It would be nice to have a reference for the results cited above by those who claimed that this is a known result. I would also find it surprising if this result hadn't been established by some USSR/EasternEuro bros in the 70s. At least at a level of a "folk theorem".
A Modern GaussMarkov Theorem

It would be nice to have a reference for the results cited above by those who claimed that this is a known result. I would also find it surprising if this result hadn't been established by some USSR/EasternEuro bros in the 70s. At least at a level of a "folk theorem".
Either you find a reference or you don't make such a claim. I have already had to fight against referees who wrote things like: Your result is important and correct but it is so obvious that we must have already known it. Without providing a single reference! And while there were numerous published papers suggesting suboptimal methods
It is impossible to prove that nobody has ever derived a result. The burden of the proof is on the people who claim that it has already been shown.

But in a sense, using this short note in teaching would be definitely closer in spirit to modern econometric research than the traditional GaussMarkov algebra. So it has its pedagogical advantages.
I agree. But for teaching, I would appreciate it if we had an intuitive proof. Here I don't get yet the intuition.

Neat paper. Now I know why I've never been able to find a nonlinear estimator that outdoes the sample average unless I make a particular distributional assumption.
I do have a slight gripe. I'm surprised Hansen doesn't mention that the original GM theorem only assumes uncorrelatedness, not independence. So this is not, in a technical sense, a strengthening of the claim. I can think of time series models  such as those with ARCH heteroskedasticity  that satisfy the original GM assumptions (because heteroskedasticity doesn't depend on X) but are not i.i.d. draws from a population.

Can someone explain the difference between Hansen's result and Goldberger's definition of OLS as best linear predictor?
https://www.jstor.org/stable/2281645You can't generally get unbiased estimators of the linear predictor, only consistent estimators. Remember the difference between a model (or, in the LP, an equation that defines parameters) and an estimator.

The paper claims the result is a strict improvement on GaussMarkov. Wooldridge says the opposite in the tweet linked above. Who is right?
Bruce Hansen has written a revised version that discusses several points mentioned in this thread: https://www.ssc.wisc.edu/~bhansen/papers/gauss.pdf

The paper claims the result is a strict improvement on GaussMarkov. Wooldridge says the opposite in the tweet linked above. Who is right?
Bruce Hansen has written a revised version that discusses several points mentioned in this thread: https://www.ssc.wisc.edu/~bhansen/papers/gauss.pdf
I think that Bruce Hansen has restated his result such that this critique does not apply. He no longer assumes independence but only Var(YX) = (sigma^2)*I(n) (equations 3 and 4), which is exactly what Wooldridge wanted. It is interesting to see that the paper improved after constructive critiques. I have even the impression that some parts have been added in reply to some comments made in this thread. For instance:
"A caveat is that the class of nonlinear unbiased estimators is small. As shown by Koopmann (1982) and discussed in Gnot, Knautz, Trenkler, and Zmyslony (1992), any unbiased estimator of the regression coefficient can be written as a linearquadratic function of the dependent variable Y . Koopmann’s result shows that while nonlinear unbiased estimators exist, they constitute a narrow class."
was not in the previous version. 
The paper claims the result is a strict improvement on GaussMarkov. Wooldridge says the opposite in the tweet linked above. Who is right?
Bruce Hansen has written a revised version that discusses several points mentioned in this thread: https://www.ssc.wisc.edu/~bhansen/papers/gauss.pdf
I think that Bruce Hansen has restated his result such that this critique does not apply. He no longer assumes independence but only Var(YX) = (sigma^2)*I(n) (equations 3 and 4), which is exactly what Wooldridge wanted. It is interesting to see that the paper improved after constructive critiques. I have even the impression that some parts have been added in reply to some comments made in this thread. For instance:
"A caveat is that the class of nonlinear unbiased estimators is small. As shown by Koopmann (1982) and discussed in Gnot, Knautz, Trenkler, and Zmyslony (1992), any unbiased estimator of the regression coefficient can be written as a linearquadratic function of the dependent variable Y . Koopmann’s result shows that while nonlinear unbiased estimators exist, they constitute a narrow class."
was not in the previous version.yes, we made the comments but I suppose the referees also made similar comment: at the end, the result is a good exercise for 1950 statistics but it is frankly of no interest in modern statistics; unbiasedness is a terrible constraint

Just came across this. But is it really that new ? I mean yes in the realm of regression but isn’t maximum likelihood already minimum variance unbiased ? And isn’t this sufficient to say what Hansen is saying already ?
Sure. Unbiased. Don't even bother reading Hansens's paper...

You need to make assumptions on the distributions when applying MLE. That's why OLS coincides with MLE when we assume for normality  smth CramérRao proved decades ago. I have not read the new paper yet, but I think Bruce removes this restriction.
Just came across this. But is it really that new ? I mean yes in the realm of regression but isn’t maximum likelihood already minimum variance unbiased ? And isn’t this sufficient to say what Hansen is saying already ?

holy fieck another regmonkey thread on a regmonkey paper. please guys it's 2021 we can't be talking about linear regression STILL after so many years. please
there is a big difference between reg monkey and econometric theorists.
Reg monkey = low IQ applied micro monkey who just reg income educ educ^2, robust in Stata
Econometrics theorist = high IQ who developed theories, estimators and inferences in econometrics