final07 - Department of Economics ECONOMETRICS I Take Home...

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ECONOMETRICS I Take Home Final Examination Fall 2007 Professor William Greene Phone: 212.998.0876 Office: KMC 7-78 Home page:ww.stern.nyu.edu/~wgreene e-mail: [email protected] URL for course web page: www.stern.nyu.edu/~wgreene/Econometrics/Econometrics.htm Today is Tuesday, December 4, 2007. This exam is due by 3PM, Monday, December 17, 2007. You may submit your answers to me electronically as an attachment to an e-mail if you wish. Please do not include a copy of the exam questions with your submission; submit only your answers to the questions. Your submission for this examination is to be a single authored project – you are assumed to be working alone. NOTE: In the empirical results below, a number of the form .nnnnnnE+aa means multiply the number .nnnnnn by 10 to the aa power. E-aa implies multiply 10 to the minus aa power. Thus, .123456E-04 is 0.0000123456. This test comprises 150 points in two parts. Part I contains 10 questions, allocated 10 points per part, based on general econometric methods and theory as discussed in class. Part II asks you to dissect a recently published article that was documented in the popular press. This course is governed by the Stern honor code: I will not lie, cheat or steal to gain an academic advantage, or tolerate those who do. Signature ___________________________________________ 1 Department of Economics
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Part I. Applied Econometrics 1. Properties of the least squares estimator a. Show (algebraically) how the ordinary least squares coefficient estimator, b , and the estimated asymptotic covariance matrix are computed. b. What are the finite sample properties of this estimator? Make your assumptions explicit. c. What are the asymptotic properties of the least squares estimator? Again, be explicit about all assumptions, and explain your answer carefully. 2. The paper “Learning About Heterogeneity in Returns to Schooling,” Koop, G. and J. Tobias, Journal of Applied Econometrics , 19, 7, 2004, pp. 827-849, is an analysis of an unbalanced panel of data on 2,178 individuals, 17,919 observations in total. The variables in the data set are EDUC = Education WAGE = Log of hourly wage EXP = Potential experience ABILITY = Ability MED = Mother’s education FED = Father’s education BROKEN = Broken home dummy variable SIBS = Number of siblings I propose first to analyze the log wage data with a linear model. My first model is WAGE it = β 1 + β 2 EXP it + β 3 MED i + β 4 FED i + β 5 BROKEN i + β 6 SIBS i + β 7 EDUC it + β 8 ABILITY i + ε it , ε it ~ N[0, σ 2 ]. where “i” indicates the person and “t” indicates the year. Note that some variables are time invariant. For this application, I intend to ignore any panel data aspects of the data set, and treat the whole thing as a cross section of 17,919 observations. The ordinary least squares results are shown as Regression 1 on the next page. The estimated asymptotic covariance matrix is shown on the following page. (The covariance matrices are given in two forms, a graphic image for you to look at and as text if you wish to export the numbers to a computer program. The numbers are separated by spaces.) a.
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