I have read the paper many times, thank you for trying to belittle me. I was objecting to your particular claim that women are paid less for the same work. Now you are raising completely different points about men and women doing DIFFERENT work. I don't deny that men and women do different work and that societal expectations about gender roles is the primary cause of this. I fully agree with that.
There were many claims that women were being paid less for the same work. The Department had a legal obligation to prevent this as a civil rights issue, so they tried to discover what exactly was happening. They could not determine that such a thing was happening. Of course, every economist was saying the same thing: Investors almost universally invest in the highest expected return. If women were doing the same work for less pay, investors would invest in firms that primarily or solely used women as workers, thus increasing demand, and pay, until an equilibrium is reached.
The final conclusion: "As a result, it is not possible now, and doubtless will never be possible, to determine reliably whether any portion of the observed gender wage gap is not attributable to factors that compensate women and men differently on socially acceptable bases, and hence can confidently be attributed to overt discrimination against women. In addition, at a practical level, the complex combnation of factors that collectively determine wages pad to different individuals makes the formulation of policy that will reliably redress ay overt discrimination that does exist a task that is, at least, daunting and, more likely, unachievable." (pg. 36)
The Department of Labor has not done an equivalent study since this 2009 one.