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5.4 Heteroskedasticity and Homoskedasticity 207

will be referred to as the “homoskedasticity-only” formulas for the variance and
standard error of the OLS estimators. As the name suggests, if the errors are
heteroskedastic, then the homoskedasticity-only standard errors are inappropri-
ate. Specifically, if the errors are heteroskedastic, then the t-statistic computed
using the homoskedasticity-only standard error does not have a standard normal
distribution, even in large samples. In fact, the correct critical values to use for this
homoskedasticity-only t-statistic depend on the precise nature of the heteroskedas-
ticity, so those critical values cannot be tabulated. Similarly, if the errors are hetero-
skedastic but a confidence interval is constructed as {1.96 homoskedasticity-only
standard errors, in general the probability that this interval contains the true value
of the coefficient is not 95%, even in large samples.

In contrast, because homoskedasticity is a special case of heteroskedasticity,
the estimators snbn21 and snbn20 of the variances of bn1 and bn0 given in Equations (5.4)
and (5.26) produce valid statistical inferences whether the errors are heteroske-
dastic or homoskedastic. Thus hypothesis tests and confidence intervals based on
those standard errors are valid whether or not the errors are heteroskedastic.
Because the standard errors we have used so far [that is, those based on Equations
(5.4) and (5.26)] lead to statistical inferences that are valid whether or not the
errors are heteroskedastic, they are called heteroskedasticity-robust standard
errors. Because such formulas were proposed by Eicker (1967), Huber (1967), and
White (1980), they are also referred to as Eicker–Huber–White standard errors.

What Does This Mean in Practice?

Which is more realistic, heteroskedasticity or homoskedasticity? The answer to
this question depends on the application. However, the issues can be clarified by
returning to the example of the gender gap in earnings among college graduates.
Familiarity with how people are paid in the world around us gives some clues as to
which assumption is more sensible. For many years—and, to a lesser extent, today—
women were not found in the top-paying jobs: There have always been poorly paid
men, but there have rarely been highly paid women. This suggests that the distribu-
tion of earnings among women is tighter than among men (see the box in Chapter 3
“The Gender Gap in Earnings of College Graduates in the United States”). In
other words, the variance of the error term in Equation (5.20) for women is plausi-
bly less than the variance of the error term in Equation (5.21) for men. Thus the
presence of a “glass ceiling” for women’s jobs and pay suggests that the error term
in the binary variable regression model in Equation (5.19) is heteroskedastic. Unless
there are compelling reasons to the contrary—and we can think of none—it makes
sense to treat the error term in this example as heteroskedastic.