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220B_mid10

220B_mid10 - 1 Econ 220B Winter 2010 Midterm Exam...

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–1– Econ 220B, Winter 2010 Midterm Exam DIRECTIONS: No books or notes of any kind are allowed. Answer all questions on separate paper. 150 points are possible on this exam. 1.) (20 points) Consider the following equations: y = X β + ε b = ( X 0 X ) 1 X 0 y . Here y is a ( T × 1) vector of observations on the dependent variable, X is a ( T × k ) matrix of observations on the explanatory variables with rank k , and β is the true value of a ( k × 1) vector of parameters. Let b 2 denote the second element of the vector b and let β 2 denote the second element of the vector β . Consider the following theorem: Let ˆ β 2 be any unbiased estimator of β 2 that is constructed from some function of X and y . If condition A holds, then Var( ˆ β 2 | X ) Var ( b 2 | X ) . a.) Write down an equation for what it means to say that ˆ β 2 is an unbiased estimator of β 2 . b.) State a su cient condition or conditions A for which the above theorem is true.

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220B_mid10 - 1 Econ 220B Winter 2010 Midterm Exam...

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