University of California
D. Steigerwald
Department of Economics
Economics 140A
Problem Set IX
1.
In a 2000 study of a sample of Californians, each person’s consumption
C
t
is regressed on
an intercept, their wage and salary income
W
t
and their asset income
A
t
.
The OLS
regression estimates are
P
t
c
=
)
.
(
t
)
.
(
t
)
(
a
.
w
.
3
3
5
2
50
3
5
200
+
+
R
2
= .95,
t = 1,2,...,103.
Residual Sum of Squares :
RSS
1
= 30
.
Note:
The numbers in parentheses are estimated standard errors.
a)
Given the results above, do you think multicollinearity is present?
Please explain
your answer.
b)
If a new aggregate income regressor
Y
t
= W
t
+ A
t
replaces the individual income
regressors, then the OLS regression estimates are
)
(.
t
)
(
P
t
y
.
c
25
48
75
210
+
=
R
2
= .949,
t=1,2,...103.
Residual Sum of Squares :
RSS
2
= 35
.
Briefly explain how and why things may have changed compared to the previous
results.
c)
How would you test the null hypothesis that the coefficients of
W
t
and
A
t
in the
first regression are equal?
Suppose you reject the null hypothesis, how would this
affect your answers to parts a) and b) above?
Can you think of an alternative
procedure to the one presented in part b)?
Explain.
d)
How would these tests you have constructed be affected if the errors are not
normally distributed?
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2.
Suppose output for the economy is given by the production relation
(1)
ln Q
t
=
β
0
+
β
1
ln L
t
+
β
2
ln K
t
+ U
t
t = 1,..., n
where
t
indexes the time at which the observation is recorded,
ln
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 Fall '08
 Staff
 Economics, Regression Analysis, Null hypothesis

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