David Freedman has a provocative answer in "On the so-called 'Huber sandwich
estimator' and 'robust standard errors' in the American Statistican, Vol 60
(4) 299-302, November 2006. Here is the abstract:
The "Huber Sandwich Estimator" can be used to estimate the variance of the
MLE when the underlying model is incorrect. If the model is nearly correct,
so are the usual standard errors, and robustification is unlikely to help
much. On the other hand, if the model is seriously in error, the sandwich
may help on the variance side, but the parameters being estimated by the MLE
are likely to be meaningless - except perhaps as descriptive statistics.
I think he has a valid point asking why the fuzz about standard errors when
the estimates may be wrong.
Thanks German. I've read the paper (it is only 4 pages long but to
me reads more like it is 40!). If I understand it correctly, he says
people who use robust standard errors make this big deal about
getting the standard errors right, but they pay little attention to
the fact that their parameter estimates are biased, sometimes seriously so.