Econ220B_final_11

# Econ220B_final_11 - 1 Econ 220B Final Exam Winter 2011...

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–1– Econ 220B Final Exam Winter 2011 DIRECTIONS: No books or notes of any kind are allowed. Answer all questions on separate paper. 250 points are possible on this exam. 1.) (85 points total) Consider the following regression model: y t = α + βx t + ε t ε | X N ( 0 , V ) V = exp( γx 1 )0 ··· 0 0e x p ( 2 ) 0 . . . . . . . . . 00 exp( T ) . Here γ is a known scalar and α and β must be estimated from the data. a.) (20 points) Give an expression for the OLS estimate of α and β. Is this estimate unbiased under the conditions stated? (Note: you do not have to prove whether it is unbiased, just answer yes or no). b.) (20 points) Give an expression for the GLS estimate of α and Is this estimate unbiased under the conditions stated? (Note: you do not have to prove whether it is unbiased, just answer yes or no). c.) (10 points) What are the main advantages of GLS relative to OLS for this particular example? d.) (15 points) Suggest a statistic you could use to test the hypothesis that β =0 and state its distribution. Is that distribution exact or only an approximation? (Again, you do not have to derive the distribution, only state what it is) e.) (20 points) Suppose now that you don’t know the true value of γ but would have to estimate it along with α and Give speci f c details of how you would go about estimating α, β, and γ in this case. Suggest the statistic that you could use to test the hypothesis that β in this case and state its distribution.

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## This note was uploaded on 03/02/2012 for the course ECON 220b taught by Professor Hamilton,j during the Spring '08 term at UCSD.

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Econ220B_final_11 - 1 Econ 220B Final Exam Winter 2011...

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