4. Testing Discrimination (in Theory) Joe Biden has appointed you to the Supreme Court, and you have to decide whether Bank of America (BOA) is discriminating against Asians in its mortgage lending. You view "dis- crimination" through the lens of the following model. Mass 1 of Asians and Whites apply for a mortgage; Asians have continuously distributed default probability A ~f(0A), whereas Whites have continuously distributed default probability Ow ~g(0w). These distributions may differ. BoA observes the default probability of each applicant, and issues mortgages to Asians below and Whites below 0w. Assume that the worst applicants of either race are not accepted. We say that BoA discriminates against Asians if 0 <0. a) Suppose BoA approves 40% of White applicants and 30% of Asian applicants. Does this mean BoA discriminates against Asians? b) Suppose you additionally observe the average default rate of Asian and White borrow- ers, and observe that A < 0w. Does this mean BoA discriminates against Asians? c) Suppose you could observe BoA's risk assessments of applicants, and observe that the default probability for the worst approved White applicant is above the worst approved Asian applicant. Does this mean BoA discriminates? Ол A = 7% for Asians. In period t = = d) Suppose you observe only average default rates, as in (b). However, you observe the average in two periods. In period t = 1, BoA approves 40% of White applicants and 30% of Asian applicants. The average default rate is ow 16% for Whites and 2, BoA has fewer funds so and approves 36% of White applicants and 27% of Asian applicants. The average default rate drops to Ow 15% for Whites and OA = 5% for Asians. Formally, we say there is no discrimination if BoA approves applicants with default probability below 0* in period 1 and below * -8 in period 2, where > 0. Assume the distribution of applicants' default rates is constant over time. Do the above numbers mean BoA discriminates against Asians?³ =