A recent study by John Richwine and Andrew Biggs of the Heritage Foundation and the American Enterprise Institute purports to show that teachers are on average overpaid. I do not find their evidence convincing, and the reasons have less to do with their affilitations than the technical nature of their work. My problems with their paper are:

(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:

w=(d-a)/(b+f) +(g-c)X1/(b+f)+(e2-e1)/(b+f)

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:

(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:

w=(d-a)/(b+f) +(g-c)X1/(b+f)+(e2-e1)/(b+f)

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:

"

*Table 2 shows how teacher salaries change depending on whether education or AFQT is included in the regression. The first row is the "standard" regression based on our CPS analysis in the previous section: Years of education are controlled for, but AFQT is not. The standard regression shows a teacher salary penalty of 12.6 percent.**The second row includes both education and AFQT in the same regression. The impact on teacher wages is small: The penalty decreases by less than two percentage points. The third row again includes AFQT but now omits education. With this specification, the change is dramatic: The teaching penalty is gone, replaced by a statistically insignificant premium.*

*How to interpret these results? On the one hand, the difference in IQ between teachers and other college graduates*

*by itself has only a small effect on estimates of the teacher penalty. As the second row indicates, teachers with both the same education and AFQT score as other workers still receive 10.7 percent less in wages.*

*However, as we have shown, education is a misleading measure of teacher skills in several ways. In addition to the IQ difference between teachers and non-teachers, the education major is among the least challenging fields of study, and years of education subsequently have little to no effect on teacher quality. This suggests that eliminating education as a control variable and letting AFQT alone account for skills (as in the third row) may provide the most accurate wage estimates.*

*Replacing education with an objective measure of skills eliminates the observed teacher penalty, indicating that non-teachers with the same education as a typical teacher will likely have more applicable skills. We emphasize that a job is not necessarily less important or less challenging when the credentials for it are easier to obtain. Indeed, effective teachers are highly valuable to society and the economy."*

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).

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