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# Use economic theory past exam practice question

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Unformatted text preview: lid! To remember: Bias deals with expectation of estimator OVB intuition goes through to models with more than 2 regressors Introduction Omitting Relevant Variable Including Irrelevant Variables Detection & Remedy OVB Detection & Remedy Detection: Use economic theory. Look at other tests of mispeciﬁcation (example: DW test). Get the most out of your residuals. Past Exam Practice Question Introduction Omitting Relevant Variable Including Irrelevant Variables Detection & Remedy OVB Detection & Remedy Detection: Use economic theory. Look at other tests of mispeciﬁcation (example: DW test). Get the most out of your residuals. Remedy: Include omitted variable! Use proxy variable if not available. Past Exam Practice Question Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Deﬁnition Disease 2: Including Irrelevant Variables True Model: Y = β1 + β2 X2 + u But estimate β2 with OLS estimator using (incorrect) model: Y = β1 + β2 X2 + β3 X3 + u → We include an irrelevant variable (X3 ) in the regression model. (9) Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Consequences IIV Consequences In general OLS still unbiased. s.e.’s and test statistics valid. GENERALLY estimator more erratic, loss of efﬁciency and higher s.e.’s. Introduction Omitting Relevant Variable Including Irrelevant Variables Consequences Unbiasedness Under IIV We saw that OLS still unbiased under IIV. Despite misspeciﬁcation, why do we have unbiasedness? Past Exam Practice Question Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Consequences Unbiasedness Under IIV We saw that OLS still unbiased under IIV. Despite misspeciﬁcation, why do we have unbiasedness? X3 is irrelevant so β3 = 0. By including X3 you are letting regression discover by itself that X3 is irrelevant. Therefore estimator of β2 is not effected by including a variable whose coefﬁcient is 0 already. 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 . 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 est...
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