Take a regression model Y Xe with E e j X 0 and i i d observations (Yi ,Xi ) and scalar X The parameter of interest is 2 Consider the OLS estimators b and b b2 (a) Find E b j X using our knowledge of E b j X and Vb var b j X Is b biased for (b) Suggest an (approximate) biased corrected estimator b using an estimator b Vb for Vb (c) For b to be potentially unbiased, which estimator of Vb is most appropriate Under which conditions is b unbiased

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Question: Take a regression model Y Xe with E[e j X] 0 and i.i.d. observations (Yi ,Xi ) and scalar X. The parameter of

Take a regression model Y Æ X¯Åe with E[e j X] Æ 0 and i.i.d. observations (Yi ,Xi ) and scalar X. The parameter of interest is µ Æ ¯2. Consider the OLS estimators b¯ and bµ Æ b¯2.

(a) Find E

£bµ j X

using our knowledge of E

£ b¯ j X

and Vb¯

Æ var

£ b¯ j X

. Is bµ biased for µ?

(b) Suggest an (approximate) biased-corrected estimator bµ¤ using an estimator b Vb¯ for Vb¯.

(c) For bµ¤ to be potentially unbiased, which estimator of Vb¯ is most appropriate?

Under which conditions is bµ¤ unbiased?

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