econ583lab8fall2009

Econ583lab8fall2009 - = I T = V which is of dimension 2 T 2 T and where is a 2 2 matrix with elements ij i j = 1 2 1 Show that OLS on the giant

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Econ 583 Lab 8 (really lab 7) Eric Zivot Fall 2009 Due: Wednesday, December 2. 1 Reading 1. Hayashi, Chapter 4. 2 Hayahsi Exercises 1. Chapter 4, Page 285, Questions For Review 8 and 9. . 2. Chapter 4, Page 294, Questions For Review 3. 3. Chapter 4, Pages 308-316 , Analytic Exercises 2, 5, 8 3 Seemingly Unrelated Regressions Consider a SUR model with 2 regression equations y 1 y 2 ¸ = X 1 0 0 X 2 ¸ β 1 β 2 ¸ + ε 1 ε 2 ¸ (1) where y 1 and y 2 are T × 1 vectors, X 1 is a T × k 1 matrix, X 2 is a T × k 2 matrix, β 1 is a k 1 × 1 vector, β 2 is a k 2 × 1 vector and ε 1 and ε 2 are T × 1 vectors. Assume that X 1 and X 2 contain exogenous variables independent of the error terms. The error terms satisfy E [ ε 1 ε 0 1 ]= σ 11 I T ,E [ ε 2 ε 0 2 ]= σ 22 I T and E [ ε 1 ε 0 2 ]= E [ ε 2 ε 0 1 ]= σ 12 I T where I T is the T dimensional identity matrix. The SUR model can be written as the giant regression y = X β + ε (2) 1
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where y =( y 0 1 , y 0 2 ) 0 and X and ε are obtained similarly from the SUR model. y and ε are 2 T × 1 , X is 2 T × k and β is k × 1 where k = k 1 + k 2 . The stacked errors ε have covariance matrix E
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Unformatted text preview: [ ] = I T = V which is of dimension 2 T 2 T and where is a 2 2 matrix with elements ij ( i, j = 1 , 2) . 1. Show that OLS on the giant regression (2) is the same as OLS on each equation in (1) taken separately. 2. Compare the estimated variance-covariance matrix of the coe cients computed from the giant regression (2) and from OLS on each equation in (1). Are they the same? 3. Is the OLS estimate of from the giant equation unbiased? 4. What is the (infeasible) GLS estimator of in the giant regression (2) ? Is b GLS unbiased? 5. Show that b GLS is numerically equivalent to b OLS when is a diagonal matrix . (Hint: write 1 = 1 11 1 22 and crank away.) 2...
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This note was uploaded on 08/23/2010 for the course ECON 583 taught by Professor Zivot during the Fall '09 term at W. Alabama.

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Econ583lab8fall2009 - = I T = V which is of dimension 2 T 2 T and where is a 2 2 matrix with elements ij i j = 1 2 1 Show that OLS on the giant

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