Use the notional_summer_educ data set.4 The idea behind this exercise is that 3rd-grade students who are at a reading level under 85 (one standard deviation below the mean of 100) are required to...

Use the notional_summer_educ data set.4 The idea behind this exercise is that 3rd-grade students who are at a reading level under 85 (one standard deviation below the mean of 100) are required to attend summer school. But, some students below the threshold do not attend, while some students above the threshold choose to attend voluntarily. We want to estimate how summer school improves the reading test scores for the students. Given that the threshold does not automatically dictate summer-school attendance, this is a Fuzzy RD model. The variables are: test3 = a test at the end of 3rd grade; test4 = a test at the end of 4th grade;

summer = a dummy variable for whether the student went to summer school between 3rd and 4th grades. a. Estimate a Fuzzy RD model with an instrumental-variables model to estimate the effect of summer school (summer) on 4th-grade test performance (test4). Use just a linear model to capture the discontinuity in summer-school attendance from test3. b. Estimate the same model, but use a quadratic function from both below and above the threshold of 85 for the effects of test3 on test4. c. From (b), what is the interpretation of the estimated effect of summer school?