The study suggests that the birth of a first or a second child briefly increases the level of their parents' happiness, but the birth of a third child does not have the same effect.
However, the researchers are keen to point out this doesn't mean the third child is any less loved.
The research also found that couples who postpone becoming parents until later in life experience the highest and most lasting levels of happiness following the birth of their children.
According to the study by the London School of Economics and Western University, Canada, parents' happiness increases in the years before and after the birth of a first child. It then quickly decreases and returns to their 'pre-child' level of happiness.
When the couple's second child is on the way, they again experience a boost in happiness - although this time around the increase is approximately half of that for first births.
The researchers report that when a couple are expecting their third child, the increase in their happiness is negligible.
Professor Mikko Myrskylä from LSE said: "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.
"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.
"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."
The research also found that the parents who experienced the greatest and most long lasting boost to their happiness following the birth of their children, were those aged between 35 and 49 years old.
"The fact that among older and better-educated parents, wellbeing 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 assistant professor Rachel Margolis from Western University.
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