[dp-tyvek]

According to my understanding, rimliu is proposing that

  wage ~ education + experience + gender + race + additional_factors + error

where additional_factors consists of other unknown factors (e.g. charisma, intelligence, appearance?). In which case, if education, experience, gender and race are kept constant, there is still going to be a fair bit of variance in wage caused by these unknown factors.

Either way, it would be pretty hard to model when these factors are far from orthogonal. Imagine the impact race would have on work experience if race is a big factor when hiring people.

[xapata]

Looking at it a different way, if productivity is defined as the combination of all relevant features (education, experience, ethics, etc.) then racism/sexism imply non-zero coefficients in

    wage ~ productivity + race + gender

This also assumes a competitive market where wage will asymptotically approach productivity.