UCSD ECON120C Midterm I Summer '08 - Key

# UCSD ECON120C Midterm I Summer '08 - Key - Economics 120C...

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Economics 120C Name: _________________________ Professor Yongil Jeon Summer 2008-2 Student ID#: _________________________ Answer keys to Homework #1 – Summer 2008-Session 2, Econ 120C (Answer keys to Midterm Exam, Summer 2008-Session 1, Econ 120C) Answer all questions on separate paper. This problem set should be handed in to Professor Jeon at the beginning of your class on Monday, August 18, 2008 . 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) One of differences between the central limit theorems for a scalar and vector-valued random variables is a. that n approaches infinity in the central limit theorem for scalars only. b. the conditions on the variances. c. that single random variables can have an expected value but vectors cannot. d. the homoskedasticity assumption in the former but not the latter. Answer : b 2) (3 points) The linear multiple regression model can be represented in matrix notation as =+ YX U β , where X is of order n × ( k +1). k represents the number of a. regressors. b. observations. c. regressors excluding the “constant” regressor for the intercept. d. unknown regression coefficients Answer : c 3) (3 points) One implication of the “extended” least squares assumptions in the multiple regression model is that a. feasible GLS should be used for estimation. b. E ( U | X ) = I n . c. X X is singular. d. the conditional distribution of U given X is N ( 0 n , 2 u σ I n ). Answer : d

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2 Answer to HW#1, ECON 120C, Summer 2008 – S2 4) (3 points) An estimator of β is said to be linear if a. it can be estimated by least squares. b. it is a linear function of Y 1 ,…, Y n . c. there are homoskedasticity-only errors. d. it is a linear function of X 1 ,…, X n . Answer : b 5) (3 points) The GLS estimator a. is always the more efficient estimator when compared to OLS. b. is the OLS estimator of the coefficients in a transformed model, where the errors of the transformed model satisfy the Gauss-Markov conditions. c. cannot handle binary variables, since some of the transformations require division by one of the regressors. d. produces identical estimates for the coefficients, but different standard errors. Answer : b 6) (10 points) Suppose that Y and X are related by the regression Y=1.0 +2.0X+u. A researcher has observations on Y and X, where 02 0 , X where the conditional variance is var( | ) 1 ii uX x == for 01 0 , x and var( | ) 16 = = for 10 20 x <≤ . Draw a hypothetical scatterplot of the observations ( , ), 1,. .., . X Yi n = Does WLS put more weight on observations with 10 x or 10?
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UCSD ECON120C Midterm I Summer '08 - Key - Economics 120C...

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