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Lecture11

# Lecture11 - Lecture 11 Multicollinearity Econ 444 Winter...

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Lecture 11 : Multicollinearity Econ 444, Winter 2010 Feb 22, 2010

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Fig 1. No Correlation between independent variables X1 and X2 – very rare as most economic variables are correlated with each other.
Fig 2 : Strong Correlation between independent variables X1 and X2 – case of imperfect multicollinearity.

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Fig 3. Perfect Multicollinearity-X2 is a perfect function of X1. Therefore, including X2 would be irrelevant because it does not explain any of the variation on Y that is not already accounted by X1.
Perfect Multicollinearity : imply perfect correlation between independent variables in a regression equation. Hence if we want to estimate, Y i = β 0 + β 1 X 1 i + β 2 X 2 i + i (1) then, above regression is a case of perfect multicollinearity if correlation between X 1 i and X 2 i is 1 : Perfect Multicollinearity ⇔ | Corr ( X 1 i , X 2 i ) | = 1 Perfect multicollinearity is a violation of Classical Assumption VI. In this case, OLS estimator does not exist.

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To illustrate the problem consider the following demand function for food, Y i = β 0
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