Economics 120B
Name:
_________________________
Professor Yongil Jeon
Winter 2008, March 3
Student ID#: _________________________
Answer to Exam #2 – Winter 2008:
Econometrics
120B
1.
(15 points)
A multiple regression includes two regressors:
i
i
i
i
X
X
Y
ε
β
β
β
+
+
+
=
2
2
1
1
0
(i) What is the expected change in
i
Y
if
i
X
1
increases by 3 units and
i
X
2
unchanged?
(ii) What is the expected change in
i
Y
if
i
X
2
decreased by 5 units and
i
X
1
is unchanged?
(iii) What is the expected change in
i
Y
if
i
X
1
increases by 3 units and
i
X
2
decreased by
5 units?
Answer
If
i
X
1
increases by 3 units and
i
X
2
unchanged, then
i
Y
is expected to change by
1
3
β
units.
If
i
X
2
decreased by 5 unites and
i
X
1
is unchanged,
then
i
Y
is expected to change by
2
5
β
−
units.
If
i
X
1
increases by 3 units and
i
X
2
decreased by 5 unites,
then
i
Y
is expected to change
by
2
1
5
3
β
β
−
units.
2.
(15 points)
Consider the regression model
i
i
i
i
u
X
X
Y
+
+
+
=
2
2
1
1
0
β
β
β
. Transform the
regression to use a t-statistic to get
1
2
1
β
β
+
= −
.
Answer
1
2
1
β
β
+
= −
(Hint: You must define the dependent variable in the regression).
0
1
2
1
θ
β
β
=
+
+
. Thus,
1
0
2
1
β
θ
β
=
−
−
0
0
2
1
2
2
(
1)
i
i
i
i
Y
X
X
u
β
θ
β
β
=
+
−
−
+
+
(
)
1
0
0
1
2
2
1
i
i
i
i
i
i
Y
X
X
X
X
u
β
θ
β
+
=
+
+
−
+
And test whether
0
0
=
θ
.

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