Consider the Following Earnings Function

Essay

Consider the following earnings function:
ahe_i= β₀ + β₁×DFemme_i + β₂×educ_i+...+ u_i
versus the alternative specification
ahe_i= γ₀ × DMale + γ₁×DFemme_i + γ₂×educ_i+...+ u_i
where ahe is average hourly earnings, DFemme is a binary variable which takes on the value of "1" if the individual is a female and is "0" otherwise, educ measures the years of education, and DMale is a binary variable which takes on the value of "1" if the individual is a male and is "0" otherwise. There may be additional explanatory variables in the equation.
a. How do the βs and γs compare? Putting it differently, having estimated the coefficients in the first equation, can you derive the coefficients in the second equation without re-estimating the regression?
b. Will the goodness of fit measures, such as the regression R², differ between the two equations?
c. What is the reason why economists typically prefer the second specification over the first?