Differences between the sexes in educational attainment are of interest to many people. In Ireland, as elsewhere, males are being left behind by females in key exams and university entrance. So where does it all start and is it the same for everyone?
Using the Growing up in Ireland data I look at differences in maths score: I estimate quantile regressions controlling for a bunch of chararacteristics (SES, birthweight, maternal smoking, income and more). These show the effect of being male on the maths score at different points of the conditional distribution : so high quantiles are not "high test scores" but "high test scores conditional on the covariates one has included". I interpret this as proxying unobserved ability, this could be cognitive ability but not necessarily. The outcome is scaled to have a mean of 100 and a std deviation of 15.
The results are striking. Boys do better on average so a linear regression gives a coefficient of about 1.2. By comparison, being right-handed or having been breastfed is worth an extra 1.4 points. But at lower quantiles the effects are smaller and are not statistically significant. At higher quantiles the effect is around 4 points.
So I interpret this as saying that at low levels of unobserved ability it doesn't matter if the child is a boy or girl. But for "smarter" children being a boy is an advantage i.e. being male and being "smart" are complements.