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

FIGURE 12.11
Regression residuals
from the Nerlove
study. (Adapted from
Marc Nerlove, “Return
to Scale in Electric
Supply,” in Carl F.
Christ et al.,
Measurement in
Economics,
Stanford
University Press,
Stanford, Calif., 1963.)
Time
0
u
t
Regression residuals
×
×
×
× ×
×
×
×
×
×
×
×
×
×
×
×
×
FIGURE 12.12
Hypothetical
regression residuals
plotted against time.
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Part Two
Relaxing the Assumptions of the Classical Model
large amount, perhaps three or four standard deviations away from the mean value of
all the observations.
a.
What are the reasons for the existence of the outlier(s)?
b.
If there is an outlier(s), should that observation(s) be discarded and the regres-
sion run on the remaining observations?
c.
Is the Durbin–Watson 
d
applicable in the presence of the outlier(s)?
12.13. Based on the Durbin–Watson 
d
statistic, how would you distinguish “pure’’ auto-
correlation from specification bias?
12.14. Suppose in the model
Y
t
=
β
1
+
β
2
X
t
+
u
t
the 
u
’s are in fact serially independent. What would happen in this situation if, as-
suming that 
u
t
=
ρ
u
t
−
1
+
ε
t
, we were to use the following generalized difference
regression?
Y
t
−
ρ
Y
t
−
1
=
β
1
(1
−
ρ
)
+
β
2
X
t
−
ρβ
2
X
t
−
1
+
ε
t
Discuss in particular the properties of the disturbance term 
ε
t
.
12.15. In a study of the determination of prices of final output at factor cost in the United
Kingdom, the following results were obtained on the basis of annual data for the
period 1951–1969:
PF
t
=
2.033
+
0.273
W
t
−
0.521
X
t
+
0.256
M
t
+
0.028
M
t
−
1
+
0.121
PF
t
−
1
se 
=
(0.992)
(0.127)
(0.099)
(0.024)
(0.039)
(0.119)
R
2
=
0.984
d
=
2.54
where PF
=
prices of final output at factor cost, 
W
=
wages and salaries per employee,
X
=
gross domestic product per person employed, 
M
=
import prices, 
M
t
−
1
=
import prices lagged 1 year, and PF
t
−
1
=
prices of final output at factor cost in the
previous year.
* 
“Since for 18 observations and 5 explanatory variables, the 5 percent lower and
upper 
d
values are 0.71 and 2.06, the estimated 
d
value of 2.54 indicates that there
is no positive autocorrelation.’’ Comment.
12.16. Give circumstances under which each of the following methods of estimating the
first-order coefficient of autocorrelation