2009_ECON0701_tutorial_2

2009_ECON0701_tutorial_2 - ECON0701 Econometrics Tutorial 2...

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ECON0701 Econometrics Tutorial 2 Question 1 a) n n X E n X E n X n E X E n i i n i i n i i 1 ) ( 1 ) ( 1 ) 1 ( ) ( 1 1 1 b) ) 2 ( 2 1 X X Var ) ( ) 2 1 ( 2 1 2 X X Var ) , ( 2 ) ( ) ( 4 1 2 1 2 1 X X Cov X Var X Var 0 ) , ( 2 1 X X Cov as 2 1 , X X are independent ) ( ) ( 4 1 2 1 X Var X Var 2 2 2 2 4 1
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c) ) 3 ( 3 2 1 X X X Var ) ( ) 3 1 ( 3 2 1 2 X X X Var ) ( ) ( ) ( 9 1 3 2 1 X Var X Var X Var 3 2 1 , , X X X are independent 3 2 2 2 2 9 1
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d) ) ( X Var ) 1 ( 1 n i i X n Var ) ( 1 1 2 n i i X Var n ) ( 1 1 2 n i i X Var n n X X ,..., 1 are independent 2 2 1 n n n 2 Question 2 a) False. Should be 0 and 1 instead of 0 and 1 . b) True. i i x y 1 0
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c) True. Sum of OLS residuals=0 0 ) ( 1 1 i n i i n i i y y d) False.
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