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Wooldridge PPT ch5

Fall 2008 under econometrics prof keunkwan ryu 18

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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

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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 = + + + + = - -
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

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

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