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# 220B_mid07_answers - t p v E ± x t t ± c b ± ² T" 1...

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Answer key for the midterm in 2007 1.) The sample correlation of e t and x t is always zero in OLS because from the normal equation ! t ± 1 T e t x t ± 0. 2.) When E ± // U   ± @ 2 V ± X   , premultiply the regression model by P " 1 where V ± X   ± PP U .Then E ± / ±/ ± U   ± @ I T where / ± ± P " 1 / . Therefore, the transformed regression model satisfies all the assumptions for Gauss-Markov Theorem. 3.) a.) As x t / t is a martingale difference sequence, E ± x t / t | x t " 1 / t " 1 , T , x 1 / 1   ± 0 , E ± x t / t   ± 0 by the law of iterated expectations. b.) By Ergodic theorem, T " 1 ! x t /
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Unformatted text preview: t p v E ± x t / t ± c.) b ± * ² T " 1 ! x t x t U " 1 T " 1 ! x t / t p v * d.) T ± b " * L v N ± , Q " 1 SQ " 1 e.) Let R ± 1 0 C 0 1 C . Then, we can use the following test statistic. W T ± T ± Rb U ¡ RV ² T R U " 1 Rb , where V ² T ± T " 1 ! t ± 1 T x t x t U " 1 T " 1 ! t ± 1 T e t 2 x t x t U T " 1 ! t ± 1 T x t x t U " 1 . f.) W T L v D 2 ± 2...
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