How to test (in Stata) whether the gender distribution of employees to jobs differs across two companies? I have data on several companies where some are headed by a male CEO while others by a female CEO. As you can imagine, the jobs within these companies have different gender compositions. What I am trying to do is compare the gender distribution of employees across jobs for companies led by a male versus a female CEO. 
For example - Co A has a FEMALE CEO where Job1 is 40% female, Job2 is 30% female, Job3 is 15% female. Co B has a MALE CEO where Job1 is 60% female, Job2 is 40% female, Job3 is 20% female. Clearly Co B has a greater proportion of female employees, but my question is whether the distribution of female employees across jobs is significantly different for Co A and Co B. What is the appropriate statistical test and command in Stata for testing this?
Assume these jobs are identical for simplicity. 
 A: If you are willing to assume that all the jobs are identical, then you can do logistic regression. The DV would be "female in job" and the IV would be "female CEO"; you  might want other IVs as well (you probably do).
I don't know Stata, so I can't help there. 
A: If you're willing to treat each job category separately (and maybe use a more stringent threshold for statistical significance to adjust for the multiple comparison problem), take a look at Chris Baum's Stata Tip #63. Another related approach is user-written betafit from SSC. For many of these, the two extremes of no women and all women will pose a problem. The glm way is a notable exception.
For a multivariate approach that can accommodate proportions that don't sum to one, I would think about a Hotelling's T-squared generalized means test (which can be shoe-horned into a regression setting). It's hotelling in Stata. Equivalently, an F-test from a regression of a female CEO dummy on all the proportion variables whose means should be equal across groups. This F-test can be found right under the sample size in Stata's regress output. If you have other controls like industry dummies or if you want more elaborate standard errors, the regression method might be better.
On second thoughts, I am not so sure if using controls and testing only the proportion coefficients is a good idea. Maybe someone can else can comment on this.
