. Problem 2-[50 points] You are interested in estimating the effect of teacher quality. Imagine a scenario where you have two mathematics teachers in grade 5 for a given school. Both teachers have the same number of students in their classrooms and all students are randomly assigned to teachers in this school. Teacher A is teaching grade 5 mathematics for a 6th year (they have 5 years of previous experience teaching grade 5 mathematics) and Teacher B is teaching grade 5 mathematics for a 4th year (they have 3 year of previous experience teaching grade 5 mathematics). Suppose you also have historical information on both teachers' past student performance. In particular you have information on how better or worse past students have performed in grade 5 compared to their performance in grade 4. A summary of their performance is as follows: . Average grade 5 mathematics performance (compared to grade 4) of all students taught by teacher A in: 2 Year 1: Students scored 4 points higher in grade 5 in mathematics as compared to when they were in grade 4 (with a previous teacher). Year 2: Students scored 2 points higher in grade 5 in mathematics as compared to when they were in grade 4 (with a previous teacher). Year 3: Students scored the same in grade 5 in mathematics as compared to when they were in grade 4 (with a previous teacher). Year 4: Students scored 2 points lower in grade 5 in mathematics as compared to when they were in grade 4 (with a previous teacher). Year 5: Students scored 10 points lower in grade 5 in mathematics as compared to when they were in grade 4 (with a previous teacher). . Average grade 5 mathematics performance (compared to grade 4) of all students taught by teacher B in: Year 1: Students scored 2 points higher in grade 5 in mathematics as compared to when they were in grade 4 (with a previous teacher). Year 2: Students scored 4 points higher in grade 5 in mathematics as compared to when they were in grade 4 (with a previous teacher). Year 3: Students scored 8 points higher in grade 5 in mathematics as compared to when they were in grade 4 (with a previous teacher). a) (10 points) Compute the Value-added of Teacher A in their 6th year of teaching. Compute the Value-added of Teacher B in their 4th year of teaching. Show your work and provide details (You need to provide a numerical answer here). b) (10 points) Based on your answers in part a), who do you think is the better overall mathe- matics teacher? Explain? c) (10 points) Who was the better teacher during their 2nd year of teaching? Provide details. d) (10 points) Using the given information on student performance, would you say teaching experience matters a lot? Explain and give details by comparing Teacher A to Teacher B and by also comparing each teacher to their own performance over the years. e) (10 points) Suppose a policy maker critiques the above information as not being indicative of the quality of a teacher. How would you respond? Give details and imagine a scenario where you have all the data on students you could imagine. Could you construct a better measure of teacher quality