Exercise 6

Exercise 6 - Economics 241B Exercise 6 1. Asymptotic...

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Economics 241B Exercise 6 1. Asymptotic Behavior of Hypothesis Tests H 0 : k = k vs. H 1 : k 6 = k . a. You know that under H 0 , p n B k k ± d ! N (0 ;Avar ( B k )) (1) \ Avar ( B k ) p ! Avar ( B k ) ; where \ Avar ( B k ) = S 1 xx ^ SS 1 xx . To perform your test, you wish to use a t -statistic and you want to make sure that the limit distribution is standard normal. Show that (1) implies that under H 0 , B k k SE ± ( B k ) d ! N (0 ; 1) ; (2) where SE ± ( B k ) = q 1 n \ Avar ( B k ) . b. When performing the test, under what circumstances would you select the critical values from a normal distribution versus a t distribution? c. Show what SE ± ( B k ) converges in probability to. d. With your answer from part c , intuitively explain the convergence in (2). 2. Consider the model Y t = 01 X t 1 + 02 X t 2 + U t t = 1 ;:::;n (3) where U t iid ± N (0 2 ) while X t 1 and X t 2 are scalars such that E ( X t 1 X t 2 ) 6
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This note was uploaded on 12/26/2011 for the course ECON 241b taught by Professor Staff during the Fall '08 term at UCSB.

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Exercise 6 - Economics 241B Exercise 6 1. Asymptotic...

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