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

question 31

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.

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Definitions:

Subscapular Vein

A vein located beneath the scapula, responsible for draining blood from the shoulder and upper back areas.

Internal Thoracic Vein

A vein located along the inner side of the thoracic wall, draining blood from the chest wall and breasts back to the heart.

Superior Vena Cava

A large vein carrying deoxygenated blood from the upper half of the body to the heart's right atrium.

Inferior Vena Cava

The largest vein in the human body, carrying deoxygenated blood from the lower half of the body to the heart.