It would help if you posted the empirical data you refer to.
There are some good studies on this subject that I've read over the years though, for instance one among lawyers in a firm in which women were paid about 2-3% lower than men, on average IIRC. But these often don't or can't take into account personality characteristics. For instance, women on average are more agreeable and so often don't negotiate as hard as men on their salary.
When controlling for all factors, wage differences largely disappear.
https://www.epi.org/publication/womens-work-and-the-gender-p...
The authors also conjecture that this is due to cultural biases, but obviously cannot prove this.
For instance, their overview that women arrive in college less interested in STEM, and they hint suggestively that this is due to discrimination. Except this hypothesis doesn't at all explain the gender equality paradox; in fact, it predicts the exact opposite of what we see.
Normally in science, a falsification this strong would immediately dismiss a hypothesis as a viable candidate theory. It's suggestive that it hasn't.