Some of our data does ask questions like that. Again, it's often debatable whether you should include measures such as that in a gender wage gap study. Analyses that fully omit occupation and industry, let's say, tend to say that choice doesn't matter, or preferences don't matter, whereas analyses that include variables like that tend to undervalue any labour market constraints on wages. Oftentimes a lot of these analyses will have a model with these variables in and a model without the variables, and the reader can then decide what's what.
On May 2nd, 2016. See this statement in context.