Lecture32-2010 - System Estimators - Least Squares and...

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Unformatted text preview: System Estimators - Least Squares and Maximum Likelihood: Lecture XXXII Charles B. Moss November 28, 2010 I. Iterative Seemingly Unrelated Regression A. Consider the derived demand equations x 1 t = 01 + 11 w nt + 21 w pt + 1 c t + 1 t x 2 t = 02 + 12 w nt + 22 w pt + 2 c t + 2 t (1) where 12 = 21 by Youngs theorem applied to the cost function. B. First, consider the spreadsheet SystemExample2.csv available on the course Web page. This spreadsheet contains the stacked dataset so that the first 50 observations are observe rations for the derived demand for nitrogen and the second 50 observations are the de- rived demand for phosphorous. 1. From this we form the y vector and x matrix for system re- gression y = 211 . 275 189 . 379 . . . 201 . 329 214 . 046 197 . 990 . . . 204 . 331 , x = 1 0 . 5567 1 0 . 0971 . . . . . . . . . . . . . . . . . . . . . 1 0 . 8286 ... 1 0 . 05216 132 . 013 1 . 0971 129 . 425 . . . . . . . . . . . . . . . . . . . . . 1 0 . 08286 130 . 731 (2) 1 AEB 6571 Econometric Methods I Professor Charles B. Moss Lecture XXXII Fall 2010 2. First, consider estimating the parameters in Equation 1 (see the code SystemExample2.R) OLS = ( x x )- 1 ( x y ) OLS = 300 . 7493- 432 . 0741- 218 . 4566- . 4029 424 . 4358- 151 . 6394- 482 . 0754- 1 . 3543...
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Lecture32-2010 - System Estimators - Least Squares and...

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