Consider a model where the return to education depends upon the amount of work experience (and vice versa):

log1wage2 5 b0 1 b1educ 1 b2exper 1 b3educ # exper 1 u.

(i) Show that the return to another year of education (in decimal form), holding exper fixed, is b1 1 b3exper.

(ii) State the null hypothesis that the return to education does not depend on the level of exper.

What do you think is the appropriate alternative?

(iii) Use the data in WAGE2 to test the null hypothesis in (ii) against your stated alternative.

(iv) Let u1 denote the return to education (in decimal form), when exper 5 10: u1 5 b1 1 10b3.

Obtain u^

1 and a 95% confidence interval for u1. (Hint: Write b1 5 u1 2 10b3 and plug this into the equation; then rearrange. This gives the regression for obtaining the confidence interval for u1.)