3. Gifted and talented programs provide extra services for academically high-performing students. Eligibility for these programs is typically based on having a test score above a threshold. Suppose you want to estimate the effect of participating in these programs on achievement of the students using a regression discontinuity design.

a. Explain in words how the regression discontinuity method leads to a valid estimated of the causal effect. What are the assumptions needed? b. Draw the two figures that you would need to show if you are doing this estimation in Stata (Obviously you dont have the data here, use your imagination). Assume the test score is only determinant of the participation in the program.

c. Can this method tell us how very high-achieving students are affected by the program? d. Would it be a problem for this approach if not all students who were eligible for the program decided to enroll in it? Why or why not?