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
Residency i,t
=β 0
+β 1
Scholarship i,t−1
+ε i
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
Residency i,t
= (0.0023)
0.721
− (0.00078)
0.043
Scholarship p i,t−1
a) Interpret
β
^
0
and
β
^
1
. b) Do you believe that
β
^
1
=−0.043
is the causal effect of scholarship on residency? c) Do you believe that
β
^
1
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. Explain intuitively what the connection is and what the instrumental variable is in a regression discontinuity.
