{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Wooldridge PPT ch5

Fall 2008 under econometrics prof keunkwan ryu 18

Info iconThis preview shows pages 18–21. Sign up to view the full content.

View Full Document Right Arrow Icon
Fall 2008 under Econometrics Prof. Keunkwan Ryu 18 Lagrange Multiplier statistic Once we are using large samples and relying on asymptotic normality for inference, we can use more that t and F stats The Lagrange multiplier or LM statistic is an alternative for testing multiple exclusion restrictions Because the LM statistic uses an auxiliary regression it’s sometimes called an nR 2 stat
Background image of page 18

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 19 LM Statistic (cont) Suppose we have a standard model, y = β 0 + 1 x 1 + 2 x 2 + . . . k x k + u and our null hypothesis is H 0 : k-q+1 = 0, ... , k = 0 First, we just run the restricted model reg this from is where , ) variables the (i.e. ,..., , on ~ regress and , ~ residuals, the take Now ~ ~ ... ~ ~ 2 2 2 1 1 1 0 u u k q k q k R nR LM all x x x u u u x x y = + + + + = - -
Background image of page 19
Fall 2008 under Econometrics Prof. Keunkwan Ryu 20 LM Statistic (cont) 2 2 2 for value - p a calculate just or on, distributi a from , value, critical a choose can so , ~ q q q a c LM χ With a large sample, the result from an F test and from an LM test should be similar Unlike the F test and t test for one exclusion, the LM test and F test will not be identical
Background image of page 20

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 21 Asymptotic Efficiency Estimators besides OLS will be consistent However, under the Gauss-Markov assumptions, the OLS estimators will have the smallest asymptotic variances We say that OLS is asymptotically efficient Important to remember our assumptions though, if not homoskedastic, not true
Background image of page 21
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page18 / 21

Fall 2008 under Econometrics Prof Keunkwan Ryu 18 Lagrange...

This preview shows document pages 18 - 21. Sign up to view the full document.

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