THIS week’s Free exchange column looks at a fascinating bit of statistical work on the value of a good teacher. Economists Raj Chetty, John Friedman, and Jonah Rockoff obtained a massive data set from a large, urban school system, which covered 2.5m students (and 18m test scores) over two decades. With it, they were able to calculate a “value added” score (showing how a teacher could be expected to influence a student’s test scores) for every teacher in the sample—and demonstrate that the score didn’t simply represent a child’s background advantages, of parental income, for example. Even better, they were able to track the performance of the earliest pupils in the sample into early adulthood, and therefore see how exposure to teachers of various quality really mattered. The results are remarkable:

They find, for instance, that the quality of teachers varies much more within schools than among them: a typical school has teachers spanning 85% of the spectrum for the school system as a whole. Not only do teachers matter, in other words, but the best teachers are not generally clumped within particular schools.

Across schools, however, better pupils are assigned to slightly better teachers on average…

[E]xposure to better teachers is associated with an increased probability of attending university and, among pupils who go on to university, with attendance at better ones, as well as with higher earnings. Somewhat more unexpectedly, good teachers also seem to reduce odds of teenage pregnancy and raise participation in retirement-savings plans. Effects seem to be stronger for girls than for boys, and English teachers have a longer-lasting influence on their pupils’ futures than maths teachers.

The authors reckon that swapping a teacher at the bottom of the value-added spectrum with one of average quality raises the collective lifetime income of each class they teach by $1.4m. That rise would apply across all the teacher’s classes and over the whole of his or her career.

In present discounted value terms that works out to $250,000. That is vastly more than teachers are typically paid per year. And it is vastly more than school systems typically offer teachers unions in exchange for accepting rigorous assessments, performance pay, and the ability to sack poor teachers. That is understandable; as the gains accrue to the students themselves over a long period of time, school systems can’t very well dip into them in order to boost teacher compensation today. It does suggest, however, that reforms which focus on assessing and improving teacher quality are likely to pay off handsomely down the line. And a school system deciding how to deploy scarce resources across teaching, administration, technology and other amenities should keep that in mind.