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Unformatted text preview: 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 + b = ( X X ) 1 X 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 is the true value of a ( k 1) vector of parameters. Let b 2 denote the second element of the vector b and let 2 denote the second element of the vector . Consider the following theorem: Let 2 be any unbiased estimator of 2 that is constructed from some function of X and y . If condition A holds, then Var( 2 | X ) Var ( b 2 | X ) . a.) Write down an equation for what it means to say that 2 is an unbiased estimator of 2 . b.) State a su cient condition or conditions A for which the above theorem is true....
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This note was uploaded on 03/02/2012 for the course ECON 220b taught by Professor Hamilton,j during the Spring '08 term at UCSD.
- Spring '08