Is my gender wage gap view a Motte and Bailey Doctrine?

Commenter Julien Couvreur taught me a fantastic new term today: the motte and bailey fallacy. I don't think his comment is persuasive at all, but it's interesting enough to spend some time talking about. A motte and bailey fallacy (for those of you who, like me, weren't aware of it) is according to Nicholas Shackel less a fallacy and more of a doctrine - or if you'd like a style of presenting an argument. You can read the Shackel link for background but the gist is that you promote and live in and enjoy in a less defensible but more desirable argumentative terrain when you can (the bailey), but when things get tough you retreat to the more defensible but less desirable terrain (the motte) and you treat them like the same thing. Julien alleges this is what I'm doing. Absolutely unequivocally I am not, but let's start with his comment:


"I smell a mote-and-bailey fallacy. Activists stretch and go wild with their interpretations, and when called on it, they fall back to the uncontroversial facts ("that's what we meant all along, you denier!"). The aggregate gender pay gap is real, and I doubt Bob questions it. But it is usually stated as women getting payed less "for the same job" or "for the same skills", explicitly or implicitly as the result of employer discrimination. That is simply incorrect and deserves to be called false, fallacious, a myth. Plus it offers no legs to the associated policy recommendation (forcing employers to pay "fairly")."


The problem here is I am not an activist. I am not Obama. I am not Arquette. My bailey is what I posted, and as far as I know I don't have a motte. Now Obama or Arquette might be guilty of the motte and bailey fallacy if they were pressed but I am absolutely not. I've never made anything like the switch that Julien describes.


A possible candidate for this (although I don't want to be too accusatory because I can't read his mind or his intentions) is Steve Horwitz's video on the wage gap. He leads with calling the wage gap a fallacy and only in the last minute or so of the video does he get into some of the qualifications that should lead to the conclusion that it's not a fallacy at all. So if one wanted to accuse him of a motte and bailey fallacy the first four minutes or so are his bailey and the last minute is his motte. Because of the time ordering that is possibly appropriate. Certainly enough people have mistakenly thought the first four minutes were his position that he had to do damage control and write a post correcting them. I don't want to push that too hard because keeping the qualifications towards the end doesn't in and of itself guarantee a motte and bailey fallacy (although it might not be the most strategic approach if you think that last minute is important to your point).


I also want to reemphasize an analytic point that I think Julien might have missed. He writes "The aggregate gender pay gap is real, and I doubt Bob questions it." I want to be clear that I am not concerned that anyone thinks the aggregate pay gap isn't real. I'm assuming everyone thinks it's real. I'm concerned that people are badly misinterpreting the meaning of the coefficients on the occupational dummies.