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

under both heteroscedasticity and autocorrelation the usual
OLS estimators, although linear, unbiased, and asymptotically (i.e., in large samples)
normally distributed,
1
are no longer minimum variance among all linear unbiased
estimators. In short, they are not efficient relative to other linear and unbiased
estimators. Put differently, they may not be best linear unbiased estimators (BLUE).
As a result, the usual,
t
,
F
, and 
χ
2
may not be valid.
12.1
The Nature of the Problem
The term 
autocorrelation
may be defined as “correlation between members of series of
observations ordered in time [as in time series data] or space [as in cross-sectional data].’’
2
In the regression context, the classical linear regression model assumes that such autocor-
relation does not exist in the disturbances 
u
i
. Symbolically,
cov(
u
i
,
u
j
|
x
i
,
x
j
)
=
E
(
u
i
u
j
)
=
0
i
=
j
(3.2.5)
Put simply, the classical model assumes that the disturbance term relating to any observa-
tion is not influenced by the disturbance term relating to any other observation. For exam-
ple, if we are dealing with quarterly time series data involving the regression of output on
labor and capital inputs and if, say, there is a labor strike affecting output in one quarter,
there is no reason to believe that this disruption will be carried over to the next quarter. That
is, if output is lower this quarter, there is no reason to expect it to be lower next quarter.
Similarly, if we are dealing with cross-sectional data involving the regression of family
consumption expenditure on family income, the effect of an increase of one family’s income
on its consumption expenditure is not expected to affect the consumption expenditure of
another family.
However, if there is such a dependence, we have autocorrelation. Symbolically,
E
(
u
i
u
j
)
=
0
i
=
j
(12.1.1)
In this situation, the disruption caused by a strike this quarter may very well affect output
next quarter, or the increases in the consumption expenditure of one family may very well
prompt another family to increase its consumption expenditure if it wants to keep up with
the Joneses.
Before we find out why autocorrelation exists, it is essential to clear up some termino-
logical questions. Although it is now a common practice to treat the terms