Consider the Following Two Models Involving Binary Variables as Explanatory

Essay

Consider the following two models involving binary variables as explanatory
variables: $$\widehat { \text { Wage } } = \widehat { \beta } _ { 0 } + \widehat { \beta } _ { 1 } D \text { Femme and } \widehat { \text { Wage } } = \widehat { \phi } _ { 1 } D \text { Femme } + \widehat { \phi } _ { 2 } \text { Male }$$ where Wage is the hourly wage rate, DFemme is a binary variable that is equal to 1 if the person is a female, and 0 if the person is a male. Male $= 1 -$ DFemme. Even though you have not learned about regression functions with two explanatory variables (or regressions without an intercept), assume that you had estimated both models, i.e., you obtained the estimates for the regression coefficients.
What is the predicted wage for a male in the two models? What is the predicted wage for a female in the two models? What is the relationship between the $\beta \mathrm { s }$ and the $\phi s$ ? Why would you prefer one model over the other?