> We estimate several models with an extensive list of control variables and high school fixed effects. Results consistently show that high school GPA is a positive and statistically significant predictor of educational attainment and earnings in adulthood. Moreover, the coefficient estimates are large and economically important for each gender.
I doubt there will ever be a way to satisfactorily control for other variables when it comes to these sorts of real-life studies (there is a reason the majority of social science isn't reproducible[1])
I know that personally my grades don't tend to correlate with my actual knowledge at all. I've failed things because I've been bored with them, and I've gotten perfect grades on things I don't understand at all outside the tested material.
My guess is it is similar to IQ results - does a good job weeding out people who know nothing, but does worse differentiating between students who are satisfactory and those who are exceptional