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

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12.4
Consequences of Using OLS in the Presence 
of Autocorrelation
As in the case of heteroscedasticity, in the presence of autocorrelation the OLS estimators
are still linear unbiased as well as consistent and asymptotically normally distributed, but
they are no longer efficient (i.e., minimum variance). What then happens to our usual hy-
pothesis testing procedures if we continue to use the OLS estimators? Again, as in the case
of heteroscedasticity, we distinguish two cases. For pedagogical purposes we still continue
to work with the two-variable model, although the following discussion can be extended to
multiple regressions without much trouble.
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OLS Estimation Allowing for Autocorrelation
As noted, 
ˆ
β
2
is not BLUE, and even if we use var (
ˆ
β
2
)
AR1
, the confidence intervals derived
from there are likely to be wider than those based on the GLS procedure. As Kmenta
shows, this result is likely to be the case even if the sample size increases indefinitely.
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That is, 
ˆ
β
2
is not asymptotically efficient
. The implication of this finding for hypothesis test-
ing is clear: We are likely to declare a coefficient statistically insignificant (i.e., not differ-
ent from zero) even though in fact (i.e., based on the correct GLS procedure) it may be.
This difference can be seen clearly from Figure 12.4. In this figure we show the 95% OLS
[AR(1)] and GLS confidence intervals assuming that true 
β
2
=
0. Consider a particular
estimate of 
β
2
, say, 
b
2
. Since 
b
2
lies in the OLS confidence interval, we could accept the
hypothesis that true
β
2
is zero with 95 percent confidence. But if we were to use the (cor-
rect) GLS confidence interval, we could reject the null hypothesis that true 
β
2
is zero, for
b
2
lies in the region of rejection.