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Econ 220B, Winter 2009
James Hamilton
Midterm Exam
DIRECTIONS: No books or notes of any kind are allowed.
Answer all questions on
separate paper. 150 points are possible on this exam.
1.) (50 points) Consider the following regression model:
y
=
X
β
+
ε
ε

X
∼
N
(
0
,σ
2
V
(
X
))
.
Here
y
is a
(
T
×
1)
vector of observations on the dependent variable,
X
is a
(
T
×
k
)
matrix
of observations on the explanatory variables with rank
k
,
β
is an unknown
(
k
×
1)
vector
of parameters that must be estimated from the data,
σ
2
is an unknown scalar that must be
estimated from the data, and
V
(
X
)
is a known nonsingular
(
T
×
T
)
matrix. The regression
includes a constant term, so that each element of the
f
rst column of
X
is equal to unity.
a.) Give the formula for the OLS estimate of
β
,denoted
ˆ
β
OLS
.
b.) Give the formula for the GLS estimate of
β
,denoted
ˆ
β
GLS
.
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 Spring '08
 Hamilton,J

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