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# m2_ak - Introduction to Econometrics Fall 2006 You have one...

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Midterm Exam 2 Introduction to Econometrics - Fall 2006 You have one hour and 15 minutes to answer the questions below. You are not allowed to use any kind of notes or to consult formulas stored in your calculator; all the formulas you need are in the attached sheet. The value of each question is given; manage your time remembering that the results of the exam will be curved. When asked to test a null hypothesis, use a two sided alternative hypothesis and a 5% signi…cance level, unless otherwise speci…ed. PLEASE SHOW YOUR WORK 1. (a) e fl 1 = n P i =1 a i Y i = n P i =1 a i ( fl 0 + fl 1 X i + u i ) = fl 0 n P i =1 a i + fl 1 n P i =1 a i X i + n P i =1 a i u i = fl 1 + n P i =1 a i u i Because the least squares assumptions hold, we know: E ( u i j X 1 ;:::;X n ) = E ( u i j X i ) = 0 ; so we have: E ³ e fl 1 j X 1 ;:::;X n ´ = fl 1 (b) When the three least squares assumptions hold and the error term is homoskedastic, the Gauss- Markov Theorem says that the OLS estimator b fl 1 has the smallest variance, conditional on X 1 ; ::::;X n ; of all linear conditionally unbiased estimators (in other words it is the BLUE). In

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