Thanks to Robert Dawson (again), Steve Simon, and Rich
Ulrich for their responses.
What begins to dawn on me is that I might be confusing
residuals (as taken into account when estimating
regression equations or as displayed in the respective
plots after a regression has been estimated) and
unobserved, true random disturbances. So, my second
question was based on a misunderstanding on my part.
Would anyone care to correct the following, if necessary?
My intuition now is (and was all the time, but I was
unable to sort it out) that there is no reason to treat
systematically inhomogeneous observed residuals
differently from homogeneous residuals, IF one had not
accepted randomness of the disturbances in the first place
as one of the core assumptions of OLS in the first place.
Inefficiency of the estimates only results if one can
claim that these observed residuals represent
inhomogeneous (random) unobserved disturbances -- which
is, of course, the common textbook assumption. Only then
weighting down observations with larger variability is an
obvious cure. If we don't know about the source of the
inhomogeneous residuals (which I deliberatly don't call
disturbances), we also cannot claim randomness, and we
don't have justification to artificially decrease the
weight of the more variable observations.
Rather, we might be forced to state that the population as
such is inhomogeneous and a single model might not fit two
or more different subpopulations, or we should consider
conditional effects which only work in the
high-variability regions of the model. In any case, the
issue is misspecification.
Regarding the question of how standard errors become
inflated, your explanations make sense given the above,
and I shall also follow the references provided.
Thanks again to you all!
MQ
--
________________________________________________________________
Markus Quandt
===========================================================================
This list is open to everyone. Occasionally, less thoughtful
people send inappropriate messages. Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.
For information about this list, including information about the
problem of inappropriate messages and information about how to
unsubscribe, please see the web page at
http://jse.stat.ncsu.edu/
===========================================================================
