Question

) In the case of perfect multicollinearity, OLS is unable to estimate the slope coefficients of the variables involved. Assume that you have included both X1 and X2 as explanatory variables, and that X2 = 2 X1 , so that there is an exact relationship between two explanatory variables. Does this pose a problem for estimation? Why or why not? Also, explain what perfect multicollinearity is and why it is problematic in general in your answer.

Answer 1

Perfect multicollinearity exists when there is an exact linear relationship between two or more variables.

Imperfect multicollinearity exists where there is a linear relationship between two or more variables with some error term involved.

X2 = 2 X1, this will cause a problem in the estimation as the perfect collinearity between X2 and X1 would make the estimation of both difficult. The standard errors become infinite and no structural inferences can be drawn.

Perfect multicollinearity is problematic because it makes the estimators indeterminate. OLS estimation would, therefore, go for a toss.