econ582mt02 - Econ 582 Midterm Exam Instructions This is an...

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Econ 582 Midterm Exam Instructions : This is an open book and open notes exam. Answer all question. Time limit is 2 hours. Total points = 100. 1. (15 points) Consider the linear regression model with normal errors conditional on the x ’s: 2 ~ ( 0 , ) ii i i y iid N ε σ =+ β x a) Recall, the maximum likelihood estimator of maximizes () ( ) ( ) SSR −= ββ y-X Show that the Newton-Raphson algorithm for maximizing () SSR converges in 1 iteration to the least squares estimate 1 ˆ = X'X X'y regardless of the initial value chosen for the iteration. 2. (25 points) Let 1 ,, n X X K be an iid sample with 2 ~( , ) XN µσ . Consider the maximum likelihood estimator (mle) of 2 22 1 1 ˆ n mle i i x x n = =− a) What is the asymptotic distribution of 2 ˆ mle ? b) What is the mle for ? c) Using the delta method, derive the asymptotic distribution for ˆ mle Hint : 2 4 0 0 2 n I n θ   =  3. (30 points) Consider the consumption function regression 01 2 tt t t cy r ∆= +∆+ + where ln( ) cC ∆= denotes real consumption growth, ln( ) yY =∆

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econ582mt02 - Econ 582 Midterm Exam Instructions This is an...

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