,1_ In many US states; high school students are offered scholarships are given to students to students who remain inestate for university or college. For example: Kansan high school students can receive scholarships for $12,500 if they go to a university within Kansas. These types of policies are often thought to ght braindrain from states that lack a highskill workforce. Suppose that you are a policy analyst investigating the effect of scholarship provision on braindrain. As a baseline model you estimate Hesidencyiat 2 {5'0 + lSchofm'shipl-y l + ea- where Residency is a binary variable indicating whether or not Kansas high school student 15 resided in Kansas in time t and Scholarship is a binary variable indicating whether or not Kansas high school student 16 received a scholarship to attend an instate university in time t i 1. Suppose the estimated model was Residency\" = 0.721 0.043 Srholarshpz-It 1 " (0.0023) (0.00078) ' a) Interpret {in and 51. b) Do you believe that Ii; 2 0.f}/13 is the causal eect of scholarship on residency? c) Do you believe that 31 is biased up or down? lf not: why not? If so, explain the direction of the hypothesized bias. d) Suppose that the scholarship was contingent on a high school student's GPA being at least 3.2. How could you use this threshold in regression discontinuity design? Illustrate with a graph showing the elTect of scholarship as a function of GPA. Bonus: I mentioned in class that Regression discontinuity is a type of instrumental variable design. Ex plain intuitively what the connection is and what the instrumental variable is in a regression discontinuity