In many US states, high school students are offered scholarships are given to students to students who remain in-state 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 fight brain-drain from states that lack a high-skill workforce. Suppose that you are a policy analyst investigating the effect of scholarship provision on brain-drain. As a baseline model you estimate Residencyi,to + B1 Scholarshipi,t-1 + Ei where Residency is a binary variable indicating whether or not Kansas high school student i resided in Kansas in time t and Scholarship is a binary variable indicating whether or not Kansas high school student i received a scholarship to attend an in-state university in time t - 1. Suppose the estimated model was Residencyi,t 0.721 0.043 Scholarshipi,t-1 (0.0023) (0.00078) a) Interpret 30 and 3. b) Do you believe that = -0.043 is the causal effect of scholarship on residency? c) Do you believe that is biased up or down? If 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 effect 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.