Is the relationship between experience and wages constant over one’s lifetime? To investigate we will fit a quadratic model using the data file cps4_small.dat, which contains 1,000 observations on hourly wage rates, experience and other variables from the 2008 Current Population Survey (CPS).

(a) Create a new variable called EXPER30 ¼ EXPER 30.

Construct a scatter diagram with WAGE on the vertical axis and EXPER30 on the horizontal axis.

Are any patterns evident?

(b) Estimate by least squares the quadratic model WAGE ¼ g1 þ g2ð Þ EXPER30 2 þ e.

Are the coefficient estimates statistically significant? Test the null hypothesis that g2  0 against the alternative that g2 < 0 at the a ¼ 0.05 level of significance. What conclusion do you draw?

(c) Using the estimation in part (b), compute the estimated marginal effect of experience upon wage for a person with 10 years’ experience, 30 years’

experience, and 50 years’ experience. Are these slopes significantly different from zero at the a ¼ 0.05 level of significance?

(d) Construct 95% interval estimates of each of the slopes in part (c). How precisely are we estimating these values?

(e) Using the estimation result from part

(b) create the fitted values WAGE b¼ g^1 þ g^2ð Þ EXPER30 2

, where the ^ denotes least squares estimates.

Plot these fitted values and WAGE on the vertical axis of the same graph against EXPER30 on the horizontal axis. Are the estimates in part

(c) consistent with the graph?

(f) Estimate the linear regression WAGE ¼ b1 þ b2EXPER30 þ e and the linear regression WAGE ¼ a1 þ a2EXPER þ

e. What differences do you observe between these regressions and why do they occur? What is the estimated marginal effect of experience on wage from these regressions? Based on your work in parts

(b) – (d), is the assumption of constant slope in this model a good one? Explain.

(g) Use the larger data cps4.dat (4838 observations) to repeat parts (b), (c), and (d).

How much has the larger sample improved the precision of the interval estimates in part (d)?