Imagine you want to estimate the effect of getting affordable student housing in Uppsala on university students' probability of finishing their degree at Uppsala University. You know that student housing for first-year students in Lund is determined randomly to be as fair as possible. The housing company (Student Living) assigns every new student a slot in the housing queue using a lottery. Students who get a low number are placed first in the queue and will get a housing contract quickly, whereas students with a high number will have to wait very long to be able to get a student housing contract. Student Living has full control of the student housing contracts and there is no way to skip the queue. a) You want to use the housing lottery as an instrument for getting student housing during a person's first year of university studies, but you expect thetreatment effects to be heterogeneous. What are the assumptions that need to hold for your IV analysis to work when treatment effects are heterogeneous? Name the assumptions and explain what they mean. (5p) b) Name the four sub-groups of the population that exist with respect to the treatment effects and explain who they are in this scenario. Is it likely that they all exist in this scenario? (5p) c) Write down the equations you will estimate to get the causal effect of student housing on the probability of students finishing their degree. Clearly explain what all components of the equations represent, and which parameter that gives you the causal effect. (5p) d) What is the causal effect you can obtain called? What does it measure? (5p)