03.05.2024 OLS Distribution and Tests#

Sampling Distribution of OLS-Estimator#

Assumption:

  • error \(\epsilon\)​​ = independent of explanatory variables

  • normally distributed with mean = 0 and sd = \(\sigma^2\)

=> depends on empirical topic

e.g Wage regression

  • wage > 0 \(\neq\) normal distributed

  • minimum wage => population eran exaclty minimum

=> solve with log

Theorem

\[\begin{split} \implies \hat{ \beta_j } \sim Normal[\beta_j, Var(\beta_j)] \\ \end{split}\]

t-statistic#

4.2!