This preview shows pages 1–2. Sign up to view the full content.
Econ 220B
James Hamilton
Final Exam
Winter 2008
DIRECTIONS: No books or notes of any kind are allowed.
Answer all questions on
separate paper. 250 points are possible on this exam
1.) (80 points total) This question concerns the following regression model:
y
=
X
β
+
ε
where
y
is a
(
T
×
1)
vector consisting of
T
di
f
erent observations on a variable
y
t
to be
explained,
X
is a
(
T
×
k
)
matrix of observations on
k
explanatory variables, and
ε
is a
(
T
×
1)
vector of residuals. Suppose that
X
has rank
k
and
ε

X
∼
N
(
0
,σ
2
I
T
)
for
I
T
the
(
T
×
T
)
identity matrix.
a.) (10 points) Write down the formula for the OLS estimate of
β
.
b.) (20 points) Consider the special case when there are
K
=2
explanatory variables, so
that the
t
th row of the above vector system looks like
y
t
=
β
1
x
1
t
+
β
2
x
2
t
+
ε
t
.
Write down the formula for the OLS
F
test of the hypothesis that
β
1
=2
β
2
. State (but do
not derive) the distribution of this statistic under the assumptions given above.
c.) (15 points) Suppose instead that you wanted to test the hypothesis that
β
1
=2
β
2
using a
t
test rather than an
F
test. Write down the expression for the statistic you would
use and state (but do not derive) its distribution.
d.) (15 points) How would your answer to part (b) change if you were to base your test
statistic on White (robust) standard errors rather than the usual OLS standard errors?
e.) (20 points) How would your answer to part (b) change if your null hypothesis were
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Hamilton,J

Click to edit the document details