Using the SLID data, Table 12.1 (on page 313) reports the results of a regression of log wages on sex, the square of education, a quadratic in age, and interactions between sex and education-squared,...

Using the SLID data, Table 12.1 (on page 313) reports the results of a regression of log wages on sex, the square of education, a quadratic in age, and interactions between sex and education-squared, as well as between sex and the quadratic for age.

(a) Estimate the age γ₁
at which women attain on average their highest level of wages, controlling for education. Use the delta method to estimate the standard error of γ₁. Note: You will need to fit the model yourself to obtain the covariance matrix for the estimated regression coefficients, which is not given in the text.

(b) Estimate the age γ₂
at which men attain on average their highest level of wages, controlling for education. Use the delta method to estimate the standard error of b₂.

(c) Let γ₃
[ γ₁
- γ₂, the difference between the ages at which men and women attain their highest wage levels. Compute bγ3. Use the delta method to find the standard error of γ₃
and then test the null hypothesis H₀: γ₃
= 0.