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!