220B_mid08_answers

220B_mid08_answers - " * v t ! t 1 T z t v t 2...

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Answer key for the midterm in 2008 1.) a.) ± There is no difference in estimating * between Option 1 and Option 2. ± Validity of t test: - Advantage: t test using Option 2 is asymptotically valid in the presence of an unknown form of heteroskedasticity. - Disadvantage: If there is no heteroskedasticity, t test using Option 1 may perform better than Option 2 in a small sample. b.) ± Estimate of * : - Advantage: FGLS is asymptotically more efficient. - Disadvantage: If V ² X   is misspecified or not well estimated, FGLS is still consistent but may not be more efficient than OLS. ± Validity of t test: -Advantage:If V ² X   is well estimated, t statistic using Option 3 can be close to t distribution in a small sample. - Disadvantage: If V ² X   is misspecified, t test based on Option 3 is not valid. 2.) See the textbook. 3.) a.) No. A Gaussian regression model satisfies / | X L N ² 0, @ / 2 I T   , which implies that / and X are independent. But E / t x t ± E ² u t " * v t  ² z t ² v t   ± @ v 2 . b.) b ± ! t ± 1 T x t y t ! t ± 1 T x t 2 ± * ² ! t ± 1 T ² z t ² v t  ² u t
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Unformatted text preview: " * v t ! t 1 T z t v t 2 * T " 1 ! t 1 T z t u t v t u t " * z t v t " * v t 2 T " 1 ! t 1 T z t 2 v t 2 2 z t v t Therefore, p lim T v . b * " *@ v 2 @ z 2 @ v 2 * ' c.) When a researcher is interested in forecasting y with x . d.) As b " * ' ! t 1 T z t v t u t " * v t ! t 1 T z t v t 2 *@ v 2 @ z 2 @ v 2 , T b " * ' L v T " 1/2 ! t 1 T z t v t u t " * v t *@ v 2 @ z 2 @ v 2 . Let q t z t v t u t " * v t *@ v 2 . Then E q t 0, q t L i . i . d E q t 2 @ z 2 @ u 2 @ v 2 @ u 2 * 2 @ z 2 @ v 2 2 * 2 @ v 4 . Therefore, T b " * ' L v N 0, V , where V @ z 2 @ u 2 @ v 2 @ u 2 * 2 @ z 2 @ v 2 2 * 2 @ v 4 @ z 2 @ v 2 2 e.) T b " * L v N 0, @ u 2 / @ z 2 ,...
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220B_mid08_answers - " * v t ! t 1 T z t v t 2...

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