The properties of the OLS estimator in the static model

Summary

Setup:

• The linear regression model with the GM assumptions

$$y_t=β_1+β_2x_{t,2}+...+β_kx_{t,k}+ε_t , t=1,…,T$$

• $b_1,b_2,…,b_k$ are the OLS estimators of $β_1,β_2,…,β_k$

Result:

• The OLS estimator is unbiased.
• The OLS estimator is consistent (under weak assumptions).
• The OLS estimator is BLUE
• The OLS standard errors are consistent.
• Inference is correct if error terms are normal, approximately correct if $T$ is large.