"I see no reason to reject ... as one of the factors"
Such agnostic logic is unassailable. You don't know; the powers that be don't know; the courts & lawsuits don't know. You're right not to reject the possibility.
However, you'd be wrong the assert the certainty "... disparity is also caused by discrimination" with such flimsy evidence.
We know for an incontrovertible fact that a few decades back women faced wage discrimination, even when doing the same job, with the same experience.
We know this from explicit records, with Lilly Ledbetter being one example. There is a reason why the various civil rights laws were enacted.
Therefore, to argue that wage discrimination does not now exist, the proof must be more rigorous than "we can't explain the remaining gap, but it can't be wage discrimination."
I have pointed to recent (within the last 10 years) court cases where the court determined that there was wage discrimination on the basis of sex. Thus, we know for certain that some wage discrimination exists.
If you want to have an argument that it's small - sure, I'll accept that. If you want to say it's hard to measure its magnitude - sure, I'll accept that too. But there's zero justification to state that it does not exist, when we have evidence that it does exist.
I can be wrong. I could have missed some recent study which resolves this more clearly. There may be a report which shows that the court cases I came across happen to be the only ones that have happened i the last 10 years. Such things would be evidence that my position is weak or untenable.
I have not seen such counter-evidence, hence I see no reason to reject my conclusion that wage discrimination on the basis of sex remains an admittedly minor contribution to the wage gap.
"We know this from explicit records, with Lilly Ledbetter being one example."
I'm not tremendously familiar with this case, but according to the gods of wikipedia, the evidence for discrimination consisted of nothing but evidence of difference.
"It is unfair, however, to give no guidelines of what you think might be acceptable."
If you do not accept a jury's decision that there was pay discrimination on the basis of sex, then you have ridiculously high bar that precludes effectively all evidence.
The same court decision that was thrown out by the SCOTUS? The same jury that used the 51% "more likely than not" standard to assume that the difference in pay was due to discrimination, there being no actual clear evidence?
Such agnostic logic is unassailable. You don't know; the powers that be don't know; the courts & lawsuits don't know. You're right not to reject the possibility.
However, you'd be wrong the assert the certainty "... disparity is also caused by discrimination" with such flimsy evidence.