Lecture 31-2007 - Exceptions to Ordinary Least Squares...

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1 Exceptions to Ordinary Least Squares Lecture XXXI I. Heteroscedasticity A. Using the derivation of the variance of ordinary least squares estimator 1 1 1 11 ˆˆ ˆ : X X X V X X X X X X V X X X SX X X S E under the Gauss-Markov assumptions 2 TT S E I . B. However, if we assume that 2 S E I the ordinary least squares estimator is still unbiased, but is no longer efficient. In this case, we use the generalized least squares estimator 1 X AX X Ay 1. The variance of this estimator is then 1 1 X AX X AX X A X AX X AX X AX X A X AX X A V X AX X A A X X AX X AX X ASA X X AX 2. Setting 1 AS 1 : V X AX X A X X AX A A X AX C. Seemingly Unrelated Regressions 1. One of the uses of generalized least squares is the estimation of simultaneous systems of equations without endogeneity. a) Derived input demand equations derived from cost minimization implies relationship between the parameters 1 1 11 1 12 2 11 1 2 2 21 1 22 2 21 2 x A w A w y x A w A w y
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AEB 6933 – Mathematical Statistics for Food and Resource Economics Lecture XXXI Professor Charles Moss Fall 2007 2 where 1 x and 2 x are input levels, 1 w and 2 w are the respective input prices, y is the level of output, and 1 , 2 , 11 A , 12 A , 21 A , 22 A , 11 and 21 are estimated parameters.
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This note was uploaded on 07/18/2011 for the course AEB 6933 taught by Professor Carriker during the Fall '09 term at University of Florida.

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Lecture 31-2007 - Exceptions to Ordinary Least Squares...

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