Richard Posner is probably the most prominent judge in the U.S. not on the Supreme Court. He has to be the hardest working, as a judge on the 7th Circuit Court of Appeals and a senior lecturer at the U. of Chicago Law School. The author of approaching 40 books, by one measure, he's the most cited judge of the 20th Century. 

Posner has a joint blog with Gary Becker, the Nobel-winning UC economist, where they discuss a topic every week. Awhile back, they took on "Rating Teachers." Judge Posner wrote:

I don’t think varying salaries on the basis of measures of teacher quality are a feasible reform. My reasons for this pessimistic judgment are several. First, teaching below the college level tends not to be attractive to competitive people. I happen to have a job, as a federal court of appeals judge, in which everyone is securely tenured and paid the same salary, even though the judges vary in ability, experience, and effort.

I.e., nobody works as hard as Posner.

There are many jobs of that sort, they have their pluses and their minuses, and it would be a mistake to think that all such jobs would be performed better if they were restructured along the Darwinian lines that prevail in business. It’s a mistake to think that everyone is a natural risk taker. Tenure, a wage that varies with seniority rather than measured output, and long summer vacations create a compensation package that is attractive to a certain kind of person.  

Second, while in a sample of millions, as in the study by Chetty et al. that Becker cites, it may well be inferrable, as the study finds, that teachers vary in the value they add to their students, within an individual school such an inference will be very difficult to draw. The average IQ and home environment of students in different classes may differ significantly, random factors may affect their future success, and there can be spillover effects from other classes. 

I know a lot about the history of the evolution of baseball statistics over the last 150 years, a lot more than I know about the development of teacher rating statistics. Maybe I'm not up to date, but my general impression is that teacher rating stats are about where baseball stats were in the late 1800s.

Here's a concept for a nonfiction book. A lot of books come out that focus on schools, with journalists visiting KIPP schools, charter schools, etc. etc., and there's always talk about value added test scores being used to evaluate teachers, but I've never seen a journalist follow some teachers, sitting in the back of the classroom, and then watch them get back their value-added test scores. Do the value-added scores match up with the journalists' subjective impressions?

You may be saying, "Subjective? Everybody knows we have to trust only objective statistical measures, even if they were just made up this year!" In truth, subjective and objective evaluations improve each other. Right now, we have a bunch of brand new complicated value-added measurement systems with few ways of checking whether they seem plausible or not.

Suppose for example that a mediocre teacher teaches English, and a superb teacher teaches the same students history. Both teachers require essays. The superb teacher improves the students’ writing skills, and that in turn improves their performance in their English class, making the English teacher look better than he or she really is.  

Third, and related, varying teachers’ salaries by some output measure will induce all sorts of wasteful strategizing—office politics—what organization economists call “influence activities,” an aspect of agency costs—by teachers hoping to get a good quality rating. They will angle to get the best students assigned to their classes, even when salary is tied to “value added,” as discussed by Becker, because smarter students are likely to improve more.  

Fourth, although in principle the cost of higher salaries for the better teachers could be offset by reducing the salaries of the worse teachers, that is surely infeasible; so the Darwinian approach would cost more than the existing system, and maybe as much more as raising teacher salaries by a uniform percentage.  

Finally, I am not clear what we should think the problem of American education (below the college level) is. Most children of middle-class (say upper quartile of households, income starting at $80,000) Americans are white or Asian and attend good public or private schools, usually predominantly white. The average white IQ is of course 100 and the Asian (like the Jewish) almost one standard deviation higher, that is, 115. The average black IQ is 85, a full standard deviation below the white average, and the average Hispanic IQ has been estimated recently at 89. 

Black children in particular often come from disordered households, which has a negative effect on ability to learn and perhaps indeed on IQ (which is only partly hereditary) as well. Increasingly, black and Hispanic students find themselves in schools with few white or Asian students. The challenge to American education is to provide a useful education to the large number of Americans who are unlikely to benefit from a college education or from high school courses aimed at preparing students for college. The need is for a different curriculum and for a greater investment in these children’s preschool environment. We should recognize that we have different populations with different schooling needs and that  curricula and teaching methods should be revised accordingly. This recognition and response should precede tinkering with compensations systems.