326_midterm-11

326_midterm-11 - UBC, ECONOMICS 326 - 003 2011 MIDTERM...

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UBC, ECONOMICS 326 - 003 2011 MIDTERM EXAMINATION You have 80 minutes. There are 3 question (100 points total). Answer all questions. Question 1 (30 points) Consider a simple linear regression model Y i = α + βX i + U i , where E ( U i | X 1 ,...,X n ) = 0 . Let ˜ β be a conditionally unbiased estimator of β , i.e. E ( ˜ β | X 1 ,...,X n ) = β . Define ¯ Y = n - 1 n i =1 Y i and ¯ X = n - 1 n i =1 X i . Show that ˆ α = ¯ Y - ˜ β ¯ X is an unbiased estimator of α . Question 2 (40 points) Find A-D in the Stata output below if the number of observa- tions is 23. ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x | .0910863 A B 0.191 C D _cons | .3599422 .0241652 14.90 0.000 .3096879 .4101965 ------------------------------------------------------------------------------ Question 3 (30 points) Consider a regression of
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326_midterm-11 - UBC, ECONOMICS 326 - 003 2011 MIDTERM...

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