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1
Econ 120C
Ramu Ramanathan
Fall 2003
First Midterm answers
I.
Consider the model
Y
t
=
b
1
+
b
2
X
t
+
b
3
S
t
+
u
t
,
where
Y
= percapita expenditure
on health care,
X
is percapita personal income, and
S
is the percent of seniors (that
is, percent of population 65 years or over). Using data for the U.S. states and the
District of Columbia (51 observations), the model was estimated by OLS, and the
auxiliary regression for testing for heteroscedasticity is given next (it had
R
2
=
0.417).
2
2
003
.
0
063
.
0
017
.
0
683
.
0
619
.
6
ˆ
t
t
t
t
t
S
S
X
X
u

+
+

=
Ia.
(3 points)
Write down in symbolic terms the auxiliary equation that specifies
how heteroscedasticity is determined. In it write down the null hypothesis of homo
scedasticity.
Note that your equation should not have any numerical values.
t
s
=
1
a
+
2
a
X
t
+
3
a
2
t
X
+
4
a
S
t
+
5
a
S
2
t
H
0
:
2
a
=
3
a
=
4
a
=
5
a
= 0
Ib. (5 points)
Compute the test statistic, state its distribution under the null and d.f.,
carry out the test at the 1 percent level, and state your conclusion about homo
/heteroscedasticity in words.
LM = nR
2
= 51
·
0.417 = 21.267.
Under H
0
LM has the Chisquare distribution
with 4 d.f.
For a 1 percent test, the critical value is LM* = 13.2767.
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This note was uploaded on 04/21/2008 for the course ECON 120C taught by Professor Stohs during the Spring '08 term at UCSD.
 Spring '08
 Stohs

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