hw1_answer_120c_su07_S2 - Economics 120C Professor Yongil...

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Economics 120C Name: _________________________ Professor Yongil Jeon Summer 2007-2 Student ID#: _________________________ Answer to Homework #1 – Summer 2007-Session 2, Econ 120C (Midterm Exam, Summer 2007-Session 1, Econ 120C) Answer all questions on separate paper. This problem set should be handed in to your TA at the beginning of your review session on Tuesday, August 21, 2007. Problem sets may not be handed in once solutions have been distributed. Please write down your name and PID clearly. Good luck! 1) (3 points) When the errors are heteroskedastic, then a. WLS is efficient in large samples, if the functional form of the heteroskedasticity is known. b. OLS is biased. c. OLS is still efficient as along as there is no serial correlation in the error terms. d. weighted least squares is efficient. Answer : a 2) (3 points) It is possible for an estimator of Y µ to be inconsistent while a. converging in probability to Y . b. S n p Y . c. unbiased. d. Pr[| S n Y | δ ] 0. Answer : c 3) (3 points) The following is not one of the Gauss-Markov conditions a. var( u i | X 1 ,…, X n ) = 2 u σ , 0 < 2 u < for i = 1,…, n ,. a. the errors are normally distributed. c. E ( u i u j | X 1 ,…, X n ) = 0, i = 1,…, n , j = 1,…, n , i j . d. E ( u i | X 1 ,…, X n ) = 0 Answer : b 4) (3 points) The WLS estimator is called infeasible WLS estimator when a. the memory required to compute it on your PC is insufficient. b. the conditional variance function is not known. c. the numbers used to compute the estimator get too large. d. calculating the weights requires you to take a square root of a negative number. Answer : b
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2 Answer to HW #2, ECON 120C, Summer 2007 – S2 5) (13 points) Discuss the properties of the OLS estimator when the regression errors are homoskedastic and normally distributed. What can you say about the distribution of the OLS estimator when these features are absent? Answer : In the initial discussion of the OLS estimator, it was established that if the three least squares assumptions hold, then the OLS estimator is unbiased, consistent, and has an asymptotically normal distribution. Small sample properties are more difficult to establish, at least in the case when the regressors are random variables. If the assumption of homoskedasticity is added to the previous assumptions, then the OLS estimator is efficient in the class of linear and conditionally unbiased estimators. This result is known as the Gauss-Markov Theorem. Since the proof depends on the assumption of homoskedasticity, OLS is not efficient in its absence. In that case, an alternative estimator, WLS, is
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This note was uploaded on 07/17/2008 for the course ECON 120C taught by Professor Stohs during the Spring '08 term at UCSD.

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hw1_answer_120c_su07_S2 - Economics 120C Professor Yongil...

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