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.