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Unformatted text preview: 1 Lecture Notes 5: Multicollinarity and Heteroskedasticity Multicollinearity Multicollinearity refers to fact that one of the regressor is a perfect linear function of the other regressors. Example: For the regression model g G G G G G G three explanators G u G and G are perfectly collinear if G G G and , are nonzero. h Implications: Regression coefficients remain indeterminate and their standard errors are infinite. Example: For the model g G G G G the estimated version is (in deviation form) G G G G , where G G , G G . If G = G , then and . Example: Consumption = + Income + Wealth + G Problem: Here Income and Wealth highly correlated  wealthier people generally tend to have higher incomes. Solution: We need a sufficient number of sample observations of wealthy individuals with lowincome and highincome individuals with lowwealth. h Practical Consequences: 1. OLS estimators have large variances and covariances making precise estimation difficult 2. Wider confidence intervals implying acceptance of zero null hypothesis more likely 3. Insignificant tratio of one or more coefficients 4. Higher R 2 2 h Detection: 1. Higher R 2 but few significant tratios 2. Higher pairwise correlations among regressors (say, in excess of 0.8) 3. Look at Variance Inflation Factor (VIF). If VIF=1, there exists no collinearity. In a multiple regression model (with k regressors) one can calculate k different VIFs, one for each g G , by running an OLS regression that has g G as a function of all the other explanatory variables in the original regression. For example, one of all the other explanatory variables in the original regression....
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 Fall '08

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