{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 31-2007

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

This preview shows pages 1–3. Sign up to view the full content.

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 1 1 ˆ ˆ 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 T T S E I . B. However, if we assume that 2 T T 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 1 1 1 1 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 A S 1 1 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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online