I am unsure as to whether my calculations are correct. Currently, the model given is:
The first question was to derive an equation for the marginal effects of EDU on In(Wage).
I obtained the following equation:
The second question asked was obtaining the value for EXPER, at EDU = 12, for which the value of ln(Wage) was at its maximum.
When I equated the derivative of the estimated equation to zero, and used the value of 12 for EDU:
The value obtained for EXPER was 107.25; this value confused me.
In truth, for the model, EDU = Years of Education, and EXPER = years of experience in the job, and the WAGE was the wage per hour. As such, it would be extremely unrealistic to only have maximum wage after 107 years of working experience.
Should I derive an equation for the marginal effects of Experience (EXP) on ln (Wage) instead?
Thank You.
You are working with the wrong derivative. If, given $\text{EDU}=12$, you want to find the best choice for $\text{EXPER}$, we need to calculate the derivative with respect to $\text{EXPER}$ and set the derivative equal to $0$. (And we need to check that we really do get a maximum, but that is clear in this case.)