–1–
Econ 220B
Final Exam
Winter 2007
DIRECTIONS: No books or notes of any kind are allowed.
Answer all questions on
separate paper.
250 points are possible on this exam
1.) (115 points total) Consider the following regression model,
y
t
=
α
+
γ
0
z
t
+
ε
t
for
z
t
a
(
q
×
1)
vector of explanatory variables.
Let
ε
= (
ε
1
,
ε
2
, ...,
ε
T
)
0
and suppose that
ε

z
1
,
z
2
, ...,
z
T
∼
N
(
0
,
σ
2
I
T
)
.
a.) (20 points) Write down the formula that characterizes the OLS estimate of
γ
as a
function of
{
y
1
, ..., y
T
,
z
1
, ...,
z
T
}
.
b.) (20 points) The OLS
F
test of the null hypothesis that
γ
=
0
can be written as
F
=
(
SSR
R
−
SSR
U
)
/m
SSR
U
/
(
T
−
k
)
where
SSR
R
denotes the restricted sum of squared residuals and
SSR
U
denotes the unre
stricted sum of squared residuals.
What are the values of
m
and
k
in this case?
Explain
exactly which regressions you would use to calculate
SSR
R
and
SSR
U
.
c.) (20 points) What additional assumptions (if any) beyond those stated above would
you need in order to conclude that
F
has an exact
F
(
n
1
, n
2
)
distribution?
What are the
values of
n
1
and
n
2
?
d.) (20 points) The centered
R
2
for a regression is de
fi
ned by
R
2
= 1
−
P
T
t
=1
e
2
t
P
T
t
=1
(
y
t
−
y
)
2
for
y
the sample mean of
y
1
, ..., y
T
and
e
t
the OLS residual for observation
t
.
Calculate
R
2
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 Spring '08
 Hamilton,J

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