4818-Exam1a

# 4818-Exam1a - Economics 4818 - Introduction to Econometrics...

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Economics 4818 - Introduction to Econometrics Midterm 1 - Answers 1. Discuss the e/ect of the following phenomena on the unbiasedness and the variance of the OLS estimators, c j : 1. heteroskedasticity Answer: Heteroskedasticity means that the error variance is not a constant and so Assumption 5 of the Gauss-Markov assumptions is violated, that is V ar ( u ) 6 = ± 2 . (3 points) E/ect on the unbiasedness of c j : Heteroskedasticity does not a/ect the unbiasedness of the OLS estimators, c j . (3 points) E/ect on the variance of c j : Under heteroskedasticity, the usual formula for the variance of OLS estimators, V ar c j ± = 2 SST j ( 1 R 2 j ) , is no longer valid. 2. perfect collinearity Answer: Perfect collinearity means that some independant variable, x j , is a perfect linear combination of other independent variables. (3 points) E/ect on the unbiasedness of c j : Perfect collinearity violates Assumption 3 for the unbiasedness of OLS estimators, c j . In fact, under perfect collinearity, the OLS estimators, c j , practically cannot be computed. one of the variables in the perfect linear combination. (3 points) E/ect on the variance of c j : If the independant variable, x j , is a perfect linear combination of other independent variables, then R 2 j = 1 and the variance of c j , which is given by V ar c j ± = 2 SST j ( 1 R 2 j ) , is not de±ined (or it is in±nitely large). 3. multicollinearity Answer: Multicollinearity means that some independant variables are higly corre- lated with each other. (3 points) E/ect on the unbiasedness of c j : Multicollinearity does not a/ect the unbiasedness of the OLS estimators, c j . (3 points)

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## This note was uploaded on 05/13/2008 for the course ECON 4818 taught by Professor Platikanova during the Spring '08 term at Colorado.

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4818-Exam1a - Economics 4818 - Introduction to Econometrics...

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