(Regular readers of this blog will know that I consider that a good thing.)

It is rare that I even understand a seminar in econometric theory let alone come away being able to explain it in words but this one was exceptionally clear.

A perennial applied topic is to try to measure the returns to education.  If someone attends an extra year of school how does that affect, say, their lifetime earnings? Absent a controlled experiment, the question is plagued with identification problems.  You can’t just measure the earnings of someone with N years of education and compare that with the earnings of someone with N-1 years because those people will be different along other, unobservable, dimensions.  For example, if intrinsically smarter students go to school longer and earn more, then that difference will be at least partially attributable to intrinsic smartness, independent of the extra year of school.

Even a controlled experiment has confounding factors.  Say you divide the population randomly into two groups and lower the cost of schooling for one group. Then you see the difference in education levels and lifetime earnings among these groups.  These data are hard to interpret because different people in the treated group will respond differently to the cost reduction, probably again depending on their unobserved characteristics.  Those who chose to get an extra year of education are not a random sample from the treated group.

Torgovitzky shows that under a natural assumption you can nevertheless identify the returns to additional schooling for students of all possible innate ability levels, even if those are unobservable.  The assumption is that the ranking of students by educational attainment is unaffected by the treatment.  That is, if students of ability level A get more education than students of ability level B when education is costly, they would also get more education than B when education is less costly.  (Of course their absolute level of education will be affected.)

The logic is surprisingly simple.  Under this assumption, when you look at students in the Qth percentile of education attainment in the treated and control groups, you know they have the same distribution of unobserved ability.  So whatever their difference in earnings is fully explained by their difference in education attainment. (Remember that the Qth percentile measures the relative position in the distributions.  The Qth percentile of the treated groups education distribution is a higher raw number of years of schooling.)

Not only that, but after some magic (see figure 1 in the paper), the entire function mapping (quantiles of) ability level and education to earnings can be identified from data.