321w11p1

# 321w11p1 - Multicollinearity Perfect Multicollinearity one...

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Multicollinearity Perfect Multicollinearity – one regressor is a perfect linear combination of one or more of the other regressors. perfect multicollinearity: x j = 1 x 1  2 x 2 ...  k x k , where i 0for at least one i. It is easy to solve the problem of perfect multicollinearity by dropping or combining one or more of the independent variables.

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However, with Imperfect Multicollinearity, we face a different dillemna. Imperfect Multicollinearity – two or more regressors are highly correlated. There are no theoretical issues with OLS estimators in the case of imperfect multicollinearity.
But if there is a very high correlation between two variables, at least one coefficient will be imprecisely estimated. Recall: Var j = 2 SST j 1 R j 2 The higher the correlation among the regressors, the higher is R j , the smaller the denominator and the higher the variance of j . So when you include highly correlated variables, you are likely to see imprecise estimates for at least one regressor.

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How much correlation is too much? Addressing Multicollinearity: 1. Use joint hypothesis tests instead of individual t-ratios 2. Factor Analysis 3. Drop one or more variables
Ex/ Suppose we wish to estimate the effect of University quality on wages and estimate the following regression for Canadian students:

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## This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.

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321w11p1 - Multicollinearity Perfect Multicollinearity one...

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