(CNN) There may be a downside for a man who is the breadwinner in a household -- at least if he's younger.

It turns out that as married millennial men take on more economic responsibility in their households, their psychological well-being and overall physical health slightly suffer, according to a new working paper. However, as millennial women take on more economic responsibility, their psychological well-being may get a boost.

"So, the effect is kind of opposite here for this psychological well-being component," said Christin Munsch, an assistant professor of sociology at the University of Connecticut and lead author of the paper. She presented the research at the annual meeting of the American Sociological Association on Sunday.

"In some ways, I was surprised," she said of the findings. "But there's no one-size-fits-all solution for all families. This is just showing trends in the data. There are women who want to stay home or men who really want to be breadwinners, and similarly, there are women who want to be breadwinners and men who prefer to stay home. So, I think that the take-home is that we need to have these conversations with our partners."

Measuring the well-being of breadwinners

Munsch and her colleagues examined data on 9,000 heterosexual married couples between the ages of 18 and 32. The data, which date from 1997 to 2011, came from the Bureau of Labor Statistics' National Longitudinal Survey of Youth

The researchers tracked changes in each couple's individual and household incomes, self-reported psychological well-being and self-reported physical health. They controlled for total income, education, age, working long hours and children.

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The researchers found that men whose wives contributed equally to the household income had an average psychological well-being score of about 3.33 on a four-point scale, whereas men who contributed twice as much as their wives had a 3.27 score.

What about men who were complete breadwinners? Their psychological well-being score was 3.17. A small decline in physical health was seen among men who contributed more, as well.

However, for women, the lowest psychological well-being scores -- around 3.08 -- were associated with those who were completely dependent on their husbands. Women who were the least economically dependent scored 3.17. There was no shift in the women's overall physical health.

Why the gender gap?

"The positives are that it's nationally representative, which is an important thing in social science research. It's longitudinal, which is also a really excellent thing, and specifically, they looked at these young couples over 15 time points," said Mary Noonan, associate professor of sociology at the University of Iowa, who was not involved in the paper.

"But why are the results different for men and women? It seems a little funny. Is there something else that's causing these men breadwinners to feel a decline in their health? Why are female breadwinners saying their health is better?" Noonan asked. "What I'm a little suspicious about is, is there an outlier that might be driving these results? ... But it's great to see this study, and income dynamics within couples is an important area to study."

Noonan added that it would be interesting to replicate the research and indicate whether there are different outcomes across various socioeconomic groups.

Nonetheless, "being a breadwinner is a different psychological experience for men than for women," Munsch said.

Based on traditional gender expectations, "for men, it's sort of what's expected for you in many ways. You're not getting any brownie points for being a breadwinner," Munsch said. "Whereas, for a woman, if you're a breadwinner, you are not status quo."

Additionally, Munsch said, men may be more inclined to accept a higher-paying, more stressful job because they feel the pressure to climb the corporate ladder and make as much money as possible for their families, whether they enjoy their work or not.

"For women, because there isn't the expectation that you're going to make as much money as possible for your family no matter the cost, I think they're much more likely to ask themselves, 'Oh, is this what I really want to do?' " Munsch said. "And so when women do go into these high-level occupations, there's more of a match between their preferences. So their psychological well-being is going to improve, whereas for men, it's not."

More research is needed to determine whether the study results would be similar among married couples in their 40s, 50s or older, Munsch added.

"But I can't help to think that part of the findings are being driven by the fact that these are millennials," she said.

"Essentially, young people, millennials, really do want egalitarian relationships. This is what they prefer when you ask 'what kind of relationship do you want?' They envision both partners contributing financially and both partners taking care of domestic responsibilities," Munsch said. "That might not have been the case in a previous generation ... but I don't know that."

'The second wave of the gender revolution'

The paper seems to build on a wave of recent millennial-focused studies that indicate younger couples increasingly hold egalitarian aspirations, said Kathleen Gerson, a professor of sociology at New York University who was not involved in the new paper.

She added that, as more young couples share responsibilities in their households, more institutional structures and support should be made available to them.

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"In some sense, this is the second wave of the gender revolution. If the first wave was understandably focused on opening doors to women's participation outside of the home; the second wave is asking, how do we make adjustments at work and in men's lives to that revolutionary change?" Gerson said.

"The answer for women and men alike is that we begin to restructure our workplaces, our child-rearing institutions and other supports so that both men and women are able to blend and balance breadwinning with caregiving and share it in the way they deem best in their relationships," she said. "Now, we need to create the institutional structures. ... And this study shows that men need them every bit as much as women do."