Consider the following earnings function:
ahei= β0 + β1×DFemmei + β2×educi+...+ ui
versus the alternative specification
ahei= γ0 × DMale + γ1×DFemmei + γ2×educi+...+ ui
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?

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The Answer of Consider the following earnings function:
ahei= β0 + β1×DFemmei + β2×educi+...+ ui
versus the alternative specification
ahei= γ0 × DMale + γ1×DFemmei + γ2×educi+...+ ui
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?

Consider the Following Earnings Function