Econ220B_final_04

Econ220B_final_04 - 1 Econ 220B James Hamilton Final Exam Winter 2004 DIRECTIONS No books or notes of any kind are allowed separate paper 250

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–1– Econ 220B James Hamilton Final Exam Winter 2004 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 total) State (but do not prove) the Gauss-Markov Theorem. 2.) (30 points total) Consider the following regression model: y = X β + ε where y is a ( T × 1) vector, X is a ( T × k ) matrix, ε is a ( T × 1) vector with the property that ε | X N ( 0 , σ 2 I T ) . Suppose you wanted to test the single nonlinear hypothesis g ( β )=0 . Give the formula for a statistic you could use to test this hypothesis and state (but do not prove) the distribution you would use to interpret this statistic. 3.) (40 points total) Consider the following regression, which includes a lagged dependent variable: y t = α + β y t 1 + γ z t + ε t . Let ε =( ε 1 , ε 2 , ..., ε T ) 0 be the ( T × 1) vector containing all the epsilons where T is the sample size and let z =( z 1 ,z 2 ,...,z T ) 0 . Suppose that ε | z N ( 0 , σ 2 I T ) and y 0 =0 . Suppose further that the true value of β satis f es 0 < β < 1 and that { z t ,y t } are stationary and ergodic with E 1 y t 1 z t £ 1 y t 1 z t ¤ = Q where Q hasrank3w itha l le lemen tso f Q strictly positive. Let ˆ α , ˆ β ,and ˆ γ be the OLS estimates de f ned by ˆ α ˆ β ˆ γ = T Σ y t 1 Σ z t Σ y t 1
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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_04 - 1 Econ 220B James Hamilton Final Exam Winter 2004 DIRECTIONS No books or notes of any kind are allowed separate paper 250

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