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On a recent work trip in Belgium, I met a fascinating woman in her late 40s. Elizabeth had a PhD in history and was working on a book about the First World War. She taught at a respected American university and had a long and impressive publication list. Because of the nature of the trip, we talked mostly about work before moving on to more personal subjects. It wasn't until the second day of the trip that I asked Elizabeth casually if she had any children. "Yes," she said rather cryptically, but offered nothing more.

"How many?" I said, thinking with a resume like hers, one kid, maybe two.

"Seven," she said with an apologetic smile.

My reaction, which was to spit out my wine and scream "seven children are you out of your mind woman?!!" probably explains why Elizabeth offered up this information somewhat unwillingly. But once I calmed down and I found myself asking the age-old working-mother question: How on earth did she do it?

Her answer was instructive.

"I'm just very, very careful with my time," she said. And that was all. Because an accomplished working mother of seven children isn't going to bother mincing words, is she?

A U.S. study that came out this week shows us that not only is Elizabeth not alone, as an over-achieving working mother, she is typical (though obviously not her extreme fecundity, which is highly unusual). Economists at the research arm of the Federal Reserve Bank of St. Louis found that, over the course of a 30-year career, women with children are more productive in terms of output than anyone else in the workplace, including men with and without children and childless females.

The study, which was published in the Washington Post, will have been met with incredulity from ambitious, unencumbered types and a big fat "Well duh," from driven working moms, who are well aware of the truth in the old adage: If you want a job done, give it to a busy person.

The researchers got their results by analyzing academic research completed by a group of more than 10,000 academic economists – a profession which requires a post-graduate degree and in which work is heavily ranked and recorded, making it easy to measure precise productivity.

The results were counterintuitive, if you assume (as most do) that children are a drag on anyone's career.

While men with one child or fewer performed more or less consistently throughout their career, men with two or more children were more productive. And for women, this effect was even more profound: Women with two or more children were markedly more productive throughout their career than anyone else in their field, both before and after they had children.

So Sheryl Sandberg needn't have told us to "lean in" after all. It turns out those of us in the game are as bent as the Tower of Pisa. The real question of course is why our superior efforts have not yet resulted in superior pay or promotions. Mothers, after all, tend to be the hardest workers in even the poorest societies – but our labour doesn't usually equate to power. If anything, the opposite is true.

But talking to harassed working mothers, you will not find a group of people celebrating their success but instead a group lamenting their failures and collective anxiety. We might be the most productive demographic in terms of raw output, but we sure don't feel that way. It's likely this tendency to self-criticize is the secret to our "success," but what good are the bountiful fruits of our labours if we are barely capable of enjoying them at the end of the long day?

Tova White, head of human resources for Coca-Cola Canada and a working mother of two children herself, says that's the risk she sees with high-producing working mothers. "The busier these women are, the more energized they are, and there's always a danger with that. For many ambitious women, performing at a high level in all aspects of life offers an adrenaline rush they can't get anywhere else."

But does productivity actually increase because of having children, or do productive women simply choose to keep working after they reproduce?

White says it's probably a bit of both. "Having a child makes you approach tasks in a smarter way, and in HR, we know time-management and prioritization are teachable skills," White says. "But I think there's also a strong element of self-selection here. Those mothers who decide to stay in the workforce and advance their careers are an unbelievable group of individuals with an amazing host of skills to begin with."

Either way, it's clear that the moms in the study were both educated and economically privileged, which means they likely benefited from planned pregnancies and were able to afford decent childcare. No one would argue that poor, less-educated and low-skilled mothers are likely to boost their careers by having more children. To be a successful working mother, it takes a village, as they say, and if you don't happen to have a village, it takes a supportive spouse and a significant chunk of money.

And it's also important to remember that the home-life burdens don't simply evaporate with small children. By the time our kids are ready for university, our aging parents are often beginning to ail. Allison Pearson, the author of the bestselling novel I Don't Know How She Does It, now writes a column for the Daily Telegraph called Sandwich Woman – which places the same character, beleaguered working mother Kate Reddy, 10 years later and still struggling be all things to all people – only this time her days are spent rushing from the office to the nursing home instead of the nursery school.

So if you want to get something done, give it to a busy, privileged working mother with multiple children older than three. If you can catch her, that is.