Department of Economics
Fall 2007
University of California
Prof. Woroch
Economics 140
: MIDTERM #2 ANSWERS
I.
SHORT QUESTIONS
: Give a concise but complete answer to each of the following 4 questions for a total
of 50 points.
1.
[10]
Consider the following regression of wages (
wage
i
) on education (
edu
i
):
i
i
i
i
i
i
i
i
u
edu
DM
edu
edu
DF
DF
wage
+
×
+
+
×
+
+
=
)
(
)
(
4
3
2
1
0
β
β
β
β
β
,
where
DM
i
= 1 if person is male and 0 otherwise and
DF
i
= 1 if person is female and 0 otherwise.
a)
Explain why this regression has a multicollinearity problem.
Be specific to this problem.
Answer:
Perfect multicolinearity arises when one or more independent variables is a linear function of other
independent variables in the regression. In this case:
i
i
i
i
i
edu
edu
DM
edu
DF
=
×
+
×
)
(
)
(
b)
Assume you drop the variable
)
(
i
i
edu
DM
×
from the above regression. Interpret
β
2
.
Answer:
These are all correct answers to this question:
1.
2
β
is the effect of education on wages for females vs. males.
2.
2
β
is the effect of education on wages for females minus the effect of education on wages for
males.
3.
2
β
is the change in wages associated with an additional year of education for females compared to
this change for males.
4.
2
β
is the difference in slopes between females and males in the wage-education relationship.
2.
[15]
Consider the wage regression
i
i
i
i
i
i
i
i
i
u
Z
X
Z
D
X
D
X
Y
+
×
+
+
×
+
+
+
=
)
(
)
(
5
4
3
2
1
0
β
β
β
β
β
β
where
X
is years of education,
D
is a dummy variable indicating college graduation and Z is family income level.
a)
How would you test the hypothesis that graduating from college has no effect on wages for all values of
X
?
Answer:
i)
The relevant hypothesis for this test is:
H
o
:
β
2
=0 and
β
3
=0
H
1
:
β
2
≠
0 and/or
β
3
≠
0
ii)
Using this hypothesis, I would obtain an F statistic
iii)
I would reject the hypothesis if this statistic is larger than the critical value corresponding to a 5% test in an
F
(2, n-5-1)
distribution: 3.00. Rejecting the hypothesis means that I reject that college graduation has no effect
on wages for all values of
X
.
b)
Write an expression for the effect of a small increase in X, i.e.,
X
Y
Δ
Δ
, in terms of the coefficients and
variables in the above wage regression model.
Answer:
i
i
i
i
Z
D
X
Y
5
3
1
β
β
β
+
+
=
Δ
Δ

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Economics 140
Page 2
Midterm #2 Answers
c)
You think that rather than affecting the level of wages, education and family incomes are best thought of as
changing the wage in percentage terms. What change would you make to the above regression specification
to reflect this?
Answer:
These are all correct answers to this question:
1.
i
i
i
i
i
i
i
i
i
u
Z
X
Z
D
X
D
X
Y
+
×
+
+
×
+
+
+
=
)
(
)
(
ln
5
4
3
2
1
0
β
β
β
β
β
β
A unit increase in education generates a percentage increase in wages.

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