# Econometric Theory/Multicollinearity

## Detecting Multicollinearity

Detecting multicollinearity can be more difficult than in the above example. But the first step that should be taken is an examination of the theory that is being tested. Is it redundant to have both mother's level and father's level? If this does not yield any results, probably because the theory is more complex, causing multicollinearity to be hidden, several econometric techniques can be used to find problems.

1) Large changes in the estimated regression coefficients when a predictor variable is added or deleted. Running the regression first with 'FatherLevel' and then without it may yield large variation, indicating that there is an error.

2) Non-significant results of simple linear regressions. Obviously if we find that with both FatherLevel and MotherLevel that neither are significant, than again there is something strange happening signaling possible multicollinearity.

3) Estimated regression coefficients have an opposite sign from predicted If in a regression with both FatherLevel and MotherLevel, b is positive, but c is negative; we know from theory that a higher reading level of the mother does not cause the child to be a worse reader. This is a possible sign of multicollinearity.

4)formal detection-tolerance or the variation inflation factor (VIF)

$\mathrm {tolerance} =1-R^{2},\quad \mathrm {VIF} ={\frac {1}{\mathrm {tolerance} }}.$

A tolerance of less than 0.1 indicates a multicollinearity problem.