Thursday, February 26, 2015

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.


  1. "Real productivity" should probably be "marginal product", I was just using Scott's language. It's not an important point for this discussion, obviously.

  2. This is something that I've been trying to explain to people without econometric training but could not provide such a cogent explanation. Thank you very much!

  3. I don't think this works, Daniel. Assume for the moment that we had a list of variables that were perfect proxies for marginal product. If all workers (men & women) were paid in accordance with their marginal product, then an apparent wage gap would disappear as we included more of the variables in the regression, eventually disappearing altogether. So people who pointed to such evidence as refuting the "pay gap myth" would be on solid ground, right?

    In actual labor markets, it's not going to be an all-or-nothing thing, right? It's not that 0 women will be in occupation X because of rampant discrimination. Instead, it will be that only the incredibly qualified women will be in occupation X, working alongside less competent males, and getting similar pay. So that would show up in the regression as a gap that doesn't go away, even as we include more proxies.


    1. Exactly but I don't understand why that means this doesn't work. I'm not claiming that it's an all or nothing thing and I'm not claiming that the entire gap is due to discrimination. I'm claiming the coefficients in the wage regression - particularly occupation but also education (which we haven't talked about as much) do not have the interpretation people give them. All they can really tell you is how much of the variation is within-occupation and how much of the variation is between-occupation, NOT how much of the variation is and isn't discrimination.

      I think it all depends on how they're "refuting the pay gap myth". Like I've said some approaches are stronger than others. Steve Horwitz's video was much better than Perry and Biggs's op-ed.


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