It’s curious that I get economic questions a lot. But let’s roll.
Does the gender wage gap exist? I think it does. My priors are that it does because we know that in experimental settings, employment discrimination is very real. But what does the observed evidence in the labor market tell us?
First of all, good interpretation of statistical evidence requires that we evaluate not just individual studies and papers, but the entire literature. Reviews of this literature suggest that “there is considerable agreement that gender wage discrimination exists“.
The parsimonious “let’s control for observables” approaches have yielded mixed results. Most of the wage gap disappears, but leaving some significant difference behind. That difference has been the subject of many arguments on both sides. But let me suggest a different way to think about the wage data (or any kind of data).
For many things in life, the fact that you can observe something is information in and of itself. The fact that for a specific individual, a wage is offered and accepted (and then by random chance recorded in population surveys) is telling. Surveys generally do a great job of randomly selecting a sample from the population, but the market does not do a good job of randomly choosing who works at what wage, or whether certain people work at all. Selection bias is at work, whether you like it or not. The only thing I want to convince you of is that the existence of selection bias is something to really consider when thinking about “controlling for other factors”.
Selection, its effects and more specifically how to correct for them, is the area of research that got James Heckman his Nobel Prize in Economics in 2000. Most interestingly, it has been used extensively to study the determinants of wages.
How exactly does selection work in our setting? Let me draw you a few pictures! But I don’t have my awesome graphic design software installed, so I’ll have to do with MS Paint.
If controlled wages for females (sorry everyone, the U.S. surveys don’t code for third gender or anything like that) are lower, and if we want to think about selection into the sample, then we have to ask, “what would make a a person work?”
We all have an intuition that there’s a wage low enough where we would choose not to work. We call it the reservation wage. There are many reasons to think why this wage is nontrivial. Maybe spousal income might be a good substitution for individual income, so we choose to work only if we have to or we’re paid a lot for it. Maybe you believe that the evil welfare state is causing many low-wage workers to rely on unemployment benefits and food stamps because welfare is supposedly better than working at some low wage.
The effect of this reservation wage, if it were a strict thing, would mask more of the lower end of the lower distribution than the lower end of the higher distribution. Take a look at the graph, and imagine all the points under the black horizontal line are not observed. In reality, it would mean that many women choose not to work, which is empirically true because female labor force participation is not all that high.
When there’s selection on the lower end of the spectrum, it makes the slope of the line flatter, which means it makes the estimate of the gender wage gap smaller than it actually is.
An important point is that the graph is a little exaggerated. Specifically, the reservation wages are different for everyone. So there’s no clear black line you can draw on the graph where all the points below that line are unobserved. Instead, we should think of the appearance of a point in the data as a probability–a probability that increases as the wage gets higher because you are more likely to work!
I’m still trying to find a really good paper on specifically the U.S. gender wage gap and selection bias correction (across all different kinds of ways to correct for it), and it’s not been going well. There’s this paper using data from Columbia that suggests “that self selection into the labor force is crucial for gender gaps: if all women participated in the labor force, the observed gap would be roughly 50% larger at all quantiles.” Of course, we need to review the entire literature.