Wage gaps and occupational coefficients: with a specific example from a commenter

I've said here before that in work I've done I've often used the word "disparity" rather than "discrimination" because "discrimination" confuses people - they think they know what it is, but it's a wishy-washy term. "Disparity" is broad but at least it's clear.


At Bob's blog I asked commenter Scott D to be more specific about what he meant by "discrimination" (how you interpret a wage regression can vary dramatically depending on how you conceptualize "discrimination"). His response is fine I think - a perfectly reasonable definition - and it's also a great opportunity to illustrate why I think people often misinterpret occupational coefficients in wage regressions. Scott D writes: "Discrimination in this context would constitute an error in decision-making. It would be a case of a worker’s real productivity being discounted irrationally, resulting in them losing out to another candidate with weaker credentials."


I think other people would have other definitions of discrimination but this is a great one. I'm willing to run with it.


So let's say a woman faces discrimination by this definition - she loses out to a man with weaker credentials. "Loses out" itself is pretty vague and could reasonably be consistent with several different observed labor market outcomes, two of which are:


Outcome A: She gets hired to the same job as the man but at lower pay, and
Outcome B: She doesn't get the job and instead takes her next best offer in a different occupation at lower pay. Let's further say that she is paid her real productivity in this job.


Let's say the woman's wage in Outcome A and the wage in Outcome B is exactly the same.


Under Outcome A, a wage regression with occupational dummies and a gender dummy is going reliably report the magnitude of the discrimination in the gender dummy. Under Outcome B, a wage regression with occupational dummies and a gender dummy is going to report all of the discrimination under the occupational dummies. If you interpret the results thinking that "discrimination" as Scott D defines it is only in the gender coefficient, you would say there is discrimination in the case of Outcome A, but that there's no discrimination in the case of Outcome B.


It would be one thing if these were very, very different sorts of discrimination but these are two reasonable outcomes from the exact same act of discrimination.


This is why people like Claudia Goldin see occupational dummies as describing the components of the wage gap and not as some way of eliminating part of the gap that isn't really about gender.


"Equal pay for equal work" is a principle that I should hope everyone can agree on. It's great stuff. And I for one think the courts might have some role to play in ensuring the principle is abided by in our society. But it's a pretty vacuous phrase when it comes to economic science. It's not entirely clear what it means or how it can be operationalized. Outcome A is clearly not equal pay for equal work, but what about Outcome B? After all the woman is being paid "fairly" for the work she ended up doing. Is that equal pay for equal work? You could make the argument but it doesn't feel right and in any case it's clearly incommensurate with the data analysis we're doing. When two things are incommensurate it's typically a good idea to keep them separate. Let "equal pay for equal work" ring out as a rallying call for a basic point of fairness and don't act like you can either affirm it or refute it with economic science. As far as I can tell you can't.