Imagine you regressed earnings of individuals on a constant (intercept), a dummy variable (‘male’) which takes on the value 1 for males and is 0 otherwise, and another dummy variable (‘female’) which takes on the value 1 for females and 0 otherwise. Because females typically earn less than males, you would expect ________. a. none of the OLS estimators to exist because there is perfect multicollinearity b. both coefficients to be the same distance from the constant, one above and the other below c. the coefficient for ‘male’ to have a positive sign, and for ‘female’ a negative sign d. the coefficient for ‘male’ to have a negative sign, and for ‘female’ a positive sign
Question
Imagine you regressed earnings of individuals on a constant (intercept), a dummy variable (‘male’) which takes on the value 1 for males and is 0 otherwise, and another dummy variable (‘female’) which takes on the value 1 for females and 0 otherwise. Because females typically earn less than males, you would expect ________.
a. none of the OLS estimators to exist because there is perfect multicollinearity
b. both coefficients to be the same distance from the constant, one above and the other below c. the coefficient for ‘male’ to have a positive sign, and for ‘female’ a negative sign
d. the coefficient for ‘male’ to have a negative sign, and for ‘female’ a positive sign
Solution
The correct answer is a. None of the OLS estimators to exist because there is perfect multicollinearity.
This is because the 'male' and 'female' dummy variables are perfectly multicollinear, meaning they perfectly predict each other. In a regression model, this would lead to a situation where it is impossible to estimate the individual effect of these variables on the dependent variable (earnings in this case). This is a violation of one of the key assumptions of the OLS model, which states that the independent variables should not be perfectly multicollinear.
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