ProblemSet3 - Econ 103 UCLA Spring 2011 Problem Set 3 Due...

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Unformatted text preview: Econ 103 UCLA, Spring 2011 Problem Set 3 Due: Tuesday, May 3 in hardcopy at the beginning of class Note: Please attach the Homework Cover Page from Classweb to the front of your home- work. Part 1: True or False and explain brie y why. 1. The assumption that E ( u i | X i = x i ) = 0 says that the expected value of u i changes depending on the value of X i . 2. If Cov ( X i ,u i ) > , then the OLS estimator ˆ β 1 will tend to be higher than β 1 . 3. Consider an omitted variable V i that is negatively correlated with X i . Also suppose that V i positively a ects Y i . Then the OLS estimator ˆ β 1 is negatively biased. 4. Suppose you run a regression and obtain the estimate ˆ β 1 = 3 . 4 . STATA tells you that the t-statistic for the null hypothesis that β 1 = 0 is equal to 1.7. This implies that SE ( ˆ β 1 ) is equal to 2. 5. Under perfect multicollinearity, the OLS estimator cannot be computed. 6. The Adjusted R 2 can be used to compare models with di erent numbers of regressors. Part 2: Analytical questions. Question 1: The cost of attending your university/college has once again gone up. Although you have been told that education is an investment in human capital, which carries a return of roughly 10% a year, you (and your parents) are not pleased. One of the administrators at your university/college does not make the situation better by telling you that you pay more because the reputation of your institution is better than that of others. To investigate this hypothesis, you collect data randomly for 100 national universities and liberal arts colleges from the U.S. News and World Report annual rankings. Next you perform the following regression: [ Cost i = 7 , 311 . 17 (2 , 058 . 63) + 3 , 985 . 20 (664 . 58) Reputation- . 20 (0 . 13) Size + 8 , 406 . 79 (2 , 154 . 85) Dpriv- 416 . 38 (1 , 121 . 92) Dlibart- 2 , 376 . 51 (1 , 007 . 86) Dreligion R 2 = 0 . 72 , SER = 3 , 773 . 35 where Cost is Tuition, Fees, Room and Board in dollars, Reputation is the index used in...
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