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HW5_S2010

HW5_S2010 - Problem Set 5 Practice for Prelim 2 Due Tuesday...

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Problem Set 5 ° Practice for Prelim 2 Due Tuesday 04/13/10 at the beginning of class Econ 3200 - Introduction to Econometrics Spring 2010 Cornell University Prof. Molinari The exam will consist of TWO parts totaling 100 points. It will be a CLOSED BOOK exam. However, useful formulae will be provided, and you can ±nd them here on pages 5+. Calculators will be permitted ° but graphic calculators are prohibited. Please, use the Tables for the Normal, t , ° 2 and F distributions at the end of the textbook °during the test the same copies of these Tables will be attached to the text of the exam. You will have 75 minutes to complete the exam. Part 1 ° 20 points (4 points each) In WORDS , brie²y (1 paragraph maximum) describe the following: 1. OLS Estimator. 2. Total Sum of Squares. 3. Multicollinearity. 4. Interpreting the slope coe¢ cient of a log-level regression. 5. Variance-Covariance Matrix. 1

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Part 2 ° 80 points (Each sub-question has the number of corresponding points in brackets) This part of the homework consists of a series of questions related to real empirical appli- cations. 1. We have often talked in class about regression models that are used to explain wages. In this question we take a closer look at a wage regression. A random sample of 936 individuals was gathered for the following variables: ln( wage ) = natural log of hourly wage, educ = years of education, exper = years of experience. Assume for now that assumptions MLR1-MLR5 hold for ln( wage i ) = ± 0 + ± 1 educ i + ± 2 exper i + u i : (1) This regression was estimated by OLS yielding the following: ln( w b age i ) = 0 : 42 +0 : 072 educ i +0 : 020 exper i (0 : 0072) R 2 = 0 : 096 SSR = 173 : 4 SST = 192 : 0 (2) In addition, the following two variable regression models were estimated. Standard errors are in parentheses: ln( w b age i ) = 0 : 91 +0 : 053 educ i R 2 = 0 : 0658 SSR = 179 : 4 SST = 192 : 0 (0 : 052) (0 : 006) (3) ln( w b age i ) = 1 : 57 +0 : 004 exper i R 2 = 0 : 0016 SSR = 191 : 7 SST = 192 : 0 (0 : 042) (0 : 0033) (4) e b duc i = 16 : 11 ° 0 : 229 exper i R 2 = 0 : 207 SSR = 3571 : 4 SST = 4506 : 8 (0 : 181) (0 : 014) (5) (a) Interpret the estimates of ± 1 and ± 2 in the regression of ln( wage ) on educ and exper . Do these estimates make sense? Do the estimates suggest that education and experience have a big e/ect on wages? Why or why not? (5 points) (b) Test the null hypothesis that ± 1 = 0 in regression (1). Use a 5% signi±cance level and assume that MLR.6 holds. Show the rejection rule that you are using and justify your choice of critical values.
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