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

EXAMPLE 11.6
White’s
Heteroscedasticity
Test
From cross-sectional data on 41 countries, Stephen Lewis estimated the following regres-
sion model:
26
ln
Y
i
=
β
1
+
β
2
ln
X
2
i
+
β
3
ln
X
3
i
+
u
i
(11.5.24)
where 
Y
=
ratio of trade taxes (import and export taxes) to total government revenue,
X
2
=
ratio of the sum of exports plus imports to GNP, and 
X
3
=
GNP per capita; and ln
stands for natural log. His hypotheses were that 
Y
and 
X
2
would be positively related (the
higher the trade volume, the higher the trade tax revenue) and that 
Y
and 
X
3
would be
(
Continued
)
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Part Two
Relaxing the Assumptions of the Classical Model
A comment is in order regarding the White test. If a model has several regressors, then
introducing all the regressors, their squared (or higher-powered) terms, and their cross
products can quickly consume degrees of freedom. Therefore, one must use caution in
using the test.
28
In cases where the White test statistic given in Eq. (11.5.25) is statistically significant,
heteroscedasticity may not necessarily be the cause, but specification errors, about which
more will be said in Chapter 13 (recall point 5 of Section 11.1). In other words, 
the White
test can be a test of (pure) heteroscedasticity or specification error or both.
It has been
argued that if no cross-product terms are present in the White test procedure, then it is a test
of pure heteroscedasticity. If cross-product terms are present, then it is a test of both het-
eroscedasticity and specification bias.
29
Other Tests of Heteroscedasticity
There are several other tests of heteroscedasticity, each based on certain assumptions. The
interested reader may want to consult the references.
30
We mention but one of these tests
because of its simplicity. This is the