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yiE(eixi)=xi+ei,i=1,,n=0,Var(ei)=2 The parameter of interest is =2. Consider the OLS estimates ^ and ^=^2. (a) Find E(^X) using our knowledge of E(^X) and Var(^X). Is ^ biased for ? (b) Suggest an (approximate) biased-corrected estimator ^, and show ^ is unbiased. (c) Is ^ consistent for when sample size n is large? If yes, establish the consistency of ^. (d) Establish the asymptotic distribution (limiting distribution) of ^ when sample size n is large (hint: first derive the limiting distribution of ^, then use the Delta method)..

yiE(eixi)=xi+ei,i=1,,n=0,Var(ei)=2 The parameter of interest is =2. Consider the OLS estimates ^
and ^=^2. (a) Find E(^X) using our knowledge of E(^X) and Var(^X). Is ^ biased for ? (b) Suggest
an (approximate) biased-corrected estimator ^, and show ^ is unbiased. (c) Is ^ consistent for
when sample size n is large? If yes, establish the consistency of ^. (d) Establish the asymptotic
distribution (limiting distribution) of ^ when sample size n is large (hint: first derive the limiting
distribution of ^, then use the Delta method).

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