This is my Econ453 Question:

. 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;) = a + BSFU; + Xiyte (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 8 = 0.10. Describe briefly what this coefficient 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 S 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 specific 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 specific about what comparisons you would make.Problem 2[50 points] You are interested in estimating the effect of class size on students' academic performance. Students are divided into either small or large classes, and you want to study the effect of being \"treated\" with a small class size on students' scores on a standardized test. Y, is student i's score on the standardized test. D, is a dummy variable that is equal to 1 if student '32 is in a small class and 0 if he / she is in a large class. a) (20 points) You collect data on whether students were in small or large classes, student performance and various student characteristics (such as parents' income, parentsI education, etc.). Assume that treatment is not randomized. Explain why you cannot estimate the causal effect of class size on student performance by running the following regression: YiZO'l'lD-lui b) (15 points) What can you do to with the data you have to decrease bias and get closer to estimating the causal effect? c) (15 points) Suppose you learn that when a classroom has 30 students or more, then students are divided into two smaller classrooms. In other words if a classroom has a class size of 30 students, the students will then be divided into two classes of 15 students each. Describe in words how you would use this natural experiment to identify the causal effects of class size