Gender segregation at work is one of the biggest contributors to the wage gap between women and men–in 2014, women cashed in at about 79 cents per men’s dollar. Much of the difference is explained by the fact that women overwhelmingly dominate “pink-collar jobs” that generally pay less, like teaching, nursing, and waitressing, and men dominate in higher-paying positions, like physicians, sales directors, and CEOs. However, even when men and women start in the same field, men are much more likely to advance. For instance, in June, The Washington Post reported that the number of Fortune 500 companies led by women was at an all-time high: 5%. (Less heralded? That women make up 45% of the labor force in these companies.)

While the number is small, clearly some women do make it to the top. So, when women are employed in upper level positions, what happens to women left near the bottom?

Researchers Stainback, Kleiner, and Skaggs studied the association between women in leadership positions and gender segregation in lower-level positions across 86 Fortune 1000 firms in Texas. Using statistical models, they tested the level of gender segregation across eight non-managerial occupational categories based on the percentage of women in managerial and executive positions. Overall, the researchers found that having more women in leadership positions is associated with less gender segregation in lower level jobs. However, this relationship gets much smaller when the percentage of women on corporate boards approaches 20%.

Since none of the firms actually has women as 20% of its corporate board, their finding is telling of the gross inequality between men’s and women’s representation in executive positions. Put differently, because corporate board membership hasn’t surpassed 20% female, the authors cannot make any conclusions about what would happen if it did.

Still, the association between more women at the top and less gender segregation below leads the authors to conclude that women who make it to the top can–and do–act as “agents of change” across organizations.