Question

Briefly explain what perfect multicollinearity is and how it relates to what is often called the ”dummy variable trap”. This is where if you have multiple binary regressors (variables that are either 0 or 1) to represent a series of groups, you have to leave the variable that represents one of the groups out of the regression.   

Answer 1

Multicollinearity refers to a situation when two or more than two independent variables are correlated with each other in a regression equation. Perfect multicollinearity occurs when the regressors are perfectely correlated that is the correlation is either 1 or -1.

Example: Let the regression equation be Y=b1+b2X2+b3X3+ui. If X3=5X2, there is perfect multicollinearity.

Dummy variable trap refers to a situation where the dummy variables in the regression equations are correlated that is there is multicollinearity in the equation. This occurs when a person introduces as many dummies as the number of categories ina regression equation with intercept term.

Example: Let there be two categories of gender (independent variable), male and female, and let the dependent variable be income.

The regression equation is Y=b1+b2D2+b3D3+ui, where D2=1 for males and 0 for females and D3=1 for females and 0 for males.

This example shows a situation of dummy variable trap as there is no unique base category and the variables D2 and D3 are correlated with each other.