final07

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

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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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