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You will have found in Exercise 7.7 that the estimates of the coefficients of PWEBEF and TENURE are different. This raises the issue of whether the difference is due to random factors or whether the coefficients are significantly different. Set up the null hypothesis H0: δ1 = δ2, where δ1 is the coefficient of PWEBEF and δ2 is the coefficient of TENURE. Explain why the regression with PWE is the correct specification if H0 is true, while the regression with PWEBEF and TENURE should be used if H0 is false. Perform an F test of the restriction using RSS for the two regressions. Do this for the combined sample and also for males and females separately.

Exercise 7.7

Length of work experience is generally found to be an important determinant of earnings. The data set does not contain this variable, but TENURE, tenure with the current employer, could be taken as a proxy. An alternative is to calculate years of potential work experience, PWE, as a proxy. This is defined to be current age, AGE, less age of completion of full-time education. The latter can be estimated as years of schooling plus 5, assuming that schooling begins at the age of 6. Hence

PWE = AGE – S – 5.

Using your EAEF data set, regress LGEARN on S, ASVABC, MALE, ETHBLACK, ETHHISP, and PWE .Compare the results with the corresponding regression without PWE. You are likely to find that the coefficient of S is greater than before. Can you explain why? The data set includes TENURE, tenure with current employer. This allows one to divide PWE into two components: potential work experience with previous employers, PWEBEF, and TENURE. Define PWEBEF as

PWEBEF = PWE – TENURE

and regress LGEARN on the variables as before, replacing PWE by PWEBEF and TENURE. Compare the result with that of the previous regression. Variation: PWE is not likely to be a satisfactory proxy for work experience for females because it does not take into account time spent out of the labor force rearing children. Investigate this by running the regressions with PWE for the male and female subsamples separately. You must drop the MALE dummy from the specification (explain why). Do the same for the regressions with PWEBEF and TENURE.

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