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STOC.5953.CH04.089-141 6/27/02 12:46 PM Page 129
4.10
Conclusion
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any reason to believe that the errors are homoskedastic. It therefore is prudent to
assume that the errors might be heteroskedastic unless you have compelling reasons to believe otherwise.
Practical implications. The main issue of practical relevance in this discussion is whether one should use heteroskedasticity-robust or homoskedasticityonly standard errors. In this regard, it is useful to imagine computing both, then
choosing between them. If the homoskedasticity-only and heteroskedasticityrobust standard errors are the same, nothing is lost by using the heteroskedasticity-robust standard errors; if they differ, however, then you should use the more
reliable ones that allow for heteroskedasticity. The simplest thing, then, is always
to use the heteroskedasticity-robust standard errors.
For historical reasons, many software programs use the homoskedasticity-only
standard errors as their default setting, so it is up to the user to specify the option
of heteroskedasticity-robust standard errors. The details of how to implement
heteroskedasticity-robust standard errors depend on the software package you use.
All the empirical examples in this book employ heteroskedasticity-robust standard errors unless explicitly stated otherwise.2
4.10 Conclusion
Return for a moment to the problem that started this chapter, the superintendent
who is considering hiring additional teachers to cut the student-teacher ratio.
What have we learned that she might find useful?
Our regression analysis, based on the 420 observations for 1998 in the California test score data set, showed that there was a negative relationship between
the student-teacher ratio and test scores: districts with smaller classes have higher
test scores. The coefficient is moderately large, in a practical sense: districts with
2 fewer students per teacher have, on average, test scores that are 4.6 points higher.
This corresponds to moving a district at the 50th percentile of the distribution of
test scores to approximately the 60th percentile.
2
In case this book is used in conjunction with other texts, it might be helpful to note that some
textbooks add homoskedasticity to the list of least squares assumptions. As just discussed, however, this additional assumption is not needed for the validity of OLS regression analysis as long
as heteroskedasticity-robust standard errors are used.