Question

When the conditions for linear regression are met, the OLS estimator is the BLUE estimator. Discuss this argument.

Answer 1

The Gauss-Markov Theorem states that if a linear regression model fulfils the assumptions of the classical linear regression model the ordinary least squares estimator is the best linear unbiased estimator (BLUE).

When the conditions for linear regression are met, the OLS estimator is the only BLUE estimator. The B in BLUE stands for best, and in this context best means the unbiased estimator with the lowest variance.

If the regression conditions aren't met - for instance, if heteroskedasticity is present - then the OLS estimator is still unbiased but it is no longer best. Instead, a variation called general least squares (GLS) will be BLUE.