midterm2_ans - Department of Economics University of...

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Department of Economics Fall 2007 University of California Prof. Woroch Economics 140 : MIDTERM #2 ANSWERS I. SHORT QUESTIONS : Give a concise but complete answer to each of the following 4 questions for a total of 50 points. 1. [10] Consider the following regression of wages ( wage i ) on education ( edu i ): i i i i i i i i u edu DM edu edu DF DF wage + × + + × + + = ) ( ) ( 4 3 2 1 0 β , where DM i = 1 if person is male and 0 otherwise and DF i = 1 if person is female and 0 otherwise. a) Explain why this regression has a multicollinearity problem. Be specific to this problem. Answer: Perfect multicolinearity arises when one or more independent variables is a linear function of other independent variables in the regression. In this case: i i i i i edu edu DM edu DF = × + × ) ( ) ( b) Assume you drop the variable ) ( i i edu DM × from the above regression. Interpret 2 . Answer: These are all correct answers to this question: 1. 2 is the effect of education on wages for females vs. males. 2. 2 is the effect of education on wages for females minus the effect of education on wages for males. 3. 2 is the change in wages associated with an additional year of education for females compared to this change for males. 4. 2 is the difference in slopes between females and males in the wage-education relationship. 2. [15] Consider the wage regression i i i i i i i i i u Z X Z D X D X Y + × + + × + + + = ) ( ) ( 5 4 3 2 1 0 where X is years of education, D is a dummy variable indicating college graduation and Z is family income level. a) How would you test the hypothesis that graduating from college has no effect on wages for all values of X ? Answer: i) The relevant hypothesis for this test is: H o : 2 =0 and 3 =0 H 1 : 2 0 and/or 3 0 ii) Using this hypothesis, I would obtain an F statistic iii) I would reject the hypothesis if this statistic is larger than the critical value corresponding to a 5% test in an F (2, n-5-1) distribution: 3.00. Rejecting the hypothesis means that I reject that college graduation has no effect on wages for all values of X . b) Write an expression for the effect of a small increase in X, i.e., X Y Δ Δ , in terms of the coefficients and variables in the above wage regression model. Answer: i i i i Z D X Y 5 3 1 + + = Δ Δ
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Economics 140 Page 2 Midterm #2 Answers c) You think that rather than affecting the level of wages, education and family incomes are best thought of as changing the wage in percentage terms. What change would you make to the above regression specification to reflect this? Answer: These are all correct answers to this question: 1. i i i i i i i i i u Z X Z D X D X Y + × + + × + + + = ) ( ) ( ln 5 4 3 2 1 0 β A unit increase in education generates a percentage increase in wages.
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This note was uploaded on 10/21/2008 for the course ECON 140 taught by Professor Duncan during the Fall '08 term at University of California, Berkeley.

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midterm2_ans - Department of Economics University of...

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