Loans are made to black versus white males in 3 consecutive stages across 100 banks. These banks vary in selectivity of moving the loan application to the next stage.
Each of the three stages are eliminatory, with variation across banks in how many cuts are made per stage. Some banks cut 40% of applications at every stage, some cut 80%, and some cut 20%. All potential male recipients apply to all banks for loans.
I want to test mean differences in the (unobserved) risk distribution across races. Can I compare the (within bank) success rates across groups and use variation in selectivity across banks to see if mean risk is the same across groups?
For example, if I find that black applications are, on average, only cut at the very end, would this be evidence of potential discrimination (assuming minimum selection on other observables)?