Studies are offering new observations on how being a mom or dad is impacted by how many kids a parent has. But it's not easy to tease out how the findings might converge.

One study says having two or more kids makes moms and dads more productive at work, compared to those who have fewer or no children. And an entirely different study says that after a second child, the initial happiness that surrounds birth starts to decline and a third child won't bring it back up much.

For the first study, researchers at the Federal Reserve Bank of St. Louis looked at the productivity of 10,000 "highly skilled" economists to conclude that both moms and dads are more productive at work, overall, if they have at least two children children, compared to those who have one or no children.

They measured productivity through the proxy of published work.

But it's not a simple math equation. Their study, presented as a working paper, noted that the productivity boost is over the course of a 30-year career. There are dips in productivity when the kids are very young, but it's made up as the kids get older.

And mothers at every stage outperformed women without children, it noted. But as Christian Zimmermann, one of the study's authors, told TODAY.com, "It's all about timing. It's really when the children are younger that there is an impact, but if you consider the whole career of the person, then on average, the person (with at least two kids) is doing better."

Wrote the Washington Post's Ylan Q. Mui, "It's important to point out that the authors are examining a very narrow group of women with privileged circumstances. Parenthood was likely planned for many of them, with benefits such as maternity leave and paid sick time. They can also better afford to pay for resources like reliable childcare that allow them to work longer. Low-income or low-skilled mothers often face a very different working environment."

Meanwhile, the other study tackled not performance, but happiness. "Parents often say that nothing compares to the joy of welcoming their new baby into the family. But all newborns are not equal in the happiness they bring mom and dad," Smithsonian.com's Rachel Nuwer wrote of the study published in Demography. "By the time couples reach their third baby, the thrill of pregnancy and birth has worn off, the researchers find."

Those researchers collected data on 7,000 parents in Europe who each provided information for more than 10 years for either the German Socio-Economic Panel or the British Household Panel Survey. They found that while "parents’ happiness increases in the year before and after the birth of a first child, it then quickly decreases and returns to their ‘pre-child’ level of happiness," according to a written statement.

And so it goes through a second birth, with the happiness before and at the time "roughly half of that for first births." There's no real increase in the joy level of parents with a third child.

But lest that third or sixth or seventh child feel unloved, “the arrival of a third child is not associated with an increase in the parents’ happiness, but this is not to suggest they are any less loved than their older siblings," the release said. "Instead, this may reflect that the experience of parenthood is less novel and exciting by the time the third child is born or that a larger family puts extra pressure on the parents’ resources. Also, the likelihood of a pregnancy being unplanned may increase with the number of children a woman already has — and this brings its own stresses.”

The researchers said that women's happiness increases more, compared to men, during the pregnancy and around the time of birth, but they also see bigger declines than men in a child's first year of life. That might simply reflect the difference in the initial happiness boost, they said. Over time, there are no differences in the happiness levels of men and women related to having children.

Parents who are older and better-educated at the time of a first child's birth have a particularly great happiness reaction, and that sense doesn't drop off as much, according to Rachel Margolis, assistant professor from Western University’s Faculty of Social Science.

“The fact that among older and better-educated parents, well-being increases with childbearing, but the young and less-educated parents have flat or even downward happiness trajectories, may explain why postponing fertility has become so common,” she said.

Wrote Smithsonian's Nuwer: "For the youngest parents, the team found, having a baby markedly detracts from their happiness. 'Those who become parents in their teens,' they write, 'have a predominantly declining pattern of happiness that does not increase above the baseline even during the year of birth.’ ”

Email: lois@deseretnews.com, Twitter: Loisco