Women score just as high as men on the four factors that determine who becomes a CEO, Steve Kaplan and Morten Sørensen find in their study. Yet when those factors are held constant, female candidates for a CEO position are 28 percent less likely to be hired.

“That was a disappointing finding,” Kaplan says in an interview. “Is there any discrimination going on, or are women not trying to be CEOs? It could be one or the other, or both.”

Overall, roughly 10 percent of the candidates in his study with Sørensen are female. That includes 5 percent of CEO candidates and 8 percent of both CFO and COO candidates.

There’s no dispute that women lag in reaching the C-suite. Chicago Booth’s Marianne Bertrand and Kevin F. Hallock, now at Cornell University, found in a 2001 study that women were underrepresented among the five highest-paid executives at S&P 500 firms from 1992 to 1997. Only 2.5 percent of those executives were female, and just 0.5 percent of CEO or chairperson roles were held by women.

The numbers have improved, but only slightly. As of February 2016, just 20 of the S&P 500 companies are run by women, according to Catalyst, a nonprofit research group that promotes workplace inclusion.

Bertrand argues that women face a stronger trade-off than men between career and family. In a 2010 study, she and her coresearchers, Harvard’s Claudia Goldin and Lawrence F. Katz, find that MBAs experience huge wage penalties for taking any work leave, which women are likely to do. In a 2009 survey of CEO research, Bertrand wrote that it is likely that “women’s ability to hold top-level jobs is primarily constrained by either their desire to spend time with family or the continued relevance of strong gender norms in terms of the allocation of childcare duties, both of which may constrain career advancement given a working environment that offers limited tolerance for anything less than full commitment to work.” Her work indicates that until stereotyped gender roles change, women are unlikely to get equal billing at the top.