ECON 483K: Economics of Education
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.”)
(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?
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