Advanced econometrics

Chapter 6 : The statistics of the linear regression model, large samples

By Lund University

The statistics of the linear regression model, large samples

Large sample properties of the OLS estimator

In this section, we investigate the large sample properties of the OLS estimator. We show that the OLS estimator is consistent. We also show that the OLS estimator is approximately normally distributed no matter what the distribution of the error terms. Therefore, inference results developed under the assumption of normally distributed errors will approximately correct even when errors are nor normal, as long as the Gauss-Markov assumptions hold and n is large enough.

Regressor moments

Probability limit of X’X/n

Probability limit of X’ε/n

Consistency of the OLS estimator

Limit of X’ε/√n

Limit of √n(b-β)

Problems

Problems

Moments of X’X/n

Moments of X’ε/n

Consistency of the OLS estimator