Does the return to education differ by race and gender? For this exercise use the file cps5. [This is a large file with 9799 observations. If your software is a student version, you can use the smaller file cps5_small if your instructor permits]. In this exercise, you will extract subsamples of observations consisting of (i) white males, (ii) white females, (iii) black males, and (iv) black females.

a. For each sample partition, obtain the summary statistics of WAGE.

b. A variable's coefficient of variation \((\mathrm{CV})\) is 100 times the ratio of its sample standard deviation to its sample mean. For a variable \(y\), it is

It is a measure of variation that takes into account the size of the variable. What is the coefficient of variation for WAGE within each sample partition?

c. For each sample partition, estimate the log-linear model

What is the approximate percentage return to another year of education for each group?

d. Create \(95 \%\) interval estimates for the coefficient \(\beta_{2}\) in each partition. Identify partitions for which the \(95 \%\) interval estimates of the rate of return to education do not overlap. What does this imply about the population relations between wages and education for these groups? Are they similar or different? For the nonoverlapping pairs, test the null hypothesis that the parameter \(\beta_{2}\) in one sample partition (the larger one, for simplicity) equals the estimated value in the other partition, using the \(5 \%\) level of significance.

e. Create \(95 \%\) interval estimates for the intercept coefficient in each partition. Identify partitions for which the \(95 \%\) interval estimates for the intercepts do not overlap. What does this imply about the population relations between wages and education for these groups? Are they similar or different? For the nonoverlapping pairs, test the null hypothesis that the parameter \(\beta_{1}\) in one sample partition (the larger one, for simplicity) equals the estimated value in the other partition, using the 5\% level of significance.

f. Does the model fit the data equally well for each sample partition?

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CV = 100 x