a Problem 1[50 points] Imagine that the only two universities in the world are Simon Fraser University (SFU) and University of British Columbia (UBC). You have data on a large number of students who attend either one of those schools and may or may not have applied to both. Assume that everyone who attends a university graduates from one of those schools. a) (15 points) Suppose you are trying to discover the return to attending SFU in this world, in order to explain it to the provincial legislature. We have access to a large number of control variables (like gender, race, parental income, etc.) on students who attend SFU and students who attend UBC. You run the following regression using Ordinary Least Squares: log(Wage,-) = o: + BSFU, + Xi? + e,- (1) The dependent variable is the log of each individual i's wage. SFU,- is a variable that equals 1 if student i attended SFU and 0 otherwise.X,; are the extensive set of controls for factors like demographics, high school grades, SAT scores, and so on. Suppose ,6 = 0.10. Describe briey what this coefcient means; be thorough and complete, as if you are explaining it to someone with no knowledge of statistics or the economics of education. b) (10 points) Is this estimate of 3 likely to be accurate (i.e. causal)? Explain carefully why or why not. [10 points] c) (15 points) One of your research colleagues suggests an instrumental variable Z for the SFU variable: having a family member who attended SFU. Is this a valid instrument? Explain carefully in no more than two sentences for the specic example described in this question. (Have at least one sentence for each IV assumption.) d) (10 points) In an ideal world (from a researcher's perspective), how would you get a causal answer to this question? Be specic about what comparisons you would make