Asymptotically normal OLS estimator

An asymptotically normal OLS estimator is an estimator that, as the amount of data available to it increases, follows a normal distribution in its estimates. This property of the estimator comes from the fact that the OLS (ordinary least squares) method relies on the Central Limit Theorem, which states that when independent variables have identical and independent distributions, the average of those distributions tends towards a normal distribution. Thus, an asymptotically normal OLS estimator is an estimator that, as it receives more information, has its estimates converge on a normal distribution. The practical implication of this property is that, if one has enough data, one can assume that the estimates of the OLS estimator are normally distributed.