Two summers ago, I wrote on this blog about Kylie, a little girl who had lived with only her mother for the first five years of her life, but whose father had just proposed marriage to her mother. On the surface, marriage between biological parents represents a good scenario for children of single mothers: Marriage is more stable than cohabitation, and marriage between parents is more stable than marriage involving stepparents. Scratch beneath the surface, and two other truths quickly emerge regarding Kylie’s situation: 1) all union transitions put stress on children, and 2) a parent undergoing a union transition is likely to undergo more than only one.

That first point bucks conventional wisdom. We all know that breaking up is stressful, but maybe we like to imagine that the child of a single mother is better off when the mother gains a partner—someone to pool income with, and someone to share chores and joys with. If that partner has a direct interest in the child, such as a biological connection, then it is even better. But research has shown that children suffer from family transitions of all types. Educational, social, and behavioral outcomes decline with each additional transition, even though only every other transition is a breakup. The type of transition matters far less than the number. Even though Kylie’s dad has a lot to offer, family transitions disrupt routines and disrupt healthy development.

The difficulties involved with incorporating a new person into an established household may help explain the second point: If a mother forms a union after childbirth, the odds of it lasting aren’t very good. In fact, new research by Susan Brown, J. Bart Stykes, and Wendy Manning showed that many single mothers who entered a cohabiting union became single again before their child reached age 12 (the average number of transitions was 2.1: one for starting a cohabitation, plus an average of 1.1 more). Children born to single mothers who married did a little better with 1.8 transitions on average; even so, a large share of these children experienced parental divorce before age 12.

So what about births to cohabiting couples? If Kylie’s parents haven’t moved in together in all this time, it might signal a problem in their relationship. But if a couple that is already living together has a child together, doesn’t that child have a better chance at family stability than poor Kylie who can’t even have two parents in her house without undergoing a huge transition? One of the biggest take-a-ways from Brown, Stykes, and Manning’s study is that children born to cohabiting couples experience almost as much union instability as children born to single mothers (see Table 4 in study).

Among children born in the early 1980s, there was no difference at all between those born to single moms and those born to cohabiting couples: an average of 1.4 transitions by age 12 in both groups. That means that most women who had a child while single didn’t stay single, and many of them became single again. It also means that most women who had a child while cohabiting broke off with their partner (transitioning to marriage wasn’t included in the count), and many of them entered a new union. Children born outside marriage averaged the same number of transitions regardless of whether their parents were cohabiting or not.

Among children born about a decade later in the 1990s, children born to cohabiting parents did have an advantage, but not because cohabitation has become more stable. The average number of family transitions before age 12 stayed put at 1.4 among children born to cohabiting couples. But among children born to single mothers, it grew to 1.7. Why? More women who give birth while single start cohabiting now than in the past. Over this same period, the instability for children born inside marriage decreased modestly from 0.6 to 0.5.

Brown and her colleagues show that family instability is down among children born to married couples, but fewer births are marital. Family instability is the same—but still high—among children born to cohabiting couples, and there are many more of them. Instability is up among children born to single mothers whose numbers have increased modestly. This leads them to conclude that, “recent changes in U.S. family life portend greater family instability for today’s children.”

If that conclusion wasn’t depressing enough, they also show that the burden of family instability is not shared equally across racial groups and that black children’s disadvantage has increased. Black children born in the early 1980s experienced about 0.4 more transitions by age 12 than either White or Hispanic children; the racial gap had grown to 0.7 transitions a decade later. Again, most of the change over time is due to the fact that single mothers have become more likely to cohabit, and this affects black children disproportionately. Thankfully, the consequences of family instability do not seem to be as extreme among black children, but being taxed at a lower rate is still draining if you are taxed over and over again.

The aggregate numbers in the study also mask growing inequality among white families. White kids born to marriage average 0.5 family transitions before age 12 today, when it used to be 0.7. But for white kids born in cohabiting unions, transitions are up from 1.1 to 1.6.

Step back and think for a moment about what happens when cohabitation becomes a more common institution: It becomes an increasingly accessible alternative to both marriage and singleness. The data Brown and her colleagues present support the interpretation that whites have used cohabitation more as an alternative to marriage, while blacks have used it more as an alternative to singleness.

What happens when cohabitation becomes a more common institution? It becomes an increasingly accessible alternative to both marriage and singleness.

Here is what I mean: The vast majority of white children born in the early 1980s were born inside of marriage. Over the following decade, the share of births to cohabiting couples grew especially rapidly among white couples. In contrast, among blacks, births to cohabiting mothers increased, even as births to single mothers fell (and the share of marital births was relatively stable).

Unfortunately, neither substitution increases stability for children. When cohabitation starts to substitute for marriage as a context for births, it seems that parents making the substitution are selected on the basis of less stable relationships. For example, the Brown study shows that family instability among white children born to cohabiting parents increased rapidly. The substitution of cohabitation for single motherhood might hold more promise for increasing children’s stability, except that parents also tend to make that substitution after childbirth. More single mothers are now entering cohabiting unions while raising their children, and that explains the rise in instability among children born to black single mothers. In the very recent past, a larger share of these children were raised by their single mothers without having to adjust to their mother’s partner moving in (and often back out).

There are clearly “diverging destinies” between children born to married parents, and those born to either cohabiting or single parents. Even though the Brown study shows that most of the growth in instability over time is among children born to single parents, the growth of cohabitation is an important part of why children of single parents have less stable family lives.