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.