HW03_Econ140A_2011Fall

HW03_Econ140A_2011Fall - Economics 140A Fall 2011 Professor...

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Unformatted text preview: Economics 140A Fall 2011 Professor Startz Homework 3 1. The variance of the OLS estimator is ¡¢(£ ̂ ) ¤ ¥ ¦ §¨ © ¦ , where ª « ¬ ­ ®« ¦ § . You're hired to estimate £ and you're going to be paid according to the accuracy of your estimate. Specifically, your revenue is ¯ °±²³²´µ(¶ · ) . You can buy as many observations as you want at price ¸ . The sample variance of ¹ , ª « ¬ , never changes. How many observations should you buy? 2. Suppose that you have º ¤ » observations on ¼ , that ¼ ½ ¤ ¾ ¿ À ½ , that ÁÂÀà ¤ Ä , ¡¢ÂÀà ¤ Å ¬ , and that ÆÇ ÂÀ È É À ¬ à ¤ Ä . Prove that the sample mean, ¾Ê , is the best, linear, unbiased estimator of ¾ . Feel free to cite previous results about the variance of ¾Ê , but carry out the proof rather than simply citing the Gauss-Markov theorem. 3 a. Find the formula for ¡¢(£ ̂ È Ë £ ̂ ¬ ) ....
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This note was uploaded on 12/26/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.

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HW03_Econ140A_2011Fall - Economics 140A Fall 2011 Professor...

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