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

Part Two
Relaxing the Assumptions of the Classical Model
43
N. Gregory Mankiw, “A Quick Refresher Course in Macroeconomics,” 
Journal of Economic Literature,
vol. XXVIII, December 1990, p. 1648.
44
John Fox, 
Applied Regression Analysis, Linear Models, and Related Methods, 
Sage Publications, 
California, 1997, p. 306.
45
Ibid., p. 307.
46
Note that we have squared the standard errors to obtain the variances.
1. A critical assumption of the classical linear regression model is that the distur-
bances
u
i
have all the same variance, 
σ
2
. If this assumption is not satisfied, there is
heteroscedasticity.
2. Heteroscedasticity does not destroy the unbiasedness and consistency properties of OLS
estimators.
3. But these estimators are no longer minimum variance or efficient. That is, they are not
BLUE.
Summary and
Conclusions
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Chapter 11
Heteroscedasticity: What Happens If the Error Variance Is Nonconstant?
401
4. The BLUE estimators are provided by the method of weighted least squares, provided
the heteroscedastic error variances, 
σ
2
i
, are known.
5. In the presence of heteroscedasticity, the variances of OLS estimators are not provided
by the usual OLS formulas. But if we persist in using the usual OLS formulas, the 
t
and
F
tests based on them can be highly misleading, resulting in erroneous conclusions.
6. Documenting the consequences of heteroscedasticity is easier than detecting it. There
are several diagnostic tests available, but one cannot tell for sure which will work in a
given situation.
7. Even if heteroscedasticity is suspected and detected, it is not easy to correct the problem.
If the sample is large, one can obtain White’s heteroscedasticity-corrected standard er-
rors of OLS estimators and conduct statistical inference based on these standard errors.
8. Otherwise, on the basis of OLS residuals, one can make educated guesses of the likely
pattern of heteroscedasticity and transform the original data in such a way that in the
transformed data there is no heteroscedasticity.