FRM Part I · FRM Exam Part I · Linear Regression
Under the Gauss-Markov conditions, OLS is described as BLUE. What does the term 'best' mean in this context?
In BLUE, 'best' means OLS has the smallest variance among all linear unbiased estimators, given the Gauss-Markov conditions. It does not guarantee the lowest variance among all estimators, including nonlinear or biased ones, and it still requires errors uncorrelated with the regressors.
- AIt has the smallest variance among all linear unbiased estimatorsCorrect
- BIt has the smallest variance among all estimators, linear or not
- CIt has the highest R-squared of any possible estimator
- DIt is unbiased even if the errors are correlated with the regressors
Explanation
Gauss-Markov states OLS has minimum variance within the class of linear unbiased estimators when the errors have zero mean, constant variance, and no serial correlation. It does not claim superiority over nonlinear or biased estimators, and exogeneity is still required for unbiasedness.
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