Every time a woman in America gets put in charge of a Fortune 500 company we hear proclamations that the glass ceiling holding women back from top leadership positions is finally cracking, along with more measured responses observing how far we still have to go. Indra Noori and Virginia Rometty notwithstanding, it’s been a long, slow march toward gender equality in the C-suite over the last couple of decades.

Such news also provokes the occasional discussion of what things would be like if more women were in charge: Would we see kinder, gentler, more empathetic work environments, and maybe even world peace? Or the same harsh corporate world, run by women preaching the same gospel of shareholder profits as their male predecessors?

In America, we’re not going to find out anytime soon, given that companies continue to appoint mostly male boards and executives. The Norwegians, however, haven’t left gender equity to the whims of market forces: In 2006, the government mandated that every company traded on the Oslo Stock Exchange increase the fraction of women on its board to at least 40 percent by February 2008. Four years later, we’re now starting to see how this social experiment has affected Norway’s companies. The results are described in a study released last year by economists David Matsa and Amalia Miller. Companies where women were given a strong voice in decision-making were less likely to react to short-term dips in profits by shedding employees. It seems a world run by women may indeed be kinder and gentler, though also one with lower profits, at least in the short run.

Why should we expect women bosses to be any different from men? Most people, when asked, believe that women are cooperative and emotional whereas men are cold, rational, and competitive. Some even go so far as to suggest that women are more honest and less corruptible than their male counterparts. It follows that women would run more open, democratic organizations, and perhaps even allow more than just the bottom line to guide their decisions.

But are women and men really so unlike one another that they may as well be from different planets, or is this more a matter of perception than reality? And even if they are different now, would women be corrupted by the power of being the boss?

It’s hard to determine the effect of female leadership by comparing women-run companies like IBM and Pepsi to their male-run competitors like Dell and Coke—a company that puts women in charge presumably values gender equity and diversity, which might also mean it’s a kinder, gentler organization to begin with. Companies that are nice might put women in charge, not the other way around.

Matsa and Miller get around the chicken-egg problem by tracing the effects of the large-scale social experiment engineered by the Norwegian government in 2006. The mandated gender quota applied only to companies listed on the Oslo Stock Exchange; at the time, the boards of Oslo-listed firms were, on average, 20 percent female. These companies had two years to up that percentage to 40, regardless of whether the company valued gender equity. Meanwhile, there were no new pressures to hire women at Norwegian companies not listed on the exchange, so the researchers also had a natural point of comparison to assess whether changes in the way listed companies operated were due to having more women on the board, or something else that changed in Norway at the same time the quota law was passed. And since no comparable law was passed elsewhere in the region, Matsa and Miller also compare what happened to the management of companies on the Oslo Exchange to companies listed on exchanges in Denmark, Sweden, and Finland.

Matsa and Miller found that strategic decisions made by corporate boards were unaffected by having more women involved: Between 2006 and 2009, listed Norwegian companies didn’t get involved in more mergers, acquisitions, or joint ventures relative to listed companies elsewhere in Scandinavia. Nor did they generate higher revenues than companies that didn’t face quotas. However, the companies run by boards newly influenced by women became about 4 percent less profitable relative to the control companies that Matsa and Miller use as a benchmark.

Were women simply unqualified to guide large, publicly traded enterprises? A Norwegian acquaintance of mine recalls that, when the law went into effect, many in the business community were skittish about whether enough qualified women could be found to fill all the open board seats. But the source of lower profitability suggests that it’s not that men have bigger brains or more experience. The lower profits are more likely the result of how Mars-Venus gender differences play out in boardroom discussions. The listed Norwegian companies made less money mainly because they handed out fewer pink slips. In fact, the entire gap in profits can be accounted for by a swelling of the wage bill. (Employment actually went up more than total wages did, implying a drop in average salaries. Matsa and Miller speculate that this is because the women-led companies were particularly protective of low-skill jobs that were vulnerable to layoffs.)

So having women in charge is good for workers. And maybe it’s not so bad for shareholders – for years now, we’ve heard about the excessive short-termism of corporate leaders who can’t look past the next quarterly earnings report. While it’s too early to tell what the longer-term effects will be of giving women a voice in the boardroom, perhaps their kinder, gentler management style will be more effective in retaining talent and motivating employees, which will eventually give a boost to the bottom line.

Based on the results of the Norwegian quota experiment, it’s tempting to imagine that we could cure corporate America’s obsession with short-term profits, and perhaps make a dent in the wealth gap between workers and capitalist investors in the process, simply by getting more women into corner offices. But there are lots of ways that live-free-or-die America differs from the workers’ utopias of northern Europe. First, Norwegians are used to having the government stick its nose into their affairs, whether it involves health care, personal data, or taxation. It’s unlikely we could simply legislate gender equality in America.

If American women aren’t going to be the beneficiaries of large-scale affirmative action anytime soon, they can at least continue to chip away at the glass ceilings of corporate America. In work published recently in the American Economic Review, Matsa and Miller give reason for at least some optimism; they open with a quote from Sam Walton, who in 1987 describes Wal-Mart board member Hillary Clinton as a “strong-willed young lady on the board … who has already told the board it should do more to ensure the advancement of women.” Their study goes on to present evidence that Clinton is not alone in her efforts: Companies that appoint more women to their boards are more likely to hire female executives in the years that follow. The resulting virtuous circle of women promoting women may mean not just better opportunities for the fairer sex, but also for the workers at the companies they lead.