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

Dummy Variables and Heteroscedasticity
Let us revisit our savings–income regression for the United States for the periods
1970–1981 and 1982–1995 and for the entire period 1970–1995. In testing for structural
stability using the dummy technique, we assumed that the error var (
u
1
i
)
=
var (
u
2
i
)
=
σ
2
,
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Chapter 9
Dummy Variable Regression Models
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that is, the error variances in the two periods, were the same. This was also the assumption
underlying the Chow test. If this assumption is not valid—that is, the error variances in the
two subperiods are different—it is quite possible to draw misleading conclusions. There-
fore, one must first check on the equality of variances in the subperiod, using suitable
statistical techniques. Although we will discuss this topic more thoroughly in the chapter
on heteroscedasticity, in Chapter 8 we showed how the 
F
test can be used for this purpose.
20
(See our discussion of the Chow test in that chapter.) As we showed there, it seems the error
variances in the two periods are not the same. Hence, the results of both the Chow test and
the dummy variable technique presented before may not be entirely reliable. Of course, our
purpose here is to illustrate the various techniques that one can use to handle a problem
(e.g., the problem of structural stability). In any particular application, these techniques
may not be valid. But that is par for most statistical techniques. Of course, one can take
appropriate remedial actions to resolve the problem, as we will do in the chapter on
heteroscedasticity later (however, see Exercise 9.28).