When estimating wage equations, we expect that young, inexperienced workers will have relatively low wages and that with additional experience their wages will rise, but then begin to decline after middle age, as the worker nears retirement. This lifecycle pattern of wages can be captured by introducing experience and experience squared to explain the level of wages. If we also include years of education, we have the equation WAGE ¼ b1 þ b2EDUC þ b3EXPER þ b4EXPER2 þ e

(a) What is the marginal effect of experience on wages?

(b) What signs do you expect for each of the coefficients b2, b3, and b4? Why?

(c) After how many years of experience do wages start to decline? (Express your answer in terms of b’s.)

(d) The results from estimating the equation using 1000 observations in the file cps4c_small.dat are givenin Table 5.9 on page 204. Find 95%interval estimates for

(i) The marginal effect of education on wages

(ii) The marginal effect of experience on wages when EXPER ¼ 4

(iii) The marginal effect of experience on wages when EXPER ¼ 25

(iv) The number of years of experience after which wages decline 

Table 5.9 Wage Equation with Quadratic Experience Variable Coefficient Std. Error 1-Stat Prob. C -13.4303 2.0285 -6.621 0.000 EDUC 2.2774 0.1394 16.334 0.000 EXPER 0.6821 0.1048 6.507 0.000 EXPER -0.0101 0.0019 -5.412 0.000 Covariance Matrix for Least Squares Estimates C C 4.114757339 EDUC -0.215505842 EXPER -0.124023160 EXPER 0.001822688 EDUC EXPER EXPER -0.215505842 -0.124023160 0.001822688 0.019440281 -0.000217577 -0.000217577 0.000015472 0.010987185 -0.000189259 0.000015472 -0.000189259 0.000003476