236. An economic assignment. 5 questions, High level


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An economic assignment. 5 questions, High level

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All the work has to be 100 percent original.

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ECON 483K: Economics of Education Homework 5 Define any variables you need to answer the problems. You are welcome to discuss the problems with other students but you should write out and turn in your own answers. This homework is due at the start of class on Tuesday, May 1. 1. Chetty, Friedman, and Rockoff use a teacher switching quasi-experiment to study measures of teacher value-added. (a) What were they trying to demonstrate with the teacher switching quasiexperiment? (b) Suppose that teachers only switch between schools with very similar types of students. What would that say about their results? Explain. 2. What do the findings of Chetty et al. (Tennessee STAR paper) and Chetty, Friedman, and Rockoff (long-run effects paper) imply about the human capital vs. signaling models of the returns to schooling? 3. In class, we discussed a particular definition of what it means for teacher ratings to be “unbiased.” In particular, our definition was that θ̂ is a forecast unbiased way of guessing θ if E(θi | θ̂i ) = θ̂i . (a) Suppose that there are exactly two types of basketball players, those who make 75% of their shots and those who make 25% of their shots. Let θi be the fraction of shots that player i generally makes. I make a guess θ̂i about a player i’s fraction of shots made by (i) observing one shot that the player took, and then (ii) guessing .75 if the shot was made and .25 if the shot was missed. Is this estimate forecast unbiased? Why not? (Hint: Check if the forecast unbiasedness condition holds for each value of my guess θ̂i .) (b) Would it be any better if I had guessed 1 when the shot was made and 0 when it was not? Why not? (c) In statistics and econometrics, a more common definition of unbiasedness is that θ̂i is an unbiased way to estimate θi if E(θ̂i | θi ) = θi . Translate this definition into words. (Suggestion: You can refer to θ̂i as “the guess about person i’s value of theta” or “the estimate of i’s value of theta.”) 1 (d) Consider the way I produced the estimate θ̂i in part (b). What is E(θ̂i | θi = .75)? How about E(θ̂i | θi = .25)? (Hint: When Y is a dummy variable, E(Y ) = P r(Y = 1).) What do you conclude about whether or not this estimator is unbiased in the sense described in part (c)? 4. We have seen evidence that teachers produce skills which are not captured by contemporaneous test scores. Should we interpret those skills as being noncognitive, or do you think they might represent other kinds of cognitive skills which are simply not measured by the exam? 5. In a couple of paragraphs, what are your thoughts on the use of value-added models to evaluate teachers in schools? 6. Which question did you find hardest? 2 ...
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