Question

Heteroskedasticity in OLS estimators has several consequences. State and explain the consequences.

Answer 1

1. Unbiasedness; the presence of heteroskedasticity does not affect the unbiasedness character of the OLS estimators (α & β) and they would still be linear. Thus the OLS estimators are unbiased even under heteroskedasticity conditions.

2. Efficiency; under sconditions of heteroskedasticity, the OLS estimators will not have minimum variance among the class of unbiased estimators rendering them inefficient in small samples.

3. Assymptotic Efficiency; the OLS estimators are also innefficient for large samples in the presence of heteroskedasticity. This means that as n moves towards infinity, an alternative estimator can be found with a smaller asymptotic variance than the OLS estimator

4. Inapplicability of OLS estimator variance for hypothesis testing; when a model suffers heteroskedasticity problem, the formulae for variance of OLS estimators would be under/over stated.

5. Inefficiency of prediction; a high variance due to the presence of heteroskedasticity. The prediction of Y for a given value X would be inefficient since the variance of prediction would include the variance of the error term.

Heteroskedasticity causes unbiasedness and efficiency of OLS estimators. It causes the tests of hypothesis to be no longer valid.