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Econ220B_final_07

# Econ220B_final_07 - 1 Econ 220B Final Exam Winter 2007...

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–1– Econ 220B Final Exam Winter 2007 DIRECTIONS: No books or notes of any kind are allowed. Answer all questions on separate paper. 250 points are possible on this exam 1.) (115 points total) Consider the following regression model, y t = α + γ 0 z t + ε t for z t a ( q × 1) vector of explanatory variables. Let ε = ( ε 1 , ε 2 , ..., ε T ) 0 and suppose that ε | z 1 , z 2 , ..., z T N ( 0 , σ 2 I T ) . a.) (20 points) Write down the formula that characterizes the OLS estimate of γ as a function of { y 1 , ..., y T , z 1 , ..., z T } . b.) (20 points) The OLS F test of the null hypothesis that γ = 0 can be written as F = ( SSR R SSR U ) /m SSR U / ( T k ) where SSR R denotes the restricted sum of squared residuals and SSR U denotes the unre- stricted sum of squared residuals. What are the values of m and k in this case? Explain exactly which regressions you would use to calculate SSR R and SSR U . c.) (20 points) What additional assumptions (if any) beyond those stated above would you need in order to conclude that F has an exact F ( n 1 , n 2 ) distribution? What are the values of n 1 and n 2 ? d.) (20 points) The centered R 2 for a regression is de fi ned by R 2 = 1 P T t =1 e 2 t P T t =1 ( y t y ) 2 for y the sample mean of y 1 , ..., y T and e t the OLS residual for observation t . Calculate R 2

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Econ220B_final_07 - 1 Econ 220B Final Exam Winter 2007...

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