Imagine you regressed earnings of individuals on a constant, a binary variable ("Male")which takes on the value 1 for males and is 0 otherwise, and another binary variable ("Female")which takes on the value 1 for females and is 0 otherwise. Because females typically earn less than males, you would expect
A)the coefficient for Male to have a positive sign, and for Female a negative sign.
B)both coefficients to be the same distance from the constant, one above and the other below.
C)none of the OLS estimators to exist because there is perfect multicollinearity.
D)this to yield a difference in means statistic.

Question

Quizplus · Accepted Answer

Including both a "Male" and a "Female" binary variable in a regression model where these two variables perfectly predict each other (since if one is 0, the other is 1, and vice versa) leads to perfect multicollinearity. This means the ordinary least squares (OLS) estimators cannot be uniquely determined because the design matrix does not have full rank.

Imagine You Regressed Earnings of Individuals on a Constant, a Binary