1. Chetty, Friedman, and Rocko use a teacher switching quasi

1. Chetty, Friedman, and Rocko use a teacher switching quasi-experiment tostudy measures of teacher value-added.(a) What were they trying to demonstrate with the teacher switching quasi-experiment?(b) Suppose that teachers only switch between schools with very similar typesof students. What would that say about their results? Explain.2. What do the ndings of Chetty et al. (Tennessee STAR paper) and Chetty,Friedman, and Rocko (long-run eects paper) imply about the human capitalvs. signaling models of the returns to schooling?3. In the lecture, we discussed a particular denition of what it means for teacherratings to be unbiased.’ In particular, our denition was that ^ is a forecastunbiased way of guessing if E(i j ^i) = ^i. (Equivalently, but using slightlydierent notation, it is forecast unbiased if E(i j ^i = k) = k for all values ofk.)(a) Suppose that there are exactly two types of basketball players, those whomake 75% of their shots and those who make 25% of their shots. Let ibe the fraction of shots that player i generally makes. I make a guess ^iabout a player i’s fraction of shots made by (i) observing one shot thatthe player took, and then (ii) guessing :75 if the shot was made and :25 ifthe shot was missed. Is this estimate forecast unbiased? Why not? (Hint:Check if the forecast unbiasedness condition holds for each value of myguess ^i.)(b) Would it be any better if I had guessed 1 when the shot was made and 0when it was not? Why not?(c) In statistics and econometrics, a more common denition of unbiasednessis that ^i is an unbiased way to estimate i if E(^i j i) = i. Translatethis denition into words. (Suggestion: You can refer to ^i as the guessabout person i’s value of theta’ or the estimate of i’s value of theta.’)(d) Consider the way I produced the estimate ^i in part (b). What is E(^i ji = :75)? How about E(^i j i = :25)? (Hint: When Y is a dummyvariable, E(Y ) = Pr(Y = 1).) What do you conclude about whether ornot this estimator is unbiased in the sense described in part (c)?4. We have seen evidence that teachers produce skills which are not captured bycontemporaneous test scores. Should we interpret those skills as being non-cognitive, or do you think they might represent other kinds of cognitive skillswhich are simply not measured by the exam?5. In a couple of paragraphs, what are your thoughts on the use of value-addedmodels to evaluate teachers in schools?