Patricia Arquette recently promoted gender equality particularly as it relates to the wage gap at the Oscars. Some Facebook discussion followed, and Bob Murphy encouraged me to put my position in a blog post, so here it is.
My frustration with the empirics of the wage gap come in whenever - following something like the Arquette statement, or a mention of "77 cents on the dollar" in the State of the Union - people get up and assert that the wage gap is a "myth" or a "fallacy" simply because there are explanations for different contributions to the gap (some of these explanations are better than others). I think that's very misleading and that it's a mistake to use conditional mean differences in a regression to argue that the gap is mythical. I have always liked Claudia Goldin's approach (I linked to her first thing when I saw the Arquette news). Goldin says of the 77 cents on the dollar figure that "it's an accurate statement of what it is". The gap isn't a myth - it's real. The question is, what is the gap?
Some people are tempted to perform the following exercise:
1. Add a bunch of controls in a wage regression.
2. Note that the difference in conditional means between men and women shrinks when you do that.
3. Call the gap a "myth" or a "fallacy".
This is wrong for a number of reasons, and how it's wrong largely depends on how it's executed, interpreted, and qualified by the author. In other words doing steps 1 and 2 is totally fine. The problem comes in with step 3.
All adding occupational and educational controls does is parse out the within-occupation/education and between-occupation/education variation in the gap. Specifically, you are removing the between-occupation/education variation and leaving behind the within-occupation/education variation. Economists think wages and employment - prices and quantities - are jointly determined by supply and demand. Labor market disparities facing women are going to express themselves partly in the wage determination in a given occupation, and partly through the distribution of women across occupations. The analogy I made yesterday is that it would be nonsensical to say that blacks didn't face labor market discrimination in the postbellum South because black sharecroppers were approximately as a dirt poor as white sharecroppers (hypothetically - I'm not sure what the disparity was in sharecropping). That ignores the fact that differential treatment of blacks by employers lowered within-occupation wages and drove them to lower wage occupations. You can't separate the two points and you certainly can't dismiss the disparity because it shows up between occupations rather than within occupations.
The picture of between- and within-variation gets even more complicated when you consider the point that women are not passive actors in the labor market. They sort across occupations in response to anticipated earnings and other benefits. Women will sort into occupations where they have the greatest comparative advantage and likewise for men. If within-occupation variation (which drives this sorting behavior) is random this sorting won't matter much, but if within-occupation variation is correlated with between-occupation variation then it can matter a lot. This sort of effect was pointed out a long time ago by Roy (1951), and it's going to lead to bias in the coefficients on occupation (or perhaps it's better to say it's going to impact how you interpret the coefficients on occupation). Claudia Goldin has done a lot of work on where the within-occupation wage gaps are, but I'm not sure that she has looked into how this has impacted sorting behavior.
The take-away from all this is that it's misleading to say the wage gap is a myth by pointing at occupational controls. It is much sounder to follow Goldin's lead in her AEA presidential address and treat them as clues for understanding the various factors driving a very non-mythical wage gap.
Now if you want to go a step further and assert that you, individually, don't care about certain parts of the wage gap that's one thing. This gets very heated when we think about employment practices around pregnancy, for example. You're welcome to do that. But don't mislead about what the data say.
The good news is things are getting better. The wage gap has shrunk, female labor force participation and human capital investment is up. The last big thing to tackle is how the labor market handles pregnancy and children.