Multicollinearity arises when a linear relationship exists between two or more independent variables in a regression model. In practice, you rarely encounter perfect multicollinearity, but high multicollinearity is quite common and can cause substantial problems for your regression analysis.
Two types of multicollinearity exist:
Perfect multicollinearity occurs when two or more independent variables in a regression model exhibit a deterministic (perfectly predictable or containing no randomness) linear relationship. When perfectly collinear variables are included as independent variables, you can’t use the OLS technique to estimate the value of the parameters. Perfect multicollinearity, therefore, violates one of the classical linear regression model (CLRM) assumptions.
High multicollinearity results from a linear relationship between your independent variables with a high degree of correlation but aren’t completely deterministic (in other words, they don’t have perfect correlation). It’s much more common than its perfect counterpart and can be equally problematic when it comes to estimating an econometric model.
In practice, perfect multicollinearity is uncommon and can be avoided with careful attention to the model’s independent variables. However, high multicollinearity is quite common and can create severe estimation problems. For this reason, when econometricians point to a multicollinearity issue, they’re typically referring to high multicollinearity rather than perfect multicollinearity.