Want to make your company more profitable? Promote more women.

A new study says hiring more women in leadership roles literally pays off — big time.

The study, released Monday by the Peterson Institute for International Economics, finds that companies with more women executives tend to be more profitable.

This study isn’t the first to find that better gender balance in leadership can be good for business. But it is the most extensive, sampling 21,980 firms with headquarters in 91 countries. Most other studies looking at this issue have been more limited or have just focused on one country.

Researchers found that companies with at least 30 percent of women in their most senior “C-suite” management positions are about 15 percent more profitable than firms with no top women executives.

This huge difference is probably because gender diversity is also correlated with skill diversity, which improves corporate performance on average. It’s not that individual women will always outperform individual men in leadership. It’s that women often bring different skills to the table — and firms that discriminate against women won’t benefit from those skills.

Despite the profit-boosting power of women leaders, the report found a relative lack of women in upper management worldwide. Sixty percent of the companies studied had no women board members. Just over 50 percent had no women in C-suite executive positions, and 57 percent of the remaining half had just one woman executive. Fewer than 5 percent had a woman CEO. (Women CEOs also lead fewer than 5 percent of US companies on the S&P 500 index.)

But it’s important to note: Having a woman CEO didn’t actually have a measurable effect on a firm’s performance one way or another. Having other women senior executives did, though — so much that the authors wonder if the same effect would apply to women in leadership below the C-suite level. Having women board members helps too, but not as much as having women executives.

“This pattern underscores the importance of creating a pipeline of female managers and not simply getting lone women to the top,” the report reads.

Some countries, like Norway, have gender quotas for corporate boards. But, the report notes, these quotas don’t seem to do much to help companies’ performances.

One reason for this is the so-called “golden skirt effect,” where a small number of women sit on the boards of several different companies and perform worse because they’re overcommitted.

There could still be a role for quotas — especially ones that companies impose on themselves — in helping fight gender discrimination, the authors note. But it depends on a lot of different factors, including how far down the corporate ladder the glass ceiling reaches. If women struggle even just to reach upper management, it’s more helpful to pursue policies to help mid-career women before tackling corporate board representation.

What definitely does help? Being located in countries that are really good at gender equity overall.

There’s a positive correlation between companies with more women executives (and thus better profit potential) and countries where girls do better at math and where the public has less discriminatory attitudes toward women executives.

The researchers said that when women get a better education and have a better chance to get work experience free of discrimination, it fills the pipeline with lots of women who are qualified to serve in executive-level positions.

Paid paternity leave also makes a huge difference — but paternity leave specifically, not maternity leave.

This makes sense because, as other research has found, paid leave for dads boosts gender equality overall. It helps shift social norms away from the expectation that women are always going to be the primary caregivers for children, which helps remove a big stumbling block that keeps women from participating as fully as men in work and society.

This is another reason why boardroom quotas may not work — they can easily operate at a surface level. They can help companies look more diverse without solving the broader, deeper problems that hold down women’s workplace advancement in the first place.