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Problem Set 1 702 2011

Problem Set 1 702 2011 - Problem Set 1 Due Jan 25 Resource...

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Problem Set 1 Resource Economics 702 Due Jan. 25 Econometrics I 1. Show or derive the following: a. Show that the following three estimators are equivalent: 1 2 2 2 i i i i i i i i i i i X Y Y X x y x Y b X X X x x ; where ( ) and ( ) i i i i x X X y Y Y . (2 pts.) b. If i u u n , what is 2 nu ? Reduce this to its simplest form (1 pt.) c. Show that 1 1 ( ) ( ) i i i e u u b x ; where ( ) i i x X X . (1 pt.) d. We know that 2 2 2 1 1 0 0 2 2 ~ , ~ , i i i X b N and b N x n x . Show that 2 2 0 1 2 1 ( ) ~ , i i i i X X Y X N X n x (3 points). (Note: here we are predicting the value of Y at X i . Logically, what comprises the variance?) 2. Explain, in an essay, the process of estimation using the simple linear model for your example. You
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