How much does education affect wage rates? The data file cps4_small.dat contains 1000 observations on hourly wage rates, education, and other variables from the 2008 Current Population Survey (CPS). (a) Estimate the linear regression WAGE = B1 B2EDUC + € (use the command lm ( ) ) What is the average effect of an aditional year of education on wage? (b) Calculate the least squares residuals and plot them against EDUC. Should any patterns be evident in the least squares residuals? Hint: suppose you call your regression as reg, then you can plot the residuals using the command: plot(cps4_small$educ, reg$resid, xlab = 'educ', ylab = 'residuals') (e) Estimate the quadratic regression WAGE ' = α1 + α2EDUC² + e. Estimate the marginal effect (that is the slope Ay/Ax) of an additional year of education on wage for a person with 12 years of education, and for a person with 14 years of education. Compare these values to the estimated marginal effect of education from the linear regression in part (b). (f) Plot a scatter plot of wage and eductaion with the fitted linear model from part (b) and the fitted values from the quadratic model from part (e) in the same graph with the data on WAGE and EDUC. Which model appears to fit the data better? Hint: If you call your first regression as reg and your second regression as reg2, You can generate the plot using the following commands: plot(cps4_small$educ, cps4_small$wage) i <- order(cps4_small$educ) (get indices that order the vector) lines (cps4_small$educ[i], fitted (reg) [i], col = 'blue') lines (cps4_small$educ[i], fitted (reg2) [i], col = 'red') (g) Construct a histogram of In(WAGE). Compare the shape of this histogram to that for WAGE from part a. Which appears more symmetric and bell-shaped? Hint: The histograms can be generated using the following commands: hist (cps4_small$wage,20) hist (log(cps4_small$wage), 20) (h) Estimate the log-linear regression In(WAGE) = Y1 + Y2EDUC + e. Estimate the marginal effect of another year of education on wage for a person with 12 years of education, and for a person with 14 years of education.