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

Part Two
Relaxing the Assumptions of the Classical Model
presence is detected, then one can take corrective action, such as using the weighted least-
squares regression or some other technique. Before we turn to examining the various cor-
rective procedures, however, we must first find out whether heteroscedasticity is present or
likely to be present in a given case. This topic is discussed in the following section.
A Technical Note
Although we have stated that, in cases of heteroscedasticity, it is the GLS, not the OLS, that
is BLUE, there are examples where OLS can be BLUE, despite heteroscedasticity.
8
But
such examples are infrequent in practice.
11.5
Detection of Heteroscedasticity
As with multicollinearity, the important practical question is: How does one know that
heteroscedasticity is present in a specific situation? Again, as in the case of multicollinearity,
there are no hard-and-fast rules for detecting heteroscedasticity, only a few rules of thumb. But
this situation is inevitable because
σ
2
i
can be known only if we have the entire
Y
population
corresponding to the chosen
X
’s, such as the population shown in Table 2.1 or Table 11.1.
But such data are an exception rather than the rule in most economic investigations. In this
respect the econometrician differs from scientists in fields such as agriculture and biology,
where researchers have a good deal of control over their subjects. More often than not, in
economic studies there is only one sample
Y
value corresponding to a particular value of
X
.
And there is no way one can know
σ
2
i
from just one
Y
observation. Therefore, in most cases
involving econometric investigations, heteroscedasticity may be a matter of intuition, edu-
cated guesswork, prior empirical experience, or sheer speculation.
With the preceding caveat in mind, let us examine some of the informal and formal
methods of detecting heteroscedasticity. As the following discussion will reveal, most of
these methods are based on the examination of the OLS residuals 
ˆ
u
i
since they are the ones
we observe, and not the disturbances 
u
i
. One hopes that they are good estimates of 
u
i
, a
hope that may be fulfilled if the sample size is fairly large.