Part I. We are interested in the causal effect of attending a KIPP charter school on students' academic performances. Given that there were more applications than the number of seats at this KIPP school, school seats were offered to a random set of students. Let Z be a dummy variable indicating whether an applicant was offered a seat or not, and X be a dummy variable indicating whether an applicant actually attended the KIPP school or not. Consider the causal model YzalXlu where Y is the standardized math score a year later (Y is measured in terms of how many standard deviations away from a state average). (a) Is the OLS estimator of based on the above model likely to be unbiased? What is the direction of the bias if it is inconsistent? Explain. (b) Is Z a good instrument for X? Be as Specic as possible. (c) Now suppose that 79% of those who were oEered a seat (i.e., those with Z : 1) actually attended the KIPP school and 4% of those who were not oEered a seat (i.e., those with Z = 0) managed to attend the school. Also, the average value of Y for those who were offered a seat (i.e., those with Z = 1) is 0, and the average value of Y for those who were not offered a seat (i.e., those with Z : 0) is 0.3. Do we have enough information to compute the IV estimate? If yes, what is the IV estimate? If no, what else do we need in order to compute the IV estimate