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Is OLS consistent under heteroskedasticity?
[IMPORTANT] OLS estimators are still unbiased and consistent under heteroskedasticity. Under heteroskedasticity, OLS is no longer the best linear unbiased estimator (BLUE); there might be more efficient linear estimator.
Does heteroskedasticity make OLS estimator biased?
Heteroscedasticity does not cause ordinary least squares coefficient estimates to be biased, although it can cause ordinary least squares estimates of the variance (and, thus, standard errors) of the coefficients to be biased, possibly above or below the true of population variance.
Is the OLS estimator efficient under heteroscedasticity?
No, OLS is not efficient under heteroscedasticity. Efficiency of an estimator is obtained if the estimator has the least variance among other possible estimators. Statements about efficiency in OLS are made regardless of the limiting distribution of an estimator.
Is the MMSE estimator asymptotically efficient under heteroscedasticity?
The MMSE estimator is asymptotically unbiased and it converges in distribution to the normal distribution: n ( x ^ − x) → d N ( 0, I − 1 ( x)) , where I (x) is the Fisher information of x. Thus, the MMSE estimator is asymptotically efficient. MMSE is claimed to be asymptotically efficient. I am a little confused here.
What happens if error term μ I is heteroscedastic?
If error term ( μ i) is heteroscedastic, then the OLS estimates do not have the minimum variance property in the class of unbiased estimators, i.e. they are inefficient in small samples. Furthermore they are asymptotically inefficient. The estimated coefficients remain unbiased statistically.
Why is GLS blue if you know the form of heteroskedasticity?
Because GLS is BLUE if you know the form of heteroskedasticity (and correlated errors). If you misspecify the form of heteroscedasticity, GLS estimates will lose their nice properties. Under heteroscedasticity, OLS remains unbiased and consistent, but you lose efficiency.