## CLRM – Assumption 5: Normal Distributed Error Terms in Population

Assumption 5 is often listed as a Gauss-Markov assumption and refers to normally distributed error terms $\epsilon$ in the population. Overall, assumption 5 is not a Gauss-Markov assumption in that sense that the OLS estimator will still be the best linear unbiased estimator (BLUE) even if the error terms $\epsilon$ are not normally distributed in the population. The fact that OLS estimator is still BLUE even if assumption 5 is violated derives from the central limit theorem, which ensures that when n goes to infinity (basically for very large samples) the estimated coefficients are asymptomatically normal distributed even if the error terms $\epsilon$ are not.

Overall, OLS estimator remains BLUE even if assumption 5 violated. However, normal distributed error terms $\epsilon$ in the population come in handy for small sample sizes. That follows from the property of normal distributed error terms, allows hypothesis testing even when the number of observations in a sample is rather small.