Chapter 5 Linear Regression

Estimator Desirable Properties

1. Unbiased

2. Consistency

• $$plim\hat{\beta_n}=\beta$$
• based on the law of large numbers, we can derive consistency
• More observations means more precise, closer to the true value.
1. Efficiency
• Minimum variance in comparison to another estimator.
• OLS is BlUE (best linear unbiased estimator) means that OLS is the most efficient among the class of linear unbiased estimator Gauss-Markov Theorem
• If we have correct distributional assumptions, then the Maximum Likelihood is asymptotically efficient among consistent estimators.