Why do women bid less for gigs?

They offer 4% lower prices, win jobs more frequently, and earn higher expected revenue (prob[win]*price) than men:  New working paper:

...we provide empirical evidence for a statistically significant 4% gender wage gap among workers, at the project level. We also find that female workers propose lower wage bills and are more likely to win the competition for contracts.

This raises the obvious question, whether women bid more aggressively than men because they think that the opportunity cost of their time is lower, or because they are bidding optimally, and men are not.