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If both the asymptotic Variance-Covariance matrix estimators (robust and non-robust) are consistent to the same matrix, i.e., both will have the same efficiency (True?), then what is the advantage of using SE estimators assuming Conditionally Homoskedasticity, when we have Conditionally Homoskedasticity?

Hayashi's Econometrics book states that «the finite-sample properties of an estimator are generally better, the fewer the number of population parameters estimated to form the estimator.», i.e., under conditional homoskedasticity we should use non-robust estimators. I understand that with the robust estimator we estimate more population parameters. But what are these properties that Hayashi speaks of? and how can we prove that they are better?

Any help would be appreciated.

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  • $\begingroup$ @AlecosPapadopoulos, this question arose from Hayashi's book page 130. The sentence is for us to assume conditional homoskedasticity. Aand under this assumption, he states that it's better to use the estimators that are not robust since they have better properties in this case. Which properties are these, and why are their better? I don't think this is answered in that question,or at least not it's not apparent to me how it is... $\endgroup$ – An old man in the sea. Dec 28 '14 at 7:33
  • $\begingroup$ The finite sample properties of estimators usually examined in econometrics relate to bias and efficiency. I though this was understood. Estimating fewer unknowns reduces overall error. But if the post I linked too does not cover you, certainly I have no problem in retracting my "close as duplicate" vote, just let me know. $\endgroup$ – Alecos Papadopoulos Dec 28 '14 at 7:52
  • $\begingroup$ @AlecosPapadopoulos But in this case both have the same asymptotic efficiency (under conditional homoskedasticity). Do they have a different bias? $\endgroup$ – An old man in the sea. Dec 28 '14 at 9:33
  • $\begingroup$ I thought we were discussing finite-sample properties (for which there are no mathematically derived results in this case as far as I know, but rather accumulated experience from applications and simulations). $\endgroup$ – Alecos Papadopoulos Dec 28 '14 at 9:41
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    $\begingroup$ In principle, you should open a new question, asking about references to, and summary of, specific studies that deal with the issue and make finite-sample comparisons between the contestants here. But then again, this would be very open-ended... you must understand that this is not an issue solved through mathematical statistics, but spread over various papers and books, and in reality, it may not even be "well-documented" -maybe just researchers making side-notes, like the one Hayashi makes in his book. $\endgroup$ – Alecos Papadopoulos Dec 28 '14 at 17:53