Final Exam
ECON 3210 O: Use of Economic Data
Laura Salisbury
York University
April 16, 2014
This exam contains 7 questions and 12 pages (including this one), for a total of 108 points.
Read questions carefully, and answer all questions in the booklets provided.
Formulas and
tables are provided on the last 5 pages of the exam. You may use a calculator. You have 180
minutes. Good luck!
1
1. For each of the following, indicate whether the statement is true or false.Explain youranswers
(a)
(4 pts)
Econometric forecasting is more accurate for values of explanatory variables
that are closer to the sample mean.
True. Forecasts based on values of
x
that are far away from the sample mean have
a larger variance. Intuitively, we are better able to forecast based on values of
x
we
have better information about, i.e. values that are close to the sample mean.
(b)
(4 pts)
Linear regression models are flawed because it is impossible for them to
capture nonlinear relationships between variables.
False.
It is possible to approximate nonlinear relationships between variable in a
linear regression by including polynomial terms or logs.
(c)
(4 pts)
In the presence of heteroskedasticity, least squares estimates are biased.
False. In the presence of heteroskedasticity, conventional standard errors for coef
ficient estimates are not appropriate; however, the coefficient estimates themselves
are still unbiased.
(d)
(4 pts)
You are testing a null hypothesis, and the pvalue associated with your test
is 0.025. You should only reject the null hypothesis if you are willing to accept a
probability of type I error of 2.5% or greater.
True. If the pvalue is 0.025, you reject
H
0
for tests at the 2.5% level or greater.
The size of the test is exactly the probability of type I error you are willing to accept.
2. You are estimating the following regression equation:
y
=
β
1
+
β
2
x
2
+
β
3
x
3
+
e
2
You are given the following information:
R
2
= 0
.
4631
R
2
= 0
.
4233
N
X
i
=1
(
y
i

y
)
2
= 1425
.
68
N
X
i
=1
x
2
2
i
= 855
.
17
N
X
i
=1
x
2
3
i
= 1252
.
33
x
2
= 4
.
252
x
3
= 86
.
71
r
23
=

0
.
676
(a)
(4 pts)
Calculate the sum of squared errors (SSE).
You are given
R
2
= 0
.
4631
, and
SST
≡
∑
N
i
=1
(
y
i

y
)
2
= 1425
.
68
.
So, use the
formula for
R
2
and solve for SSE:
R
2
= 1

SSE
SST
⇒
0
.
4631 = 1

SSE
1425
.
68
⇒
SSE
= 765
.
4476
(b)
(4 pts)
Calculate N.
Use the SSE calculated in part (a),
R
2
, and SST to solve for N:
R
2
= 1

SSE/
(
N

K
)
SST/
(
N

1)
⇒
0
.
4233 = 1

765
.
4476
/
(
N

3)
1425
.
68
/
(
N

1)
⇒
N
= 30
(c)
(4 pts)
Calculate the standard error of
b
2
.
You know that
∑
(
x
2
i

x
2
)
2
=
∑
x
2
2
i

N
x
2
2
= 855
.
17

30(4
.
252)
2
= 312
.
785
. And,
because
r
23
=

0
.
676
, it follows that
1

r
2
23
= 1

(

0
.
676)
2
= 0
.
543
. Finally, we
3
know that
ˆ
σ
2
=
SSE
N

K
= 765
.
4476
/
(30

3) = 28
.
350
. So:
\
var
(
b
2
) =
ˆ
σ
2
(1

r
2
23
)
∑
(
x
2
i

x
2
)
2
=
28
.
350
0
.
543(312
.
785)
= 0
.
1669
Then,
se
(
b
2
) =
q
\
var
(
b
2
) = 0
.
4086
.
3. Sean the econometrician is studying the effect of the price of flour on the price of crois
sants. He is also interested in how the price of butter affects the price of croissants. He
estimates the following regression models:
CR
=
β
1
+
β
2
FL
+
e
(1)
CR
=
β
1
+
β
2
FL
+
β
3
BU
+
e
(2)
CR is the price of croissants (in dollars), FL is the price per pound of flour (in cents),
and BU is the price per pound of butter (in dollars). Sean obtains the following results,