I heard this paper discussed on Freakonomics. The lead author, John List, is totally qualified and has lots of Uber driving data. They found that women made 7 percent less per hour than man. The reasons were time/location of driving (20%), experience (30%), and driving faster/more rides per hour (50%).
According to the authors, these differences are "inherent" to gender, i.e., women prefer to drive on Sunday afternoons, women are more likely to quit uber (76% vs 63% for men, within 6 months) and women "prefer" to drive slower.
I find that logic to be sound (or at least reasonable) but not adequate as an excuse to stop the analysis. Why not take risk (of incidents at certain places and times, the kinds of random passengers you get, and of accidents and damage from driving too fast, respectively) into account? I'm guessing that women are "willing to pay" 7 percent to avoid the risks that men might not notice or worry about.
When I give travel advice to women, I tell them that they have to pay the "girl surcharge" when they are alone in strange new places to make sure they are safe. That means taking a taxi instead of walking or hitchhiking, getting their own room instead of sleeping in dorms (let alone men's dorms), saying no to potential dates instead of "going for it" and so on...
Bottom line: The gender pay gap has a lot to do with the risk of being a women. The safer women are, the smaller that gap will be.