[datascience] R: R: OLS is BUE


Cronologico Percorso di conversazione 
  • From: "Gianluca Cubadda" < >
  • To: "'Alessandro Casini'" < >, < >
  • Subject: [datascience] R: R: OLS is BUE
  • Date: Tue, 10 May 2022 14:08:36 +0200

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 < >
Inviato: martedì 10 maggio 2022 12:51
A: Gianluca Cubadda < >;
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 (
 
 ">
 )
Department of Economics and Finance 
University of Rome Tor Vergata
Via Columbia 2
00133 Rome, Italy
http://alessandro-casini.com
-- 
Alessandro Casini (
 
 ">
 )
Department of Economics and Finance 
University of Rome Tor Vergata
Via Columbia 2
00133 Rome, Italy
http://alessandro-casini.com



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