–1–
Econ 220B, Winter 2011
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.) (55 points total) An economist is interested in comparing the wages earned by male
and female workers.
Let
x
t
1
=
½
1
if worker
t
is male
0
otherwise
x
t
2
=
½
1
if worker
t
is female
0
otherwise
y
t
=
wage earned by worker
t.
We have an observed sample of
t
= 1
, ..., T
workers of whom
n
M
are male and
n
F
are female,
so that
n
M
+
n
F
=
T.
Consider the following regression model:
y
t
=
x
t
1
β
1
+
x
t
2
β
2
+
ε
t
ε

X
∼
N
(
0
, σ
2
I
T
)
.
a.) (15 points) Calculate the OLS estimates of
β
1
and
β
2
.
What is the relation between
the OLS estimate
b
1
and the average wage earned by male workers in the sample?
b.) (15 points) Propose an unbiased estimate of
σ
2
.
(You do not need to prove that it is
unbiased— just state the formula).
c.) (15 points) Give a formula for the OLS
F
test of the null hypothesis that
β
1
=
β
2
.
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 Spring '08
 Hamilton,J

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