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[datascience] Re: R: R: R: OLS is BUE


Cronologico Percorso di conversazione 
  • From: Alessandro Casini < >
  • To: Gianluca Cubadda < >,
  • Subject: [datascience] Re: R: R: R: OLS is BUE
  • Date: Wed, 11 May 2022 15:12:57 +0200

Dear Gianluca,

I see your point. I agree that labeling the result in Hansen as modern GM theorem is misleading given the new evidence that has appeared recently. However, the discussion has led to some scientific progress. If you call Hansen's restriction on unbiasedness U*, then the statement "OLS is BU*E" is a technically correct statement. We did not know this before. Ok, I agree this is not the kind of result one was hoping for. One would like to have a result saying that OLS is best in a certain class where linear as well as nonlinear estimators are allowed. Here instead we get that OLS is best in a class where there are only linear estimators. That's not really the kind of modern GM theorem one would expect.

I noticed that you were implicitly referring to what we discussed previously and to Heckman's paper.  However, my impression is that this was not the case for this paper. Ex-ante it looked an interesting result. It was reviewed by three referees. I do not think that Hansen needs +1 paper in Ecma or any favor whatsoever. The topic of the paper is foundational. I thought it was relevant also in view of the recent growing interest on machine learning methods which are highly non-linear (the discussion here may have something to say about the difference between machine learning methods and more traditional methods?). So I thought it was nice to have a note in Ecma about this. BTW, this paper generates lots of discussion around. In the end, this is the goal of scientific research. When Ecma twitted this paper from its account, it received >1000 likes and many comments. The twits about the other accepted papers receive on average 100 likes each. Likes do not mean anything, but it showed it turned heads up.

I had no doubt that you agree on ethical considerations.

BTW, your Inter Milan has spent much more money than my AC Milan this year, but it looks like you are having hard time to win the title this season! :)

Alessandro 

On 5/11/2022 9:23 AM, Gianluca Cubadda wrote:
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Dear Alessandro,

 

my own reading of the paper by Pötscher and Preinerstorfer is that the claim that OLS is BUE is, if not wrong, at least misleading because the class of unbiased estimator that Hansen uses (that is not the usual one) includes linear estimators only.

So, I think it’s fair to conclude that NOW there is no such a thing as a modern GM theorem, given that what we still know is that OLS is BLUE and not BUE.

 

However, I agree that we need to understand better the relation between non-linearity and unbiasedness.

I would not exclude that in the mathematical statistics literature one can find examples of non-linear unbiased estimators that are more efficient than OLS under the classical GM assumptions, even if Pötscher and Preinerstorfer do not provide any of them in their paper (at least in the version that I read).

We’ll see.

 

Finally, I think that any man of reason couldn’t agree more that no human activity is flawless but that was not my point.

My remark was rather intended to point towards what James Heckman calls the tyranny of the top five, a phenomenon that is idiosyncratic in economics and, I believe, absolutely deleterious to the profession.

However, I admit that I was likely too implicit.

Of course, I agree with your ethical considerations.

 

Ciao,

 

Gianluca

 

 

 

 

Dear Gianluca,

yes, several people out there behave aggressively. This time was about Potscher; surely he is not alone.

The whole point is that we need better understanding of this relation between unbiased and non-linearity. That's the key behind the claim whether OLS is BUE or not.

Gianluca, we are all humans. We can have mistakes in our papers. Also Hansen can have it. And it may happen that the Editor (Imbens here) and two referees did not see these issues in Hansen's paper. So also Ecma can publish a paper with mistakes. Outside Economics, Man City have been spending millions and millions in recent years and have not managed to win the Champions League. How about PSG?

You see, failures happen in any profession. I am sure weird things also happen in other fields/professions.

Anyway, my conclusion is the same as last time. Weird things happen and will continue to happen. The important is to maintain integrity, be professional and work on things you think are worth being explored.

Best,

Alessandro 

On 5/10/2022 2:08 PM, Gianluca Cubadda wrote:

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

 

 

 

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
-- 
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
-- 
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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