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Econ220B_final_06

# Econ220B_final_06 - 1 Econ 220B Final Exam Winter 2006...

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–1– Econ 220B Final Exam Winter 2006 DIRECTIONS: No books or notes of any kind are allowed. Answer all questions on separate paper. 250 points are possible on this exam 1.) (25 points) State (but do not prove) the Gauss-Markov Theorem. 2.) (80 points total) Consider the following model: y ( T × 1) = X ( T × k ) β ( k × 1) + u ( T × 1) E ( u | X ) = 0 E ( uu 0 | X ) = V ( α , X ) plim T 1 ( X 0 X ) = Q where Q has rank k plim T 1 ( X 0 u ) = 0 . You need not prove or derive any of the following statements; just give the expression and answer “yes” or “no”. a.) (30 points) Give the formula for the OLS estimate b . Is b unbiased? Is b consistent? b.) (30 points) Suppose that the value of α is known. Give the formula for the GLS estimate ˆ β GLS . Is ˆ β GLS biased? Is ˆ β GLS consistent? c.) (20 points) If instead α has to be estimated consistently from the data (so that ˆ α T p α ), how would that change your answers to part (b)?

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–2– Econ 220B 3.) (90 points total) Consider the following model: y t = z 0 t β + u t E ( x t z 0 t ) = A E ( x t x 0 t ) = B E ( u 2 t ) = σ 2 E ( u 2 t x t x 0 t ) = σ 2 B
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