Essay
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.
Correct Answer:

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(a)The OLS estimator in this case is
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