Collinearity refers to linear relationships between two X variables. Multicollinearity encompasses linear relationships between more than two X variables. Multiple regression is impossible in the presence of perfect collinearity or multicollinearity. If X1 and X2 have no independent variation, we cannot estimate the effects of X1 adjusting for X2 or vice versa. One of the variables must be dropped. This is no loss, since a perfect relationship implies perfect redundancy. Perfect multicollinearity is, however, rarely practice problem. Strong (not perfect) multicollinearity, which permits estimation but makes it less precise, is more common. When the multicollinearity is present, the interpretation of. | Applied Econometrics 1 Multicollinearity Applied Econometrics Lecture 7 Multicollinearity Double whom you will but never yourself 1 Introduction Multiple regression can be written as follows Yi bo biXi b2X2 . bkXk Collinearity refers to linear relationships between two X variables. Multicollinearity encompasses linear relationships between more than two X variables. Multiple regression is impossible in the presence of perfect collinearity or multicollinearity. If X1 and X2 have no independent variation we cannot estimate the effects of X1 adjusting for X2 or vice versa. One of the variables must be dropped. This is no loss since a perfect relationship implies perfect redundancy. Perfect multicollinearity is however rarely practice problem. Strong not perfect multicollinearity which permits estimation but makes it less precise is more common. When the multicollinearity is present the interpretation of the coefficients will be quite difficult. 2 Practice consequences of multicollinearity Standard errors of coefficients The easiest way tell whether multicollinearity is causing problems is to examine the standard errors of the coefficients. If several coefficients have high standard errors and dropping one or more variables from the equation lowers the standard errors of the remaining variables. Multicollinearity will be the source of the problem. A more sophisticated analysis would take into account the fact that the covariance between estimated parameters may be sensitive to multicollinearity aq high degree of multicollinearity will be associated with a relatively high covariance between estimated parameters . This suggests that if one estimated parameter bi overestimates the true parameter pi a second parameter estimates bj is likely to underestimates P_j and vice versa. Because of the large standard errors the confident intervals for the relevant population parameters tend to be larger. Written by Nguyen Hoang Bao May 24 2004 Applied Econometrics 2 .
