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):

I 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:

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:

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.