Has your relationship with your spouse or live-in partner taken a recent hit after adding a new child to your family? Are you too tired to put much effort into improving it? A new study may offer you another reason to keep working on it: do it for the kids.

Confirming and extending earlier research findings, G. Cole Ratcliffe, Aaron M. Norton, and Jared A. Dutschi write in the Journal of Family Issues that mothers’ and fathers’ relationship quality when their child is one year old predicts their parental engagement two years later. That is, parents who report having an affectionate, positive relationship with their spouse or live-in partner engage in more positive parenting activities—reading to, singing to, and playing with their child—down the road.

Mothers’ positive parental engagement when a child is three years old, in turn, is associated with a lower incidence of negative child behavior (disobedience, irritability, temper tantrums, clinginess, restlessness, etc.) when the child is five, controlling for earlier relationship quality.

Ratcliffe, Norton, and Dutschi consider their findings to confirm the “spillover hypothesis” about how parents’ relationship affects their parenting: the idea that “high or low relationship quality ‘spills over’ to how the child is parented.” It’s easy to imagine how such spillover works on the ground: A man or woman who feels loved and supported is more apt to have the patience and energy that good parenting requires, whereas someone worn out by a romantic conflict has little appetite for yet another round of “The Itsy-Bitsy Spider.”

One downside of the study, from my perspective, was the way it controlled for marital status, rather than examining how outcomes might differ between couples who are married and those who are cohabiting. (The researchers examined all parents who lived together and were romantically involved, whether or not they were married, without exploring differences between the two groups.) It seems to me that the greater psychological security of marriage—spouses’ confidence in each other’s commitment—as well as the higher costs of ending a marriage, compared to ending a cohabiting relationship, may make married couples more determined to maintain a positive relationship and to support each other’s parenting efforts, with obvious benefits for their kids. Cohabiting couples, on the other hand, may be less likely to think that relationship-building efforts are worthwhile or likely to pay off. Perhaps that could be the subject of a future study.