# pq2 - Econ 410 - Fall 2006 Practice Questions for the...

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Econ 410 - Fall 2006 Practice Questions for the Second Midterm 1. Consider the following linear model: Y i = β 0 + β 1 X i + u i Assume that all the least square assumptions for the model with one re- gressor hold. You want to estimate the coe cient β 1 using the following estimator: e β 1 = n X i =1 ¡ d i d ¢¡ Y i Y ¢ where d i is some function of the observations X 1 , ..., X n and d = 1 n n P i =1 d i (a) Is e β 1 a linear estimator? Can you write it as: e β 1 = n P i =1 a i Y i ?I fth i s is the case, what is a i equal to? Explain. (b) Using the fact that Y i = β 0 + β 1 X i + u i ,showthat : e β 1 = β 1 n P i =1 ¡ d i d ¢ X i + n P i =1 ¡ d i d ¢ u i (c) What are the conditions under which e β 1 is conditionally unbiased? (d) Assume that Var ( u i | X i )= σ 2 u . According to the Gauss-Markov Theorem, what are the conditions on d i under which e β 1 has the lowest variance, conditional on X 1 , .... , X n

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## This note was uploaded on 07/28/2010 for the course ECON 410 taught by Professor Staff during the Fall '08 term at University of Wisconsin Colleges Online.

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pq2 - Econ 410 - Fall 2006 Practice Questions for the...

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