{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Wooldridge PPT ch3

Fall 2008 under econometrics prof keunkwan ryu 25

Info iconThis preview shows pages 25–33. Sign up to view the full content.

View Full Document Right Arrow Icon
Fall 2008 under Econometrics Prof. Keunkwan Ryu 25 Variance of OLS (cont) Let x stand for ( x 1 , x 2 ,…x k ) Assuming that Var( u | x ) = σ 2 also implies that Var( y | x ) = 2 The 4 assumptions for unbiasedness, plus this homoskedasticity assumption are known as the Gauss-Markov assumptions
Background image of page 25

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

View Full Document Right Arrow Icon
Fall 2008 under Econometrics Prof. Keunkwan Ryu 26 Variance of OLS (cont) ( 29 ( 29 ( 29 s ' other all on regressing from the is and where , 1 ˆ s Assumption Markov - Gauss Given the 2 2 2 2 2 x x R R x x SST R SST Var j j j ij j j j j - = - = σ β
Background image of page 26
Fall 2008 under Econometrics Prof. Keunkwan Ryu 27 Components of OLS Variances The error variance: a larger σ 2 implies a larger variance for the OLS estimators The total sample variation: a larger SST j implies a smaller variance for the estimators Linear relationships among the independent variables: a larger R j 2 implies a larger variance for the estimators
Background image of page 27

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

View Full Document Right Arrow Icon
Fall 2008 under Econometrics Prof. Keunkwan Ryu 28
Background image of page 28
Fall 2008 under Econometrics Prof. Keunkwan Ryu 29 Misspecified Models ( 29 ( 29 ( 29 same the re ' then they ed, uncorrelat are and unless ˆ ~ Thus, ~ that so , ~ ~ ~ model ed misspecifi again the Consider 2 1 1 1 1 2 1 1 1 0 x x Var Var SST Var x y β σ < = + =
Background image of page 29

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

View Full Document Right Arrow Icon
Fall 2008 under Econometrics Prof. Keunkwan Ryu 30 Misspecified Models (cont) While the variance of the estimator is smaller for the misspecified model, unless β 2 = 0 the misspecified model is biased As the sample size grows, the variance of each estimator shrinks to zero, making the variance difference less important
Background image of page 30
Fall 2008 under Econometrics Prof. Keunkwan Ryu 31 Estimating the Error Variance We don’t know what the error variance, σ 2 , is, because we don’t observe the errors, u i What we observe are the residuals, û i We can use the residuals to form an estimate of the error variance
Background image of page 31

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

View Full Document Right Arrow Icon
Fall 2008 under Econometrics Prof. Keunkwan Ryu 32 Error Variance Estimate (cont) ( 29 ( 29 ( 29 ( 29 [ ] 2 1 2 2 2 1 ˆ ˆ thus, 1 ˆ ˆ j j j i R SST se df SSR k n u - = - - = σ β df = n – ( k + 1), or df = n k – 1 df (i.e. degrees of freedom) is the (number of observations) – (number of estimated parameters)
Background image of page 32
Fall 2008 under Econometrics Prof. Keunkwan Ryu 33 3.5The Gauss-Markov Theorem Given our 5 Gauss-Markov Assumptions it can be shown that OLS is “BLUE” Best Linear Unbiased Estimator Thus, if the assumptions hold, use OLS
Background image of page 33
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page25 / 33

Fall 2008 under Econometrics Prof Keunkwan Ryu 25 Variance...

This preview shows document pages 25 - 33. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online