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課程名稱︰計量
課程性質︰選修
課程教師︰劉錦添
開課學院：
開課系所︰經濟系
考試日期（年月日）︰2013.5.2
考試時限（分鐘）：120mins
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
1. Let S*t be the desired savings of a household and Y*t be its expected
income. The relationship between these two variables is of the form S*t = α
+ βY*t.
According ti the partial adjustment and adaptive expectations rules,
St= S(t-1)+ λ(S*(t-1)-S(t-1))
Y*t= Y*(t-1)+ μ(Y(t-1)-Y*(t-1))
where St is actual saving and Yt is actual income. You have data on only St
and Yt, and none on S*t and Y*t.
(a) State the signs and other restrictions you would expect for the unkonwn
parameters α, β , λ, and μ. Explain your reasons.
(b) Derive a relationship that can be used to estoimate α, β , λ, and μ.
Add an error tern ut at the end.
(c) State all the assumptions on ut that will make OLS you got in part (b)
consistent. Are the estimates BLUE? Why or why not?
(d) Can α, β , λ, and μestimated? If not, explain why. If yes, describe
how they can be estimated: that is, express α , β , λ, and μ in terms of
the estimates of the model in part (b).
2. Suppose annual earnings and marijuana usage are determined jointly by
log(earnings) = β0 + β1 gMINt+β2educ + u1
marijuana = γ0 + γ1 log(earnings) + γ2 educ + γ3 fine + γ4 prison + u2
where fine is the typical fine for people possessing small amounts of
marijuana and prison is a dummy variable equal to one if a person can serve
prison time for being in possession of marijuana. Assume fine and prison can
vary with the country of residence.
(a) If educ, fine, and prison are exogenous, what do you need to assume about
the parameters in the system in order to consistently estimate beta s?
(b) Explain how would you estimate the beta s, assuming the parameters are
identified.
(c) Do you have over identification?
3.
Suppose that, for a given state in the United States, you wish to use annual
time
series data to estimate the effect of the state-level minimum wage on the
employment
of those 18 to 25 years old (EMP). A simple model is
gEMPt=β0+β1gMINt+β2gPOPt+β3gGSPt+β4gGDPt+ut,
where MINt is the minimum wage, in real dollars, POPt is the population from
18 to 25
years old, GSPt is gross state product, and GDPt is U.S. gross domestic
product. The g
prefix indicates the growth rate from year (t-1) to year t, which would
typically be
approximated by the difference in the logs.
(a) If we are worried that the state chooses its minimum wage partly based
on unobserved (to us) factors that affect youth employment, what is the
problem with OLS estimation?
(b) Let USMINt be the U.S. minimum wage, which is also measured in real
terms. Do you think gUSMINt is uncorrelated with ut?
(c) By law, any state’s minimum wage must be at least as large as the U.S.
minimum. Explain why this makes gUSMINt a potential IV candidate
for gMINt.
4.
Suppose that, for one semester, you can collect the following data on a random
sample of college juniors and seniors for each class taken: a standardized
final exam
score, percentage of lectures attended, a dummy variable indicating whether
the class
is within the student’s major, cumulative grade point average prior to the
start of the semester, and SAT score.
(a) Why would you classify this data set as a cluster sample? Roughly how
many observations would you expect for the typical student?
(b) Write a model that explains final exam performance in terms of attendance
and the other characteristics. Use s to subscript student and c to subscript
class. Which variables do not change within a student?
(c) If you pool all of the data together and use OLS, what are you assuming
about unobserved student characteristics that affect performance
and attendance rate? What roles do SAT score and prior GPA play in
this regard?
(d) If you think SAT score and prior GPA do not adequately capture student
ability, how would you estimate the effect of attendance on final exam
performance?
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