Amelia is interested in understanding the factors surrounding fringe benefits and salary packages in Australia. She estimates the model: Annbens = β0 + β1 lannearn + β3exper + β4expersq + β5educ + β6male + β7 male_educ + u Using STATA she estimates Model (F1) by OS and obtains the following results:
Amelia is interested in understanding the factors surrounding fringe benefits and salary packages in Australia. She estimates the model:
Annbens = β0 + β1 lannearn + β3exper + β4expersq + β5educ + β6male + β7 male_educ + u
Using STATA she estimates Model (F1) by OS and obtains the following results:
| Source | SS | df | MS |
|
Model Residual |
702938241 427363687 |
7 602 |
100419749 709906.456 |
| Total | 1.1303e+09 | 609 | 1855996.6 |
| annbens | coef. | std. err. | t | P > |t| | [95% Conf. Interval] | |
| lannhrs | -1180.478 | 181.3568 | -6.51 | 0.000 | -1536.647 | -824.3093 |
| lannearn | 2033.2 | 91.60081 | 22.20 | 0.000 | 1853.304 | 2213.096 |
| exper | 24.83705 | 11.12976 | 2.23 | 0.026 | 2.97918 | 46.69493 |
| expersq | -0.4499223 | 0.2366406 | -1.90 | 0.058 | -0.9146638 | 0.0148192 |
| educ | -3.846457 | 21.41313 | -0.18 | 0.858 | -45.89996 | 38.20705 |
| male | -21.9345 | 328.8641 | -0.07 | 0.947 | -667.7947 | 623.9257 |
| male_educ | 5.905139 | 25.45598 | 0.23 | 0.817 | -44.08817 | 55.89845 |
| _cons | -8190.175 | 1319.71 | -6.21 | 0.000 | -10781.97 | -5598.38 |
Number of obs = 610
F (7, 602) = 141.45
Prob > F = 0.0000
R-squared = 0.6219
Adj R-squared = 0.6175
Root MSE = 842.56
Where:
- annbens is the dollar value of the individual's annual benefits, which are the sum of paid annual leave, sick leave and superannuation (retirement saving)
- lanhrs is the natural log of the hours worked per year by the individual
- lannearn is the natural log of the annual earnings of the individual
- exper is the individual's experience in the workforce (in years)
- expersq is the square of exper
- educ is the individual's education attainment (in years)
- male is a dummy variable equal to 1 if the individual identifies as male and 0 otherwise
- male_educ is equal to male×educ, that is, the interaction of male and educ
Using the information above, answer the following questions.
[i] Mary and her colleague Rebecca are chatting, and they notice that they both started working on this same day of the year but many years ago. As of today, Mary has been working for 12 years while Rebecca has been working for 8 years. Does an additional year of work experience have the same effect on their annual benefits? If yes, explain why. If not, find the difference in the effect of an additional year of experience on Mary and Rebecca.
[ii] Graph the relationship between the dollar value of annual benefits and the number of years of education for males and females. Be sure to fully label your graph.
[iii] Your friend states that the effect of education on the dollar value of annual benefits does not differ by gender, that is, between males and females. Compute and report the 90% confidence interval that you can use to test this hypothesis at the 10% level of significance. Conduct the hypothesis test. Be sure to state the null and alternative hypotheses and provide a conclusion.
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