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

Empirical Exercises
7.16.
The demand for roses.
*
Table 7.6 gives quarterly data on these variables:
Y
=
quantity of roses sold, dozens
X
2
=
average wholesale price of roses, $/dozen
X
3
=
average wholesale price of carnations, $/dozen
X
4
=
average weekly family disposable income, $/week
X
5
=
the trend variable taking values of 1, 2, and so on, for the period 1971–III to
1975–II in the Detroit metropolitan area
You are asked to consider the following demand functions:
Y
t
=
α
1
+
α
2
X
2
t
+
α
3
X
3
t
+
α
4
X
4
t
+
α
5
X
5
t
+
u
t
ln
Y
t
=
β
1
+
β
2
ln
X
2
t
+
β
3
ln
X
3
t
+
β
4
ln
X
4
t
+
β
5
X
5
t
+
u
t
a.
Estimate the parameters of the linear model and interpret the results.
b.
Estimate the parameters of the log–linear model and interpret the results.
guj75772_ch07.qxd 11/08/2008 04:22 PM Page 218

---

Chapter 7
Multiple Regression Analysis: The Problem of Estimation
219
c.
β
2
,
β
3
, and
β
4
give, respectively, the 
own-price, cross-price,
and 
income elastici-
ties 
of demand. What are their a priori signs? Do the results concur with the a
priori expectations?
d.
How would you compute the own-price, cross-price, and income elasticities for
the linear model?
e.
On the basis of your analysis, which model, if either, would you choose and why?
7.17.
Wildcat activity. 
Wildcats are wells drilled to find and produce oil and/or gas in an
improved area or to find a new reservoir in a field previously found to be productive
of oil or gas or to extend the limit of a known oil or gas reservoir. Table 7.7 gives data
on these variables:
*
Y
=
the number of wildcats drilled
X
2
=
price at the wellhead in the previous period 
(in constant dollars, 1972
=
100)
X
3
=
domestic output
X
4
=
GNP constant dollars (1972
=
100)
X
5
=
trend variable, 1948
=
1, 1949
=
2, . . . , 1978
=
31
See if the following model fits the data:
Y
t
=
β
1
+
β
2
X
2
t
+
β
3
ln
X
3
t
+
β
4
X
4
t
+
β
5
X
5
t
+
u
t
a.
Can you offer an a priori rationale to this model?
b.
Assuming the model is acceptable, estimate the parameters of the model and their
standard errors, and obtain 
R
2
and 
¯
R
2
.
c.
Comment on your results in view of your prior expectations.
d.
What other specification would you suggest to explain wildcat activity? Why?
7.18.
U.S. defense budget outlays, 1962–1981
. In order to explain the U.S. defense budget,
you are asked to consider the following model:
Y
t
=
β
1
+
β
2
X
2
t
+
β
3
X
3
t
+
β
4
X
4
t
+
β
5
X
5
t
+
u
t
where 
Y
t
=
defense budget-outlay for year 
t
, $ billions
X
2
t
=
GNP for year 
t
, $ billions
X
3
t
=
U.S. military sales/assistance in year 
t
, $ billions
X
4
t
=
aerospace industry sales, $ billions
X
5
t
=
military conflicts involving more than 100,000 troops. This variable
takes a value of 1 when 100,000 or more troops are involved but is
equal to zero when that number is under 100,000.
To test this model, you are given the data in Table 7.8.
a.
Estimate the parameters of this model and their standard errors and obtain 
R
2
,
modified 
R
2
, and 
¯
R
2
.
b.
Comment on the results, taking into account any prior expectations you have
about the relationship between 
Y
and the various 
X
variables.
c.
What other variable(s) might you want to include in the model and why?
*
I am indebted to Raymond Savino for collecting and processing these data.
guj75772_ch07.qxd 11/08/2008 04:22 PM Page 219

---

220