The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

Empirical Exercises
8.12. Refer to Exercise 7.21.
a.
What are the real income and interest rate elasticities of real cash balances?
b.
Are the preceding elasticities statistically significant individually?
c.
Test the overall significance of the estimated regression.
d.
Is the income elasticity of demand for real cash balances significantly different
from unity?
e.
Should the interest rate variable be retained in the model? Why?
8.13. From the data for 46 states in the United States for 1992, Baltagi obtained the
following regression results:
†
log
C
=
4.30
−
1.34 log
P
+
0.17 log
Y
se
=
(0.91) (0.32)
(0.20)
¯
R
2
=
0
.
27
where 
C
=
cigarette consumption, packs per year
P
=
real price per pack
Y
=
real disposable income per capita
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Chapter 8
Multiple Regression Analysis: The Problem of Inference
265
a.
What is the elasticity of demand for cigarettes with respect to price? Is it statisti-
cally significant? If so, is it statistically different from 1?
b.
What is the income elasticity of demand for cigarettes? Is it statistically signifi-
cant? If not, what might be the reasons for it?
c.
How would you retrieve 
R
2
from the 
adjusted R
2
given above?
8.14. From a sample of 209 firms, Wooldridge obtained the following regression results:
*
log (
salary)
=
4.32
+
0.280 log (sales)
+
0.0174 roe
+
0.00024 ros
se
=
(0.32)
(0.035)
(0.0041) (0.00054)
R
2
=
0.283
where salary
=
salary of CEO
sales
=
annual firm sales
roe
=
return on equity in percent
ros
=
return on firm’s stock
and where figures in the parentheses are the estimated standard errors.
a.
Interpret the preceding regression taking into account any prior expectations that
you may have about the signs of the various coefficients.
b.
Which of the coefficients are 
individually
statistically significant at the 5 percent
level?
c.
What is the overall significance of the regression? Which test do you use? 
And why?
d.
Can you interpret the coefficients of roe and ros as elasticity coefficients? Why or
why not?
8.15. Assuming that 
Y
and 
X
2
,
X
3
,
. . .
,
X
k
are jointly normally distributed and assuming
that the null hypothesis is that the population partial correlations are individually
equal to zero, R. A. Fisher has shown that
t
=
r
1 2
.
3 4
...
k
√
n
−
k
−
2
1
−
r
2
1 2
.
3 4
...
k
follows the 
t
distribution with 
n
−
k
−
2 df, where 
k
is the 
k
th-order partial correla-
tion coefficient and where 
n
is the total number of observations. (
Note: r
1 2.3
is a first-
order partial correlation coefficient, 
r
1 2.3 4
is a second-order partial correlation
coefficient, and so on.) Refer to Exercise 7.2. Assuming 
Y
and 
X
2
and 
X
3
to be
jointly normally distributed, compute the three partial correlations 
r
1 2.3
, 
r
1 3.2,
and
r
2 3.1
and test their significance under the hypothesis that the corresponding popula-
tion correlations are individually equal to zero.
8.16. In studying the demand for farm tractors in the United States for the periods
1921–1941 and 1948–1957, Griliches
†
obtained the following results:
log
Y
t
=
constant
−
0.519 log
X
2
t
−
4.933 log
X
3
t
R
2
=
0.793
(0.231)
(0.477)
*
See Jeffrey M. Wooldridge, 
Introductory Econometrics,
South-Western Publishing Co., 2000, 
pp. 154–155.
†
Z. Griliches, “The Demand for a Durable Input: Farm Tractors in the United States, 1921–1957,” in
The Demand for Durable Goods,
Arnold C. Harberger (ed.), The University of Chicago Press, Chicago,
1960, Table 1, p. 192.
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