Econometrics HT 18

Chapter 12 : The properties of the OLS estimator, lectures

By Lund University

The OLS estimator has some nice properties in the linear regression model.

The properties of the OLS estimator

In order to evaluate the usefulness of an estimator, we introduced to properties held by good estimators, unbiasedness and consistency. It turns out that the OLS estimator has favorable properties as long as the explanatory variable is exogenous. However, it is possible to find many different estimators with these properties. Therefore, we need some method of distinguishing between them. To do that, we begin by assuming that the error terms are homoscedastic, that is, they all have the same variance. With this assumption, we can find the variance of the OLS estimators and show that the OLS estimator has the lowest variance among all linear unbiased estimators. This result is called the Gauss Markov theorem.

When are the OLS estimators unbiased and consistent?

Homoscedasticity, heteroscedasticity and the Gauss-Markov assumptions

The variance of the OLS estimators

Estimating σ2

Estimating the variance of the OLS estimators

The Gauss-Markov theorem