An NBER working paper from Jonah Rockoff and Mariesa Hermann has quantified what every school-age child knows: not much learning happens with a substitute teacher.

Looking at the impact of teachers' absences on elementary student achievement in New York City from 1999 to 2009, the researchers calculate a jaw-dropping estimate of the productivity lost when a sub is in the room for just a single day: about the same as replacing an average teacher with one who is at the absolute bottom-of-the-barrel.

When teachers are absent also matters a lot. Teachers who are absent close to the start of the annual state testing period (within five days) wreak havoc on student performance on such tests, having a negative impact that is nine times greater than if they were absent other times during the school year (20 or more days before the tests).

Although it is possible that students perform more poorly on the tests because they are more anxious with a sub, the researchers posit a host of other reasons, some suggesting that teachers routinely skirt very close to the edge of cheating. Absent teachers are of course unable to do test prep, remind students of effective test-taking strategies or clarify instructions, but they are also unable to overtly, covertly, or inadvertently prompt students to fill in the correct answers. (By some reports, New York State makes the process of teaching to the test very easy.)

Perhaps we ought to replace classroom teachers with substitutes several weeks in advance of testing, just the tonic needed to ensure that teachers focus from day one of school on real learning, knowing that they can't salvage test scores with quick fixes in the weeks before testing. We're only half kidding.