2007 Midterm Exam 1

2007 Midterm Exam 1 - Midterm Exam 1 Econ 360 - Fall 2007...

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Midterm Exam 1 Econ 360 - Fall 2007 Professor Mumford Thursday, September 27, 2007 mumford@purdue.edu RAWL 2077 3:00 – 4:15pm 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 one hour and ten minutes to complete the exam. Good luck! 1. (12 points) Define or explain the following terms: a. (3 points) sum of squared residuals (SSR) b. (3 points) R-squared c. (3 points) covariance between two random variables x and y d. (3 points) endogenous explanatory variable
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2. (16 Points) For each of the 4 Gauss-Markov assumptions in the multiple regression model (E.1 - E.4), state the assumption and explain how it could be violated by describing an example in which the assumption does not hold (graphically if desired). a. (4 points) E.1 b. (4 points) E.2 c. (4 points) E.3 d. (4 points) E.4
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3. (12 Points) In the multiple regression model, derive the OLS estimator, ˆ β , as the solution to the problem of minimizing the sum of squared residuals min ˆ β u 0 ˆ u ) .
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4. (33 Points) Consider a standard wage equation that accounts for race: log ( wage ) = β 0 + β 1 age + β 2 educ + β 3 race + u. (1) Here, race = 1 indicates that the individual is black, while race = 0 indicates non-black. The Bell Curve was a controversial best-selling 1994 book by Herrnstein and Murray. It attempts to answer the question of “how much of the wage gap between blacks and whites can be explained by ability?” To answer this question, they estimated the following equation using data from the National Longitudinal Survey of Youth (NLSY): log ( wage ) = β 0 + β 1 age + β 2 educ + β 3 race + β 4 AFQT + u. (2) where AFQT is the “Armed Forces Qualifying Test”, an achievement exam given in 1979 to all youth in the NLSY. The AFQT variable is the individual’s percentile (99th percentile is the best) in the distribution of all scores received. Herrnstein and Murray claim that nearly all of the wage gap between blacks and whites can be explained by differences in ability. We will examine this claim using more recent NLSY data for males from 2004. Note that the
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2007 Midterm Exam 1 - Midterm Exam 1 Econ 360 - Fall 2007...

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