Women are paid more than men and are promoted more often

 
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This is the way the world ends. Not with a bang but a whimper.
If you control for background and exit rate.

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Our empirical analysis shows that female executives have different backgrounds and experience from male executives and that women are paid more and have higher pay-for-performance sensitivity than men conditional on rank, background, and experience. We also find that women are promoted more quickly internally but display similar rates of external promotion to men; however, women and men have similar demotion rates. The higher rate of promotion results in female executives at the upper levels of the hierarchy having significantly less job experience than male executives. Female executives, however, have a higher exit rate than men and the probability of a female executive becoming CEO is less than half that of male executives at every age. Our decomposition shows that the male executive survival rate is twice that of female executives. The gender differences in career length are accounted for completely by the difference in exit rates, and, conditional on survival as an executive at any age, women have a higher probability of becoming a CEO. The average career compensation of female executives is lower than that of male executives, but it is higher than male executives if female executives are assigned the male initial experience, the male initial rank assignment, or the male career experience distribution