I've written a few times about the gender composition of corporate boards, not the most important manifestation of entrenched sexist practices in the business world but the most blatantly obvious one since it would be totally trivial for a firm that actually cared about gender equity to have an equitable board.
In "When All Are Abord: Does The Gender of Directors Matter", Miriam Schwartz-Ziv looks at one sub-set of firms that do have to take women's representation on corporate boards seriously—Israel firms in which the State of Israel owns a substantial financial stake. Such firms are required by law to have women on their boards and have been for about twenty years:
How does gender-balance affect the working of boards of directors? I examine boards that have been required for two decades to be relatively gender-balanced: boards of business companies in which the Israeli government holds a substantial equity interest. I construct a novel database based on the detailed minutes of 402 board- and board-committee meetings of eleven such companies. I find that boards that had critical masses of at least three directors of each gender in attendance, and particularly of three women, were approximately twice as likely both to request further information and to take an initiative, compared to boards that did not have such critical masses. A 2SLS model confirms these results. Consistent with these findings, the ROE and net profit margin of these type of companies is significantly larger in companies that have at least three women directors. In addition, boards that included a critical mass of women directors were more likely to experience CEO turnover when firm performance was weak. At the level of the individual directors, both men and women directors were more active when at least three women directors were in attendance.
This is important not only for what it reveals about gender, but for the fact that it suggests that firms are being systematically mismanaged.
There's a simplistic theoretical argument that sexism in general can't be systematically present in a competitive market economy, since firms that irrationally discriminate against women will lose out in the marketplace. But male-dominated boards have been very persistent, not necessarily "despite" the fact that more balanced boards might do better but perhaps in part because firms don't boards that are inclined to "request further information" and otherwise make trouble.
Meanwhile in "Gender and Connections Among Wall Street Analysts" Lily Fang and Sterling Huang find that the main driver of whether a woman analyst is rated a "star" is her actual performance, whereas for men connections are the main driver. I don't have empirical proof that connections rather than abilities are what puts men on corporate boards, but frankly nobody even seems to deny that that's how it works.