Consider the model Yi – β1Xi + ui, where the Xi and ui the are mutually independent i.i.d. random variables with finite fourth moment and E(ui)= 0.
(a)Let 1 denote the OLS estimator of β1. Show that ( 1- β1)= (b)What is the mean and the variance of ? Assuming that the Central Limit Theorem holds, what is its limiting distribution?
(c)Deduce the limiting distribution of ( 1 – β1)? State what theorems are necessary for your deduction.