Heckman (1998) argues that, if the bar for acceptance is high (so most applicants are rejected), then belonging to a group who quality has high variance tends to help you. The argument is something like this: if employers only hire people whose quality exceeds a certain cutoff, but most people fail the cutoff, then if your group's distribution of quality has higher variance it will have more mass above the cutoff.
Aigner and Cain (1977) also discuss variance based discrimination. Assuming that you send a signal equal to your group's mean, the only effect of higher variance is to dissuade risk averse employers to hire you. There is no Heckman style mechanism where high variance can help you if most people get rejected.
I would be very grateful if someone could explain what leads to this contrast.
My (possibly confused) thoughts on this: the Heckman model makes sense if employers decide whether to grant an interview based on whether the probability that someone's quality is above a certain level exceeds a certain cutoff. But that is a crazy hiring rule! Instead, they should just look at whether expected quality exceeds a certain cutoff (to be fair to Heckman, this is supposed to be the hiring rule.)
OK suppose that this is the hiring rule: can high variance still help you (in the context of an audit/correspondence study)? Well, I can see how this works if the researcher perfectly controls on one dimension (e.g. what the auditors say) but doesn't control on another (e.g. attractiveness), and one group has higher variance on that second dimension, which means more of them get over the bar. But that logic totally breaks down in correspondence studies (supposedly also a target). Here the employer does not get to see some realisation from a distribution of quality that is unobserved by the researcher. At best, the employer can say: that group's high variance, so more likely to exceed the cutoff. But that brings us back to the crazy hiring strategy already discussed.