# economics of education s homework

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

study 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 types

of 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 capital

vs. signaling models of the returns to schooling?

3. In the lecture, we discussed a particular denition of what it means for teacher

ratings to be unbiased.” In particular, our denition was that ^ is a forecast

unbiased way of guessing if E(i j ^i) = ^i. (Equivalently, but using slightly

dierent notation, it is forecast unbiased if E(i j ^i = k) = k for all values of

k.)

(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 i

be the fraction of shots that player i generally makes. I make a guess ^i

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 ^i.)

(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 denition of unbiasedness

is that ^i is an unbiased way to estimate i if E(^i j i) = i. Translate

this denition into words. (Suggestion: You can refer to ^i as the guess

about 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 j

i = :75)? How about E(^i j i = :25)? (Hint: When Y is a dummy

variable, E(Y ) = Pr(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 non-

cognitive, 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?