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# final - ECON 139 Duke University Spring 2008 Final Exam...

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ECON 139 Duke University Spring 2008 Final Exam Instructions (PLEASE READ CAREFULLY before starting): This test has a total of 4 problems and 100 points . You have 150 minute Remember to Show Your Work and please be sure that your handwriting is legible ! Be precise but brief. If a correct reply is hidden among wrong, or irrelevant, arguments, you will not get full credit. We will grade only what is written on your exam sheet. There should be plenty of space for all your calculations. There are two extra pages included at the end of the exam to be used as scratch paper. Do not turn in anything besides your exam sheet . Standard errors are in parentheses (unless otherwise noted). Name: 1

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1. (20 points total) Consider the basic panel data set-up in which the population regression model is given by Y it = & 0 + 1 X it + ± i + u it (1) for i = 1 ;:::;n; t = 1 ;:::;T and where we can assume E ( ± i ) = 0 (because we have included an intercept) and E ( u it j X it ) = 0 . a. (3 points) Given (1), show that the following relation also holds Y i = & 0 + 1 X i + ± i + u i (2) where the overbar represents the average over time for a given individual. b. (6 points) Suppose that u i is uncorrelated with X i ; but cov ( X it i ) = ² for all t and i: Show that cov X i i + u i ± = ² 2
c. (5 points) Let e 1 be the OLS estimate of 1 obtained from estimating equation (2). This is plim e 1 = 1 + ± V ar X i ± where the probability limit is de²ned as N ! 1 : d. (3 points) Assume further that the X it ; for all t = 1 ;:::;T are uncorrelated with constant variance ± 2 X : Show that plim e 1 = 1 + T ± ± 2 X 3

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e. (3 points) If the explanatory variables are indeed uncorrelated across time, what does the result more time periods? 4
2. (34 points total) Continuing a theme from the last exam, we are now going to use the data from the airline airfare question on Midterm 2 to estimate airline demand. Recall from before that we connecting Raleigh-Durham (RDU) and Washington National (DCA) airports). We have information on

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## This note was uploaded on 08/02/2011 for the course ECON 139 taught by Professor Alessandrotarozzi during the Spring '08 term at Duke.

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final - ECON 139 Duke University Spring 2008 Final Exam...

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