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I keep hearing my professor try to explain that we can use robust standard errors when we run a regression to confront the issue of heteroskedasticity. However I don't quite understand how telling Stata to use the robust standard errors is different than using regular standard errors. If the regular standard errors have a risk of being a problem wouldn't we always want to use robust standard errors then?

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    $\begingroup$ Yes, you are right. In situations where they provide well-calibrated inference (large samples, not too many covariates, nothing with a really extreme distribution) there's at worst a small loss of efficiency estimating the standard error - the efficiency of the point estimate is of course unchanged. Compared to everything else that could be going wrong, this is usually a small price to pay. $\endgroup$
    – guest
    Nov 17 '12 at 6:46
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    $\begingroup$ Arguably, you want to avoid using them! A simple message for autocorrelation correctors: Don't. by Grayham Mizon (1995) - Journal of Econometrics. $\endgroup$ Mar 21 '15 at 21:18
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If the assumption of homoskedasticity is truly valid, the simple estimator of the VCE is more efficient than the robust sandwich version. That means it has smaller variance, so your estimates are less uncertain.

Of course, you can always do a heteroskedasticity test first and estimate accordingly.

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  • $\begingroup$ As with almost all mis-specification tests, choosing your analysis based on how the test comes out has problems; the mis-specification test and the post-test inference are not independent, which messes up the frequentist properties of the post-test inference, as it's typically implemented. $\endgroup$
    – guest
    Nov 17 '12 at 6:47
  • $\begingroup$ Can you give/cite an example of where heteroskedasticity testing will cause inference to go awry? $\endgroup$
    – dimitriy
    Nov 17 '12 at 16:18
  • $\begingroup$ For one example, see Rasch et al (2009) The two-sample t test: pre-testing its assumptions does not pay off. For lots more, google "homoskedasticity pre-test", or consult the literature on the lack of power of omnibus specification tests. $\endgroup$
    – guest
    Nov 19 '12 at 23:46
  • $\begingroup$ @DimitriyV.Masterov, +1, but the gain in efficiency of classical standard errors is only given in finite samples, as both classical and robust s.e.s have the same plim under homoskedasticity. $\endgroup$ Jul 5 '16 at 14:29
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There's also an interesting point raised by King & Roberts (2014): if your classical and robust standard errors diverge, your model suffers from misspecification that need to be fixed. "Settling" for the misspecified model and just correcting the standard errors will lead to "biased estimators of all but a few quantities of interest."

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    $\begingroup$ That's an interesting point. Can you clarify how it speaks to the OP's question? Are you arguing the we should always try both? $\endgroup$ Mar 21 '15 at 21:21
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    $\begingroup$ As far as I understand, OP wonders whether we should always use robust rather than "classic" standard errors. The answer is yes and no. It makes sense to report robust rather than "classic" standard errors, but they are no silver bullet. If they're too far apart, your model suffers from misspecification and standard error robustness won't fix that. $\endgroup$
    – Durden
    Mar 22 '15 at 3:19
  • $\begingroup$ Haven't read the King paper, but it sounds like David Freedman makes the same points in On The So-Called “Huber Sandwich Estimator” and “Robust Standard Errors”. Angrist and Pischke make an another point in Mostly harmless econometrics, in small samples the variance + bias of robust standard errors can make rejection rates much worse than simply using the biased estimates of the conventional standard errors (which have a smaller variance). $\endgroup$
    – Andy W
    Mar 22 '15 at 13:33

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