does the above rd approach represent an example for a sharp or a fuzzy rd design

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Let us assume that before being admitted to High School, students are required to take a test. Based on how well they do, they are either assigned to a regular High School (scores of at least 50) or a special program (scores less than 50). A group of researchers decides they want to test for effects of being enrolled in the special program on earnings later in life. a) First, the researcher decides to estimate the following OLS regression: Earningsi = β0 + β1program + ui . Earningsi represents later life earning for individual i, while program is an indicator whether the individual attended the special program. Comment on this approach. In your opinion, does the estimate for β1 represent the causal effect of the special program on earnings? Why or why not? Provide examples to back up your answer b) Next, the researchers decide to estimate the following Regression Discontinuity model: Earningsi = β0 + β1test-performance + β2program + ui . (i) What advice would you give the researchers for this RD approach in terms of sample selection? In your answer, list two examples for challenges of an RD design. (ii) If the researchers follow your advice, do you think the estimate for β2 represents the causal effect of the special program on earnings? (iii) Does the above RD approach represent an example for a sharp or a fuzzy RD design? (iv) Now let’s assume that students with scores less that 50 are given a voucher to participate in the special program. Is this now a sharp or a fuzzy RD design?

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