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

robust standard errors.
34
See H. White, op. cit.
35
More technically, they are known as 
heteroscedasticity-consistent covariance matrix 
estimators.
36
William H. Greene, 
Econometric Analysis, 
2d ed., Macmillan, New York, 1993, p. 385.
37
T. Dudley Wallace and J. Lew Silver, 
Econometrics: An Introduction, 
Addison-Wesley, Reading, Mass.,
1988, p. 265. 
EXAMPLE 11.8
Illustration of
White’s Procedure
As an example, we quote the following results due to Greene:
36
ˆ
Y
i
=
832.91
− 
1834.2 (Income) 
+
1587.04 (Income)
2
OLS se 
=
(327.3) (829.0)
(519.1)
t
=
(2.54) (2.21)
(3.06)
(11.6.4)
White se 
=
(460.9) (1243.0)
(830.0)
t
=
(1.81) (
−
1.48)
(1.91)
where 
Y
=
per capita expenditure on public schools by state in 1979 and Income
=
per
capita income by state in 1979. The sample consisted of 50 states plus Washington, DC.
As the preceding results show, (White’s) heteroscedasticity-corrected standard errors are
considerably larger than the OLS standard errors and therefore the estimated
t
values are
much smaller than those obtained by OLS. On the basis of the latter, both the regressors
are statistically significant at the 5 percent level, whereas on the basis of White estimators
they are not. However, it should be pointed out that White’s heteroscedasticity-corrected
standard errors can be larger or smaller than the uncorrected standard errors.
Since White’s heteroscedasticity-consistent estimators of the variances are now avail-
able in established regression packages, it is recommended that the reader report them. As
Wallace and Silver note:
Generally speaking, it is probably a good idea to use the WHITE option [available in regres-
sion programs] routinely, perhaps comparing the output with regular OLS output as a check to
see whether heteroscedasticity is a serious problem in a particular set of data.
37
Plausible Assumptions about Heteroscedasticity Pattern
Apart from being a large-sample procedure, one drawback of the White procedure is that
the estimators thus obtained may not be so efficient as those obtained by methods that
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