(1) They estimate a reduced form, which means it is difficult to interpret the meaning of their coefficients.
(2) Even if we accept their reduced form, there are issues in how the authors specify their explanatory variables.
(3) The authors' specification has a serious selectivity problem and
(4) Most disturbingly, they ignore their most convincing spefication, a specification that supports the idea that teachers get paid 10 percent less in wages than those in other professions.
Let's turn to each problem in turn:
(1) Underlying any wage equation is a supply curve for labor and a demand curve for labor. Let's write these out:
L(s) = a + bw +cX1+ e1
L(d) =d - fw +gX2 + e2
X1 and X2 are vestors of explanatory variables, e1 and e2 are residuals from a regression equation.
Let's say one of the elements in X2 is years of education--the demand for labor goes up in years of education after controlling for wages. The coefficient g that is multiplied by years of education is thus easy to interpret--it is a wage premium associated with education.
The problem is that the authors estimate a reduced from, where they put L(s)=L(d). The resulting equation they arrive at is
w = d/(b+f)+gX2/(b+f)+e2/(b+f)-a/(b+f)-cX1/(b+f)-e1/(b+f)
If X2 is education, and is in both the supply and deman equation, the reduced form wage equation reduces to:
So the coefficient on X1 is (g-c)/(b+f). This coefficient helps with prediction of wages, but it does not allow us to disintangle the stuctural foundation of wages. This why why when we are trying to determine the impact of policy on outcomes, reduced forms are problematic.
(2) The authors assume that wages are linear in years of education. This is clearly not true--the impact of education on wages tends to fall into "buckets;" < 12 years, 12-15 years, 16 years, and > 16 years. You get the idea. Their mis-specification of the educational variable could bias their other findings.
(3) People who select themselves into teaching might have skills that do not show up in educational levels or on aptitude tests. I have lots of education and do well on aptitude tests, but I think I would be at sea teaching second graders and REALLY at sea teaching middle schoolers. Teaching students at these levels requires patience, insight and social skills that are not measured by aptitude tests.
The authors point to the interesting fact that people generally make less money when they move from teaching to non-teaching jobs. There are alternative interpretations to there. One is that teaching is a hard job, and so people willingly leave at lower wages. The second is that those who select out of teaching are those who have decided they are not very good at it.
(4) The most disturbing part of the paper is this:
So the authors have a regression with both education (which reflects Spence-type signalling, among other things) and IQ. The reduction in the R-squared when education is dropped suggests that after controlling for IQ, the coefficient on education continues to be statistically different from zero. When both IQ and education are included, teachers suffer a 10 percent wage discount relative to the private sector. Yet the authors ignore this result for the rest of the paper.
(FWIW, I really admire Michelle Rhee).