I am attempting to see how different tiers of collegiate institutions have contributed to the change in female collegiate attendance. For example, let's say that the female share of college attendance has risen by 5% (meaning that the male share has fallen by 5%), how much of that 5% is from elite schools (Harvard, Yale, etc.) vs middle of the road schools vs for-profits (ex. Univ. Phoenix)? Someone suggested that I use the Oaxaca decomposition but I'm not sure how to to make it work with my data. In the data set, I have a list of institutions (sorted by tier), and their gender make-up for several different years. Any guidance would be much appreciated!