I doubt this. See the HN post from a few days ago ("I put Mr. on my CV and got a job"). It would seem that employers not only pay their females employees less, but have little faith in them to get the job done, thus they wouldn't hire them in the first place.
Thus, we have two possibilities: either nobody in the world is both aware of the potential for arbitrage and unethical enough to exploit the situation, or the wage gap is smaller than these estimates suggest.
In fact, many new-economy juggernauts like Microsoft, Google, and Facebook do precisely this. Their employee marketing aggressively recruits women. Are they doing this out of the goodness of their hearts, or because they see an economic opportunity? Ultimately it doesn't really matter - the effect is that more women get employed in positions of power. But it's quite possible that the economic arbitrage that people are pointing out is happening in practice, right now, you just don't hear about it because most arbitragers are not dumb enough to let you know what they're doing. And the effect, over a long time scale, is that businesses run by bigots are replaced by businesses with a more accurate perception of personal productivity, which leads to a more equitable world for everyone.
There really doesn't seem to be any alternative besides these three:
- Women are not underpaid or more efficient.
- There is not a noticeable number of unethical people seeking to get rich.
- People are getting rich by hiring lots of women and outcompeting everybody else who prefers men.
The last two don't look true to me, which suggests that the first one is true. I certainly could be wrong about the assumptions or conclusion, but it does suggest that.
But many of them did...
Which is exactly what happened over the past 30 or so years.
I'm not saying that this is the case, just pointing out that you missed options that would allow the hypothesised discrimination to exist.