220B_mid12

# 220B_mid12 - 1 Econ 220B Winter 2012 Midterm Exam...

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–1– Econ 220B, Winter 2012 Midterm Exam DIRECTIONS: No books or notes of any kind are allowed. Answer all questions on separate paper. 150 points are possible on this exam. 1.) (60 points total) Let y t and z t be stationary and ergodic scalars which are related according to y t = φy t 1 + αz t + γz t 1 + ε t where ε t i.i.d. N (0 2 ) . a.) (20 points) Write the above equation in the form of a regression model y t = x 0 t β + ε t . What is the value of x t and β ? Use this notation to characterize the OLS estimate of the vector ( φ, α, γ ) 0 and of σ 2 . b.) (25 points) Suppose you wanted to test the null hypothesis H 0 : α = γ. Suggest a statistic that you could compare with a Student t distribution to test this null hypothesis. What are the degrees of freedom? Would the test have an exact Student t distribution or only approximately Student t under the assumptions stated? c.) (15 points) Now propose an alternative test statistic that you could use to test the

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220B_mid12 - 1 Econ 220B Winter 2012 Midterm Exam...

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