To allow for possibly nonlinear and interaction effects, consider the following regression estimates (standard errors in parentheses): Iwage= 0.720 0.0195 educ+ 0.00477 educ² (0.0583) (0.00204) (0.430) + 0.0457 exper - (0.0133) 0.000857 exper²-0.000145 educx exper. (0.000156) (0.000774) We will call the estimated coefficients Bo, B₁,---, Bs. (a) What is the marginal effect of education (for example, consider a one year increase in education) for someone who already has 12 years of education and 5 years of work experience? (b) Based on the estimated regression coefficients, are education and work experience comple ments or substitutes? That is, does the effect of education on wage increase or decrease as one gets more work experience? (c) Use the p-value approach to conduct a formal statistical test at the 5% level that there is no interaction effect between education and experience. (d) To test whether education has a constant percentage effect on wage, a researcher considers the hypothesis that 3₂ = ßs=0. (i) How many restrictions are involved in this hypothesis? (ii) For a Bonferroni test at the 1% level, which critical value should be used? (iii) Do we reject this hypothesis? (e) Now consider the hypothesis that there is no nonlinear or interaction effect. That is, ₂ = B=Bs = 0. The F statistic is 12. (i) For a 5% test, which critical value should be used? (ii) Do we reject this hypothesis?
