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pqf2_ak - Econ 410 Introduction to Econometrics Practice...

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Econ 410 - Introduction to Econometrics Practice Questions for the Final Exam II - Answer Key 1. (a) E ( Y t ) = E à 0 + t P j =1 u j ! = 0 + t P j =1 E ( u j ) = 0 because from the conditional mean assumption we know that E ( u j ) = 0 for all j 0 s . This value is a linear function of t , so it is not constant over time. (b) var ( Y t ) = var à 0 + t P j =1 u j ! = t P j =1 var ( u j ) = 2 u because the conditional mean assumption implies that the error term is serially uncorrelated, so that cov ( u t , u t j ) = 0 for any j 6 = 0 . This value is a linear function of t , so it is not constant over time. (c) cov ( Y t , Y t j ) = cov à 0 + t P j =1 u j , ( t j ) β 0 + t j P k =1 u k ! = cov à t P j =1 u j , t j P k =1 u k ! = ( t j ) σ 2 u again because the conditional mean assumption implies that the error term is serially uncorrelated, so that cov ( u t , u t j ) = 0 for any j 6 = 0 . This value is a linear function of t , so it is not constant over time. (d) E ( Y t ) = E ( β 0 + u t ) = β 0 This value is just a constant, so it does not change over time. (e) var ( Y t ) = var ( β 0 + u t ) = var ( u t ) = σ 2 u This value is just a constant, so it does not change over time. (f) cov ( Y t , Y t j ) = cov ( β 0 + u t , β 0 + u t j ) = cov ( u t , u t j ) = 0 because cov ( u t , u t j ) = 0 for any j 6 = 0 .
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