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Economics 120C
Name:
_________________________
Professor Yongil Jeon
Summer 20072
Student ID#: _________________________
Answer to Homework #1 – Summer 2007Session 2, Econ 120C
(Midterm Exam, Summer 2007Session 1, Econ 120C)
Answer all questions on separate paper. This problem set should be handed in to your TA at the
beginning of your review session on Tuesday, August 21, 2007.
Problem sets may not be handed
in once solutions have been distributed.
Please write down your name and PID clearly. Good
luck!
1)
(3 points)
When the errors are heteroskedastic, then
a.
WLS is efficient in large samples, if the functional form of the
heteroskedasticity is known.
b.
OLS is biased.
c.
OLS is still efficient as along as there is no serial correlation in the error
terms.
d.
weighted least squares is efficient.
Answer
: a
2)
(3 points)
It is possible for an estimator of
Y
µ
to be inconsistent while
a.
converging in probability to
Y
.
b.
S
n
p
→
Y
.
c. unbiased.
d. Pr[
S
n
–
Y

≥
δ
]
→
0.
Answer
: c
3)
(3 points)
The following is not one of the GaussMarkov conditions
a. var(
u
i

X
1
,…,
X
n
) =
2
u
σ
, 0 <
2
u
<
∞
for
i
= 1,…,
n
,.
a.
the errors are normally distributed.
c.
E
(
u
i
u
j

X
1
,…,
X
n
) = 0,
i
= 1,…,
n
,
j
= 1,…,
n
,
i
≠
j
.
d.
E
(
u
i

X
1
,…,
X
n
) = 0
Answer
: b
4)
(3 points)
The WLS estimator is called infeasible WLS estimator when
a.
the memory required to compute it on your PC is insufficient.
b.
the conditional variance function is not known.
c.
the numbers used to compute the estimator get too large.
d.
calculating the weights requires you to take a square root of a negative
number.
Answer
: b
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Answer to HW #2, ECON 120C, Summer 2007 – S2
5)
(13 points) Discuss the properties of the OLS estimator when the regression errors
are homoskedastic and normally distributed. What can you say about the
distribution of the OLS estimator when these features are absent?
Answer
:
In the initial discussion of the OLS estimator, it was established that if
the three least squares assumptions hold, then the OLS estimator is
unbiased, consistent, and has an asymptotically normal distribution.
Small sample properties are more difficult to establish, at least in the
case when the regressors are random variables. If the assumption of
homoskedasticity is added to the previous assumptions, then the OLS
estimator is efficient in the class of linear and conditionally unbiased
estimators. This result is known as the GaussMarkov Theorem. Since
the proof
depends on the assumption of homoskedasticity, OLS is not
efficient in its absence. In that case, an alternative estimator, WLS, is
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This note was uploaded on 07/17/2008 for the course ECON 120C taught by Professor Stohs during the Spring '08 term at UCSD.
 Spring '08
 Stohs
 Economics

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