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# Loss of degrees of freedom what if different ways of

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Unformatted text preview: imator be when IIV happens. Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Consequences Inefﬁciency Under IIV Main problematic outcome of IIV is inefﬁciency. The estimator of β2 will be more erratic. That is because the variance of estimator will be larger than when X3 is not included. 2 σb2 = 2 σu n i =1 (X2,i 1 2 ¯ − X2 )2 1 − rX2 ,X3 (10) In above setup, loss of efﬁciency depends on correlation between X2 and X3 . Therefore the higher the correlation, the less efﬁcient will the estimator be when IIV happens. Also if X2 and X3 are uncorrelated, then there is no loss of efﬁciency by including X3 . Introduction Omitting Relevant Variable Including Irrelevant Variables Detection & Remedy IIV Detection & Remedy Detection: Look at t-statistics and F-statistics! Use economic theory. Past Exam Practice Question Introduction Omitting Relevant Variable Including Irrelevant Variables Detection & Remedy IIV Detection & Remedy Detection: Look at t-statistics and F-statistics! Use economic theory. Remedy: Exclude irrelevant variables! Past Exam Practice Question Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Comparing Misspeciﬁcations OVB vs. IIV Analysis suggests general-to-speciﬁc estimation strategy to avoid OVB: 1 Start with most general model, i.e. including all possible explanatory variables. 2 Test downwards whether to omit certain variables or not. Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Comparing Misspeciﬁcations OVB vs. IIV Analysis suggests general-to-speciﬁc estimation strategy to avoid OVB: 1 Start with most general model, i.e. including all possible explanatory variables. 2 Test downwards whether to omit certain variables or not. But testing downwards can be problematic: Multicollinearity? Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Comparing Misspeciﬁcations OVB vs. IIV Analysis suggests general-to-speciﬁc estimation strategy to avoid OVB: 1 Start with most general model, i.e. including all possible explanatory variables. 2 Test downwards whether to omit certain variables or not. But testing downwards can be problematic: Multicollinearity? Loss of degrees of freedom? Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Comparing Misspeciﬁcations OVB vs. IIV Analysis suggests general-to-speciﬁc estimation strategy to avoid OVB: 1 Start with most general model, i.e. including all possible explanatory variables. 2 Test downwards whether to omit certain variables or not. But testing downwards can be problematic: Multicollinearity? Loss of degrees of freedom? What if different ways of dropping variables lead to different speciﬁcations? Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Compari...
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