If you think people in high cost of living areas are more productive on average (agglomeration effects, and their presence their is a signal that they were productive enough at their prior employment to justify the location) and their BATNA is higher (because there are many local good employers competing for them) then CoL adjustments in function as a noisy proxy for justified supply/demand curve shifts.
If you think people in high cost of living areas are more productive on average (agglomeration effects, and their presence their is a signal that they were productive enough at their prior employment to justify the location) and their BATNA is higher (because there are many local good employers competing for them) then CoL adjustments in function as a noisy proxy for justified supply/demand curve shifts.