Lecture%20Notes%205

Lecture%20Notes%205 - 1 Lecture Notes 5 Multicollinarity...

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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 ¡ ª ¥ ¦ ¥G ¤ ª § ¦ §G and ª ¥ , ª § 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 low-income and high-income individuals with low-wealth. 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 t-ratio of one or more coefficients 4. Higher R 2 2 h Detection: 1. Higher R 2 but few significant t-ratios 2. Higher pair-wise 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 VIF’s, 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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Lecture%20Notes%205 - 1 Lecture Notes 5 Multicollinarity...

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