Your assumption in your model is wrong. You aren't assuming the same productivity of men and women, you're assuming the same observed productivity of men and wo

Your assumption in your model is wrong. You aren't assuming the same productivity of men and women, you're assuming the same observed productivity of men and women. If you're in a widget factory and both a man and a woman are producing 10 widgets per hour then your effect would be expected - because the boss would be able to evaluate true performance. In the real world however, no job is that simple. The problem with the gender pay gap partly is that women are assumed to be less productive than men in certain jobs. You don't hire a woman engineer because women are interested in people not things - so your expectation is that a women is 20% less productive than a man because you've decided being interested in people is bad for the job and that influences your expectations when hiring.