problem_set_1 - Problem Set 1 ECON 5280 Applied...

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Problem Set 1 ECON 5280: Applied Econometrics Instructor: Prof. Jin Seo Cho 1 True or False Questions Write ‘T’ or ‘F’ to the next of question numbers if you think the following statements are correct or incorrect respectively. You don’t have to justify your answers. No partial credit will be granted for your justification. 1. Classical linear model (CLM) assumes the correct model specification assumption. 2. The first moment of t 1 random variable is infinite. 3. If a matrix M is idempotent then its rank is identical to its trace. 4. If X N ( μ , Σ ) then X 0 Σ - 1 X χ 2 k , where k is the rank of Σ . 5. If the normality assumption of the CLM does not hold, the conditional distribution of the OLS estimator on the explanatory variables may not be normal. 6. The projection matrix defined as X ( X 0 X ) - 1 X 0 is idempotent, where X is the n × k rectangular matrix defined in the class. 7. tr( A + B ) = tr( A ) + tr( B ). 8. Under the CLM condition, if X t is independent of U t then the conditional homoskedasticity condition naturally holds. 9. If the joint probability density function (PDF) of random variables X and Y is given as f ( x, y ) = 1 on (0 , 1) × (0 , 1), then X and Y are independent. 10. The ordinary least squares (OLS) estimator is linear with respect to the column vector of dependent variables. 11. Let X , ˆ β n and ˆ U be the matrices defined as in our class. Then even if the normality as- sumption of the CLM violates, the conditional covariance between ˆ β n and ˆ U given X is still 0 . 1
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12. The OLS estimator is unbiased even if the normality assumption of the CLM does not hold. 13. If X i N (0 , 1) then ( n - 1) - 1 n i =1 ( X i - ¯ X n ) 2 χ 2 n - 1 . 14. The OLS estimator is a linear estimator with respect to the dependent variable. 15. CLM assumes a particular distribution condition for explanatory variables. 16. CLM assumes a linear model condition for conditional expectation. 17. Without normal distribution assumption under the CLM assumption, conditional homoskedas- ticity does not hold. 18. When explanatory variables contains a constant term, sum of the prediction errors is zero. 19. CLM assumes conditional homoskedasticity.
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