Wages, height, and gender

A loyal MR reader asks:

We know women make less than men.  We know shorter people make less than taller people.  How much of the first is explained by the second?

Not much.  Short men have less self-esteem (recall that male height at the time of high school predicts earnings better than adult male height), but short women, when they are young, feel no worse about themselves than do tall women.  Next?

#28 in a series of 50.