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

Part Two
Relaxing the Assumptions of the Classical Model
12.23. As noted in the text, Maddala has suggested that if the Durbin–Watson 
d
is smaller
than 
R
2
, one may run the regression in the first-difference form. What is the logic
behind this suggestion?
12.24. Refer to Eq. (12.4.1). Assume 
r
=
0 but 
ρ
=
0. What is the effect on 
E
(
ˆ
σ
2
) if (
a
)
0
< ρ <
1 and (
b
) 
−
1
< ρ <
0? When will the bias in 
ˆ
σ
2
be reasonably small?
12.25. The residuals from the wages–productivity regression given in Eq. (12.5.2) were
regressed on lagged residuals going back six periods (i.e., AR[6]), yielding the fol-
lowing results:
Dependent Variable: S1
Method: Least Squares
Sample (adjusted): 1966–2005
Included observations: 40 after adjustments
Coefficient
Std. Error
t
-Statistic
Prob.
S1(-1)
1.019716
0.170999
5.963275
0.0000
S1(-2)
-0.029679
0.244152
-0.121560
0.9040
S1(-3)
-0.286782
0.241975
-1.185171
0.2442
S1(-4)
0.149212
0.242076
0.616386
0.5417
S1(-5)
-0.071371
0.243386
-0.293240
0.7711
S1(-6)
0.034362
0.167077
0.205663
0.8383
R-squared
0.749857
Mean dependent var.
0.004433
Adjusted R-squared
0.713071
S.D. dependent var.
0.019843
S.E. of regression
0.010629
Durbin-Waston stat.
1.956818
Sum squared resid.
0.003841
a.
From the preceding results, what can you say about the nature of autocorrelation
in the logarithmic wages–productivity data?
b.
If you think that an AR(1) mechanism characterizes autocorrelation in our data,
would you use the first-difference transformation to get rid of autocorrelation?
Justify your answer.