Use the observations in the data file cps5_small to estimate the following model:

a. At what levels of significance are each of the coefficient estimates "significantly different from zero"?

b. Obtain an expression for the marginal effect \(\partial E[\ln (W A G E) \mid E D U C, E X P E R] / \partial E D U C\). Comment on how the estimate of this marginal effect changes as EDUC and EXPER increase.

c. Evaluate the marginal effect in part (b) for all observations in the sample and construct a histogram of these effects. What have you discovered? Find the median, 5th percentile, and 95th percentile of the marginal effects.

d. Obtain an expression for the marginal effect \(\partial E[\ln (W A G E) \mid E D U C, E X P E R] / \partial E X P E R\). Comment on how the estimate of this marginal effect changes as EDUC and EXPER increase.

e. Evaluate the marginal effect in part (d) for all observations in the sample and construct a histogram of these effects. What have you discovered? Find the median, 5th percentile, and 95th percentile of the marginal effects.

f. David has 17 years of education and 8 years of experience, while Svetlana has 16 years of education and 18 years of experience. Using a 5\% significance level, test the null hypothesis that Svetlana's expected log-wage is equal to or greater than David's expected log-wage, against the alternative that David's expected log-wage is greater. State the null and alternative hypotheses in terms of the model parameters.

g. After eight years have passed, when David and Svetlana have had eight more years of experience, but no more education, will the test result in (f) be the same? Explain this outcome?

h. Wendy has 12 years of education and 17 years of experience, while Jill has 16 years of education and 11 years of experience. Using a 5\% significance level, test the null hypothesis that their marginal effects of extra experience are equal against the alternative that they are not. State the null and alternative hypotheses in terms of the model parameters.

i. How much longer will it be before the marginal effect of experience for Jill becomes negative? Find a \(95 \%\) interval estimate for this quantity.

Transcribed Image Text:

In(WAGE) = B + BEDUC + 3EDUC + BEXPER+EXPER + (EDUC EXPER) + e