Adverse selection in teaching

"Those who cannot do, teach" is a succinct characterization of the problem of adverse selection in our profession. Now we learn two more types of teacher selection, only one of which is adverse:

Using data for New York City schools from 2000-2005, we find that first-year teachers whom we identify as less effective at improving student test scores have higher attrition rates than do more effective teachers in both low-achieving and high-achieving schools.

This sounds pretty good. But now for the rest of the story...

For teachers leaving low-performing schools, the more effective transfers tend to move to higher achieving schools, while less effective transfers stay in lower-performing schools, likely exacerbating the differences across students in the opportunities they have to learn.