To find convincing evidence for this is difficult, however, economists have come up with several strategies (e.g., the degree of competion in an industry, variation over time, et cetera).
My colleagues Mario Lackner and Christine Zulehner have a new working paper where they exploit a market where some firms have market power due to an institutionalized cartel: Universites that automatically qualify for the Bowl Championship Series (BCS) in collegiate football have greater market power than those which do not qualify automatically.
They show that a higher market share results in a greater wage difference between male and female head coaches. In addition, female coaches are being crowded out by men.
Only firms with market power can sustain the cost disadvantages resulting from discriminating against a certain type of employee.