Economics 120C
Name:
_________________________
Professor Yongil Jeon
Summer 20082
Student ID#: _________________________
Answer keys to Homework #1 – Summer 2008Session 2, Econ 120C
(Answer keys to Midterm Exam, Summer 2008Session 1, Econ 120C)
Answer all questions on separate paper. This problem set should be handed in to Professor Jeon
at
the beginning of your class on Monday, August 18, 2008
.
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)
One of differences between the central limit theorems for a scalar and
vectorvalued random variables is
a. that
n
approaches infinity in the central limit theorem for scalars only.
b.
the conditions on the variances.
c.
that single random variables can have an expected value but vectors
cannot.
d.
the homoskedasticity assumption in the former but not the latter.
Answer
: b
2)
(3 points)
The linear multiple regression model can be represented in matrix
notation as
=+
YX U
β
, where
X
is of order
n
×
(
k
+1).
k
represents the number
of
a. regressors.
b. observations.
c.
regressors excluding the “constant” regressor for the intercept.
d. unknown regression coefficients
Answer
: c
3)
(3 points)
One implication of the “extended” least squares assumptions in the
multiple regression model is that
a.
feasible GLS should be used for estimation.
b.
E
(
U

X
) =
I
n
.
c.
X
′
X
is singular.
d.
the conditional distribution of
U
given
X
is
N
(
0
n
,
2
u
σ
I
n
).
Answer
: d
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
Answer to HW#1, ECON 120C, Summer 2008 – S2
4)
(3 points)
An estimator of
β
is said to be linear if
a.
it can be estimated by least squares.
b.
it is a linear function of
Y
1
,…,
Y
n
.
c.
there are homoskedasticityonly errors.
d.
it is a linear function of
X
1
,…,
X
n
.
Answer
: b
5)
(3 points)
The GLS estimator
a.
is always the more efficient estimator when compared to OLS.
b.
is the OLS estimator of the coefficients in a transformed model, where the
errors of the transformed model satisfy the GaussMarkov conditions.
c.
cannot handle binary variables, since some of the transformations require
division by one of the regressors.
d.
produces identical estimates for the coefficients, but different standard
errors.
Answer
: b
6)
(10 points) Suppose that Y and X are related by the regression Y=1.0 +2.0X+u. A
researcher has observations on Y and X, where
02
0
,
X
≤
≤
where the conditional
variance is var(

)
1
ii
uX x
==
for
01
0
,
x
≤
≤
and var(

)
16
=
=
for
10
20
x
<≤
. Draw a hypothetical scatterplot of the observations (
, ),
1,.
.., .
X
Yi
n
=
Does WLS put more weight on observations with
10
x
≤
or
10?
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '09
 JEON,YOUNGIL
 Economics, Econometrics, Linear Regression, Regression Analysis, Yi, Linear Probability Model, Econ 120C

Click to edit the document details