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Most of the reporting you see on this stuff tends to ignore most factors which would tend to explain differences in income for different work. So it's a god of the gaps argument that you are (unwittingly?) making. If we take into account one or two things the "gap" shrinks, if we take account one or two more it shrinks further, if we take account of five or six there's maybe 5% left. And then we stop because that way leads to trouble.

So Warren Farrel identified about 20-30 factors to take into account. This included some that even by themselves reduced the gap's size of the order of over 90%. Obviously there's a lot of overlap. The point is that no study has attempted to do what you say and take into account, "all the other factors". Not even close. The studies don't even take into account the factors which are greatest in reducing the gap.

As a result your figure of 10% or so was pure bullshit. Mine was too; the data just isn't there. However the end result is certainly in favour of women because women have a greater value than men as employees because of the various anti-male laws feminists have introduced. You can certainly find some studies that result in a negative wage gap although it's usually more like 2%, but for the most part the research here is chasing ghosts. Indeed literally it uses the same technique as ghost hunters: throw out a few sensible sounding ideas for a phenomena, then after rejecting them say "therefore the answer must be ghosts" as an explanation for any remaining phenomena.

https://www.amazon.com/Why-Men-Earn-More-Startling/dp/0814472109

The single factors that tend to explain almost the entire gap by themselves tend to be something along the lines of comparing like with like as to family earning responsibilities. That is to say childless unmarried men and women tend to earn the same. Once people get married and have kids women choose to earn less and force the men to pick up the slack by earning more. So the pay gap is essentially a result of anti-male discrimination forcing men to work harder to support women's choices.

As a result you get odd results of things like black women earning more than white women (if you take into account education level) and lesbians out-earning straight women. I would explain these results in terms of the responsible-to-earn for someone else's consumption factor.

Hmm. Hard to find a nice link to a study on this one factor. But it typically knock out over 90% just by itself. These days if you Google those terms you get the various studies showing how much more young women are earning compared to young men. Of course that's mostly because women are 60% more likely to go to college.

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ETA: Also the wage gap is smaller in developing countries than in the West. As a general rule of thumb the better off you are in terms of privilege, the less you can afford to earn, which is why white women have the biggest "gap" of all. The entire topic misrepresents privilege as a oppression, which is exactly what you need to do if you're a feminist of course.

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ETA: Yeah I can't find any nice reports on family responsibility as a factor (usually it's referred to as "unmarried, childless"). It was common enough 20 years ago but these days the search results get swamped by by the stories of YOUNG and "unmarried, childless" women earning about 8% more than men. But as I say this is really more because women are getting college degrees far more than men are due to the massive amount of sex discrimination in education in the USA (though these results hold all over the English speaking world). maybe you'll have better luck if you want to pursue it.