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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

Consider the Model Yi - β1Xi + Ui,where the Xi