answers2005final

answers2005final - Answer key for the 2005 final exam (econ...

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Unformatted text preview: Answer key for the 2005 final exam (econ 220b). 1 . a . Let x t ¡ ¡ r t , y t U ,- ¢ ¡ ! x t x t U " 1 ! x t p t and z ¢ t ¡ ¡ ¢- U x t , r t U . Then we can estimate c consistently from the formula ĉ d ¢ ¡ ! z ¢ t z ¢ t U " 1 ! z ¢ t q t . b . We need to assume that S xx ¡ T " 1 X U X and S xz ¡ T " 1 X U Z have full rank and E ¡ v t 2 x t x t U ¡ @ v 2 S xx . We can rewrite our estimator as T ĉ " c d ¢ " d ¡ T " 1 ¡ Z U X ¡ X U X " 1 X U Z " 1 T " 1/2 Z U X ¡ X U X " 1 X U v with z t ¡ ¡ p t , r t U . Now apply the mds central limit theorem to T " 1/2 X U v . Then the resulting distribution for our scaled esimator is N 0, @ v 2 S xz U S xx " 1 S xz " 1 . c . Construct the t-statistic as T ĉ / @ ¢ 11 2 where @ ¢ 11 2 is the top left element of the plug-in estimator of the asymptotic covariance matrix in part (b). We would reject the two-sided null hypothesis that c ¡ 0 at the 5% level if the absolute value of the t-statistic is above 1.96.1....
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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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answers2005final - Answer key for the 2005 final exam (econ...

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