ie_Slide03_2 - Introductory Econometrics ECON2206/ECON3209...

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Introductory Econometrics ECON2206/ECON3209 Slides03_continued Multicollinearity and Misspecification Lecturer: Rachida Ouysse ie_Slides03_2 R. Ouysse, School of Economics, UNSW 1
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3. Multiple Regression Model: Estimation (Ch3) Irrelevant “explanatory” variables – What if an irrelevant x is included? “irrelevant” means the population coefficient of that variable is 0. O S as the OLS estimators are unbiased, the estimate of that coefficient will “typically” be near 0. th i l i f i l t i bl h d i bl the inclusion of irrelevant variables has undesirable effects on the variances of the OLS estimators. eg x is irrelevant in the model eg. 3 y = β 0 + β 1 x 1 + β 2 x 2 + 0 x 3 + u , the OLS estimator is unbiased: ) ˆ ( k j E 1 0 in particular, . ,..., , , j j . ) ˆ ( 0 3 3 E ie_Slides03_2 R. Ouysse, School of Economics, UNSW 2
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3. Multiple Regression Model: Estimation (Ch3) Omitted explanatory variables – What if a relevant x is omitted? the OLS estimators will generally be biased. the direction and size of bias depend on how the omitted is related to the included. – Example. When x 2 is omitted from the true model y = β 0 + β 1 x 1 + β 2 x 2 + u , it becomes: y = β 0 + β 1 x 1 + v with v = β 2 x 2 + u .
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