There isn't a huge gap, not for the same job/title combination (there are cases where the gap does exist for the same job, but it's typically less than 10%). The gap widely most widely reported, the 70% figure, is primarily caused because of the genders holding different jobs, where the average pay for female-dominated jobs is less than the average pay for male-dominated jobs.

The belief that a woman with the same experience, skill, etc. is a worse performer would lead to a lower salary for women. That's the whole point of contention.

And we should probably let go of the idea that markets are rational.

Perhaps it is due to "family costs" being carried disproportionately by women.

Leaving early to pick up kids, staying home when kids are sick, etc. Even though typical gender roles are becoming less typical, they may still result in differential output from the perspective of an employer.

Thomas Sowell (a while ago) showed a dramatic difference in salary between all women, and women who had never married, suggesting that a huge component of the pay gap was due to household and family expectations.

I imagine there is more recent research on this exact theory, but I'm not aware of it.

Perhaps the same biases that might influence career progression/pay-rise discussions could also influence hiring decisions?

Though I agree with your secondary assertion.

No, there isn't. The gap is between different professions, not intra-professional. Where it is intra-professional, men tend to work more hours, and women tend to preference conditions over monetary remuneration (i.e. flexibility over pay, extraneous benefits over direct compensation etc etc). Just to be clear, extra time off is remuneration, as are things like on-site day care centres, but they aren't ever counted in pay gap studies (that I have seen anyway).

Add to that that Lesbians make more than straight women[1] - and gay men less than straight men [2][3] - and there is a bit more at play.

The problem is that any time there is something men do better than women - like negotiate pay - rather than bring women up to the male standard (teach women to negotiate better), people want to hamstring men (no pay negotiation). Anti-worker policies and pro-gender policies are often indistinguishable, if only to me personally, and in my more cynical moments think this is a business conspiracy to deflate wages to female levels, not increase wages to male levels.

[1] http://bigthink.com/dollars-and-sex/what-explains-the-lesbia...

[2] http://onlinelibrary.wiley.com/doi/10.1111/j.1468-232X.2009....

[3] https://joeclark.org/gaymoney/findings/

> set of confounders itself is a predictor of sex. This is a technique I've seen used by people who try to deny the existence of a pay gap.

This doesn't seem invalid? If for example 'wanting to spend more time at home'/'cares about team fit more than salary' is a predictor of gender, that doesn't mean it shouldn't be excluded from analysis.

What we care about is whether the pay difference is because of people treating women unfairly. If a different trait causes lower salaries in both men and women, but is more common among women, the problem is not a gender pay gap.