Consider the following earnings function:
ahei= ?0 + ?1×DFemmei + ?2×educi+...+ ui
versus the alternative specification
ahei= ?0 × DMale + ?1×DFemmei + ?2×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 ?s and ?s 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?
What will be an ideal response?
Answer:
a. γ0 = β0; γ1 = β0+ β1; γ2 = β2
b. The regression R2 will be identical, as will be the standard error of the regression.
c. The second equation allows you to consider the difference between earnings of two sub-groups. Economists are often interested in testing for such differences, rather than to find the average level of earnings.
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