doesn’t seem to work. (I don’t share that goal, and I especially don’t think it’s relevant to determining legal access to marriage, but they brought it up.)

I’m not the first one to think of this, of course. An earlier analysis in PLoS One found no evidence that same-sex marriage affects the rate of different-sex marriage. That analysis was of marriage, and its most recent data were from 2009. I haven’t seen anyone else do this for children’s living arrangements, and the 2012 only recently became available. If Gary Gates or someone else has done this, please let me know.

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