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Unformatted text preview: Section 7 - Econ 140 GSI: Edson Severnini 1 Multicollinearity 1.1 Definition • Presence of correlation between explanatory variables. 1.2 Imperfect multicollinearity • Imperfect multicollinearity arises when one of the regressors is very highly correlated - but not perfectly correlated - with the others regressors. In other words, there is a linear function of the regressors that is highly correlated with another regressor. • Consequence s: higher SE ( ˆ β OLS ) ⇒ it is easier to fail to reject the null hypothesis. Remark : The imperfect multicollinearity does not pose any problems for the theory of the OLS esti- mators. Indeed, a purpose of OLS is to sort out the independent influences of the various regressors when these regressors are potentially correlated. • Indicator of multicollinearity : high R 2 ( ⇒ F- stat ) with few or none significant t-statistics 1.3 Extreme case: Perfect multicollinearity • Perfect multicollinearity arises when one of the regressors is perfectly correlated with the others regres- sors. In other words, one regressor can be expressed as a linear function of the others. • Consequence : ( X X ) has no rank k anymore ⇒ ( X X ) is not invertible anymore ⇒ It is not possible to get ˆ β OLS anymore (Remember that ˆ β OLS = ( X X )- 1 XY ). So, if there is perfect multicollinearity, it is not possible to compute the OLS estimates. • How to fix this problem? – Eliminating one of the explanatory variables, or – Adding new observations in the sample that you are working with, or – Finding better dataset to study the question you are interested in. Remark : If you try to run a regression with the presence of perfect multicollinearity, your software (GRETL, in this course) will let you know that you have that problem and then you have to modify your regression to eliminate it. • Dummy variable trap – Special case of perfect multicollinearity that arises when dummy (or binary) variables of all cate- gories associated with some explanatory variable are included as regressors in a regression model with intercept....
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This note was uploaded on 08/06/2009 for the course ECON 140 taught by Professor Duncan during the Summer '08 term at University of California, Berkeley.
- Summer '08