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EC 331
MIDTERM
FALL 2003
NAME:
SHOW ALL YOUR WORK AND WRITE CLEARLY TO GET CREDIT
1.
(25 points)
Consider, as an alternative to the least squares estimator, the linear estimator
[
y
C
X
X
X
⋅
+
=
−
'
)
'
(
1
β
]
, where
is some
matrix that is conformable with
.
C
xT
2
'
)
'
(
1
X
X
X
−
a)
Is
an unbiased estimator? If not, how would you make it unbiased?
b)
What is the variancecovariance expression for the unbiased version of
, that is, the
estimator
with the conditions developed in part (a).
c)
Contrast the variancecovariance matrix for
with the variancecovariance expression
for
b
. How would you reach a conclusion as to which is “best” in terms of sampling
variability?
1
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View Full Document2.
(15 points)
You are given the regression output that is obtained when you estimated
the relationship on annual data.
12
tt
tax
income
e
β
=+⋅
+
Dependent Variable: TAX
Method: Least Squares
Sample: 1 60
Included observations: 60
TAX=C(1)+C(2)*INCOME
Coefficient Std. Error
tStatistic
Prob.
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 Spring '11
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