I think there have actually been studies looking at the increase of women in work and the GDP. One article I found quickly: http://thinkprogress.org/economy/2014/04/16/3427220/women-work-hours-gdp/

I think that increasing confidence allows for women to try to do more in the workforce, or engage in it. As in, vie for bigger promotions or try to get a job, or make a startup. All three would stimulate the economy and increase the GDP.

I don’t think its a hard interchangeability, but a soft cause/effect.

Regardless, women should be more confident about their options and not feel beholden to archaic societal ideas. Men should do the same — there are many sexist policies acting against men.

If only it were easy to break free from norms and societal constructs.