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2010 Spring Final Exam

# 2010 Spring Final Exam - Final Exam Econ 360 Spring 2010...

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Final Exam Econ 360 - Spring 2010 Professor Mumford Thursday, May 6, 2010 [email protected] YOUR NAME: Answer all questions clearly and legibly. Show all of your work in the space provided. Do not use additional sheets or write on the back of the page. Do not refer to your notes, the text book, or any other materials during the exam. There are 100 points possible. Maximum points for each question are noted in parentheses. You have two hours to complete the exam. Good luck! 1. (12 points) Define or explain the following terms: a. (3 points) serial correlation b. (3 points) longitudinal data c. (3 points) heteroskedasticity d. (3 points) p -Value

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2. (9 points) Consider the multiple regression model y i = β 0 + β 1 x 1 i + . . . + β k x ki + u i . The OLS estimator ˆ β 1 can be expressed as ˆ β 1 = n X i =1 ˆ r i 1 y i n X i =1 r i 1 ) 2 where ˆ r i 1 are the residuals from a regression of x 1 on x 2 , x 3 , . . . , x k . Show that ˆ β 1 is unbiased under assumptions MLR.1 through MLR.4.
3. (16 points) a. (4 points) What does the Gauss-Markov Theorem say? b. (4 points) Explain how multicollinearity affects the OLS estimates and inference. c. (4 points) What is the Breusch-Pagan test designed to detect? Describe how to conduct this test. d. (4 points) What is the regression specification error test (RESET) designed to detect? Describe how to conduct this test.

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4. (12 points) In a very famous paper, Caroline Hoxby analyzes the effect of school compe- tition on student academic achievement (a standardized test score). She wants to examine whether more school competition from having more schools in an area from which parents can choose will increase the student’s test score. Suppose she has a student-level data set from many cities for a single year that contains student test score, the number of schools in the student’s city, and various parental and student characteristics. The number of schools is a proxy for school competition. In a regression of student test score on the number of schools and the other covariates, the estimated effect of number of schools on student test score is close to zero. However, Hoxby is concerned that good schools grow in size, reducing the number of schools in a city and thus reducing school competition. a. (3 points) What is the implicit omitted variable that is biasing the results? Use your knowledge of omitted variables bias to give the likely sign of this bias. b. (3 points) The number of schools is a proxy for competition. Under what assumptions is it a valid proxy?
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