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final_practice_problems_v1 - 1 Econ 166 Professor Altonji...

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1 1 Econ 166 Professor Altonji Practice Questions for Final Exam, version 1 , Unless otherwise stated statistical tests are to be performed at the 5% significance level. Problem 1. [15 points total] (1.1) [5 points] True or false and explain. In the regression model Y t = B 1 + B 2 X t +u t , if the assumptions E(u t )=0 and E(u t | X 1 ,X 2 ,…,X N )=0 hold for all t and Cov(u t ,u j )=( ρ) | t-j| , for all t j, ρ > 0, then the OLS estimator for B 2 is unbiased. (1.2) [5 points] True or false and explain (two sentences). Heteroscedasticity means that in a regression model (either simple or multivariate regression) the variance of the error term u i is small. (1.3) [5 points] True or false, explain in two sentences. In order to obtain unbiased OLS estimates in a multivariate regression model the researcher has to make sure that she is using explanatory variables which are uncorrelated to each other. Problem 2 [25 points total] Consider the following regression model for earnings on a sample of 20 individuals in a given occupation. You observe for each individual earnings (Y) in $, years of schooling (S) and IQ-test
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2 2 scores (this is a test for “intelligence” where points scored typically range, in random samples, from a min of approximately 50 to a max of approximately 250). Consider the regression model (XX) Y i = B 1 + B 2 S i + B 3 IQ i +u i for i=1,2 ..... ,20 Different versions of the model have been estimated by OLS providing the following Sample Regression Functions. The dependent variable is Y. In the table the columns contain estimated coefficients and corresponding standard errors (in parentheses) . When the coefficient is missing the corresponding variable has not been used in the regression. constant Schooling S IQ-test IQ R-squared Version A -6418 (3349) 1985.7 (248) ---- 0.78 Version B -29586 (4155) 1640 (151) 268 (43) 0.93 Version C -25488 (11362) --- 438 (109) 0.47 (3.1) [10 points] Consider version B. 3.1.a Explain in one or two sentences the meaning of the coefficient on IQ. 3.1.b Predict earnings for an individual with 12 years of schooling and an IQ-test score of 100.
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