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answers2010final

# answers2010final - 1 Econ 220B Winter 2010 Answers to nal...

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–1– Econ 220B, Winter 2010 Answers to f nal exam 1.) a.) plim( b )= Σ 1 xx Σ xy b.) (1) if for the β we are interested in it is the case that E ( y t x 0 t β ) x t = 0 ,then OLS is allowing us to estimate this β . (2) If our goal is to minimize the mean squared error of a forecast of y t using a linear function of x t , ˆ y t = x 0 t β , then the plim of the regression is the optimal β to use. 2a.) Let ˆ α =( X 0 X ) 1 X 0 y ,s 2 =( T 3) 1 Σ ( y t x 0 t ˆ α ) 2 , and 1 0 =( 1 , 1 , 1 ) . Then reject H 0 if 1 0 ˆ α 1 q s 2 1 0 ( X 0 X ) 1 1 <z where z is the number such that the probability that a Student t variable with T 3 degrees of freedom is less than z is equal to 0.05, so z is about 1 . 66 . This is an exact small-sample test under the assumptions. b.) Let S = Σ ˆ u 2 t x t x 0 t and reject H 0 if ( 1 0 ˆ α 1 ) 2 s 2 1 0 ( X 0 X ) 1 S ( X 0 X ) 1 1 >z where z =3 . 84 , the number such that the probability that at χ 2 ( 1 ) variable exceeds

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answers2010final - 1 Econ 220B Winter 2010 Answers to nal...

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