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,

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. none of the OLS estimators to exist because there is perfect multicollinearity.

b. the coefficient for Male to have a positive sign, and for Female a negative sign.

c. this to yield a difference in means statistic.

d. both coefficients to be the same distance from the constant, one above and the other below.

Solutions

Expert Solution

A. none of the OLS estimators exist because there is perfect multicollinearity

Because the given regression model is perfect multicollinearity and due to this it is impossible to compute the OLS estimators because it produces division by 0.

It is perfect multicollinearity because the independent variables in the given regression model example are correlated, we can see that the binary variable of Male and Female is same 1 and 0 otherwise, this will lead to the multicollinearity.

So, the answer to choose is A.

Junaid answered 1 year ago

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