“The richer the country, the more likely women and men choose different types of jobs.”
This is the very interesting finding reported by Susan Pinker in The Sexual Paradox. She is specifically studying the problem that got Laurence Summers into so much undeserved trouble: why are there many fewer women than men at the highest levels of math, science, and engineering? Her answer: when given the choice, women with high aptitude for math, science, and engineering are more likely than similarly gifted men to choose something else.
In fact, Pinker argues, it is not that the women are discriminated against or diverted, where men are not. Rather, women with high math aptitude are also likely to have high verbal aptitude and high empathy, whereas math-minded men are not. It is the men who are channeled into science and engineering because they do not have as many other choices. The women, given the choice, are more likely to take their math skill to clinical medicine. They want to do work with people that makes more of a difference in people's lives.
The countries with the highest rates of women in science and engineering are not the ones in which women are most free, but in poor and authoritarian countries where math-competent women are pushed into science and engineering by families that want them to have higher salaries, and states that want more scientists and engineers.