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Midterm Exam 2
Introduction to Econometrics  Fall 2006
You have one hour and 15 minutes to answer the questions below. You are not allowed to use any kind
of notes or to consult formulas stored in your calculator; all the formulas you need are in the attached sheet.
The value of each question is given; manage your time remembering that the results of the exam will be
curved.
When asked to test a null hypothesis, use a two sided alternative hypothesis and a 5% signi…cance level,
unless otherwise speci…ed.
PLEASE SHOW YOUR WORK
1.
(a)
e
ﬂ
1
=
n
P
i
=1
a
i
Y
i
=
n
P
i
=1
a
i
(
ﬂ
0
+
ﬂ
1
X
i
+
u
i
) =
ﬂ
0
n
P
i
=1
a
i
+
ﬂ
1
n
P
i
=1
a
i
X
i
+
n
P
i
=1
a
i
u
i
=
ﬂ
1
+
n
P
i
=1
a
i
u
i
Because the least squares assumptions hold, we know:
E
(
u
i
j
X
1
;:::;X
n
) =
E
(
u
i
j
X
i
) = 0
;
so
we have:
E
³
e
ﬂ
1
j
X
1
;:::;X
n
´
=
ﬂ
1
(b) When the three least squares assumptions hold and the error term is homoskedastic, the Gauss
Markov Theorem says that the OLS estimator
b
ﬂ
1
has the smallest variance, conditional on
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This note was uploaded on 07/28/2010 for the course ECON 410 taught by Professor Staff during the Fall '08 term at Wisconsin.
 Fall '08
 Staff
 Econometrics

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