Does word of mouth affect the demand to attend college?

Many econometric studies, particularly in the United States, conclude that neither low tuition nor high income significantly boosts the demand to enroll in college. What about other factors?  Since education is an experience good, might word of mouth affect enrollment? To find out, I gather data for a Central Asian university with a good regional reputation. I measure perceived quality as the share of respondents, in an annual survey of alumni, who said they would recommend this university to prospective students.  In panel studies of 111 observations, I regress enrollment and credit hours in more than a dozen programs, undergraduate and graduate, on perceived quality, a time trend, program dummies, and the number of survey respondents from the given program.  The dataset covers fall semesters from 2008 through 2015.  Results: A fall in perceived quality might have substantially reduced enrollment and credit hours in the period studied.  But the estimates of the response to perceived quality are so imprecise that one cannot be sure that word of mouth will continue to affect demand to study at the university. Holding quality constant, some programs are losing enrollment and hours rapidly relative to others, perhaps because of a relative decline in market demand for their graduates.  Finally, a time trend reduced enrollment and hours powerfully:  Maybe growing rivalry from other universities affects college demand.  Another possibility is that the time trend picks up a demographic pattern that reduces the number of eligible students for the university, which has selective admission.  But this is not consistent with the fact that program fixed effects were statistically significant and that they varied widely in magnitude. A demographic trend should affect all programs somewhat equally.