Question

Suppose you are interested in examining the determinants of earnings. You have information on the age of the individual as well as their level of education: high school graduate, college graduate or graduate degree. Let Y = earnings, X1 = age, X2 = 1 if the person has only a high school degree and 0 otherwise,

X3 = 1 if the person has a college degree and 0 otherwise, X4 = 1 if the person has a graduate degree and 0 otherwise. Which of the following model specifications would not work?

a. Y =0 +1X1 +2X2 +3X3
b. Y =0 +1X1 +2X2 +3X3 +4X4c. Y =1X1 +2X2 +3X3
d. None of the above.

Answer 1

From the given specification

Y is Response variable.

X1,X2,X3 and X4 are independent variables.

Here, X1 is age which is a continuous variable so it will be in the model.

Whereas variables X2, X3 and X4 are categorical variables and for categorical variables we have to take one variable as dummy variable and compare the rest two variables with respect to this dummy variable.

A) For model A , X4 is taken as dummy variable so this model will work.

B) For model B, no categorical variable is taken as dummy variable so it will not work.

C) For model C, X4 is taken as dummy variable so this model will work.

Hence, optiobn B is correct.