Are nurse anesthetists overpaid by 74%? Are telemarketers underpaid by 25%? If you accept the standard statistical model used to defend huge and sweeping pay raises for public schoolteachers, then you pretty much have to accept these conclusions, too. They derive from the same set of data.

If you follow education-policy debates, you’ve no doubt heard about the “teacher-pay penalty.” A 2020 study from a union-backed think tank estimated teachers make about 19% less, on average, than do other workers with similar levels of education.

This finding is true as far as it goes — but it doesn’t really go very far, as American Enterprise Institute scholars Andrew Biggs and Jason Richwine demonstrate in a recent study. After all, using variables such as years of education or possession of a bachelor’s degree to adjust salary data is like using an adjustable wrench with a broken thumbscrew. It will turn some big nuts. But if it can’t be tightened, there are tasks it simply cannot accomplish.

Evaluating pay differentials is one of them. The labor market is about specifics, not broad categories. Employers don’t pay “college graduates.” They pay accountants, or musicians, or nurses, or telemarketers. And employers don’t offer standardized wage premiums for “graduate degrees.” Doctors and lawyers get paid more than historians and sociologists.

Even these rules are valid only for comparing averages across broad categories. Within most professions (teaching is a familiar exception) there is often a great deal of pay variation based on scale, specialization, and performance. Some attorneys make vastly more than others despite having spent the same three years in law school. And, indeed, a few superstar musicians and bestselling historians make much more than the average attorney.

“Standard control variables, such as years of education and experience, are simply insufficient to account for important differences across occupations,” Biggs and Richwine observe. In a previous study, the authors looked not at the quantity of education received but at the performance of college graduates on standard tests of knowledge and skills. Adjusting for test scores eliminated the supposed teacher-pay gap.

For their new paper, the authors explored a different set of data: average earnings adjusted for the specific college or university attended and the specific degree received. The disadvantage of this analysis is that a college graduate could end up working in a field not clearly related to her major, such as someone with a fine-arts degree working as a financial analyst. Still, there’s a big advantage to this model, too: it allows for more granular analysis. You can, in fact, turn the thumbscrew on the wrench. And, after all, most graduates do end up in jobs related to what they study in college.

Using this approach, the authors found that the real pay differential isn’t between those with education degrees and those without them. It’s between those with degrees in a science, technology, engineering, or math (STEM) discipline and without them.

Among non-STEM graduates, education majors earn about as much as other degree-holders, both at one year out of school and at 10 years out of school. Yes, education major make less than STEM graduates — but so do most other non-STEM graduates.

To accept this more-sophisticated analysis of the issue is not necessarily to conclude that teachers shouldn’t be paid more. In fact, I think an across-the-board raise is appropriate for North Carolina teachers this year, after a couple of years of pay stagnation (caused by Gov. Roy Cooper vetoing state budgets with teacher-pay raises on the grounds that they should have been larger).

But if we stop talking in misleading generalities and get down to specifics, I think the long-term policy implications are clear. North Carolina should differentiate teacher pay more than we do. We should pay a lot more for hard-to-staff positions — math and science teachers in high schools, for example — as well as for teachers in hard-to-staff schools.

As for nurse anesthetists, I think most earn every penny they get, and then some.

John Hood is a Carolina Journal columnist and author of the forthcoming novel Mountain Folk, a historical fantasy set during the American Revolution.