The past year may have been a tough one in many respects, but there was one measure in which the country made some progress. 2016 marked the year in which there were the most women ever heading companies in the S&P 500. That’s according to S&P Global Market Intelligence, which tracks the number of women CEOs in both top U.S. and European companies.

To be sure, the number is still pitiful—out of 500 companies, only 27 have female CEOs, but it’s a sign of a good trajectory, up from 2015, when it was 22, and from 2009, when it was 18. S&P 500 companies, on average, add one female CEO a year, the report said. Among the women who head S&P 500 companies are Mary Barra of General Motors, Shira Goodman of Staples, and Debra Cafaro, who has been the CEO of Ventas, a real estate investment trust, since 1999. Women have also made in-roads in other forms of corporate leadership: About 17 percent of board members for Fortune 500 companies were women in 2013, up from 9.6 percent in 1995. And though the number of female executives at big companies is still small, it has increased in recent years.

At the same time, there are more women in the workforce than ever before—73.5 million, or 47 percent of the labor force, up from 29 percent in 1945, according to the Bureau of Labor Statistics. As more women climb to the tops of corporate hierarchies, will their being there help other women advance?

Academic evidence suggests that the answer is yes, to a degree. In particular, women who are high-performing and already successful tend to see their prospects improve under a woman’s leadership. In one study, for example, a group of Italian researchers looked at the compensation of individual workers at big Italian manufacturing firms between 1982 and 1997. They found that female leadership had a positive effect on wages for women in more senior roles (and, as it happens, that firms with more women leaders performed better).

What causes this? The study’s lead author Luca Flabbi, a professor of economics at Georgetown, told me that he believes that women are better than men at reading other women and assigning them to the jobs commensurate with their experience. When a female executive replaces a male executive at a firm, she can better see the talent of senior women and put them in positions that match their talent. Since this is a better fit for these women, they do better work, and enhance the firm’s performance.  “She puts them in more productive positions, and she is right, and that’s why the performance goes up,” he told me.

Another study looked at the role of women on corporate boards and found a similar effect: The higher the share of women on corporate boards one year, the more likely the company was to hire women executives in the following year, the study’s authors, David Matsa, a professor at the Kellogg School of Management at Northewestern, and Amalia R Miller, an economics professor at the University of Virginia, discovered. This may be because women know each other through professional networks, and when there are women at the top—say on a corporate board—they help refer women to positions that otherwise might have been filled by men, Matsa told me. The increase also could have been because women discriminate less against each other, and hire them for executive positions, he said.

This same dynamic has been identified again and again. One report on 21,000 firms from 91 countries by the Peterson Institute for International Economics concluded that having women on the board increases the ranks of women executives. (It also found that companies with women on the boards tend to be more profitable than those with just men.) And a study of New York City advertising agencies over a 13-year period found that when an agency has more female managers, more newly-created jobs are first filled by women. “Women’s desire to create distinctiveness is stronger when they work with others who are similar to them,” the authors, Lisa E. Cohen and Joseph P. Broschak, write. This finding may indicate that there may be room in women-headed companies for ambitious women to create new jobs that hadn’t already existed.

But while women who are top performers may benefit under women’s leadership, women who aren’t very good at their jobs may not. In a 2015 study,  Berkeley researchers Sameer B. Srivastava and Eliot L. Sherman found that some women actually have worse outcomes under female supervisors. They looked at five years of in-depth data from a 1,700-person firm in the information-services industry, and found that most female managers had no effect on the wages of women below them. Yet drilling down into data, they found that some lower-performing women who switched from a male supervisor to a high-performing female supervisor had a lower salary the following year than men who made the same switch. This may be because the supervisor feels threatened by the worker’s poor performance, and worries she may be implicated in it. “Female managers, perhaps responding to collective threat, appeared to act in ways that amplified, rather than diminished, the gender wage gap,” they write.

Similarly, Flabbi’s study of Italian manufacturers found that females at the bottom of the wage distribution received lower wages when a female was in charge of the company. Women at the bottom of the wage spectrum may have benefited from male CEOs, Flabbi told me, since they are lumped in with other women and assigned an average woman’s wage, which is higher than the wage they should receive. But a female CEO can come in and read these women’s capabilities more specifically, and reassign non-productive workers to even lower jobs, because she can see that these women will not be assets to the company, Flabbi said. This indicates that women who aren’t good at their jobs will see pay decrease under a woman leader.

Norway provides a good testing ground for the patterns these researchers have identified. In 2003, Norway passed a law mandating that the boards of public companies comprise at least 40 percent women. A study of Norwegian and other Scandinavian companies after the quota took effect found that the quota improved salaries for women in the top five percent of the earnings distribution. But there’s no evidence that the quotas had any effect on women lower down in the companies, nor that the companies hired more women. They also found no evidence that women were inspired to go to business school, pursue business careers, or delay having children to “fast-track” their careers once they saw more women in the boardroom. “In the short run the reform had very little discernible impact on women in business beyond its direct effect on the newly appointed female board members,” they write.

Still, regardless of their gender, workers may see better working conditions and fewer layoffs under women. That’s because women leaders may do more than male leaders to avoid laying people off, another study by Matsa and Miller found, this one of companies affected by Norway’s quota. (They did find that, as a result, this made companies less profitable, in contrast to many of the other effects of women leadership.) In yet another paper, Matsa and Miller looked at women-owned businesses in the U.S. and compared them to other business during the recent recession, and found that there were fewer workforce reductions in the women-owned businesses. That study also found that female-owned businesses were less likely to use contract employees and temp workers than male-owned companies were. They have two hypotheses about why women leaders may treat their workers differently. First, women may be more empathetic than men and thus less willing to cut people during slow periods. Second, women might be more patient than men and more willing to wait through slow times, knowing that when the economy rebounds, they’ll have the need for more employees once again.

This is perhaps not surprising. A survey of U.S. companies found that women leaders have different priorities than men do, Matsa said. “U.S. female senior executives attach the greatest importance to what they describe as the ‘communal’ aspects of the workplace, such as working relationships, customer quality focus, and communication. By contrast, male senior executives are driven more by personal reward factors, such as career development and compensation,” Matsa and Miller write.

As a recent series of essays published in The Atlantic argued, the workplace is still a notoriously tough place for women, who have to balance family and career while encountering sexism and still trying to grow in their careers. That there are more women at the top may not provide much solace to women trying to figure out how to make a go of it in the corporate world. But the evidence suggests that it should.