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Econ220B_final_08

# Econ220B_final_08 - 1 Econ 220B James Hamilton Final Exam...

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–1– Econ 220B James Hamilton Final Exam Winter 2008 DIRECTIONS: No books or notes of any kind are allowed. Answer all questions on separate paper. 250 points are possible on this exam 1.) (80 points total) This question concerns the following regression model: y = X β + ε where y is a ( T × 1) vector consisting of T di ff erent observations on a variable y t to be explained, X is a ( T × k ) matrix of observations on k explanatory variables, and ε is a ( T × 1) vector of residuals. Suppose that X has rank k and ε | X N ( 0 , σ 2 I T ) for I T the ( T × T ) identity matrix. a.) (10 points) Write down the formula for the OLS estimate of β . b.) (20 points) Consider the special case when there are K = 2 explanatory variables, so that the t th row of the above vector system looks like y t = β 1 x 1 t + β 2 x 2 t + ε t . Write down the formula for the OLS F test of the hypothesis that β 1 = 2 β 2 . State (but do not derive) the distribution of this statistic under the assumptions given above. c.) (15 points) Suppose instead that you wanted to test the hypothesis that β 1 = 2 β 2 using a t test rather than an F test. Write down the expression for the statistic you would use and state (but do not derive) its distribution. d.) (15 points) How would your answer to part (b) change if you were to base your test statistic on White (robust) standard errors rather than the usual OLS standard errors?

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