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Oh, the joys of parenting! Sort of.

Some expectant parents — both mothers and fathers — experience a surge of happiness before and after their first and second little ones arrive. But by the time child No. 3 comes around, that happiness boost is nowhere to be found, according to a new study.

Researchers at the London School of Economics, using large longitudinal survey data from Britain and Germany, found that parents — mothers in particular — experienced a huge surge in happiness during the pregnancy period for their first child, and after that child was born.

With their second child, a similar — though less intense — phenomenon occurred: Parents were about half as happy as they were during and after their first pregnancy, but they were still happier than usual.

“The fact that parental happiness increases before these children are born suggests that we are capturing broader issues relating to childbearing such as couples forming partnerships and making plans for the future,” Mikko Myrskylä, an LSE demography professor and director of German’s Max Planck Institute for Demographic Research, said in a statement.

When it comes to the third child, it isn’t so much that parents are unhappy — they simply don’t get the big happiness boosts they experienced with their first two children.

“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,” Myrskylä noted. “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, he added, “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 research was published in the October issue of the journal Demography.

The findings come with two important caveats. For both the first and second children, the happiness boost is only temporary. Both parents eventually revert back to their “pre-child” levels of happiness. And, critically, whether the happiness boost is there at all depends on the ages and education levels of the parents.

Older or more educated parents derive more happiness longer from the pregnancy period and the resulting child. Researchers note that the observation is consistent with broader trend of more educated people postponing childbirth.

But mothers who are 23 – 34 years old experience a smaller boost in happiness. And women who become mothers as teenagers don’t experience any increase in happiness above their baseline at all.

“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,” said Rachel Margolis, an assistant professor of sociology at the University of Western Ontario in Canada.

About 21 percent of families with children have three or more kids, according to U.S Census Bureau data.

A 2007 Gallup poll found that Americans, on average, believe that 2.5 children (yes, two-and-a-half) make for the ideal family size. In that poll of more than 1,000 adult Americans, nearly six in 10 people said that having two children or fewer was ideal; about a third of those polled preferred three children or more.

Last year, a Today.com survey of more than 7,000 U.S. mothers found that those with three children said they experience more stress than mothers with one or two (or even four) children.

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