sociology 362
data exercise 3
dummy variables
The following problems are to be done using dmy cps1985.dta, a file that I will distribute via email
attachment. Once you open this file using stata, type the command notes to get the identity and coding
of all the variables.
1. Fit the models hrwage =α+βfemi+iand hrwage =α+βsouthi+i;
a. interpret αand βin each fitted model.
b. satisfy yourself that the regression results do indeed correspond to what you would get with a t-test of
the difference between two population means. For example, try ttest hrwage,by(fem).
2. Fit the multiple regression model hrwage =α+βf.sfem i+βs.f south i+i.
a. Interpret the estimated coefficients of fem and south.
b. Generate the observed table of hrwage means for the four combinations of south and fem. Try the
stata command tab2 south fem,summ(hrwage),nost.
c. Generate the table of fitted means for the four combinations of south by fem. (You can just use the
estimated model for this.) What is the estimated mean hourly wage for a female working in the south?
For a male working in the non-south?
d. How does the fitted table compare to the observed? For example, is the sex difference in the observed
table the same for both regions as it is in the fitted table?
3. Suppose we are interested in the relationship of hourly wage hrwage to schooling (edyrs), but we have
reason to believe that sex (fem) may be implicated in the relationship. For each of the following,
estimate the null and alternative models, and use the F-test to arrive at your conclusions.
a. Assuming the schooling slope is the same for males and females, test the hypothesis of no difference in
intercepts, i.e., no sex difference in mean Y when schooling is controlled.
b. Assuming the male and female intercepts are the same, test the hypothesis that schooling has no effect
on earnings.
c. Assuming the male and female intercepts are different, test the hypothesis that schooling has no effect
on earnings.
d. Assuming that male and female intercepts are different, test the hypothesis that male and female slope
coefficients of schooling are equal.
e. Test the joint null hypothesis of no sex difference in intercepts or in schooling slopes. This is the
so-called test of overall homogeneity (or equality) of regressions. Use the sex dummy fem and an
interaction term that you construct to test this hypothesis.
f. Again test the hypothesis of overall homogeneity of the regression of hrwage on edyrs for males and
females, but now represent the alternative model by running separate regressions of hrwage on edyrs for
men and women.
5. The alternative model of problem 4e can be written as:
hrwage =α+β1edyrsi+β2femi+β3Ii+i(1)
where Ii=femi∗edyrsi.
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