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

TABLE 12.7
Determinants of U.S.
Domestic Price of
Copper, 1951–1980
Year
C
G
I
L
H
A
1951
21.89
330.2
45.1
220.4
1,491.0
19.00
52
22.29
347.2
50.9
259.5
1,504.0
19.41
53
19.63
366.1
53.3
256.3
1,438.0
20.93
54
22.85
366.3
53.6
249.3
1,551.0
21.78
55
33.77
399.3
54.6
352.3
1,646.0
23.68
56
39.18
420.7
61.1
329.1
1,349.0
26.01
57
30.58
442.0
61.9
219.6
1,224.0
27.52
58
26.30
447.0
57.9
234.8
1,382.0
26.89
59
30.70
483.0
64.8
237.4
1,553.7
26.85
60
32.10
506.0
66.2
245.8
1,296.1
27.23
61
30.00
523.3
66.7
229.2
1,365.0
25.46
62
30.80
563.8
72.2
233.9
1,492.5
23.88
63
30.80
594.7
76.5
234.2
1,634.9
22.62
64
32.60
635.7
81.7
347.0
1,561.0
23.72
65
35.40
688.1
89.8
468.1
1,509.7
24.50
66
36.60
753.0
97.8
555.0
1,195.8
24.50
67
38.60
796.3
100.0
418.0
1,321.9
24.98
68
42.20
868.5
106.3
525.2
1,545.4
25.58
69
47.90
935.5
111.1
620.7
1,499.5
27.18
70
58.20
982.4
107.8
588.6
1,469.0
28.72
71
52.00
1,063.4
109.6
444.4
2,084.5
29.00
72
51.20
1,171.1
119.7
427.8
2,378.5
26.67
73
59.50
1,306.6
129.8
727.1
2,057.5
25.33
74
77.30
1,412.9
129.3
877.6
1,352.5
34.06
75
64.20
1,528.8
117.8
556.6
1,171.4
39.79
76
69.60
1,700.1
129.8
780.6
1,547.6
44.49
77
66.80
1,887.2
137.1
750.7
1,989.8
51.23
78
66.50
2,127.6
145.2
709.8
2,023.3
54.42
79
98.30
2,628.8
152.5
935.7
1,749.2
61.01
80
101.40
2,633.1
147.1
940.9
1,298.5
70.87
Note:
The data were collected by Gary R. Smith from sources such as 
American Metal Market, Metals Week,
and U.S.
Department of Commerce publications.
C
=
12-month average U.S. domestic price of copper (cents per pound).
G
=
annual gross national product ($, billions).
I
=
12-month average index of industrial production.
L
=
12-month average London Metal Exchange price of copper (pounds sterling).
H
=
number of housing starts per year (thousands of units).
A
=
12-month average price of aluminum (cents per pound).
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Part Two
Relaxing the Assumptions of the Classical Model
12.28. Refer to Exercise 12.26 and the data given in Table 12.7. If the results of this exer-
cise show serial correlation,
a.
Use the Cochrane–Orcutt two-stage procedure and obtain the estimates of the
feasible GLS or the generalized difference regression and compare your results.
b.
If the 
ρ
estimated from the Cochrane–Orcutt method in (
a
) differs substantially
from that estimated from the 
d
statistic, which method of estimating 
ρ
would you
choose and why?
12.29. Refer to Example 7.4. Omitting the variables 
X
2
and 
X
3
, run the regression and
examine the residuals for “serial’’ correlation. If serial correlation is found, how
would you rationalize it? What remedial measures would you suggest?
12.30. Refer to Exercise 7.21. A priori autocorrelation is expected in such data. Therefore,
it is suggested that you regress the log of real money supply on the logs of real na-
tional income and long-term interest rate in the first-difference form. Run this
regression, and then rerun the regression in the original form. Is the assumption un-
derlying the first-difference transformation satisfied? If not, what kinds of biases
are likely to result from such a transformation? Illustrate with the data at hand.
12.31.
The use of Durbin–Watson d for testing nonlinearity.
Continue with Exercise 12.29.
Arrange the residuals obtained in that regression according to increasing values of
X
. Using the formula given in Eq. (12.6.5), estimate 
d
from the rearranged residu-
als. If the computed 
d
value indicates autocorrelation, this would imply that the lin-
ear model was incorrect and that the full model should include 
X
2
i
and 
X
3
i
terms.
Can you give an intuitive justification for such a procedure? See if your answer
agrees with that given by Henri Theil.
*
12.32. Refer to Exercise 11.22. Obtain the residuals and find out if there is autocorrelation
in the residuals. How would you transform the data in case serial correlation is de-
tected? What is the meaning of serial correlation in the present instance?