ProblemSet8 Answers

ProblemSet8 Answers - Professor Mumford Econ 360 - Fall 2010

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Unformatted text preview: Professor Mumford Econ 360 - Fall 2010 mumford@purdue.edu Problem Set 8 Answers True/False (18 points) Please write the entire word. No explanations are required. 1. FALSE Heteroskedasticity does not cause the OLS estimator to be inconsistent. 2. FALSE Heteroskedasticity does not cause the OLS estimator to be biased. 3. TRUE Heteroskedasticity causes the usual estimator of the variance of the OLS esti- mator to be biased. 4. FALSE Heteroskedasticity does not cause R 2 and R 2 to be inconsistent estimators of the population R-squared. 5. TRUE Heteroskedasticity-robust standard errors are valid only if the sample size is large. 6. FALSE Heteroskedasticity-robust standard errors are valid if the error term is ho- moskedastic, even with a large sample size. 7. TRUE Heteroskedasticity-robust standard errors enable computing t statistics that are asymptotically t distributed whether or not heteroskedasticity is present. 8. FALSE Heteroskedasticity-robust standard errors are not always larger than the usual standard errors. 9. TRUE If heteroskedasticity is present, OLS is not the best linear unbiased estimator. 1 Long Answer Questions (82 points) 10. Tests for Heteroskedasticity (a) Estimate the model by OLS and obtain the residuals u i . Square each residual, u 2 i = ( u i ) 2 , and then estimate the model: u 2 i = + 1 mpg i + 2 weight i + 3 leather i + i . Perform an F test of the overall fit of the regression which has a null hypothesis of H : 1 = 2 = 3 = 0. If the p value is is below the chosen significance level we reject the null hypothesis of homoskedasticity. (b) Estimate the model by OLS and obtain the residuals u i and the fitted values y i . Square each residual, u 2 i = ( u i ) 2 , and fitted value price 2 i = price i 2 and then estimate the model: u 2 i = + 1 price i + 2 price 2 i + i . Perform an F test of the overall fit of the regression which has a null hypothesis of H : 1 = 2 = 0. If the p value is below the chosen significance level we reject the null hypothesis of homoskedasticity. 11. Robust Standard Errors Formula se = v u u u u u u u t n X i =1 ( x i- x ) u 2 i " n X i =1 ( x i- x ) 2 # 2 12. GPA Prediction with Robust Standard Errors (a) These coefficients have the anticipated signs. If a student takes courses where grades are, on average, higher as reflected by higher crsgpa then his/her grades will be higher. The better the student has been in the past as measured by cumgpa the better the student does (on average) in the current semester. Fi- the better the student does (on average) in the current semester....
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ProblemSet8 Answers - Professor Mumford Econ 360 - Fall 2010

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