Dear
Alessandro,
I agree that unnecessary aggressiveness should
be avoided in academic debates. Unfortunately, Potscher is
not the only guy in the profession that behaves like that.
Overall, my personal view if this kind of
“super-unbiasedness” condition that Hansen assumes is
satisfied by linear estimators only, then the BUE claim for
OLS is essentially misleading.
On the more general side, I believe that this
story provides another piece of evidence that even very good
journals may publish wrong (or, at least, useless) results
by very good people. Let me remark that this conclusion
would not be considered surprising at all in scientific
fields different from Economics.
Best,
Gianluca
Da: Alessandro Casini
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Inviato: martedì 10 maggio 2022 12:51
A: Gianluca Cubadda
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Oggetto: Re: R: OLS is BUE
Hi,
Thank
you for sharing. I was aware of this. We discussed it
briefly with other people in the department (Vincenzo Atella
and others). Before Potscher's paper appeared online in February, Hansen and
Wooldridge had exchanges on Twitter about what Potscher
later showed. If you look for it on Twitter, you should be
able to find the discussion.
Potscher is right. What he showed was already
pointed out online. So I think the way it writes is a
unnecessarily aggressive. But he has always behaved in this
way. It is not the first time that comes out with a
takedown.
Moving to the core discussion, my take is this.
Hansen showed that if you drop linearity and impose further
conditions on unbiasedness, then OLS is best in such class.
That would mean that OLS is BUE (best unbiased estimator).
Potscher showed that the restrictions on unbiasedness
introduced by Hansen actually are satisfied only by linear
estimators. Thus, it looks like that Hansen's result still
applies to linear estimators only (implying that we go back
to OLS is BLUE). However, one can interpret Potscher's
results as saying that if you want unbiasedness then you
need to drop non-linear estimators. Then, I see an argument
to say that OLS is BUE.
The
discussion on Twitter was indeed on the tension between
these unbiasedness restrictions and linearity/nonlinearity.
Regarding
the other early papers containing some related results, I do
not know anything. Some of the papers Potscher referenced are written in German...
Overall, I found the discussion
thought-provoking. Yes, this was bad for Hansen's
reputation. Potscher once again showed to be unnecessarily
aggressive.
I am curious to see how the discussion would
go. My guess is that Ecma will publish some corrigendum from
Potscher. But he has to tone down his writings. The
discussion is on the process.
There is a second version of Potscher's
paper (after communication with Hansen) here:
https://arxiv.org/pdf/2203.01425v2.pdf
Let's
see what happens.
BTW, I
presented these two papers also in my class in the PhD. Also
as a lesson on how difficult is the publishing process in
our profession. And that it is possible even for giants
people to have mistakes in their papers (or just disagree on
whether there is a mistake or not).
Best,
Alessandro
On 5/10/2022 8:38 AM, Gianluca Cubadda
wrote:
Dear
All,
you’ll find in attachment a reply by Pötscher
and Preinerstorfer to the paper by Hansen (forthcoming in
Econometrica) that Alessandro kindly brought to our
attention.
Fundamentally, the authors claim that Hansen
reinvented the wheel!
I should add that
Bruce Hansen is (was?) one of my econometric heroes, so it
was tough to become aware of this paper…
Ciao,
Gianluca
Hi,
this is not on big data but I think
still useful when teaching econometrics. A recent paper "A
Modern Gauss-Markov Theorem" by Bruce Hansen forthcoming
in Econometrica that shows that OLS is not just BLUE (best
linear unbiased estimator) but also BUE (best unbiased
estimator). So basically OLS is the best thing you can do
even when allowing for nonlinear estimators.
The proof is not as easy as for
BLUE. So I am not sure how relevant is going to be for
teaching undergraduate classes. Yet, it is worth knowing
it.
The paper is here:
https://www.econometricsociety.org/system/files/19255-3.pdf
Best,
Alessandro
--
Alessandro Casini (
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Department of Economics and Finance
University of Rome Tor Vergata
Via Columbia 2
00133 Rome, Italy
http://alessandro-casini.com
--
Alessandro Casini (
" moz-do-not-send="true" class="moz-txt-link-freetext">
)
Department of Economics and Finance
University of Rome Tor Vergata
Via Columbia 2
00133 Rome, Italy
http://alessandro-casini.com