Talent and Opportunity Cost

Alex Tabarrok has an interesting post, "Using Nature to Understand Nurture" which describes a genome-wide association study (GWAS) that tracked math courses taken in high school and ultimate educational attainment.

The study results Alex’s commentary use the implicit framing that there is unrealized talent - students that could have taken higher-level courses but didn't perhaps because their school didn't offer or route them to the right classes. But the phase "…it wouldn’t be a surprise if there were more math talent in the pool" got me thinking – of course there is more talent. There has to be, since this is just looking at math.The variable you don't see measured here is how much other (non-math) talent each student had, and how far they went with it.

In that sense, there is always going to be more talent than is made use of. The most talented people are also the ones for whom the limiting factor in their overall achievement is how much time they have. So the study is aggregating students who are talent-limited and those who are not, and it’s easy to then conclude that the achievement deficit is caused by a lack of educational opportunity within the schools. In fact, the greater the level of students’ talent outside of math, the more students will take their advanced courses outside of math, and this would be tabulated as unrealized math potential.

Essentially, this is all attrition, but we need to differentiate between attrition due to lack of opportunity vs. attrition due to the existence of even better opportunities. A student who’s talented in only math will try to max out on the math path. But someone who’s talented in both math and art (or science, or english), has a choice to make. Thus, schools with good curricula in areas outside of math would appear to underperform precisely because they're giving their more broadly-talented students a wider array of options. Looks like there's a Simpson's paradox at work here.